%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN507-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:23 AM UTC 2025
% Result : Unsatisfiable 1.77s 1.92s
% Output : Proof 2.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN507-1 : TPTP v9.0.0. Released v2.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:36:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.77/1.92 % SZS status Unsatisfiable
% 1.77/1.92 % SZS output start Proof
% 1.77/1.92 tff(c0_1_type, type, (
% 1.77/1.92 c0_1: $i > $o)).
% 1.77/1.92 tff(a606_type, type, (
% 1.77/1.92 a606: $i)).
% 1.77/1.92 tff(c2_1_type, type, (
% 1.77/1.92 c2_1: $i > $o)).
% 1.77/1.92 tff(a604_type, type, (
% 1.77/1.92 a604: $i)).
% 1.77/1.92 tff(a599_type, type, (
% 1.77/1.92 a599: $i)).
% 1.77/1.92 tff(c3_1_type, type, (
% 1.77/1.92 c3_1: $i > $o)).
% 1.77/1.92 tff(hskp11_type, type, (
% 1.77/1.92 hskp11: $o)).
% 1.77/1.92 tff(a636_type, type, (
% 1.77/1.92 a636: $i)).
% 1.77/1.92 tff(a607_type, type, (
% 1.77/1.92 a607: $i)).
% 1.77/1.92 tff(a601_type, type, (
% 1.77/1.92 a601: $i)).
% 1.77/1.92 tff(a598_type, type, (
% 1.77/1.92 a598: $i)).
% 1.77/1.92 tff(c1_1_type, type, (
% 1.77/1.92 c1_1: $i > $o)).
% 1.77/1.92 tff(ndr1_0_type, type, (
% 1.77/1.92 ndr1_0: $o)).
% 1.77/1.92 tff(hskp10_type, type, (
% 1.77/1.92 hskp10: $o)).
% 1.77/1.92 tff(a633_type, type, (
% 1.77/1.92 a633: $i)).
% 1.77/1.92 tff(a612_type, type, (
% 1.77/1.92 a612: $i)).
% 1.77/1.92 tff(hskp17_type, type, (
% 1.77/1.92 hskp17: $o)).
% 1.77/1.92 tff(a587_type, type, (
% 1.77/1.92 a587: $i)).
% 1.77/1.92 tff(hskp3_type, type, (
% 1.77/1.92 hskp3: $o)).
% 1.77/1.92 tff(hskp22_type, type, (
% 1.77/1.92 hskp22: $o)).
% 1.77/1.92 tff(a623_type, type, (
% 1.77/1.92 a623: $i)).
% 1.77/1.92 tff(hskp6_type, type, (
% 1.77/1.92 hskp6: $o)).
% 1.77/1.92 tff(hskp20_type, type, (
% 1.77/1.92 hskp20: $o)).
% 1.77/1.92 tff(a583_type, type, (
% 1.77/1.92 a583: $i)).
% 1.77/1.92 tff(hskp26_type, type, (
% 1.77/1.92 hskp26: $o)).
% 1.77/1.92 tff(a590_type, type, (
% 1.77/1.92 a590: $i)).
% 1.77/1.92 tff(a586_type, type, (
% 1.77/1.92 a586: $i)).
% 1.77/1.92 tff(hskp4_type, type, (
% 1.77/1.92 hskp4: $o)).
% 1.77/1.92 tff(hskp2_type, type, (
% 1.77/1.92 hskp2: $o)).
% 1.77/1.92 tff(a603_type, type, (
% 1.77/1.92 a603: $i)).
% 1.77/1.92 tff(hskp14_type, type, (
% 1.77/1.92 hskp14: $o)).
% 1.77/1.92 tff(hskp29_type, type, (
% 1.77/1.92 hskp29: $o)).
% 1.77/1.92 tff(a588_type, type, (
% 1.77/1.92 a588: $i)).
% 1.77/1.92 tff(a678_type, type, (
% 1.77/1.92 a678: $i)).
% 1.77/1.92 tff(a595_type, type, (
% 1.77/1.92 a595: $i)).
% 1.77/1.92 tff(hskp9_type, type, (
% 1.77/1.92 hskp9: $o)).
% 1.77/1.92 tff(a593_type, type, (
% 1.77/1.92 a593: $i)).
% 1.77/1.92 tff(hskp8_type, type, (
% 1.77/1.92 hskp8: $o)).
% 1.77/1.92 tff(hskp23_type, type, (
% 1.77/1.92 hskp23: $o)).
% 1.77/1.92 tff(hskp27_type, type, (
% 1.77/1.92 hskp27: $o)).
% 1.77/1.92 tff(a589_type, type, (
% 1.77/1.92 a589: $i)).
% 1.77/1.92 tff(hskp5_type, type, (
% 1.77/1.92 hskp5: $o)).
% 1.77/1.92 tff(a611_type, type, (
% 1.77/1.92 a611: $i)).
% 1.77/1.92 tff(a592_type, type, (
% 1.77/1.92 a592: $i)).
% 1.77/1.92 tff(hskp7_type, type, (
% 1.77/1.92 hskp7: $o)).
% 1.77/1.92 tff(hskp12_type, type, (
% 1.77/1.92 hskp12: $o)).
% 1.77/1.92 tff(a600_type, type, (
% 1.77/1.92 a600: $i)).
% 1.77/1.92 tff(a585_type, type, (
% 1.77/1.92 a585: $i)).
% 1.77/1.92 tff(hskp1_type, type, (
% 1.77/1.92 hskp1: $o)).
% 1.77/1.92 tff(hskp16_type, type, (
% 1.77/1.92 hskp16: $o)).
% 1.77/1.92 tff(a584_type, type, (
% 1.77/1.92 a584: $i)).
% 1.77/1.92 tff(hskp0_type, type, (
% 1.77/1.92 hskp0: $o)).
% 1.77/1.92 tff(hskp28_type, type, (
% 1.77/1.92 hskp28: $o)).
% 1.77/1.92 tff(a610_type, type, (
% 1.77/1.92 a610: $i)).
% 1.77/1.92 tff(hskp18_type, type, (
% 1.77/1.92 hskp18: $o)).
% 1.77/1.92 tff(hskp15_type, type, (
% 1.77/1.92 hskp15: $o)).
% 1.77/1.92 tff(a651_type, type, (
% 1.77/1.92 a651: $i)).
% 1.77/1.92 tff(hskp25_type, type, (
% 1.77/1.92 hskp25: $o)).
% 1.77/1.92 tff(a617_type, type, (
% 1.77/1.92 a617: $i)).
% 1.77/1.92 tff(hskp19_type, type, (
% 1.77/1.92 hskp19: $o)).
% 1.77/1.92 tff(hskp13_type, type, (
% 1.77/1.92 hskp13: $o)).
% 1.77/1.92 tff(a629_type, type, (
% 1.77/1.92 a629: $i)).
% 1.77/1.92 tff(hskp21_type, type, (
% 1.77/1.92 hskp21: $o)).
% 1.77/1.92 tff(1,assumption,(~c0_1(a607)), introduced(assumption)).
% 1.77/1.92 tff(2,plain,
% 1.77/1.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(3,plain,
% 1.77/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[2])).
% 1.77/1.92 tff(4,plain,
% 1.77/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(5,plain,
% 1.77/1.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(6,plain,
% 1.77/1.92 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[5])).
% 1.77/1.92 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.77/1.92 tff(8,plain,
% 1.77/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.77/1.92 tff(9,plain,
% 1.77/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.77/1.92 tff(10,plain,(
% 1.77/1.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.77/1.92 inference(skolemize,[status(sab)],[9])).
% 1.77/1.92 tff(11,plain,
% 1.77/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.77/1.92 tff(12,plain,
% 1.77/1.92 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(13,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[12])).
% 1.77/1.92 tff(14,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(15,plain,
% 1.77/1.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(16,plain,
% 1.77/1.92 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[15])).
% 1.77/1.92 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.77/1.92 tff(18,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.77/1.92 tff(19,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.77/1.92 tff(20,plain,(
% 1.77/1.92 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.77/1.92 inference(skolemize,[status(sab)],[19])).
% 1.77/1.92 tff(21,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.77/1.92 tff(22,assumption,(~c2_1(a607)), introduced(assumption)).
% 1.77/1.92 tff(23,plain,
% 1.77/1.92 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(24,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[23])).
% 1.77/1.92 tff(25,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(26,plain,
% 1.77/1.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(27,plain,
% 1.77/1.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[26])).
% 1.77/1.92 tff(28,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.77/1.92 tff(29,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.77/1.92 tff(30,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.77/1.92 tff(31,plain,(
% 1.77/1.92 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.77/1.92 inference(skolemize,[status(sab)],[30])).
% 1.77/1.92 tff(32,plain,
% 1.77/1.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.77/1.92 tff(33,assumption,(~c3_1(a607)), introduced(assumption)).
% 1.77/1.92 tff(34,plain,
% 1.77/1.92 (^[U: $i] : refl((hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(35,plain,
% 1.77/1.92 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[34])).
% 1.77/1.92 tff(36,plain,
% 1.77/1.92 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(37,plain,
% 1.77/1.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp6) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp6))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp6) <=> (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp6) <=> (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(38,plain,
% 1.77/1.93 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp6) <=> ![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[37])).
% 1.77/1.93 tff(39,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.77/1.93 tff(40,plain,
% 1.77/1.93 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.77/1.93 tff(41,plain,
% 1.77/1.93 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.77/1.93 tff(42,plain,(
% 1.77/1.93 ![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.77/1.93 inference(skolemize,[status(sab)],[41])).
% 1.77/1.93 tff(43,plain,
% 1.77/1.93 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.77/1.93 tff(44,assumption,(~hskp22), introduced(assumption)).
% 1.77/1.93 tff(45,assumption,(~c0_1(a590)), introduced(assumption)).
% 1.77/1.93 tff(46,plain,
% 1.77/1.93 (^[U: $i] : refl((hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(47,plain,
% 1.77/1.93 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[46])).
% 1.77/1.93 tff(48,plain,
% 1.77/1.93 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(49,plain,
% 1.77/1.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(50,plain,
% 1.77/1.93 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[49])).
% 1.77/1.93 tff(51,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.77/1.93 tff(52,plain,
% 1.77/1.93 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.77/1.93 tff(53,plain,
% 1.77/1.93 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.77/1.93 tff(54,plain,(
% 1.77/1.93 ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.93 inference(skolemize,[status(sab)],[53])).
% 1.77/1.93 tff(55,plain,
% 1.77/1.93 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.77/1.93 tff(56,plain,
% 1.77/1.93 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(57,plain,
% 1.77/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[56])).
% 1.77/1.93 tff(58,plain,
% 1.77/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(59,plain,
% 1.77/1.93 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(60,plain,
% 1.77/1.93 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[59])).
% 1.77/1.93 tff(61,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.77/1.93 tff(62,plain,
% 1.77/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.77/1.93 tff(63,plain,
% 1.77/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[62, 58])).
% 1.77/1.93 tff(64,plain,(
% 1.77/1.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.77/1.93 inference(skolemize,[status(sab)],[63])).
% 1.77/1.93 tff(65,plain,
% 1.77/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[64, 57])).
% 1.77/1.93 tff(66,assumption,(~c1_1(a607)), introduced(assumption)).
% 1.77/1.93 tff(67,assumption,(~hskp6), introduced(assumption)).
% 1.77/1.93 tff(68,assumption,(~ndr1_0), introduced(assumption)).
% 1.77/1.93 tff(69,plain,
% 1.77/1.93 ((ndr1_0 | (~hskp17)) <=> (ndr1_0 | (~hskp17))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(70,plain,
% 1.77/1.93 (((~hskp17) | ndr1_0) <=> (ndr1_0 | (~hskp17))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(71,axiom,((~hskp17) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 1.77/1.93 tff(72,plain,
% 1.77/1.93 (ndr1_0 | (~hskp17)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.77/1.93 tff(73,plain,
% 1.77/1.93 (ndr1_0 | (~hskp17)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[72, 69])).
% 1.77/1.93 tff(74,plain,
% 1.77/1.93 (~hskp17),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[73, 68])).
% 1.77/1.93 tff(75,plain,
% 1.77/1.93 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(76,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 1.77/1.93 tff(77,plain,
% 1.77/1.93 ((~hskp29) | ndr1_0),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.77/1.93 tff(78,plain,
% 1.77/1.93 ((~hskp29) | ndr1_0),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[77, 75])).
% 1.77/1.93 tff(79,plain,
% 1.77/1.93 ((~hskp29) | ndr1_0),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[78, 75])).
% 1.77/1.93 tff(80,plain,
% 1.77/1.93 ((~hskp29) | ndr1_0),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.77/1.93 tff(81,plain,
% 1.77/1.93 ((~hskp29) | ndr1_0),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[80, 75])).
% 1.77/1.93 tff(82,plain,
% 1.77/1.93 (~hskp29),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[81, 68])).
% 1.77/1.93 tff(83,plain,
% 1.77/1.93 ((ndr1_0 | (~hskp22)) <=> (ndr1_0 | (~hskp22))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(84,plain,
% 1.77/1.93 (((~hskp22) | ndr1_0) <=> (ndr1_0 | (~hskp22))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(85,axiom,((~hskp22) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause9')).
% 1.77/1.93 tff(86,plain,
% 1.77/1.93 (ndr1_0 | (~hskp22)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.77/1.93 tff(87,plain,
% 1.77/1.93 (ndr1_0 | (~hskp22)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[86, 83])).
% 1.77/1.93 tff(88,plain,
% 1.77/1.93 (~hskp22),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[87, 68])).
% 1.77/1.93 tff(89,plain,
% 1.77/1.93 ((hskp29 | hskp22 | hskp17) <=> (hskp29 | hskp22 | hskp17)),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(90,plain,
% 1.77/1.93 (((hskp29 | hskp22) | hskp17) <=> (hskp29 | hskp22 | hskp17)),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(91,plain,
% 1.77/1.93 ((hskp29 | hskp22) <=> (hskp29 | hskp22)),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(92,plain,
% 1.77/1.93 (((hskp29 | hskp22) | hskp17) <=> ((hskp29 | hskp22) | hskp17)),
% 1.77/1.93 inference(monotonicity,[status(thm)],[91])).
% 1.77/1.93 tff(93,plain,
% 1.77/1.93 (((hskp29 | hskp22) | hskp17) <=> (hskp29 | hskp22 | hskp17)),
% 1.77/1.93 inference(transitivity,[status(thm)],[92, 90])).
% 1.77/1.93 tff(94,axiom,((hskp29 | hskp22) | hskp17), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.77/1.93 tff(95,plain,
% 1.77/1.93 (hskp29 | hskp22 | hskp17),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.77/1.93 tff(96,plain,
% 1.77/1.93 (hskp29 | hskp22 | hskp17),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[95, 89])).
% 1.77/1.93 tff(97,plain,
% 1.77/1.93 (hskp29 | hskp22 | hskp17),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[96, 89])).
% 1.77/1.93 tff(98,plain,
% 1.77/1.93 (hskp29 | hskp22 | hskp17),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[97, 89])).
% 1.77/1.93 tff(99,plain,
% 1.77/1.93 (hskp29 | hskp22 | hskp17),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[98, 89])).
% 1.77/1.93 tff(100,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[99, 88, 82, 74])).
% 1.77/1.93 tff(101,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(102,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(103,plain,
% 1.77/1.93 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607))) <=> (hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(104,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[103])).
% 1.77/1.93 tff(105,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[104, 102])).
% 1.77/1.93 tff(106,plain,
% 1.77/1.93 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(107,plain,
% 1.77/1.93 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.77/1.93 tff(108,plain,
% 1.77/1.93 (hskp6 | c1_1(a607) | (~c0_1(a607))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[107, 101, 44, 22, 43])).
% 1.77/1.93 tff(109,plain,
% 1.77/1.93 (~c0_1(a607)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[108, 67, 66])).
% 1.77/1.93 tff(110,assumption,(hskp4), introduced(assumption)).
% 1.77/1.93 tff(111,plain,
% 1.77/1.93 (((~hskp4) | (~c2_1(a588))) <=> ((~hskp4) | (~c2_1(a588)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(112,plain,
% 1.77/1.93 (((~c2_1(a588)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a588)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(113,axiom,((~c2_1(a588)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.77/1.93 tff(114,plain,
% 1.77/1.93 ((~hskp4) | (~c2_1(a588))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.77/1.93 tff(115,plain,
% 1.77/1.93 ((~hskp4) | (~c2_1(a588))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[114, 111])).
% 1.77/1.93 tff(116,plain,
% 1.77/1.93 (~c2_1(a588)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[115, 110])).
% 1.77/1.93 tff(117,plain,
% 1.77/1.93 (((~hskp4) | (~c1_1(a588))) <=> ((~hskp4) | (~c1_1(a588)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(118,plain,
% 1.77/1.93 (((~c1_1(a588)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a588)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(119,axiom,((~c1_1(a588)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.77/1.93 tff(120,plain,
% 1.77/1.93 ((~hskp4) | (~c1_1(a588))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.77/1.93 tff(121,plain,
% 1.77/1.93 ((~hskp4) | (~c1_1(a588))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[120, 117])).
% 1.77/1.93 tff(122,plain,
% 1.77/1.93 (~c1_1(a588)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[121, 110])).
% 1.77/1.93 tff(123,plain,
% 1.77/1.93 (((~hskp4) | c0_1(a588)) <=> ((~hskp4) | c0_1(a588))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(124,axiom,((~hskp4) | c0_1(a588)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.77/1.93 tff(125,plain,
% 1.77/1.93 ((~hskp4) | c0_1(a588)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.77/1.93 tff(126,plain,
% 1.77/1.93 ((~hskp4) | c0_1(a588)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[125, 123])).
% 1.77/1.93 tff(127,plain,
% 1.77/1.93 ((~hskp4) | c0_1(a588)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[126, 123])).
% 1.77/1.93 tff(128,plain,
% 1.77/1.93 ((~hskp4) | c0_1(a588)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[127, 123])).
% 1.77/1.93 tff(129,plain,
% 1.77/1.93 ((~hskp4) | c0_1(a588)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[128, 123])).
% 1.77/1.93 tff(130,plain,
% 1.77/1.93 (c0_1(a588)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[129, 110])).
% 1.77/1.93 tff(131,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(132,plain,
% 1.77/1.93 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588))) <=> (hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(133,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[132])).
% 1.77/1.93 tff(134,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[133, 131])).
% 1.77/1.93 tff(135,plain,
% 1.77/1.93 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(136,plain,
% 1.77/1.93 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.77/1.93 tff(137,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[136, 101, 44, 67, 130, 122, 116, 43])).
% 1.77/1.93 tff(138,plain,((~hskp4) | hskp22 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(139,plain,
% 1.77/1.93 (~hskp4),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[138, 67, 44])).
% 1.77/1.93 tff(140,plain,
% 1.77/1.93 (^[U: $i] : refl((hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(141,plain,
% 1.77/1.93 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[140])).
% 1.77/1.93 tff(142,plain,
% 1.77/1.93 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(143,plain,
% 1.77/1.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp14) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp14))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp14) <=> (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp14) <=> (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(144,plain,
% 1.77/1.93 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp14) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[143])).
% 1.77/1.93 tff(145,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.77/1.93 tff(146,plain,
% 1.77/1.93 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.77/1.93 tff(147,plain,
% 1.77/1.93 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[146, 142])).
% 1.77/1.93 tff(148,plain,(
% 1.77/1.93 ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.77/1.93 inference(skolemize,[status(sab)],[147])).
% 1.77/1.93 tff(149,plain,
% 1.77/1.93 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[148, 141])).
% 1.77/1.93 tff(150,plain,
% 1.77/1.93 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(151,plain,
% 1.77/1.93 ((hskp14 | hskp4 | (~ndr1_0) | c2_1(a607) | c0_1(a607) | c3_1(a607)) <=> (hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(152,plain,
% 1.77/1.93 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a607) | c0_1(a607) | c3_1(a607))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607)))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[151])).
% 1.77/1.93 tff(153,plain,
% 1.77/1.93 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a607) | c0_1(a607) | c3_1(a607))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 1.77/1.93 inference(transitivity,[status(thm)],[152, 150])).
% 1.77/1.93 tff(154,plain,
% 1.77/1.93 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a607) | c0_1(a607) | c3_1(a607))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(155,plain,
% 1.77/1.93 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.77/1.93 tff(156,plain,
% 1.77/1.93 (hskp14 | hskp4 | c3_1(a607) | c0_1(a607)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[155, 101, 22, 149])).
% 1.77/1.93 tff(157,plain,
% 1.77/1.93 (hskp14),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[156, 139, 33, 109])).
% 1.77/1.93 tff(158,plain,
% 1.77/1.93 (((~hskp14) | (~c1_1(a603))) <=> ((~hskp14) | (~c1_1(a603)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(159,plain,
% 1.77/1.93 (((~c1_1(a603)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a603)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(160,axiom,((~c1_1(a603)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.77/1.93 tff(161,plain,
% 1.77/1.93 ((~hskp14) | (~c1_1(a603))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.77/1.93 tff(162,plain,
% 1.77/1.93 ((~hskp14) | (~c1_1(a603))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[161, 158])).
% 1.77/1.93 tff(163,plain,
% 1.77/1.93 (~c1_1(a603)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[162, 157])).
% 1.77/1.93 tff(164,plain,
% 1.77/1.93 (((~hskp14) | c0_1(a603)) <=> ((~hskp14) | c0_1(a603))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(165,axiom,((~hskp14) | c0_1(a603)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.77/1.93 tff(166,plain,
% 1.77/1.93 ((~hskp14) | c0_1(a603)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.77/1.93 tff(167,plain,
% 1.77/1.93 ((~hskp14) | c0_1(a603)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[166, 164])).
% 1.77/1.93 tff(168,plain,
% 1.77/1.93 ((~hskp14) | c0_1(a603)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[167, 164])).
% 1.77/1.93 tff(169,plain,
% 1.77/1.93 ((~hskp14) | c0_1(a603)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[168, 164])).
% 1.77/1.93 tff(170,plain,
% 1.77/1.93 ((~hskp14) | c0_1(a603)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[169, 164])).
% 1.77/1.93 tff(171,plain,
% 1.77/1.93 (c0_1(a603)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[170, 157])).
% 1.77/1.93 tff(172,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(173,plain,
% 1.77/1.93 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603))) <=> (hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(174,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[173])).
% 1.77/1.93 tff(175,plain,
% 1.77/1.93 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[174, 172])).
% 1.77/1.93 tff(176,plain,
% 1.77/1.93 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(177,plain,
% 1.77/1.93 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.77/1.93 tff(178,plain,
% 1.77/1.93 (c2_1(a603)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[177, 101, 44, 67, 171, 163, 43])).
% 1.77/1.93 tff(179,plain,
% 1.77/1.93 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.77/1.93 inference(bind,[status(th)],[])).
% 1.77/1.93 tff(180,plain,
% 1.77/1.93 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.77/1.93 inference(quant_intro,[status(thm)],[179])).
% 1.77/1.93 tff(181,plain,
% 1.77/1.93 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(182,plain,
% 1.77/1.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(183,plain,
% 1.77/1.94 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[182])).
% 1.77/1.94 tff(184,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.77/1.94 tff(185,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.77/1.94 tff(186,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[185, 181])).
% 1.77/1.94 tff(187,plain,(
% 1.77/1.94 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.77/1.94 inference(skolemize,[status(sab)],[186])).
% 1.77/1.94 tff(188,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[187, 180])).
% 1.77/1.94 tff(189,plain,
% 1.77/1.94 (((~hskp14) | (~c3_1(a603))) <=> ((~hskp14) | (~c3_1(a603)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(190,plain,
% 1.77/1.94 (((~c3_1(a603)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a603)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(191,axiom,((~c3_1(a603)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.77/1.94 tff(192,plain,
% 1.77/1.94 ((~hskp14) | (~c3_1(a603))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.77/1.94 tff(193,plain,
% 1.77/1.94 ((~hskp14) | (~c3_1(a603))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[192, 189])).
% 1.77/1.94 tff(194,plain,
% 1.77/1.94 (~c3_1(a603)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[193, 157])).
% 1.77/1.94 tff(195,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(196,plain,
% 1.77/1.94 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a607) | c1_1(a607) | c0_1(a607)) <=> (hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(197,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607)))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[196])).
% 1.77/1.94 tff(198,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607))),
% 1.77/1.94 inference(transitivity,[status(thm)],[197, 195])).
% 1.77/1.94 tff(199,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a607) | c1_1(a607) | c0_1(a607))),
% 1.77/1.94 inference(quant_inst,[status(thm)],[])).
% 1.77/1.94 tff(200,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.77/1.94 tff(201,plain,
% 1.77/1.94 (hskp2),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[200, 101, 33, 66, 163, 194, 188, 109, 178])).
% 1.77/1.94 tff(202,plain,
% 1.77/1.94 (((~hskp2) | (~c3_1(a586))) <=> ((~hskp2) | (~c3_1(a586)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(203,plain,
% 1.77/1.94 (((~c3_1(a586)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a586)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(204,axiom,((~c3_1(a586)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.77/1.94 tff(205,plain,
% 1.77/1.94 ((~hskp2) | (~c3_1(a586))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[204, 203])).
% 1.77/1.94 tff(206,plain,
% 1.77/1.94 ((~hskp2) | (~c3_1(a586))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[205, 202])).
% 1.77/1.94 tff(207,plain,
% 1.77/1.94 (~c3_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[206, 201])).
% 1.77/1.94 tff(208,plain,
% 1.77/1.94 (((~hskp2) | c1_1(a586)) <=> ((~hskp2) | c1_1(a586))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(209,axiom,((~hskp2) | c1_1(a586)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.77/1.94 tff(210,plain,
% 1.77/1.94 ((~hskp2) | c1_1(a586)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.77/1.94 tff(211,plain,
% 1.77/1.94 ((~hskp2) | c1_1(a586)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[210, 208])).
% 1.77/1.94 tff(212,plain,
% 1.77/1.94 ((~hskp2) | c1_1(a586)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[211, 208])).
% 1.77/1.94 tff(213,plain,
% 1.77/1.94 ((~hskp2) | c1_1(a586)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[212, 208])).
% 1.77/1.94 tff(214,plain,
% 1.77/1.94 ((~hskp2) | c1_1(a586)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[213, 208])).
% 1.77/1.94 tff(215,plain,
% 1.77/1.94 (c1_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[214, 201])).
% 1.77/1.94 tff(216,plain,
% 1.77/1.94 (((~hskp17) | c3_1(a607)) <=> ((~hskp17) | c3_1(a607))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(217,axiom,((~hskp17) | c3_1(a607)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.77/1.94 tff(218,plain,
% 1.77/1.94 ((~hskp17) | c3_1(a607)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.77/1.94 tff(219,plain,
% 1.77/1.94 ((~hskp17) | c3_1(a607)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[218, 216])).
% 1.77/1.94 tff(220,plain,
% 1.77/1.94 ((~hskp17) | c3_1(a607)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[219, 216])).
% 1.77/1.94 tff(221,plain,
% 1.77/1.94 ((~hskp17) | c3_1(a607)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[220, 216])).
% 1.77/1.94 tff(222,plain,
% 1.77/1.94 ((~hskp17) | c3_1(a607)),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[221, 216])).
% 1.77/1.94 tff(223,plain,
% 1.77/1.94 (~hskp17),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[222, 33])).
% 1.77/1.94 tff(224,plain,
% 1.77/1.94 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(225,plain,
% 1.77/1.94 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586))) <=> (hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(226,plain,
% 1.77/1.94 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586))))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[225])).
% 1.77/1.94 tff(227,plain,
% 1.77/1.94 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 1.77/1.94 inference(transitivity,[status(thm)],[226, 224])).
% 1.77/1.94 tff(228,plain,
% 1.77/1.94 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))),
% 1.77/1.94 inference(quant_inst,[status(thm)],[])).
% 1.77/1.94 tff(229,plain,
% 1.77/1.94 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.77/1.94 tff(230,plain,
% 1.77/1.94 (~c0_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[229, 101, 223, 139, 215, 207, 55])).
% 1.77/1.94 tff(231,plain,
% 1.77/1.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(232,plain,
% 1.77/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[231])).
% 1.77/1.94 tff(233,plain,
% 1.77/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(234,plain,
% 1.77/1.94 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(235,plain,
% 1.77/1.94 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[234])).
% 1.77/1.94 tff(236,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.77/1.94 tff(237,plain,
% 1.77/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.77/1.94 tff(238,plain,
% 1.77/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[237, 233])).
% 1.77/1.94 tff(239,plain,(
% 1.77/1.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.77/1.94 inference(skolemize,[status(sab)],[238])).
% 1.77/1.94 tff(240,plain,
% 1.77/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[239, 232])).
% 1.77/1.94 tff(241,plain,
% 1.77/1.94 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(242,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[241])).
% 1.77/1.94 tff(243,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(244,plain,
% 1.77/1.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(245,plain,
% 1.77/1.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[244])).
% 1.77/1.94 tff(246,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.77/1.94 tff(247,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[246, 245])).
% 1.77/1.94 tff(248,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[247, 243])).
% 1.77/1.94 tff(249,plain,(
% 1.77/1.94 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.77/1.94 inference(skolemize,[status(sab)],[248])).
% 1.77/1.94 tff(250,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[249, 242])).
% 1.77/1.94 tff(251,assumption,(~hskp29), introduced(assumption)).
% 1.77/1.94 tff(252,plain,
% 1.77/1.94 (hskp17),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[99, 251, 44])).
% 1.77/1.94 tff(253,plain,
% 1.77/1.94 (((~hskp17) | (~c2_1(a607))) <=> ((~hskp17) | (~c2_1(a607)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(254,plain,
% 1.77/1.94 (((~c2_1(a607)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a607)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(255,axiom,((~c2_1(a607)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.77/1.94 tff(256,plain,
% 1.77/1.94 ((~hskp17) | (~c2_1(a607))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.77/1.94 tff(257,plain,
% 1.77/1.94 ((~hskp17) | (~c2_1(a607))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[256, 253])).
% 1.77/1.94 tff(258,plain,
% 1.77/1.94 (~c2_1(a607)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[257, 252])).
% 1.77/1.94 tff(259,plain,
% 1.77/1.94 (((~hskp17) | (~c1_1(a607))) <=> ((~hskp17) | (~c1_1(a607)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(260,plain,
% 1.77/1.94 (((~c1_1(a607)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a607)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(261,axiom,((~c1_1(a607)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.77/1.94 tff(262,plain,
% 1.77/1.94 ((~hskp17) | (~c1_1(a607))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[261, 260])).
% 1.77/1.94 tff(263,plain,
% 1.77/1.94 ((~hskp17) | (~c1_1(a607))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[262, 259])).
% 1.77/1.94 tff(264,plain,
% 1.77/1.94 (~c1_1(a607)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[263, 252])).
% 1.77/1.94 tff(265,plain,
% 1.77/1.94 (hskp6 | (~c0_1(a607))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[107, 101, 44, 264, 258, 43])).
% 1.77/1.94 tff(266,plain,
% 1.77/1.94 (~c0_1(a607)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[265, 67])).
% 1.77/1.94 tff(267,plain,
% 1.77/1.94 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(268,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[267])).
% 1.77/1.94 tff(269,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(270,plain,
% 1.77/1.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(271,plain,
% 1.77/1.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[270])).
% 1.77/1.94 tff(272,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.77/1.94 tff(273,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.77/1.94 tff(274,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[273, 269])).
% 1.77/1.94 tff(275,plain,(
% 1.77/1.94 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(skolemize,[status(sab)],[274])).
% 1.77/1.94 tff(276,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[275, 268])).
% 1.77/1.94 tff(277,plain,
% 1.77/1.94 (c3_1(a607)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[222, 252])).
% 1.77/1.94 tff(278,plain,
% 1.77/1.94 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(279,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[278])).
% 1.77/1.94 tff(280,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(281,plain,
% 1.77/1.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(282,plain,
% 1.77/1.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[281])).
% 1.77/1.94 tff(283,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.77/1.94 tff(284,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.77/1.94 tff(285,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[284, 280])).
% 1.77/1.94 tff(286,plain,(
% 1.77/1.94 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.77/1.94 inference(skolemize,[status(sab)],[285])).
% 1.77/1.94 tff(287,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[286, 279])).
% 1.77/1.94 tff(288,assumption,(~hskp3), introduced(assumption)).
% 1.77/1.94 tff(289,plain,
% 1.77/1.94 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(290,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[289])).
% 1.77/1.94 tff(291,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(292,plain,
% 1.77/1.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(293,plain,
% 1.77/1.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[292])).
% 1.77/1.94 tff(294,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.77/1.94 tff(295,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.77/1.94 tff(296,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[295, 291])).
% 1.77/1.95 tff(297,plain,(
% 1.77/1.95 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.95 inference(skolemize,[status(sab)],[296])).
% 1.77/1.95 tff(298,plain,
% 1.77/1.95 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[297, 290])).
% 1.77/1.95 tff(299,assumption,(hskp14), introduced(assumption)).
% 1.77/1.95 tff(300,plain,
% 1.77/1.95 (~c3_1(a603)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[193, 299])).
% 1.77/1.95 tff(301,plain,
% 1.77/1.95 (~c1_1(a603)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[162, 299])).
% 1.77/1.95 tff(302,plain,
% 1.77/1.95 (c0_1(a603)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[170, 299])).
% 1.77/1.95 tff(303,assumption,(c3_1(a607)), introduced(assumption)).
% 1.77/1.95 tff(304,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(305,plain,
% 1.77/1.95 ((hskp3 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(306,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[305])).
% 1.77/1.95 tff(307,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[306, 304])).
% 1.77/1.95 tff(308,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(309,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[308, 307])).
% 1.77/1.95 tff(310,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[309, 101, 288, 303, 302, 66, 22, 301, 300, 298])).
% 1.77/1.95 tff(311,plain,((~hskp14) | hskp3 | (~c3_1(a607)) | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(312,plain,
% 1.77/1.95 (~hskp14),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[311, 288, 277, 264, 258])).
% 1.77/1.95 tff(313,plain,
% 1.77/1.95 (^[U: $i] : refl((hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.77/1.95 inference(bind,[status(th)],[])).
% 1.77/1.95 tff(314,plain,
% 1.77/1.95 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(quant_intro,[status(thm)],[313])).
% 1.77/1.95 tff(315,plain,
% 1.77/1.95 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(316,plain,
% 1.77/1.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp14) <=> ((hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp14))), rewrite(((hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp14) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.77/1.95 inference(bind,[status(th)],[])).
% 1.77/1.95 tff(317,plain,
% 1.77/1.95 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp14) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(quant_intro,[status(thm)],[316])).
% 1.77/1.95 tff(318,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.77/1.95 tff(319,plain,
% 1.77/1.95 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.77/1.95 tff(320,plain,
% 1.77/1.95 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[319, 315])).
% 1.77/1.95 tff(321,plain,(
% 1.77/1.95 ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(skolemize,[status(sab)],[320])).
% 1.77/1.95 tff(322,plain,
% 1.77/1.95 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[321, 314])).
% 1.77/1.95 tff(323,assumption,(hskp26), introduced(assumption)).
% 1.77/1.95 tff(324,plain,
% 1.77/1.95 (((~hskp26) | c1_1(a583)) <=> ((~hskp26) | c1_1(a583))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(325,axiom,((~hskp26) | c1_1(a583)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.77/1.95 tff(326,plain,
% 1.77/1.95 ((~hskp26) | c1_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.77/1.95 tff(327,plain,
% 1.77/1.95 ((~hskp26) | c1_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[326, 324])).
% 1.77/1.95 tff(328,plain,
% 1.77/1.95 ((~hskp26) | c1_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[327, 324])).
% 1.77/1.95 tff(329,plain,
% 1.77/1.95 ((~hskp26) | c1_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[328, 324])).
% 1.77/1.95 tff(330,plain,
% 1.77/1.95 ((~hskp26) | c1_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[329, 324])).
% 1.77/1.95 tff(331,plain,
% 1.77/1.95 (c1_1(a583)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[330, 323])).
% 1.77/1.95 tff(332,plain,
% 1.77/1.95 (((~hskp26) | c0_1(a583)) <=> ((~hskp26) | c0_1(a583))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(333,axiom,((~hskp26) | c0_1(a583)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.77/1.95 tff(334,plain,
% 1.77/1.95 ((~hskp26) | c0_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.77/1.95 tff(335,plain,
% 1.77/1.95 ((~hskp26) | c0_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[334, 332])).
% 1.77/1.95 tff(336,plain,
% 1.77/1.95 ((~hskp26) | c0_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[335, 332])).
% 1.77/1.95 tff(337,plain,
% 1.77/1.95 ((~hskp26) | c0_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[336, 332])).
% 1.77/1.95 tff(338,plain,
% 1.77/1.95 ((~hskp26) | c0_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[337, 332])).
% 1.77/1.95 tff(339,plain,
% 1.77/1.95 (c0_1(a583)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[338, 323])).
% 1.77/1.95 tff(340,assumption,(~hskp14), introduced(assumption)).
% 1.77/1.95 tff(341,plain,
% 1.77/1.95 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(342,plain,
% 1.77/1.95 ((hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583))) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(343,plain,
% 1.77/1.95 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[342])).
% 1.77/1.95 tff(344,plain,
% 1.77/1.95 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[343, 341])).
% 1.77/1.95 tff(345,plain,
% 1.77/1.95 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(346,plain,
% 1.77/1.95 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[345, 344])).
% 1.77/1.95 tff(347,plain,
% 1.77/1.95 (~c3_1(a583)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[346, 251, 101, 340, 339, 331, 322])).
% 1.77/1.95 tff(348,plain,
% 1.77/1.95 (^[U: $i] : refl((hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.77/1.95 inference(bind,[status(th)],[])).
% 1.77/1.95 tff(349,plain,
% 1.77/1.95 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(quant_intro,[status(thm)],[348])).
% 1.77/1.95 tff(350,plain,
% 1.77/1.95 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(351,plain,
% 1.77/1.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp22) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp22) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.77/1.95 inference(bind,[status(th)],[])).
% 1.77/1.95 tff(352,plain,
% 1.77/1.95 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp22) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(quant_intro,[status(thm)],[351])).
% 1.77/1.95 tff(353,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.77/1.95 tff(354,plain,
% 1.77/1.95 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.77/1.95 tff(355,plain,
% 1.77/1.95 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[354, 350])).
% 1.77/1.95 tff(356,plain,(
% 1.77/1.95 ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(skolemize,[status(sab)],[355])).
% 1.77/1.95 tff(357,plain,
% 1.77/1.95 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[356, 349])).
% 1.77/1.95 tff(358,plain,
% 1.77/1.95 (((~hskp26) | c2_1(a583)) <=> ((~hskp26) | c2_1(a583))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(359,axiom,((~hskp26) | c2_1(a583)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.77/1.95 tff(360,plain,
% 1.77/1.95 ((~hskp26) | c2_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.77/1.95 tff(361,plain,
% 1.77/1.95 ((~hskp26) | c2_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[360, 358])).
% 1.77/1.95 tff(362,plain,
% 1.77/1.95 ((~hskp26) | c2_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[361, 358])).
% 1.77/1.95 tff(363,plain,
% 1.77/1.95 ((~hskp26) | c2_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[362, 358])).
% 1.77/1.95 tff(364,plain,
% 1.77/1.95 ((~hskp26) | c2_1(a583)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[363, 358])).
% 1.77/1.95 tff(365,plain,
% 1.77/1.95 (c2_1(a583)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[364, 323])).
% 1.77/1.95 tff(366,plain,
% 1.77/1.95 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(367,plain,
% 1.77/1.95 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(368,plain,
% 1.77/1.95 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[367])).
% 1.77/1.95 tff(369,plain,
% 1.77/1.95 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[368, 366])).
% 1.77/1.95 tff(370,plain,
% 1.77/1.95 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(371,plain,
% 1.77/1.95 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[370, 369])).
% 1.77/1.95 tff(372,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[371, 101, 44, 340, 339, 365, 357, 347])).
% 1.77/1.95 tff(373,plain,((~hskp26) | hskp22 | hskp14 | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(374,plain,
% 1.77/1.95 (~hskp26),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[373, 312, 44, 251])).
% 1.77/1.95 tff(375,plain,
% 1.77/1.95 ((hskp26 | hskp11) <=> (hskp26 | hskp11)),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(376,axiom,(hskp26 | hskp11), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.77/1.95 tff(377,plain,
% 1.77/1.95 (hskp26 | hskp11),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.77/1.95 tff(378,plain,
% 1.77/1.95 (hskp26 | hskp11),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[377, 375])).
% 1.77/1.95 tff(379,plain,
% 1.77/1.95 (hskp26 | hskp11),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[378, 375])).
% 1.77/1.95 tff(380,plain,
% 1.77/1.95 (hskp26 | hskp11),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[379, 375])).
% 1.77/1.95 tff(381,plain,
% 1.77/1.95 (hskp26 | hskp11),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[380, 375])).
% 1.77/1.95 tff(382,plain,
% 1.77/1.95 (hskp11),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[381, 374])).
% 1.77/1.95 tff(383,plain,
% 1.77/1.95 (((~hskp11) | c3_1(a599)) <=> ((~hskp11) | c3_1(a599))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(384,axiom,((~hskp11) | c3_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.77/1.95 tff(385,plain,
% 1.77/1.95 ((~hskp11) | c3_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[384, 383])).
% 1.77/1.95 tff(386,plain,
% 1.77/1.95 ((~hskp11) | c3_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[385, 383])).
% 1.77/1.95 tff(387,plain,
% 1.77/1.95 ((~hskp11) | c3_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[386, 383])).
% 1.77/1.95 tff(388,plain,
% 1.77/1.95 ((~hskp11) | c3_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[387, 383])).
% 1.77/1.95 tff(389,plain,
% 1.77/1.95 ((~hskp11) | c3_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[388, 383])).
% 1.77/1.95 tff(390,plain,
% 1.77/1.95 (c3_1(a599)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[389, 382])).
% 1.77/1.95 tff(391,plain,
% 1.77/1.95 (((~hskp11) | (~c1_1(a599))) <=> ((~hskp11) | (~c1_1(a599)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(392,plain,
% 1.77/1.95 (((~c1_1(a599)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a599)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(393,axiom,((~c1_1(a599)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.77/1.95 tff(394,plain,
% 1.77/1.95 ((~hskp11) | (~c1_1(a599))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[393, 392])).
% 1.77/1.95 tff(395,plain,
% 1.77/1.95 ((~hskp11) | (~c1_1(a599))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[394, 391])).
% 1.77/1.95 tff(396,plain,
% 1.77/1.95 (~c1_1(a599)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[395, 382])).
% 1.77/1.95 tff(397,plain,
% 1.77/1.95 (((~hskp11) | c2_1(a599)) <=> ((~hskp11) | c2_1(a599))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(398,axiom,((~hskp11) | c2_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.77/1.95 tff(399,plain,
% 1.77/1.95 ((~hskp11) | c2_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.77/1.95 tff(400,plain,
% 1.77/1.95 ((~hskp11) | c2_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[399, 397])).
% 1.77/1.95 tff(401,plain,
% 1.77/1.95 ((~hskp11) | c2_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[400, 397])).
% 1.77/1.95 tff(402,plain,
% 1.77/1.95 ((~hskp11) | c2_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[401, 397])).
% 1.77/1.95 tff(403,plain,
% 1.77/1.95 ((~hskp11) | c2_1(a599)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[402, 397])).
% 1.77/1.95 tff(404,plain,
% 1.77/1.95 (c2_1(a599)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[403, 382])).
% 1.77/1.95 tff(405,plain,
% 1.77/1.95 (^[U: $i] : refl((hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.77/1.95 inference(bind,[status(th)],[])).
% 1.77/1.95 tff(406,plain,
% 1.77/1.95 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.95 inference(quant_intro,[status(thm)],[405])).
% 1.77/1.95 tff(407,plain,
% 1.77/1.95 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(408,plain,
% 1.77/1.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp6) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp6) <=> (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.77/1.95 inference(bind,[status(th)],[])).
% 1.77/1.95 tff(409,plain,
% 1.77/1.95 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp6) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.95 inference(quant_intro,[status(thm)],[408])).
% 1.77/1.95 tff(410,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.77/1.95 tff(411,plain,
% 1.77/1.95 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.77/1.95 tff(412,plain,
% 1.77/1.95 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[411, 407])).
% 1.77/1.95 tff(413,plain,(
% 1.77/1.95 ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.95 inference(skolemize,[status(sab)],[412])).
% 1.77/1.95 tff(414,plain,
% 1.77/1.95 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[413, 406])).
% 1.77/1.95 tff(415,plain,
% 1.77/1.95 (^[U: $i] : refl((hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.77/1.95 inference(bind,[status(th)],[])).
% 1.77/1.95 tff(416,plain,
% 1.77/1.95 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.95 inference(quant_intro,[status(thm)],[415])).
% 1.77/1.95 tff(417,plain,
% 1.77/1.95 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(418,plain,
% 1.77/1.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp23) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp23))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp23) <=> (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp23) <=> (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.77/1.95 inference(bind,[status(th)],[])).
% 1.77/1.95 tff(419,plain,
% 1.77/1.95 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp23) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.95 inference(quant_intro,[status(thm)],[418])).
% 1.77/1.95 tff(420,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.77/1.95 tff(421,plain,
% 1.77/1.95 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.77/1.95 tff(422,plain,
% 1.77/1.95 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[421, 417])).
% 1.77/1.95 tff(423,plain,(
% 1.77/1.95 ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.95 inference(skolemize,[status(sab)],[422])).
% 1.77/1.95 tff(424,plain,
% 1.77/1.95 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[423, 416])).
% 1.77/1.95 tff(425,assumption,(~c1_1(a599)), introduced(assumption)).
% 1.77/1.95 tff(426,assumption,(c3_1(a599)), introduced(assumption)).
% 1.77/1.95 tff(427,assumption,(c2_1(a599)), introduced(assumption)).
% 1.77/1.95 tff(428,plain,
% 1.77/1.95 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(429,plain,
% 1.77/1.95 ((hskp23 | hskp14 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599))) <=> (hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(430,plain,
% 1.77/1.95 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[429])).
% 1.77/1.95 tff(431,plain,
% 1.77/1.95 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[430, 428])).
% 1.77/1.95 tff(432,plain,
% 1.77/1.95 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(433,plain,
% 1.77/1.95 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[432, 431])).
% 1.77/1.95 tff(434,plain,
% 1.77/1.95 (hskp23),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[433, 101, 340, 427, 426, 425, 424])).
% 1.77/1.95 tff(435,plain,
% 1.77/1.95 (((~hskp23) | (~c1_1(a636))) <=> ((~hskp23) | (~c1_1(a636)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(436,plain,
% 1.77/1.95 (((~c1_1(a636)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a636)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(437,axiom,((~c1_1(a636)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.77/1.95 tff(438,plain,
% 1.77/1.95 ((~hskp23) | (~c1_1(a636))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.77/1.95 tff(439,plain,
% 1.77/1.95 ((~hskp23) | (~c1_1(a636))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[438, 435])).
% 1.77/1.95 tff(440,plain,
% 1.77/1.95 (~c1_1(a636)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[439, 434])).
% 1.77/1.95 tff(441,plain,
% 1.77/1.95 (((~hskp23) | (~c0_1(a636))) <=> ((~hskp23) | (~c0_1(a636)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(442,plain,
% 1.77/1.95 (((~c0_1(a636)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a636)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(443,axiom,((~c0_1(a636)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.77/1.95 tff(444,plain,
% 1.77/1.95 ((~hskp23) | (~c0_1(a636))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[443, 442])).
% 1.77/1.95 tff(445,plain,
% 1.77/1.95 ((~hskp23) | (~c0_1(a636))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[444, 441])).
% 1.77/1.95 tff(446,plain,
% 1.77/1.95 (~c0_1(a636)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[445, 434])).
% 1.77/1.95 tff(447,plain,
% 1.77/1.95 (((~hskp23) | c3_1(a636)) <=> ((~hskp23) | c3_1(a636))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(448,axiom,((~hskp23) | c3_1(a636)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.77/1.95 tff(449,plain,
% 1.77/1.95 ((~hskp23) | c3_1(a636)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[448, 447])).
% 1.77/1.95 tff(450,plain,
% 1.77/1.95 ((~hskp23) | c3_1(a636)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[449, 447])).
% 1.77/1.95 tff(451,plain,
% 1.77/1.95 ((~hskp23) | c3_1(a636)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[450, 447])).
% 1.77/1.95 tff(452,plain,
% 1.77/1.95 ((~hskp23) | c3_1(a636)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[451, 447])).
% 1.77/1.95 tff(453,plain,
% 1.77/1.95 ((~hskp23) | c3_1(a636)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[452, 447])).
% 1.77/1.95 tff(454,plain,
% 1.77/1.95 (c3_1(a636)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[453, 434])).
% 1.77/1.95 tff(455,plain,
% 1.77/1.95 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(456,plain,
% 1.77/1.95 ((hskp8 | hskp6 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(457,plain,
% 1.77/1.95 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[456])).
% 1.77/1.95 tff(458,plain,
% 1.77/1.95 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[457, 455])).
% 1.77/1.95 tff(459,plain,
% 1.77/1.95 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(460,plain,
% 1.77/1.95 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.77/1.95 tff(461,plain,
% 1.77/1.95 (hskp8 | hskp6),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[460, 101, 454, 446, 440, 414])).
% 1.77/1.95 tff(462,plain,
% 1.77/1.95 (hskp8),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[461, 67])).
% 1.77/1.95 tff(463,plain,
% 1.77/1.95 (((~hskp8) | c3_1(a593)) <=> ((~hskp8) | c3_1(a593))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(464,axiom,((~hskp8) | c3_1(a593)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.77/1.95 tff(465,plain,
% 1.77/1.95 ((~hskp8) | c3_1(a593)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[464, 463])).
% 1.77/1.95 tff(466,plain,
% 1.77/1.95 ((~hskp8) | c3_1(a593)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[465, 463])).
% 1.77/1.95 tff(467,plain,
% 1.77/1.95 ((~hskp8) | c3_1(a593)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[466, 463])).
% 1.77/1.95 tff(468,plain,
% 1.77/1.95 ((~hskp8) | c3_1(a593)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[467, 463])).
% 1.77/1.95 tff(469,plain,
% 1.77/1.95 ((~hskp8) | c3_1(a593)),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[468, 463])).
% 1.77/1.95 tff(470,plain,
% 1.77/1.95 (c3_1(a593)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[469, 462])).
% 1.77/1.96 tff(471,plain,
% 1.77/1.96 (((~hskp8) | c1_1(a593)) <=> ((~hskp8) | c1_1(a593))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(472,axiom,((~hskp8) | c1_1(a593)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.77/1.96 tff(473,plain,
% 1.77/1.96 ((~hskp8) | c1_1(a593)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.77/1.96 tff(474,plain,
% 1.77/1.96 ((~hskp8) | c1_1(a593)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[473, 471])).
% 1.77/1.96 tff(475,plain,
% 1.77/1.96 ((~hskp8) | c1_1(a593)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[474, 471])).
% 1.77/1.96 tff(476,plain,
% 1.77/1.96 ((~hskp8) | c1_1(a593)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[475, 471])).
% 1.77/1.96 tff(477,plain,
% 1.77/1.96 ((~hskp8) | c1_1(a593)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[476, 471])).
% 1.77/1.96 tff(478,plain,
% 1.77/1.96 (c1_1(a593)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[477, 462])).
% 1.77/1.96 tff(479,plain,
% 1.77/1.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(480,plain,
% 1.77/1.96 ((hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593))) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(481,plain,
% 1.77/1.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[480])).
% 1.77/1.96 tff(482,plain,
% 1.77/1.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[481, 479])).
% 1.77/1.96 tff(483,plain,
% 1.77/1.96 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(484,plain,
% 1.77/1.96 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.77/1.96 tff(485,plain,
% 1.77/1.96 (~c0_1(a593)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[484, 251, 101, 340, 478, 470, 322])).
% 1.77/1.96 tff(486,plain,
% 1.77/1.96 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(487,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[486])).
% 1.77/1.96 tff(488,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(489,plain,
% 1.77/1.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(490,plain,
% 1.77/1.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[489])).
% 1.77/1.96 tff(491,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.77/1.96 tff(492,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.77/1.96 tff(493,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[492, 488])).
% 1.77/1.96 tff(494,plain,(
% 1.77/1.96 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.96 inference(skolemize,[status(sab)],[493])).
% 1.77/1.96 tff(495,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[494, 487])).
% 1.77/1.96 tff(496,plain,
% 1.77/1.96 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(497,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[496])).
% 1.77/1.96 tff(498,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(499,plain,
% 1.77/1.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(500,plain,
% 1.77/1.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[499])).
% 1.77/1.96 tff(501,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.77/1.96 tff(502,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.77/1.96 tff(503,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[502, 498])).
% 1.77/1.96 tff(504,plain,(
% 1.77/1.96 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.77/1.96 inference(skolemize,[status(sab)],[503])).
% 1.77/1.96 tff(505,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[504, 497])).
% 1.77/1.96 tff(506,plain,
% 1.77/1.96 (((~hskp8) | (~c2_1(a593))) <=> ((~hskp8) | (~c2_1(a593)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(507,plain,
% 1.77/1.96 (((~c2_1(a593)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a593)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(508,axiom,((~c2_1(a593)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.77/1.96 tff(509,plain,
% 1.77/1.96 ((~hskp8) | (~c2_1(a593))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[508, 507])).
% 1.77/1.96 tff(510,plain,
% 1.77/1.96 ((~hskp8) | (~c2_1(a593))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[509, 506])).
% 1.77/1.96 tff(511,plain,
% 1.77/1.96 (~c2_1(a593)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[510, 462])).
% 1.77/1.96 tff(512,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(513,plain,
% 1.77/1.96 ((hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(514,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[513])).
% 1.77/1.96 tff(515,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[514, 512])).
% 1.77/1.96 tff(516,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(517,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[516, 515])).
% 1.77/1.96 tff(518,plain,
% 1.77/1.96 (~c0_1(a599)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[517, 101, 340, 427, 426, 478, 470, 511, 505])).
% 1.77/1.96 tff(519,plain,
% 1.77/1.96 (^[U: $i] : refl((hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(520,plain,
% 1.77/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[519])).
% 1.77/1.96 tff(521,plain,
% 1.77/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(522,plain,
% 1.77/1.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(523,plain,
% 1.77/1.96 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[522])).
% 1.77/1.96 tff(524,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.77/1.96 tff(525,plain,
% 1.77/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[524, 523])).
% 1.77/1.96 tff(526,plain,
% 1.77/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[525, 521])).
% 1.77/1.96 tff(527,plain,(
% 1.77/1.96 ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.77/1.96 inference(skolemize,[status(sab)],[526])).
% 1.77/1.96 tff(528,plain,
% 1.77/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[527, 520])).
% 1.77/1.96 tff(529,plain,
% 1.77/1.96 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(530,plain,
% 1.77/1.96 ((hskp6 | hskp5 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(531,plain,
% 1.77/1.96 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599)))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[530])).
% 1.77/1.96 tff(532,plain,
% 1.77/1.96 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599))),
% 1.77/1.96 inference(transitivity,[status(thm)],[531, 529])).
% 1.77/1.96 tff(533,plain,
% 1.77/1.96 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(534,plain,
% 1.77/1.96 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.77/1.96 tff(535,plain,
% 1.77/1.96 (hskp6 | hskp5 | c0_1(a599)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[534, 101, 427, 425, 528])).
% 1.77/1.96 tff(536,plain,
% 1.77/1.96 (hskp5),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[535, 518, 67])).
% 1.77/1.96 tff(537,plain,
% 1.77/1.96 (((~hskp5) | (~c2_1(a589))) <=> ((~hskp5) | (~c2_1(a589)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(538,plain,
% 1.77/1.96 (((~c2_1(a589)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a589)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(539,axiom,((~c2_1(a589)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.77/1.96 tff(540,plain,
% 1.77/1.96 ((~hskp5) | (~c2_1(a589))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[539, 538])).
% 1.77/1.96 tff(541,plain,
% 1.77/1.96 ((~hskp5) | (~c2_1(a589))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[540, 537])).
% 1.77/1.96 tff(542,plain,
% 1.77/1.96 (~c2_1(a589)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[541, 536])).
% 1.77/1.96 tff(543,plain,
% 1.77/1.96 (((~hskp5) | c1_1(a589)) <=> ((~hskp5) | c1_1(a589))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(544,axiom,((~hskp5) | c1_1(a589)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.77/1.96 tff(545,plain,
% 1.77/1.96 ((~hskp5) | c1_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[544, 543])).
% 1.77/1.96 tff(546,plain,
% 1.77/1.96 ((~hskp5) | c1_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[545, 543])).
% 1.77/1.96 tff(547,plain,
% 1.77/1.96 ((~hskp5) | c1_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[546, 543])).
% 1.77/1.96 tff(548,plain,
% 1.77/1.96 ((~hskp5) | c1_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[547, 543])).
% 1.77/1.96 tff(549,plain,
% 1.77/1.96 ((~hskp5) | c1_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[548, 543])).
% 1.77/1.96 tff(550,plain,
% 1.77/1.96 (c1_1(a589)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[549, 536])).
% 1.77/1.96 tff(551,plain,
% 1.77/1.96 (((~hskp5) | c0_1(a589)) <=> ((~hskp5) | c0_1(a589))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(552,axiom,((~hskp5) | c0_1(a589)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.77/1.96 tff(553,plain,
% 1.77/1.96 ((~hskp5) | c0_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[552, 551])).
% 1.77/1.96 tff(554,plain,
% 1.77/1.96 ((~hskp5) | c0_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[553, 551])).
% 1.77/1.96 tff(555,plain,
% 1.77/1.96 ((~hskp5) | c0_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[554, 551])).
% 1.77/1.96 tff(556,plain,
% 1.77/1.96 ((~hskp5) | c0_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[555, 551])).
% 1.77/1.96 tff(557,plain,
% 1.77/1.96 ((~hskp5) | c0_1(a589)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[556, 551])).
% 1.77/1.96 tff(558,plain,
% 1.77/1.96 (c0_1(a589)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[557, 536])).
% 1.77/1.96 tff(559,assumption,(hskp27), introduced(assumption)).
% 1.77/1.96 tff(560,plain,
% 1.77/1.96 (((~hskp27) | c3_1(a611)) <=> ((~hskp27) | c3_1(a611))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(561,axiom,((~hskp27) | c3_1(a611)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.77/1.96 tff(562,plain,
% 1.77/1.96 ((~hskp27) | c3_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[561, 560])).
% 1.77/1.96 tff(563,plain,
% 1.77/1.96 ((~hskp27) | c3_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[562, 560])).
% 1.77/1.96 tff(564,plain,
% 1.77/1.96 ((~hskp27) | c3_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[563, 560])).
% 1.77/1.96 tff(565,plain,
% 1.77/1.96 ((~hskp27) | c3_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[564, 560])).
% 1.77/1.96 tff(566,plain,
% 1.77/1.96 ((~hskp27) | c3_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[565, 560])).
% 1.77/1.96 tff(567,plain,
% 1.77/1.96 (c3_1(a611)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[566, 559])).
% 1.77/1.96 tff(568,plain,
% 1.77/1.96 (((~hskp27) | c1_1(a611)) <=> ((~hskp27) | c1_1(a611))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(569,axiom,((~hskp27) | c1_1(a611)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.77/1.96 tff(570,plain,
% 1.77/1.96 ((~hskp27) | c1_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[569, 568])).
% 1.77/1.96 tff(571,plain,
% 1.77/1.96 ((~hskp27) | c1_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[570, 568])).
% 1.77/1.96 tff(572,plain,
% 1.77/1.96 ((~hskp27) | c1_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[571, 568])).
% 1.77/1.96 tff(573,plain,
% 1.77/1.96 ((~hskp27) | c1_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[572, 568])).
% 1.77/1.96 tff(574,plain,
% 1.77/1.96 ((~hskp27) | c1_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[573, 568])).
% 1.77/1.96 tff(575,plain,
% 1.77/1.96 (c1_1(a611)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[574, 559])).
% 1.77/1.96 tff(576,plain,
% 1.77/1.96 (((~hskp27) | c0_1(a611)) <=> ((~hskp27) | c0_1(a611))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(577,axiom,((~hskp27) | c0_1(a611)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.77/1.96 tff(578,plain,
% 1.77/1.96 ((~hskp27) | c0_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.77/1.96 tff(579,plain,
% 1.77/1.96 ((~hskp27) | c0_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[578, 576])).
% 1.77/1.96 tff(580,plain,
% 1.77/1.96 ((~hskp27) | c0_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[579, 576])).
% 1.77/1.96 tff(581,plain,
% 1.77/1.96 ((~hskp27) | c0_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[580, 576])).
% 1.77/1.96 tff(582,plain,
% 1.77/1.96 ((~hskp27) | c0_1(a611)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[581, 576])).
% 1.77/1.96 tff(583,plain,
% 1.77/1.96 (c0_1(a611)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[582, 559])).
% 1.77/1.96 tff(584,plain,
% 1.77/1.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(585,plain,
% 1.77/1.96 ((hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611))) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(586,plain,
% 1.77/1.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[585])).
% 1.77/1.96 tff(587,plain,
% 1.77/1.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[586, 584])).
% 1.77/1.96 tff(588,plain,
% 1.77/1.96 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(589,plain,
% 1.77/1.96 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[588, 587])).
% 1.77/1.96 tff(590,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[589, 251, 101, 340, 583, 575, 567, 322])).
% 1.77/1.96 tff(591,plain,((~hskp27) | hskp29 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(592,plain,
% 1.77/1.96 (~hskp27),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[591, 340, 251])).
% 1.77/1.96 tff(593,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(594,plain,
% 1.77/1.96 ((hskp27 | (~ndr1_0) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593))) <=> (hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(595,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[594])).
% 1.77/1.96 tff(596,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[595, 593])).
% 1.77/1.96 tff(597,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(598,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[597, 596])).
% 1.77/1.96 tff(599,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[598, 101, 592, 470, 558, 550, 511, 542, 495, 485])).
% 1.77/1.96 tff(600,plain,(hskp6 | (~c2_1(a599)) | c1_1(a599) | hskp14 | (~c3_1(a599)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(601,plain,
% 1.77/1.96 (hskp6),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[600, 404, 396, 312, 390, 251])).
% 1.77/1.96 tff(602,plain,
% 1.77/1.96 (((~hskp6) | (~c0_1(a590))) <=> ((~hskp6) | (~c0_1(a590)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(603,plain,
% 1.77/1.96 (((~c0_1(a590)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a590)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(604,axiom,((~c0_1(a590)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.77/1.96 tff(605,plain,
% 1.77/1.96 ((~hskp6) | (~c0_1(a590))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[604, 603])).
% 1.77/1.96 tff(606,plain,
% 1.77/1.96 ((~hskp6) | (~c0_1(a590))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[605, 602])).
% 1.77/1.96 tff(607,plain,
% 1.77/1.96 (~c0_1(a590)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[606, 601])).
% 1.77/1.96 tff(608,plain,
% 1.77/1.96 (((~hskp6) | c3_1(a590)) <=> ((~hskp6) | c3_1(a590))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(609,axiom,((~hskp6) | c3_1(a590)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.77/1.96 tff(610,plain,
% 1.77/1.96 ((~hskp6) | c3_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[609, 608])).
% 1.77/1.96 tff(611,plain,
% 1.77/1.96 ((~hskp6) | c3_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[610, 608])).
% 1.77/1.96 tff(612,plain,
% 1.77/1.96 ((~hskp6) | c3_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[611, 608])).
% 1.77/1.96 tff(613,plain,
% 1.77/1.96 ((~hskp6) | c3_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[612, 608])).
% 1.77/1.96 tff(614,plain,
% 1.77/1.96 ((~hskp6) | c3_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[613, 608])).
% 1.77/1.96 tff(615,plain,
% 1.77/1.96 (c3_1(a590)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[614, 601])).
% 1.77/1.96 tff(616,plain,
% 1.77/1.96 (((~hskp6) | c2_1(a590)) <=> ((~hskp6) | c2_1(a590))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(617,axiom,((~hskp6) | c2_1(a590)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.77/1.96 tff(618,plain,
% 1.77/1.96 ((~hskp6) | c2_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.77/1.96 tff(619,plain,
% 1.77/1.96 ((~hskp6) | c2_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[618, 616])).
% 1.77/1.96 tff(620,plain,
% 1.77/1.96 ((~hskp6) | c2_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[619, 616])).
% 1.77/1.96 tff(621,plain,
% 1.77/1.96 ((~hskp6) | c2_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[620, 616])).
% 1.77/1.96 tff(622,plain,
% 1.77/1.96 ((~hskp6) | c2_1(a590)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[621, 616])).
% 1.77/1.96 tff(623,plain,
% 1.77/1.96 (c2_1(a590)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[622, 601])).
% 1.77/1.96 tff(624,plain,
% 1.77/1.96 (hskp23),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[433, 101, 312, 404, 390, 396, 424])).
% 1.77/1.96 tff(625,plain,
% 1.77/1.96 (~c1_1(a636)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[439, 624])).
% 1.77/1.96 tff(626,plain,
% 1.77/1.96 (~c0_1(a636)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[445, 624])).
% 1.77/1.96 tff(627,plain,
% 1.77/1.96 (c3_1(a636)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[453, 624])).
% 1.77/1.96 tff(628,plain,
% 1.77/1.96 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(629,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.77/1.96 inference(quant_intro,[status(thm)],[628])).
% 1.77/1.96 tff(630,plain,
% 1.77/1.96 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(631,plain,
% 1.77/1.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.77/1.96 inference(bind,[status(th)],[])).
% 1.77/1.96 tff(632,plain,
% 1.77/1.96 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.77/1.97 inference(quant_intro,[status(thm)],[631])).
% 1.77/1.97 tff(633,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.77/1.97 tff(634,plain,
% 1.77/1.97 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[633, 632])).
% 1.77/1.97 tff(635,plain,
% 1.77/1.97 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[634, 630])).
% 1.77/1.97 tff(636,plain,(
% 1.77/1.97 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.77/1.97 inference(skolemize,[status(sab)],[635])).
% 1.77/1.97 tff(637,plain,
% 1.77/1.97 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[636, 629])).
% 1.77/1.97 tff(638,assumption,(hskp20), introduced(assumption)).
% 1.77/1.97 tff(639,plain,
% 1.77/1.97 (((~hskp20) | (~c3_1(a623))) <=> ((~hskp20) | (~c3_1(a623)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(640,plain,
% 1.77/1.97 (((~c3_1(a623)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a623)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(641,axiom,((~c3_1(a623)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.77/1.97 tff(642,plain,
% 1.77/1.97 ((~hskp20) | (~c3_1(a623))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[641, 640])).
% 1.77/1.97 tff(643,plain,
% 1.77/1.97 ((~hskp20) | (~c3_1(a623))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[642, 639])).
% 1.77/1.97 tff(644,plain,
% 1.77/1.97 (~c3_1(a623)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[643, 638])).
% 1.77/1.97 tff(645,plain,
% 1.77/1.97 (((~hskp20) | (~c2_1(a623))) <=> ((~hskp20) | (~c2_1(a623)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(646,plain,
% 1.77/1.97 (((~c2_1(a623)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a623)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(647,axiom,((~c2_1(a623)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.77/1.97 tff(648,plain,
% 1.77/1.97 ((~hskp20) | (~c2_1(a623))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[647, 646])).
% 1.77/1.97 tff(649,plain,
% 1.77/1.97 ((~hskp20) | (~c2_1(a623))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[648, 645])).
% 1.77/1.97 tff(650,plain,
% 1.77/1.97 (~c2_1(a623)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[649, 638])).
% 1.77/1.97 tff(651,plain,
% 1.77/1.97 (((~hskp20) | (~c1_1(a623))) <=> ((~hskp20) | (~c1_1(a623)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(652,plain,
% 1.77/1.97 (((~c1_1(a623)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a623)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(653,axiom,((~c1_1(a623)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.77/1.97 tff(654,plain,
% 1.77/1.97 ((~hskp20) | (~c1_1(a623))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[653, 652])).
% 1.77/1.97 tff(655,plain,
% 1.77/1.97 ((~hskp20) | (~c1_1(a623))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[654, 651])).
% 1.77/1.97 tff(656,plain,
% 1.77/1.97 (~c1_1(a623)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[655, 638])).
% 1.77/1.97 tff(657,assumption,(~c1_1(a636)), introduced(assumption)).
% 1.77/1.97 tff(658,assumption,(~c0_1(a636)), introduced(assumption)).
% 1.77/1.97 tff(659,assumption,(c3_1(a636)), introduced(assumption)).
% 1.77/1.97 tff(660,assumption,(~hskp26), introduced(assumption)).
% 1.77/1.97 tff(661,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(662,plain,
% 1.77/1.97 ((hskp26 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)) | c3_1(a623) | c1_1(a623) | c2_1(a623)) <=> (hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(663,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636))))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[662])).
% 1.77/1.97 tff(664,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636)))),
% 1.77/1.97 inference(transitivity,[status(thm)],[663, 661])).
% 1.77/1.97 tff(665,plain,
% 1.77/1.97 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)) | c3_1(a623) | c1_1(a623) | c2_1(a623))),
% 1.77/1.97 inference(quant_inst,[status(thm)],[])).
% 1.77/1.97 tff(666,plain,
% 1.77/1.97 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[665, 664])).
% 1.77/1.97 tff(667,plain,
% 1.77/1.97 ($false),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[666, 660, 101, 659, 658, 657, 656, 650, 644, 637])).
% 1.77/1.97 tff(668,plain,((~hskp20) | hskp26 | (~c3_1(a636)) | c0_1(a636) | c1_1(a636)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.97 tff(669,plain,
% 1.77/1.97 (~hskp20),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[668, 374, 627, 626, 625])).
% 1.77/1.97 tff(670,assumption,(hskp12), introduced(assumption)).
% 1.77/1.97 tff(671,plain,
% 1.77/1.97 (((~hskp12) | (~c3_1(a600))) <=> ((~hskp12) | (~c3_1(a600)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(672,plain,
% 1.77/1.97 (((~c3_1(a600)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a600)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(673,axiom,((~c3_1(a600)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.77/1.97 tff(674,plain,
% 1.77/1.97 ((~hskp12) | (~c3_1(a600))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[673, 672])).
% 1.77/1.97 tff(675,plain,
% 1.77/1.97 ((~hskp12) | (~c3_1(a600))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[674, 671])).
% 1.77/1.97 tff(676,plain,
% 1.77/1.97 (~c3_1(a600)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[675, 670])).
% 1.77/1.97 tff(677,plain,
% 1.77/1.97 (((~hskp12) | c2_1(a600)) <=> ((~hskp12) | c2_1(a600))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(678,axiom,((~hskp12) | c2_1(a600)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.77/1.97 tff(679,plain,
% 1.77/1.97 ((~hskp12) | c2_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[678, 677])).
% 1.77/1.97 tff(680,plain,
% 1.77/1.97 ((~hskp12) | c2_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[679, 677])).
% 1.77/1.97 tff(681,plain,
% 1.77/1.97 ((~hskp12) | c2_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[680, 677])).
% 1.77/1.97 tff(682,plain,
% 1.77/1.97 ((~hskp12) | c2_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[681, 677])).
% 1.77/1.97 tff(683,plain,
% 1.77/1.97 ((~hskp12) | c2_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[682, 677])).
% 1.77/1.97 tff(684,plain,
% 1.77/1.97 (c2_1(a600)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[683, 670])).
% 1.77/1.97 tff(685,plain,
% 1.77/1.97 (((~hskp12) | c0_1(a600)) <=> ((~hskp12) | c0_1(a600))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(686,axiom,((~hskp12) | c0_1(a600)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.77/1.97 tff(687,plain,
% 1.77/1.97 ((~hskp12) | c0_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.77/1.97 tff(688,plain,
% 1.77/1.97 ((~hskp12) | c0_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[687, 685])).
% 1.77/1.97 tff(689,plain,
% 1.77/1.97 ((~hskp12) | c0_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[688, 685])).
% 1.77/1.97 tff(690,plain,
% 1.77/1.97 ((~hskp12) | c0_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[689, 685])).
% 1.77/1.97 tff(691,plain,
% 1.77/1.97 ((~hskp12) | c0_1(a600)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[690, 685])).
% 1.77/1.97 tff(692,plain,
% 1.77/1.97 (c0_1(a600)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[691, 670])).
% 1.77/1.97 tff(693,plain,
% 1.77/1.97 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(694,plain,
% 1.77/1.97 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600))) <=> (hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(695,plain,
% 1.77/1.97 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[694])).
% 1.77/1.97 tff(696,plain,
% 1.77/1.97 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 1.77/1.97 inference(transitivity,[status(thm)],[695, 693])).
% 1.77/1.97 tff(697,plain,
% 1.77/1.97 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))),
% 1.77/1.97 inference(quant_inst,[status(thm)],[])).
% 1.77/1.97 tff(698,plain,
% 1.77/1.97 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[697, 696])).
% 1.77/1.97 tff(699,plain,
% 1.77/1.97 ($false),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[698, 101, 44, 340, 692, 684, 676, 357])).
% 1.77/1.97 tff(700,plain,((~hskp12) | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.77/1.97 tff(701,plain,
% 1.77/1.97 (~hskp12),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[700, 312, 44])).
% 1.77/1.97 tff(702,plain,
% 1.77/1.97 ((hskp26 | hskp12 | hskp8) <=> (hskp26 | hskp12 | hskp8)),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(703,plain,
% 1.77/1.97 (((hskp26 | hskp12) | hskp8) <=> (hskp26 | hskp12 | hskp8)),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(704,plain,
% 1.77/1.97 ((hskp26 | hskp12) <=> (hskp26 | hskp12)),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(705,plain,
% 1.77/1.97 (((hskp26 | hskp12) | hskp8) <=> ((hskp26 | hskp12) | hskp8)),
% 1.77/1.97 inference(monotonicity,[status(thm)],[704])).
% 1.77/1.97 tff(706,plain,
% 1.77/1.97 (((hskp26 | hskp12) | hskp8) <=> (hskp26 | hskp12 | hskp8)),
% 1.77/1.97 inference(transitivity,[status(thm)],[705, 703])).
% 1.77/1.97 tff(707,axiom,((hskp26 | hskp12) | hskp8), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 1.77/1.97 tff(708,plain,
% 1.77/1.97 (hskp26 | hskp12 | hskp8),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[707, 706])).
% 1.77/1.97 tff(709,plain,
% 1.77/1.97 (hskp26 | hskp12 | hskp8),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[708, 702])).
% 1.77/1.97 tff(710,plain,
% 1.77/1.97 (hskp26 | hskp12 | hskp8),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[709, 702])).
% 1.77/1.97 tff(711,plain,
% 1.77/1.97 (hskp26 | hskp12 | hskp8),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[710, 702])).
% 1.77/1.97 tff(712,plain,
% 1.77/1.97 (hskp26 | hskp12 | hskp8),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[711, 702])).
% 1.77/1.97 tff(713,plain,
% 1.77/1.97 (hskp8),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[712, 701, 374])).
% 1.77/1.97 tff(714,plain,
% 1.77/1.97 (c3_1(a593)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[469, 713])).
% 1.77/1.97 tff(715,plain,
% 1.77/1.97 (c1_1(a593)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[477, 713])).
% 1.77/1.97 tff(716,plain,
% 1.77/1.97 (~c0_1(a593)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[484, 251, 101, 312, 715, 714, 322])).
% 1.77/1.97 tff(717,plain,
% 1.77/1.97 (^[U: $i] : refl((hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.77/1.97 inference(bind,[status(th)],[])).
% 1.77/1.97 tff(718,plain,
% 1.77/1.97 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.77/1.97 inference(quant_intro,[status(thm)],[717])).
% 1.77/1.97 tff(719,plain,
% 1.77/1.97 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(720,plain,
% 1.77/1.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp20) <=> ((hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp20))), rewrite(((hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp20) <=> (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp20) <=> (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.77/1.97 inference(bind,[status(th)],[])).
% 1.77/1.97 tff(721,plain,
% 1.77/1.97 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp20) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.77/1.97 inference(quant_intro,[status(thm)],[720])).
% 1.77/1.97 tff(722,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.77/1.97 tff(723,plain,
% 1.77/1.97 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[722, 721])).
% 1.77/1.97 tff(724,plain,
% 1.77/1.97 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[723, 719])).
% 1.77/1.97 tff(725,plain,(
% 1.77/1.97 ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.77/1.97 inference(skolemize,[status(sab)],[724])).
% 1.77/1.97 tff(726,plain,
% 1.77/1.97 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[725, 718])).
% 1.77/1.97 tff(727,plain,
% 1.77/1.97 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(728,plain,
% 1.77/1.97 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.77/1.97 inference(quant_inst,[status(thm)],[])).
% 1.77/1.97 tff(729,plain,
% 1.77/1.97 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[728, 727])).
% 1.77/1.97 tff(730,plain,
% 1.77/1.97 (hskp20 | hskp7),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[729, 101, 715, 714, 726, 716])).
% 1.77/1.97 tff(731,plain,
% 1.77/1.97 (hskp7),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[730, 669])).
% 1.77/1.97 tff(732,plain,
% 1.77/1.97 (((~hskp7) | (~c3_1(a592))) <=> ((~hskp7) | (~c3_1(a592)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(733,plain,
% 1.77/1.97 (((~c3_1(a592)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a592)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(734,axiom,((~c3_1(a592)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.77/1.97 tff(735,plain,
% 1.77/1.97 ((~hskp7) | (~c3_1(a592))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.77/1.97 tff(736,plain,
% 1.77/1.97 ((~hskp7) | (~c3_1(a592))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[735, 732])).
% 1.77/1.97 tff(737,plain,
% 1.77/1.97 (~c3_1(a592)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[736, 731])).
% 1.77/1.97 tff(738,plain,
% 1.77/1.97 (((~hskp7) | (~c0_1(a592))) <=> ((~hskp7) | (~c0_1(a592)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(739,plain,
% 1.77/1.97 (((~c0_1(a592)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a592)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(740,axiom,((~c0_1(a592)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.77/1.97 tff(741,plain,
% 1.77/1.97 ((~hskp7) | (~c0_1(a592))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[740, 739])).
% 1.77/1.97 tff(742,plain,
% 1.77/1.97 ((~hskp7) | (~c0_1(a592))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[741, 738])).
% 1.77/1.97 tff(743,plain,
% 1.77/1.97 (~c0_1(a592)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[742, 731])).
% 1.77/1.97 tff(744,plain,
% 1.77/1.97 (((~hskp7) | c2_1(a592)) <=> ((~hskp7) | c2_1(a592))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(745,axiom,((~hskp7) | c2_1(a592)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.77/1.97 tff(746,plain,
% 1.77/1.97 ((~hskp7) | c2_1(a592)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[745, 744])).
% 1.77/1.97 tff(747,plain,
% 1.77/1.97 ((~hskp7) | c2_1(a592)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[746, 744])).
% 1.77/1.97 tff(748,plain,
% 1.77/1.97 ((~hskp7) | c2_1(a592)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[747, 744])).
% 1.77/1.97 tff(749,plain,
% 1.77/1.97 ((~hskp7) | c2_1(a592)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[748, 744])).
% 1.77/1.97 tff(750,plain,
% 1.77/1.97 ((~hskp7) | c2_1(a592)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[749, 744])).
% 1.77/1.97 tff(751,plain,
% 1.77/1.97 (c2_1(a592)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[750, 731])).
% 1.77/1.97 tff(752,assumption,(~hskp4), introduced(assumption)).
% 1.77/1.97 tff(753,plain,
% 1.77/1.97 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.77/1.97 inference(bind,[status(th)],[])).
% 1.77/1.97 tff(754,plain,
% 1.77/1.97 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.77/1.97 inference(quant_intro,[status(thm)],[753])).
% 1.77/1.97 tff(755,plain,
% 1.77/1.97 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(756,plain,
% 1.77/1.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.77/1.97 inference(bind,[status(th)],[])).
% 1.77/1.97 tff(757,plain,
% 1.77/1.97 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.77/1.97 inference(quant_intro,[status(thm)],[756])).
% 1.77/1.97 tff(758,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.77/1.97 tff(759,plain,
% 1.77/1.97 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.77/1.97 tff(760,plain,
% 1.77/1.97 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[759, 755])).
% 1.77/1.97 tff(761,plain,(
% 1.77/1.97 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.77/1.97 inference(skolemize,[status(sab)],[760])).
% 1.77/1.97 tff(762,plain,
% 1.77/1.97 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[761, 754])).
% 1.77/1.97 tff(763,assumption,(~c3_1(a592)), introduced(assumption)).
% 1.77/1.97 tff(764,assumption,(c2_1(a592)), introduced(assumption)).
% 1.77/1.97 tff(765,plain,
% 1.77/1.97 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(766,plain,
% 1.77/1.97 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592))) <=> (hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(767,plain,
% 1.77/1.97 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[766])).
% 1.77/1.97 tff(768,plain,
% 1.77/1.97 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 1.77/1.97 inference(transitivity,[status(thm)],[767, 765])).
% 1.77/1.97 tff(769,plain,
% 1.77/1.97 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)))),
% 1.77/1.97 inference(quant_inst,[status(thm)],[])).
% 1.77/1.97 tff(770,plain,
% 1.77/1.97 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[769, 768])).
% 1.77/1.97 tff(771,plain,
% 1.77/1.97 (hskp4 | c1_1(a592)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[770, 101, 288, 764, 763, 762])).
% 1.77/1.97 tff(772,plain,
% 1.77/1.97 (c1_1(a592)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[771, 752])).
% 1.77/1.97 tff(773,assumption,(~c0_1(a592)), introduced(assumption)).
% 1.77/1.97 tff(774,plain,
% 1.77/1.97 (^[U: $i] : refl((hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.77/1.97 inference(bind,[status(th)],[])).
% 1.77/1.97 tff(775,plain,
% 1.77/1.97 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.97 inference(quant_intro,[status(thm)],[774])).
% 1.77/1.97 tff(776,plain,
% 1.77/1.97 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(777,plain,
% 1.77/1.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp4) <=> ((hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp4))), rewrite(((hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp4) <=> (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp4) <=> (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.77/1.97 inference(bind,[status(th)],[])).
% 1.77/1.97 tff(778,plain,
% 1.77/1.97 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp4) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.97 inference(quant_intro,[status(thm)],[777])).
% 1.77/1.97 tff(779,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.77/1.97 tff(780,plain,
% 1.77/1.97 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[779, 778])).
% 1.77/1.97 tff(781,plain,
% 1.77/1.97 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[780, 776])).
% 1.77/1.97 tff(782,plain,(
% 1.77/1.97 ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.97 inference(skolemize,[status(sab)],[781])).
% 1.77/1.97 tff(783,plain,
% 1.77/1.97 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[782, 775])).
% 1.77/1.97 tff(784,assumption,(c3_1(a590)), introduced(assumption)).
% 1.77/1.97 tff(785,assumption,(c2_1(a590)), introduced(assumption)).
% 1.77/1.97 tff(786,plain,
% 1.77/1.97 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(787,plain,
% 1.77/1.97 ((hskp10 | hskp4 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c3_1(a590))) <=> (hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(788,plain,
% 1.77/1.97 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c3_1(a590)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590))))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[787])).
% 1.77/1.97 tff(789,plain,
% 1.77/1.97 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c3_1(a590)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)))),
% 1.77/1.97 inference(transitivity,[status(thm)],[788, 786])).
% 1.77/1.97 tff(790,plain,
% 1.77/1.97 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c3_1(a590)))),
% 1.77/1.97 inference(quant_inst,[status(thm)],[])).
% 1.77/1.97 tff(791,plain,
% 1.77/1.97 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.77/1.97 tff(792,plain,
% 1.77/1.97 (hskp10 | hskp4),
% 1.83/1.97 inference(unit_resolution,[status(thm)],[791, 101, 785, 784, 45, 783])).
% 1.83/1.97 tff(793,plain,
% 1.83/1.97 (hskp10),
% 1.83/1.97 inference(unit_resolution,[status(thm)],[792, 752])).
% 1.83/1.97 tff(794,plain,
% 1.83/1.97 (((~hskp10) | c3_1(a598)) <=> ((~hskp10) | c3_1(a598))),
% 1.83/1.97 inference(rewrite,[status(thm)],[])).
% 1.83/1.97 tff(795,axiom,((~hskp10) | c3_1(a598)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.83/1.97 tff(796,plain,
% 1.83/1.97 ((~hskp10) | c3_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[795, 794])).
% 1.83/1.97 tff(797,plain,
% 1.83/1.97 ((~hskp10) | c3_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[796, 794])).
% 1.83/1.97 tff(798,plain,
% 1.83/1.97 ((~hskp10) | c3_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[797, 794])).
% 1.83/1.97 tff(799,plain,
% 1.83/1.97 ((~hskp10) | c3_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[798, 794])).
% 1.83/1.97 tff(800,plain,
% 1.83/1.97 ((~hskp10) | c3_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[799, 794])).
% 1.83/1.97 tff(801,plain,
% 1.83/1.97 (c3_1(a598)),
% 1.83/1.97 inference(unit_resolution,[status(thm)],[800, 793])).
% 1.83/1.97 tff(802,plain,
% 1.83/1.97 (((~hskp10) | c0_1(a598)) <=> ((~hskp10) | c0_1(a598))),
% 1.83/1.97 inference(rewrite,[status(thm)],[])).
% 1.83/1.97 tff(803,axiom,((~hskp10) | c0_1(a598)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.83/1.97 tff(804,plain,
% 1.83/1.97 ((~hskp10) | c0_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.83/1.97 tff(805,plain,
% 1.83/1.97 ((~hskp10) | c0_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[804, 802])).
% 1.83/1.97 tff(806,plain,
% 1.83/1.97 ((~hskp10) | c0_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[805, 802])).
% 1.83/1.97 tff(807,plain,
% 1.83/1.97 ((~hskp10) | c0_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[806, 802])).
% 1.83/1.97 tff(808,plain,
% 1.83/1.97 ((~hskp10) | c0_1(a598)),
% 1.83/1.97 inference(modus_ponens,[status(thm)],[807, 802])).
% 1.83/1.97 tff(809,plain,
% 1.83/1.97 (c0_1(a598)),
% 1.83/1.97 inference(unit_resolution,[status(thm)],[808, 793])).
% 1.83/1.97 tff(810,assumption,(c2_1(a598)), introduced(assumption)).
% 1.83/1.97 tff(811,assumption,(c1_1(a592)), introduced(assumption)).
% 1.83/1.97 tff(812,assumption,(c3_1(a598)), introduced(assumption)).
% 1.83/1.97 tff(813,assumption,(c0_1(a598)), introduced(assumption)).
% 1.83/1.97 tff(814,plain,
% 1.83/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 1.83/1.97 inference(rewrite,[status(thm)],[])).
% 1.83/1.97 tff(815,plain,
% 1.83/1.97 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 1.83/1.97 inference(rewrite,[status(thm)],[])).
% 1.83/1.97 tff(816,plain,
% 1.83/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607))))),
% 1.83/1.97 inference(monotonicity,[status(thm)],[815])).
% 1.83/1.97 tff(817,plain,
% 1.83/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 1.83/1.98 inference(transitivity,[status(thm)],[816, 814])).
% 1.83/1.98 tff(818,plain,
% 1.83/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))),
% 1.83/1.98 inference(quant_inst,[status(thm)],[])).
% 1.83/1.98 tff(819,plain,
% 1.83/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[818, 817])).
% 1.83/1.98 tff(820,plain,
% 1.83/1.98 ($false),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[819, 101, 303, 813, 812, 764, 66, 22, 773, 11, 811, 810])).
% 1.83/1.98 tff(821,plain,((~c2_1(a598)) | (~c3_1(a607)) | (~c0_1(a598)) | (~c3_1(a598)) | (~c2_1(a592)) | c1_1(a607) | c2_1(a607) | c0_1(a592) | (~c1_1(a592))), inference(lemma,lemma(discharge,[]))).
% 1.83/1.98 tff(822,plain,
% 1.83/1.98 (~c2_1(a598)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[821, 809, 303, 801, 764, 66, 22, 773, 772])).
% 1.83/1.98 tff(823,plain,
% 1.83/1.98 (((~hskp10) | (~c1_1(a598))) <=> ((~hskp10) | (~c1_1(a598)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(824,plain,
% 1.83/1.98 (((~c1_1(a598)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a598)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(825,axiom,((~c1_1(a598)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.83/1.98 tff(826,plain,
% 1.83/1.98 ((~hskp10) | (~c1_1(a598))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[825, 824])).
% 1.83/1.98 tff(827,plain,
% 1.83/1.98 ((~hskp10) | (~c1_1(a598))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[826, 823])).
% 1.83/1.98 tff(828,plain,
% 1.83/1.98 (~c1_1(a598)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[827, 793])).
% 1.83/1.98 tff(829,plain,
% 1.83/1.98 (~hskp14),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[311, 288, 303, 66, 22])).
% 1.83/1.98 tff(830,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(831,plain,
% 1.83/1.98 ((hskp14 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(832,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598))))),
% 1.83/1.98 inference(monotonicity,[status(thm)],[831])).
% 1.83/1.98 tff(833,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598)))),
% 1.83/1.98 inference(transitivity,[status(thm)],[832, 830])).
% 1.83/1.98 tff(834,plain,
% 1.83/1.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 1.83/1.98 inference(quant_inst,[status(thm)],[])).
% 1.83/1.98 tff(835,plain,
% 1.83/1.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[834, 833])).
% 1.83/1.98 tff(836,plain,
% 1.83/1.98 ($false),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[835, 101, 829, 809, 764, 828, 773, 763, 287, 822])).
% 1.83/1.98 tff(837,plain,(hskp4 | (~c2_1(a592)) | c0_1(a592) | c3_1(a592) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | hskp3 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.83/1.98 tff(838,plain,
% 1.83/1.98 (hskp4),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[837, 751, 743, 737, 277, 264, 258, 288, 623, 615, 607])).
% 1.83/1.98 tff(839,plain,
% 1.83/1.98 (~c2_1(a588)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[115, 838])).
% 1.83/1.98 tff(840,plain,
% 1.83/1.98 (~c1_1(a588)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[121, 838])).
% 1.83/1.98 tff(841,plain,
% 1.83/1.98 (c0_1(a588)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[129, 838])).
% 1.83/1.98 tff(842,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(843,plain,
% 1.83/1.98 ((hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(844,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592))))),
% 1.83/1.98 inference(monotonicity,[status(thm)],[843])).
% 1.83/1.98 tff(845,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592)))),
% 1.83/1.98 inference(transitivity,[status(thm)],[844, 842])).
% 1.83/1.98 tff(846,plain,
% 1.83/1.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 1.83/1.98 inference(quant_inst,[status(thm)],[])).
% 1.83/1.98 tff(847,plain,
% 1.83/1.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[846, 845])).
% 1.83/1.98 tff(848,plain,
% 1.83/1.98 ($false),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[847, 101, 312, 751, 841, 743, 737, 840, 839, 287])).
% 1.83/1.98 tff(849,plain,(hskp3 | hskp29 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.83/1.98 tff(850,plain,
% 1.83/1.98 (hskp3),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[849, 251, 44])).
% 1.83/1.98 tff(851,plain,
% 1.83/1.98 (((~hskp3) | (~c1_1(a587))) <=> ((~hskp3) | (~c1_1(a587)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(852,plain,
% 1.83/1.98 (((~c1_1(a587)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a587)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(853,axiom,((~c1_1(a587)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.83/1.98 tff(854,plain,
% 1.83/1.98 ((~hskp3) | (~c1_1(a587))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[853, 852])).
% 1.83/1.98 tff(855,plain,
% 1.83/1.98 ((~hskp3) | (~c1_1(a587))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[854, 851])).
% 1.83/1.98 tff(856,plain,
% 1.83/1.98 (~c1_1(a587)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[855, 850])).
% 1.83/1.98 tff(857,plain,
% 1.83/1.98 (((~hskp3) | c2_1(a587)) <=> ((~hskp3) | c2_1(a587))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(858,axiom,((~hskp3) | c2_1(a587)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.83/1.98 tff(859,plain,
% 1.83/1.98 ((~hskp3) | c2_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[858, 857])).
% 1.83/1.98 tff(860,plain,
% 1.83/1.98 ((~hskp3) | c2_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[859, 857])).
% 1.83/1.98 tff(861,plain,
% 1.83/1.98 ((~hskp3) | c2_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[860, 857])).
% 1.83/1.98 tff(862,plain,
% 1.83/1.98 ((~hskp3) | c2_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[861, 857])).
% 1.83/1.98 tff(863,plain,
% 1.83/1.98 ((~hskp3) | c2_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[862, 857])).
% 1.83/1.98 tff(864,plain,
% 1.83/1.98 (c2_1(a587)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[863, 850])).
% 1.83/1.98 tff(865,plain,
% 1.83/1.98 (((~hskp3) | c0_1(a587)) <=> ((~hskp3) | c0_1(a587))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(866,axiom,((~hskp3) | c0_1(a587)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.83/1.98 tff(867,plain,
% 1.83/1.98 ((~hskp3) | c0_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[866, 865])).
% 1.83/1.98 tff(868,plain,
% 1.83/1.98 ((~hskp3) | c0_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[867, 865])).
% 1.83/1.98 tff(869,plain,
% 1.83/1.98 ((~hskp3) | c0_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[868, 865])).
% 1.83/1.98 tff(870,plain,
% 1.83/1.98 ((~hskp3) | c0_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[869, 865])).
% 1.83/1.98 tff(871,plain,
% 1.83/1.98 ((~hskp3) | c0_1(a587)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[870, 865])).
% 1.83/1.98 tff(872,plain,
% 1.83/1.98 (c0_1(a587)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[871, 850])).
% 1.83/1.98 tff(873,plain,
% 1.83/1.98 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(874,plain,
% 1.83/1.98 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)))),
% 1.83/1.98 inference(quant_inst,[status(thm)],[])).
% 1.83/1.98 tff(875,plain,
% 1.83/1.98 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[874, 873])).
% 1.83/1.98 tff(876,plain,
% 1.83/1.98 (hskp14 | c3_1(a587)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[875, 101, 44, 872, 864, 357])).
% 1.83/1.98 tff(877,plain,
% 1.83/1.98 (c3_1(a587)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[876, 340])).
% 1.83/1.98 tff(878,plain,
% 1.83/1.98 (~hskp26),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[373, 340, 44, 251])).
% 1.83/1.98 tff(879,plain,
% 1.83/1.98 (~hskp12),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[700, 340, 44])).
% 1.83/1.98 tff(880,plain,
% 1.83/1.98 (hskp8),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[712, 879, 878])).
% 1.83/1.98 tff(881,plain,
% 1.83/1.98 (~c2_1(a593)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[510, 880])).
% 1.83/1.98 tff(882,plain,
% 1.83/1.98 (c3_1(a593)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[469, 880])).
% 1.83/1.98 tff(883,plain,
% 1.83/1.98 (c1_1(a593)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[477, 880])).
% 1.83/1.98 tff(884,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(885,plain,
% 1.83/1.98 ((hskp14 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(886,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593))))),
% 1.83/1.98 inference(monotonicity,[status(thm)],[885])).
% 1.83/1.98 tff(887,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.83/1.98 inference(transitivity,[status(thm)],[886, 884])).
% 1.83/1.98 tff(888,plain,
% 1.83/1.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 1.83/1.98 inference(quant_inst,[status(thm)],[])).
% 1.83/1.98 tff(889,plain,
% 1.83/1.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[888, 887])).
% 1.83/1.98 tff(890,plain,
% 1.83/1.98 ($false),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[889, 101, 340, 883, 882, 872, 864, 881, 505, 877])).
% 1.83/1.98 tff(891,plain,(hskp14 | hskp22 | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.83/1.98 tff(892,plain,
% 1.83/1.98 (hskp14),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[891, 251, 44])).
% 1.83/1.98 tff(893,plain,
% 1.83/1.98 (c0_1(a603)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[170, 892])).
% 1.83/1.98 tff(894,plain,
% 1.83/1.98 (~c3_1(a603)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[193, 892])).
% 1.83/1.98 tff(895,plain,
% 1.83/1.98 (~c1_1(a603)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[162, 892])).
% 1.83/1.98 tff(896,plain,
% 1.83/1.98 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.83/1.98 inference(bind,[status(th)],[])).
% 1.83/1.98 tff(897,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.83/1.98 inference(quant_intro,[status(thm)],[896])).
% 1.83/1.98 tff(898,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(899,plain,
% 1.83/1.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.83/1.98 inference(bind,[status(th)],[])).
% 1.83/1.98 tff(900,plain,
% 1.83/1.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.83/1.98 inference(quant_intro,[status(thm)],[899])).
% 1.83/1.98 tff(901,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.83/1.98 tff(902,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[901, 900])).
% 1.83/1.98 tff(903,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[902, 898])).
% 1.83/1.98 tff(904,plain,(
% 1.83/1.98 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.83/1.98 inference(skolemize,[status(sab)],[903])).
% 1.83/1.98 tff(905,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[904, 897])).
% 1.83/1.98 tff(906,assumption,(~c1_1(a587)), introduced(assumption)).
% 1.83/1.98 tff(907,assumption,(~c3_1(a603)), introduced(assumption)).
% 1.83/1.98 tff(908,assumption,(~c1_1(a603)), introduced(assumption)).
% 1.83/1.98 tff(909,assumption,(c2_1(a587)), introduced(assumption)).
% 1.83/1.98 tff(910,assumption,(c0_1(a587)), introduced(assumption)).
% 1.83/1.98 tff(911,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(912,plain,
% 1.83/1.98 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(913,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603)))),
% 1.83/1.98 inference(monotonicity,[status(thm)],[912])).
% 1.83/1.98 tff(914,plain,
% 1.83/1.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603))),
% 1.83/1.98 inference(transitivity,[status(thm)],[913, 911])).
% 1.83/1.98 tff(915,plain,
% 1.83/1.98 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 1.83/1.98 inference(quant_inst,[status(thm)],[])).
% 1.83/1.98 tff(916,plain,
% 1.83/1.98 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.83/1.98 tff(917,plain,
% 1.83/1.98 (hskp26 | c2_1(a603)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[916, 101, 910, 909, 908, 907, 906, 905])).
% 1.83/1.98 tff(918,plain,
% 1.83/1.98 (c2_1(a603)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[917, 660])).
% 1.83/1.98 tff(919,assumption,(c0_1(a603)), introduced(assumption)).
% 1.83/1.98 tff(920,assumption,(c2_1(a603)), introduced(assumption)).
% 1.83/1.98 tff(921,plain,
% 1.83/1.98 (hskp11),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[381, 660])).
% 1.83/1.98 tff(922,plain,
% 1.83/1.98 (~c1_1(a599)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[395, 921])).
% 1.83/1.98 tff(923,plain,
% 1.83/1.98 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.83/1.98 inference(bind,[status(th)],[])).
% 1.83/1.98 tff(924,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.83/1.98 inference(quant_intro,[status(thm)],[923])).
% 1.83/1.98 tff(925,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(926,plain,
% 1.83/1.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.83/1.98 inference(bind,[status(th)],[])).
% 1.83/1.98 tff(927,plain,
% 1.83/1.98 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.83/1.98 inference(quant_intro,[status(thm)],[926])).
% 1.83/1.98 tff(928,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.83/1.98 tff(929,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[928, 927])).
% 1.83/1.98 tff(930,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[929, 925])).
% 1.83/1.98 tff(931,plain,(
% 1.83/1.98 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.83/1.98 inference(skolemize,[status(sab)],[930])).
% 1.83/1.98 tff(932,plain,
% 1.83/1.98 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[931, 924])).
% 1.83/1.98 tff(933,plain,
% 1.83/1.98 (^[U: $i] : refl((hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.83/1.98 inference(bind,[status(th)],[])).
% 1.83/1.98 tff(934,plain,
% 1.83/1.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.83/1.98 inference(quant_intro,[status(thm)],[933])).
% 1.83/1.98 tff(935,plain,
% 1.83/1.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(936,plain,
% 1.83/1.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.83/1.98 inference(bind,[status(th)],[])).
% 1.83/1.98 tff(937,plain,
% 1.83/1.98 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.83/1.98 inference(quant_intro,[status(thm)],[936])).
% 1.83/1.98 tff(938,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.83/1.98 tff(939,plain,
% 1.83/1.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[938, 937])).
% 1.83/1.98 tff(940,plain,
% 1.83/1.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[939, 935])).
% 1.83/1.98 tff(941,plain,(
% 1.83/1.98 ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.83/1.98 inference(skolemize,[status(sab)],[940])).
% 1.83/1.98 tff(942,plain,
% 1.83/1.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[941, 934])).
% 1.83/1.98 tff(943,plain,
% 1.83/1.98 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(944,plain,
% 1.83/1.98 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | c0_1(a607)) <=> (hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.98 tff(945,plain,
% 1.83/1.98 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607)))),
% 1.83/1.98 inference(monotonicity,[status(thm)],[944])).
% 1.83/1.98 tff(946,plain,
% 1.83/1.98 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 1.83/1.98 inference(transitivity,[status(thm)],[945, 943])).
% 1.83/1.98 tff(947,plain,
% 1.83/1.98 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | c0_1(a607))),
% 1.83/1.98 inference(quant_inst,[status(thm)],[])).
% 1.83/1.98 tff(948,plain,
% 1.83/1.98 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607)),
% 1.83/1.98 inference(modus_ponens,[status(thm)],[947, 946])).
% 1.83/1.98 tff(949,plain,
% 1.83/1.98 (hskp26 | hskp0 | c0_1(a607)),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[948, 101, 66, 22, 942])).
% 1.83/1.98 tff(950,plain,
% 1.83/1.98 (hskp0),
% 1.83/1.98 inference(unit_resolution,[status(thm)],[949, 1, 660])).
% 1.83/1.98 tff(951,plain,
% 1.83/1.98 (((~hskp0) | (~c2_1(a584))) <=> ((~hskp0) | (~c2_1(a584)))),
% 1.83/1.98 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(952,plain,
% 1.83/1.99 (((~c2_1(a584)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a584)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(953,axiom,((~c2_1(a584)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.83/1.99 tff(954,plain,
% 1.83/1.99 ((~hskp0) | (~c2_1(a584))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[953, 952])).
% 1.83/1.99 tff(955,plain,
% 1.83/1.99 ((~hskp0) | (~c2_1(a584))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[954, 951])).
% 1.83/1.99 tff(956,plain,
% 1.83/1.99 (~c2_1(a584)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[955, 950])).
% 1.83/1.99 tff(957,plain,
% 1.83/1.99 (((~hskp0) | (~c0_1(a584))) <=> ((~hskp0) | (~c0_1(a584)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(958,plain,
% 1.83/1.99 (((~c0_1(a584)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a584)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(959,axiom,((~c0_1(a584)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.83/1.99 tff(960,plain,
% 1.83/1.99 ((~hskp0) | (~c0_1(a584))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[959, 958])).
% 1.83/1.99 tff(961,plain,
% 1.83/1.99 ((~hskp0) | (~c0_1(a584))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[960, 957])).
% 1.83/1.99 tff(962,plain,
% 1.83/1.99 (~c0_1(a584)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[961, 950])).
% 1.83/1.99 tff(963,plain,
% 1.83/1.99 (((~hskp0) | c1_1(a584)) <=> ((~hskp0) | c1_1(a584))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(964,axiom,((~hskp0) | c1_1(a584)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.83/1.99 tff(965,plain,
% 1.83/1.99 ((~hskp0) | c1_1(a584)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[964, 963])).
% 1.83/1.99 tff(966,plain,
% 1.83/1.99 ((~hskp0) | c1_1(a584)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[965, 963])).
% 1.83/1.99 tff(967,plain,
% 1.83/1.99 ((~hskp0) | c1_1(a584)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[966, 963])).
% 1.83/1.99 tff(968,plain,
% 1.83/1.99 ((~hskp0) | c1_1(a584)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[967, 963])).
% 1.83/1.99 tff(969,plain,
% 1.83/1.99 ((~hskp0) | c1_1(a584)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[968, 963])).
% 1.83/1.99 tff(970,plain,
% 1.83/1.99 (c1_1(a584)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[969, 950])).
% 1.83/1.99 tff(971,plain,
% 1.83/1.99 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(972,plain,
% 1.83/1.99 ((hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(973,plain,
% 1.83/1.99 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603))))),
% 1.83/1.99 inference(monotonicity,[status(thm)],[972])).
% 1.83/1.99 tff(974,plain,
% 1.83/1.99 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)))),
% 1.83/1.99 inference(transitivity,[status(thm)],[973, 971])).
% 1.83/1.99 tff(975,plain,
% 1.83/1.99 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 1.83/1.99 inference(quant_inst,[status(thm)],[])).
% 1.83/1.99 tff(976,plain,
% 1.83/1.99 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.83/1.99 tff(977,plain,
% 1.83/1.99 (hskp16),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[976, 101, 970, 908, 907, 962, 956, 932, 920])).
% 1.83/1.99 tff(978,plain,
% 1.83/1.99 (((~hskp16) | (~c3_1(a606))) <=> ((~hskp16) | (~c3_1(a606)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(979,plain,
% 1.83/1.99 (((~c3_1(a606)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a606)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(980,axiom,((~c3_1(a606)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.83/1.99 tff(981,plain,
% 1.83/1.99 ((~hskp16) | (~c3_1(a606))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[980, 979])).
% 1.83/1.99 tff(982,plain,
% 1.83/1.99 ((~hskp16) | (~c3_1(a606))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[981, 978])).
% 1.83/1.99 tff(983,plain,
% 1.83/1.99 (~c3_1(a606)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[982, 977])).
% 1.83/1.99 tff(984,plain,
% 1.83/1.99 (c3_1(a599)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[389, 921])).
% 1.83/1.99 tff(985,plain,
% 1.83/1.99 (c2_1(a599)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[403, 921])).
% 1.83/1.99 tff(986,plain,
% 1.83/1.99 (((~hskp16) | c1_1(a606)) <=> ((~hskp16) | c1_1(a606))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(987,axiom,((~hskp16) | c1_1(a606)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.83/1.99 tff(988,plain,
% 1.83/1.99 ((~hskp16) | c1_1(a606)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[987, 986])).
% 1.83/1.99 tff(989,plain,
% 1.83/1.99 ((~hskp16) | c1_1(a606)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[988, 986])).
% 1.83/1.99 tff(990,plain,
% 1.83/1.99 ((~hskp16) | c1_1(a606)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[989, 986])).
% 1.83/1.99 tff(991,plain,
% 1.83/1.99 ((~hskp16) | c1_1(a606)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[990, 986])).
% 1.83/1.99 tff(992,plain,
% 1.83/1.99 ((~hskp16) | c1_1(a606)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[991, 986])).
% 1.83/1.99 tff(993,plain,
% 1.83/1.99 (c1_1(a606)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[992, 977])).
% 1.83/1.99 tff(994,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(995,plain,
% 1.83/1.99 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(996,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606))))),
% 1.83/1.99 inference(monotonicity,[status(thm)],[995])).
% 1.83/1.99 tff(997,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606)))),
% 1.83/1.99 inference(transitivity,[status(thm)],[996, 994])).
% 1.83/1.99 tff(998,plain,
% 1.83/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 1.83/1.99 inference(quant_inst,[status(thm)],[])).
% 1.83/1.99 tff(999,plain,
% 1.83/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[998, 997])).
% 1.83/1.99 tff(1000,plain,
% 1.83/1.99 (c0_1(a606)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[999, 101, 993, 919, 985, 984, 983, 907, 922, 240, 920])).
% 1.83/1.99 tff(1001,plain,
% 1.83/1.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.83/1.99 inference(bind,[status(th)],[])).
% 1.83/1.99 tff(1002,plain,
% 1.83/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.83/1.99 inference(quant_intro,[status(thm)],[1001])).
% 1.83/1.99 tff(1003,plain,
% 1.83/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1004,plain,
% 1.83/1.99 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.83/1.99 inference(bind,[status(th)],[])).
% 1.83/1.99 tff(1005,plain,
% 1.83/1.99 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.83/1.99 inference(quant_intro,[status(thm)],[1004])).
% 1.83/1.99 tff(1006,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.83/1.99 tff(1007,plain,
% 1.83/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 1.83/1.99 tff(1008,plain,
% 1.83/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1007, 1003])).
% 1.83/1.99 tff(1009,plain,(
% 1.83/1.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.83/1.99 inference(skolemize,[status(sab)],[1008])).
% 1.83/1.99 tff(1010,plain,
% 1.83/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1009, 1002])).
% 1.83/1.99 tff(1011,plain,
% 1.83/1.99 (((~hskp16) | (~c2_1(a606))) <=> ((~hskp16) | (~c2_1(a606)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1012,plain,
% 1.83/1.99 (((~c2_1(a606)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a606)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1013,axiom,((~c2_1(a606)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.83/1.99 tff(1014,plain,
% 1.83/1.99 ((~hskp16) | (~c2_1(a606))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 1.83/1.99 tff(1015,plain,
% 1.83/1.99 ((~hskp16) | (~c2_1(a606))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1014, 1011])).
% 1.83/1.99 tff(1016,plain,
% 1.83/1.99 (~c2_1(a606)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[1015, 977])).
% 1.83/1.99 tff(1017,plain,
% 1.83/1.99 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.83/1.99 inference(bind,[status(th)],[])).
% 1.83/1.99 tff(1018,plain,
% 1.83/1.99 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/1.99 inference(quant_intro,[status(thm)],[1017])).
% 1.83/1.99 tff(1019,plain,
% 1.83/1.99 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1020,plain,
% 1.83/1.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.83/1.99 inference(bind,[status(th)],[])).
% 1.83/1.99 tff(1021,plain,
% 1.83/1.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/1.99 inference(quant_intro,[status(thm)],[1020])).
% 1.83/1.99 tff(1022,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.83/1.99 tff(1023,plain,
% 1.83/1.99 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.83/1.99 tff(1024,plain,
% 1.83/1.99 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1023, 1019])).
% 1.83/1.99 tff(1025,plain,(
% 1.83/1.99 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/1.99 inference(skolemize,[status(sab)],[1024])).
% 1.83/1.99 tff(1026,plain,
% 1.83/1.99 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1025, 1018])).
% 1.83/1.99 tff(1027,plain,
% 1.83/1.99 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1028,plain,
% 1.83/1.99 ((hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1029,plain,
% 1.83/1.99 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607))))),
% 1.83/1.99 inference(monotonicity,[status(thm)],[1028])).
% 1.83/1.99 tff(1030,plain,
% 1.83/1.99 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/1.99 inference(transitivity,[status(thm)],[1029, 1027])).
% 1.83/1.99 tff(1031,plain,
% 1.83/1.99 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.83/1.99 inference(quant_inst,[status(thm)],[])).
% 1.83/1.99 tff(1032,plain,
% 1.83/1.99 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.83/1.99 tff(1033,plain,
% 1.83/1.99 (hskp28),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[1032, 101, 303, 919, 22, 907, 1026, 1, 920])).
% 1.83/1.99 tff(1034,plain,
% 1.83/1.99 (((~hskp28) | c3_1(a612)) <=> ((~hskp28) | c3_1(a612))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1035,axiom,((~hskp28) | c3_1(a612)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.83/1.99 tff(1036,plain,
% 1.83/1.99 ((~hskp28) | c3_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.83/1.99 tff(1037,plain,
% 1.83/1.99 ((~hskp28) | c3_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1036, 1034])).
% 1.83/1.99 tff(1038,plain,
% 1.83/1.99 ((~hskp28) | c3_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1037, 1034])).
% 1.83/1.99 tff(1039,plain,
% 1.83/1.99 ((~hskp28) | c3_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1038, 1034])).
% 1.83/1.99 tff(1040,plain,
% 1.83/1.99 ((~hskp28) | c3_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1039, 1034])).
% 1.83/1.99 tff(1041,plain,
% 1.83/1.99 (c3_1(a612)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[1040, 1033])).
% 1.83/1.99 tff(1042,plain,
% 1.83/1.99 (((~hskp28) | c2_1(a612)) <=> ((~hskp28) | c2_1(a612))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1043,axiom,((~hskp28) | c2_1(a612)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.83/1.99 tff(1044,plain,
% 1.83/1.99 ((~hskp28) | c2_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.83/1.99 tff(1045,plain,
% 1.83/1.99 ((~hskp28) | c2_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1044, 1042])).
% 1.83/1.99 tff(1046,plain,
% 1.83/1.99 ((~hskp28) | c2_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1045, 1042])).
% 1.83/1.99 tff(1047,plain,
% 1.83/1.99 ((~hskp28) | c2_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1046, 1042])).
% 1.83/1.99 tff(1048,plain,
% 1.83/1.99 ((~hskp28) | c2_1(a612)),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1047, 1042])).
% 1.83/1.99 tff(1049,plain,
% 1.83/1.99 (c2_1(a612)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[1048, 1033])).
% 1.83/1.99 tff(1050,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1051,plain,
% 1.83/1.99 (((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1052,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))))),
% 1.83/1.99 inference(monotonicity,[status(thm)],[1051])).
% 1.83/1.99 tff(1053,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.83/1.99 inference(transitivity,[status(thm)],[1052, 1050])).
% 1.83/1.99 tff(1054,plain,
% 1.83/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.83/1.99 inference(quant_inst,[status(thm)],[])).
% 1.83/1.99 tff(1055,plain,
% 1.83/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 1.83/1.99 tff(1056,plain,
% 1.83/1.99 ((~c0_1(a612)) | (~c0_1(a606))),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[1055, 101, 1049, 1041, 303, 993, 66, 22, 1016, 1010])).
% 1.83/1.99 tff(1057,plain,
% 1.83/1.99 (~c0_1(a612)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[1056, 1000])).
% 1.83/1.99 tff(1058,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1059,plain,
% 1.83/1.99 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.83/1.99 inference(rewrite,[status(thm)],[])).
% 1.83/1.99 tff(1060,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))))),
% 1.83/1.99 inference(monotonicity,[status(thm)],[1059])).
% 1.83/1.99 tff(1061,plain,
% 1.83/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.83/1.99 inference(transitivity,[status(thm)],[1060, 1058])).
% 1.83/1.99 tff(1062,plain,
% 1.83/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.83/1.99 inference(quant_inst,[status(thm)],[])).
% 1.83/1.99 tff(1063,plain,
% 1.83/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))),
% 1.83/1.99 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.83/1.99 tff(1064,plain,
% 1.83/1.99 ((~c0_1(a599)) | (~c0_1(a606))),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[1063, 101, 303, 993, 985, 984, 66, 22, 1016, 1010])).
% 1.83/1.99 tff(1065,plain,
% 1.83/1.99 (~c0_1(a599)),
% 1.83/1.99 inference(unit_resolution,[status(thm)],[1064, 1000])).
% 1.83/1.99 tff(1066,plain,
% 1.83/1.99 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.83/2.00 inference(bind,[status(th)],[])).
% 1.83/2.00 tff(1067,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.00 inference(quant_intro,[status(thm)],[1066])).
% 1.83/2.00 tff(1068,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1069,plain,
% 1.83/2.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.83/2.00 inference(bind,[status(th)],[])).
% 1.83/2.00 tff(1070,plain,
% 1.83/2.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.00 inference(quant_intro,[status(thm)],[1069])).
% 1.83/2.00 tff(1071,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.83/2.00 tff(1072,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 1.83/2.00 tff(1073,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1072, 1068])).
% 1.83/2.00 tff(1074,plain,(
% 1.83/2.00 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.00 inference(skolemize,[status(sab)],[1073])).
% 1.83/2.00 tff(1075,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1074, 1067])).
% 1.83/2.00 tff(1076,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1077,plain,
% 1.83/2.00 ((hskp18 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1078,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607))))),
% 1.83/2.00 inference(monotonicity,[status(thm)],[1077])).
% 1.83/2.00 tff(1079,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.00 inference(transitivity,[status(thm)],[1078, 1076])).
% 1.83/2.00 tff(1080,plain,
% 1.83/2.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.83/2.00 inference(quant_inst,[status(thm)],[])).
% 1.83/2.00 tff(1081,plain,
% 1.83/2.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 1.83/2.00 tff(1082,plain,
% 1.83/2.00 (hskp18),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1081, 101, 303, 919, 22, 908, 907, 1075, 1])).
% 1.83/2.00 tff(1083,plain,
% 1.83/2.00 (((~hskp18) | (~c2_1(a610))) <=> ((~hskp18) | (~c2_1(a610)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1084,plain,
% 1.83/2.00 (((~c2_1(a610)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a610)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1085,axiom,((~c2_1(a610)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.83/2.00 tff(1086,plain,
% 1.83/2.00 ((~hskp18) | (~c2_1(a610))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 1.83/2.00 tff(1087,plain,
% 1.83/2.00 ((~hskp18) | (~c2_1(a610))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1086, 1083])).
% 1.83/2.00 tff(1088,plain,
% 1.83/2.00 (~c2_1(a610)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1087, 1082])).
% 1.83/2.00 tff(1089,plain,
% 1.83/2.00 (((~hskp18) | (~c0_1(a610))) <=> ((~hskp18) | (~c0_1(a610)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1090,plain,
% 1.83/2.00 (((~c0_1(a610)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a610)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1091,axiom,((~c0_1(a610)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.83/2.00 tff(1092,plain,
% 1.83/2.00 ((~hskp18) | (~c0_1(a610))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 1.83/2.00 tff(1093,plain,
% 1.83/2.00 ((~hskp18) | (~c0_1(a610))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1092, 1089])).
% 1.83/2.00 tff(1094,plain,
% 1.83/2.00 (~c0_1(a610)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1093, 1082])).
% 1.83/2.00 tff(1095,plain,
% 1.83/2.00 (((~hskp18) | c3_1(a610)) <=> ((~hskp18) | c3_1(a610))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1096,axiom,((~hskp18) | c3_1(a610)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.83/2.00 tff(1097,plain,
% 1.83/2.00 ((~hskp18) | c3_1(a610)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.83/2.00 tff(1098,plain,
% 1.83/2.00 ((~hskp18) | c3_1(a610)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1097, 1095])).
% 1.83/2.00 tff(1099,plain,
% 1.83/2.00 ((~hskp18) | c3_1(a610)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1098, 1095])).
% 1.83/2.00 tff(1100,plain,
% 1.83/2.00 ((~hskp18) | c3_1(a610)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1099, 1095])).
% 1.83/2.00 tff(1101,plain,
% 1.83/2.00 ((~hskp18) | c3_1(a610)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1100, 1095])).
% 1.83/2.00 tff(1102,plain,
% 1.83/2.00 (c3_1(a610)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1101, 1082])).
% 1.83/2.00 tff(1103,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1104,plain,
% 1.83/2.00 ((hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1105,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610))))),
% 1.83/2.00 inference(monotonicity,[status(thm)],[1104])).
% 1.83/2.00 tff(1106,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610)))),
% 1.83/2.00 inference(transitivity,[status(thm)],[1105, 1103])).
% 1.83/2.00 tff(1107,plain,
% 1.83/2.00 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 1.83/2.00 inference(quant_inst,[status(thm)],[])).
% 1.83/2.00 tff(1108,plain,
% 1.83/2.00 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 1.83/2.00 tff(1109,plain,
% 1.83/2.00 (hskp27 | (~c0_1(a606))),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1108, 101, 1102, 993, 1094, 1088, 1016, 495])).
% 1.83/2.00 tff(1110,plain,
% 1.83/2.00 (hskp27),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1109, 1000])).
% 1.83/2.00 tff(1111,plain,
% 1.83/2.00 (c3_1(a611)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[566, 1110])).
% 1.83/2.00 tff(1112,plain,
% 1.83/2.00 (c1_1(a611)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[574, 1110])).
% 1.83/2.00 tff(1113,plain,
% 1.83/2.00 (c0_1(a611)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[582, 1110])).
% 1.83/2.00 tff(1114,plain,
% 1.83/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1115,plain,
% 1.83/2.00 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1116,plain,
% 1.83/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599)))),
% 1.83/2.00 inference(monotonicity,[status(thm)],[1115])).
% 1.83/2.00 tff(1117,plain,
% 1.83/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599))),
% 1.83/2.00 inference(transitivity,[status(thm)],[1116, 1114])).
% 1.83/2.00 tff(1118,plain,
% 1.83/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 1.83/2.00 inference(quant_inst,[status(thm)],[])).
% 1.83/2.00 tff(1119,plain,
% 1.83/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.83/2.00 tff(1120,plain,
% 1.83/2.00 ($false),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1119, 101, 1049, 1041, 1113, 1112, 1111, 985, 922, 65, 1065, 1057])).
% 1.83/2.00 tff(1121,plain,(c0_1(a607) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | (~c0_1(a603)) | c3_1(a603) | (~c2_1(a603)) | c1_1(a603) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.83/2.00 tff(1122,plain,
% 1.83/2.00 (c0_1(a607)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1121, 918, 66, 22, 919, 907, 303, 908, 660])).
% 1.83/2.00 tff(1123,plain,
% 1.83/2.00 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.83/2.00 inference(bind,[status(th)],[])).
% 1.83/2.00 tff(1124,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.83/2.00 inference(quant_intro,[status(thm)],[1123])).
% 1.83/2.00 tff(1125,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1126,plain,
% 1.83/2.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.83/2.00 inference(bind,[status(th)],[])).
% 1.83/2.00 tff(1127,plain,
% 1.83/2.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.83/2.00 inference(quant_intro,[status(thm)],[1126])).
% 1.83/2.00 tff(1128,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.83/2.00 tff(1129,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 1.83/2.00 tff(1130,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1129, 1125])).
% 1.83/2.00 tff(1131,plain,(
% 1.83/2.00 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.83/2.00 inference(skolemize,[status(sab)],[1130])).
% 1.83/2.00 tff(1132,plain,
% 1.83/2.00 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1131, 1124])).
% 1.83/2.00 tff(1133,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1134,plain,
% 1.83/2.00 ((hskp1 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607))) <=> (hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1135,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607))))),
% 1.83/2.00 inference(monotonicity,[status(thm)],[1134])).
% 1.83/2.00 tff(1136,plain,
% 1.83/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607)))),
% 1.83/2.00 inference(transitivity,[status(thm)],[1135, 1133])).
% 1.83/2.00 tff(1137,plain,
% 1.83/2.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))),
% 1.83/2.00 inference(quant_inst,[status(thm)],[])).
% 1.83/2.00 tff(1138,plain,
% 1.83/2.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.83/2.00 tff(1139,plain,
% 1.83/2.00 (hskp1 | (~c2_1(a603)) | (~c0_1(a607))),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1138, 101, 919, 66, 22, 907, 1132])).
% 1.83/2.00 tff(1140,plain,
% 1.83/2.00 (hskp1),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1139, 1122, 918])).
% 1.83/2.00 tff(1141,plain,
% 1.83/2.00 (((~hskp1) | (~c0_1(a585))) <=> ((~hskp1) | (~c0_1(a585)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1142,plain,
% 1.83/2.00 (((~c0_1(a585)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a585)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1143,axiom,((~c0_1(a585)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.83/2.00 tff(1144,plain,
% 1.83/2.00 ((~hskp1) | (~c0_1(a585))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 1.83/2.00 tff(1145,plain,
% 1.83/2.00 ((~hskp1) | (~c0_1(a585))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1144, 1141])).
% 1.83/2.00 tff(1146,plain,
% 1.83/2.00 (~c0_1(a585)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1145, 1140])).
% 1.83/2.00 tff(1147,plain,
% 1.83/2.00 (((~hskp1) | c2_1(a585)) <=> ((~hskp1) | c2_1(a585))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1148,axiom,((~hskp1) | c2_1(a585)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.83/2.00 tff(1149,plain,
% 1.83/2.00 ((~hskp1) | c2_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 1.83/2.00 tff(1150,plain,
% 1.83/2.00 ((~hskp1) | c2_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1149, 1147])).
% 1.83/2.00 tff(1151,plain,
% 1.83/2.00 ((~hskp1) | c2_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1150, 1147])).
% 1.83/2.00 tff(1152,plain,
% 1.83/2.00 ((~hskp1) | c2_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1151, 1147])).
% 1.83/2.00 tff(1153,plain,
% 1.83/2.00 ((~hskp1) | c2_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1152, 1147])).
% 1.83/2.00 tff(1154,plain,
% 1.83/2.00 (c2_1(a585)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1153, 1140])).
% 1.83/2.00 tff(1155,plain,
% 1.83/2.00 (((~hskp1) | c1_1(a585)) <=> ((~hskp1) | c1_1(a585))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1156,axiom,((~hskp1) | c1_1(a585)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.83/2.00 tff(1157,plain,
% 1.83/2.00 ((~hskp1) | c1_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 1.83/2.00 tff(1158,plain,
% 1.83/2.00 ((~hskp1) | c1_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1157, 1155])).
% 1.83/2.00 tff(1159,plain,
% 1.83/2.00 ((~hskp1) | c1_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1158, 1155])).
% 1.83/2.00 tff(1160,plain,
% 1.83/2.00 ((~hskp1) | c1_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1159, 1155])).
% 1.83/2.00 tff(1161,plain,
% 1.83/2.00 ((~hskp1) | c1_1(a585)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1160, 1155])).
% 1.83/2.00 tff(1162,plain,
% 1.83/2.00 (c1_1(a585)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1161, 1140])).
% 1.83/2.00 tff(1163,plain,
% 1.83/2.00 (^[U: $i] : refl((hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.83/2.00 inference(bind,[status(th)],[])).
% 1.83/2.00 tff(1164,plain,
% 1.83/2.00 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.00 inference(quant_intro,[status(thm)],[1163])).
% 1.83/2.00 tff(1165,plain,
% 1.83/2.00 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1166,plain,
% 1.83/2.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) | hskp28) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) | hskp28) <=> (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.83/2.00 inference(bind,[status(th)],[])).
% 1.83/2.00 tff(1167,plain,
% 1.83/2.00 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) | hskp28) <=> ![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.00 inference(quant_intro,[status(thm)],[1166])).
% 1.83/2.00 tff(1168,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.83/2.00 tff(1169,plain,
% 1.83/2.00 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 1.83/2.00 tff(1170,plain,
% 1.83/2.00 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1169, 1165])).
% 1.83/2.00 tff(1171,plain,(
% 1.83/2.00 ![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.00 inference(skolemize,[status(sab)],[1170])).
% 1.83/2.00 tff(1172,plain,
% 1.83/2.00 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1171, 1164])).
% 1.83/2.00 tff(1173,plain,
% 1.83/2.00 (((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1174,plain,
% 1.83/2.00 ((hskp26 | hskp28 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1175,plain,
% 1.83/2.00 (((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 1.83/2.00 inference(monotonicity,[status(thm)],[1174])).
% 1.83/2.00 tff(1176,plain,
% 1.83/2.00 (((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.00 inference(transitivity,[status(thm)],[1175, 1173])).
% 1.83/2.00 tff(1177,plain,
% 1.83/2.00 ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 1.83/2.00 inference(quant_inst,[status(thm)],[])).
% 1.83/2.00 tff(1178,plain,
% 1.83/2.00 ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 1.83/2.00 tff(1179,plain,
% 1.83/2.00 (hskp26 | hskp28 | (~c0_1(a607))),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1178, 101, 303, 22, 1172])).
% 1.83/2.00 tff(1180,plain,
% 1.83/2.00 (hskp28),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1179, 1122, 660])).
% 1.83/2.00 tff(1181,plain,
% 1.83/2.00 (c3_1(a612)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1040, 1180])).
% 1.83/2.00 tff(1182,plain,
% 1.83/2.00 (c2_1(a612)),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[1048, 1180])).
% 1.83/2.00 tff(1183,plain,
% 1.83/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1184,plain,
% 1.83/2.00 (((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(1185,plain,
% 1.83/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607))))),
% 1.83/2.00 inference(monotonicity,[status(thm)],[1184])).
% 1.83/2.01 tff(1186,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 1.83/2.01 inference(transitivity,[status(thm)],[1185, 1183])).
% 1.83/2.01 tff(1187,plain,
% 1.83/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 1.83/2.01 inference(quant_inst,[status(thm)],[])).
% 1.83/2.01 tff(1188,plain,
% 1.83/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 1.83/2.01 tff(1189,plain,
% 1.83/2.01 (~c0_1(a612)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[1188, 101, 1182, 1181, 303, 1162, 1154, 66, 22, 1146, 11])).
% 1.83/2.01 tff(1190,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1191,plain,
% 1.83/2.01 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1192,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))))),
% 1.83/2.01 inference(monotonicity,[status(thm)],[1191])).
% 1.83/2.01 tff(1193,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 1.83/2.01 inference(transitivity,[status(thm)],[1192, 1190])).
% 1.83/2.01 tff(1194,plain,
% 1.83/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 1.83/2.01 inference(quant_inst,[status(thm)],[])).
% 1.83/2.01 tff(1195,plain,
% 1.83/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 1.83/2.01 tff(1196,plain,
% 1.83/2.01 (~c0_1(a599)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[1195, 101, 303, 985, 984, 1162, 1154, 66, 22, 1146, 11])).
% 1.83/2.01 tff(1197,plain,
% 1.83/2.01 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.83/2.01 inference(bind,[status(th)],[])).
% 1.83/2.01 tff(1198,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(quant_intro,[status(thm)],[1197])).
% 1.83/2.01 tff(1199,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1200,plain,
% 1.83/2.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.83/2.01 inference(bind,[status(th)],[])).
% 1.83/2.01 tff(1201,plain,
% 1.83/2.01 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(quant_intro,[status(thm)],[1200])).
% 1.83/2.01 tff(1202,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.83/2.01 tff(1203,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.83/2.01 tff(1204,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1203, 1199])).
% 1.83/2.01 tff(1205,plain,(
% 1.83/2.01 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(skolemize,[status(sab)],[1204])).
% 1.83/2.01 tff(1206,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1205, 1198])).
% 1.83/2.01 tff(1207,plain,
% 1.83/2.01 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.83/2.01 inference(bind,[status(th)],[])).
% 1.83/2.01 tff(1208,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(quant_intro,[status(thm)],[1207])).
% 1.83/2.01 tff(1209,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1210,plain,
% 1.83/2.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.83/2.01 inference(bind,[status(th)],[])).
% 1.83/2.01 tff(1211,plain,
% 1.83/2.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(quant_intro,[status(thm)],[1210])).
% 1.83/2.01 tff(1212,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.83/2.01 tff(1213,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 1.83/2.01 tff(1214,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1213, 1209])).
% 1.83/2.01 tff(1215,plain,(
% 1.83/2.01 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(skolemize,[status(sab)],[1214])).
% 1.83/2.01 tff(1216,plain,
% 1.83/2.01 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1215, 1208])).
% 1.83/2.01 tff(1217,plain,
% 1.83/2.01 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1218,plain,
% 1.83/2.01 ((hskp23 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1219,plain,
% 1.83/2.01 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 1.83/2.01 inference(monotonicity,[status(thm)],[1218])).
% 1.83/2.01 tff(1220,plain,
% 1.83/2.01 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.01 inference(transitivity,[status(thm)],[1219, 1217])).
% 1.83/2.01 tff(1221,plain,
% 1.83/2.01 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.83/2.01 inference(quant_inst,[status(thm)],[])).
% 1.83/2.01 tff(1222,plain,
% 1.83/2.01 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 1.83/2.01 tff(1223,plain,
% 1.83/2.01 (hskp23 | (~c0_1(a607))),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[1222, 101, 303, 66, 22, 1216])).
% 1.83/2.01 tff(1224,plain,
% 1.83/2.01 (hskp23),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[1223, 1122])).
% 1.83/2.01 tff(1225,plain,
% 1.83/2.01 (~c1_1(a636)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[439, 1224])).
% 1.83/2.01 tff(1226,plain,
% 1.83/2.01 (~c0_1(a636)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[445, 1224])).
% 1.83/2.01 tff(1227,plain,
% 1.83/2.01 (c3_1(a636)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[453, 1224])).
% 1.83/2.01 tff(1228,plain,
% 1.83/2.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1229,plain,
% 1.83/2.01 ((hskp8 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1230,plain,
% 1.83/2.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636))))),
% 1.83/2.01 inference(monotonicity,[status(thm)],[1229])).
% 1.83/2.01 tff(1231,plain,
% 1.83/2.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636)))),
% 1.83/2.01 inference(transitivity,[status(thm)],[1230, 1228])).
% 1.83/2.01 tff(1232,plain,
% 1.83/2.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 1.83/2.01 inference(quant_inst,[status(thm)],[])).
% 1.83/2.01 tff(1233,plain,
% 1.83/2.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.83/2.01 tff(1234,plain,
% 1.83/2.01 (hskp8),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[1233, 101, 1227, 1162, 1154, 1226, 1225, 1146, 1206])).
% 1.83/2.01 tff(1235,plain,
% 1.83/2.01 (c3_1(a593)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[469, 1234])).
% 1.83/2.01 tff(1236,plain,
% 1.83/2.01 (c1_1(a593)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[477, 1234])).
% 1.83/2.01 tff(1237,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1238,plain,
% 1.83/2.01 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1239,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599)))),
% 1.83/2.01 inference(monotonicity,[status(thm)],[1238])).
% 1.83/2.01 tff(1240,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599))),
% 1.83/2.01 inference(transitivity,[status(thm)],[1239, 1237])).
% 1.83/2.01 tff(1241,plain,
% 1.83/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 1.83/2.01 inference(quant_inst,[status(thm)],[])).
% 1.83/2.01 tff(1242,plain,
% 1.83/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599)),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 1.83/2.01 tff(1243,plain,
% 1.83/2.01 (~c0_1(a593)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[1242, 101, 1182, 1181, 985, 1236, 1235, 922, 65, 1196, 1189])).
% 1.83/2.01 tff(1244,plain,
% 1.83/2.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.83/2.01 inference(bind,[status(th)],[])).
% 1.83/2.01 tff(1245,plain,
% 1.83/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.01 inference(quant_intro,[status(thm)],[1244])).
% 1.83/2.01 tff(1246,plain,
% 1.83/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1247,plain,
% 1.83/2.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.83/2.01 inference(bind,[status(th)],[])).
% 1.83/2.01 tff(1248,plain,
% 1.83/2.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.01 inference(quant_intro,[status(thm)],[1247])).
% 1.83/2.01 tff(1249,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.83/2.01 tff(1250,plain,
% 1.83/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 1.83/2.01 tff(1251,plain,
% 1.83/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1250, 1246])).
% 1.83/2.01 tff(1252,plain,(
% 1.83/2.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.01 inference(skolemize,[status(sab)],[1251])).
% 1.83/2.01 tff(1253,plain,
% 1.83/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[1252, 1245])).
% 1.83/2.01 tff(1254,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1255,plain,
% 1.83/2.01 (((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(1256,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607))))),
% 1.83/2.01 inference(monotonicity,[status(thm)],[1255])).
% 1.83/2.01 tff(1257,plain,
% 1.83/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)))),
% 1.83/2.01 inference(transitivity,[status(thm)],[1256, 1254])).
% 1.83/2.01 tff(1258,plain,
% 1.83/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 1.83/2.01 inference(quant_inst,[status(thm)],[])).
% 1.83/2.01 tff(1259,plain,
% 1.83/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 1.83/2.02 tff(1260,plain,
% 1.83/2.02 (~c3_1(a587)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1259, 101, 303, 910, 909, 1162, 1154, 66, 22, 1146, 11])).
% 1.83/2.02 tff(1261,plain,
% 1.83/2.02 (~hskp20),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[668, 1227, 660, 1226, 1225])).
% 1.83/2.02 tff(1262,plain,
% 1.83/2.02 (^[U: $i] : refl((hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.83/2.02 inference(bind,[status(th)],[])).
% 1.83/2.02 tff(1263,plain,
% 1.83/2.02 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.83/2.02 inference(quant_intro,[status(thm)],[1262])).
% 1.83/2.02 tff(1264,plain,
% 1.83/2.02 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1265,plain,
% 1.83/2.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp20) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp20) <=> (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.83/2.02 inference(bind,[status(th)],[])).
% 1.83/2.02 tff(1266,plain,
% 1.83/2.02 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp20) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.83/2.02 inference(quant_intro,[status(thm)],[1265])).
% 1.83/2.02 tff(1267,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.83/2.02 tff(1268,plain,
% 1.83/2.02 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 1.83/2.02 tff(1269,plain,
% 1.83/2.02 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1268, 1264])).
% 1.83/2.02 tff(1270,plain,(
% 1.83/2.02 ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.83/2.02 inference(skolemize,[status(sab)],[1269])).
% 1.83/2.02 tff(1271,plain,
% 1.83/2.02 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1270, 1263])).
% 1.83/2.02 tff(1272,plain,
% 1.83/2.02 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1273,plain,
% 1.83/2.02 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603))) <=> (hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1274,plain,
% 1.83/2.02 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))))),
% 1.83/2.02 inference(monotonicity,[status(thm)],[1273])).
% 1.83/2.02 tff(1275,plain,
% 1.83/2.02 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.83/2.02 inference(transitivity,[status(thm)],[1274, 1272])).
% 1.83/2.02 tff(1276,plain,
% 1.83/2.02 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.83/2.02 inference(quant_inst,[status(thm)],[])).
% 1.83/2.02 tff(1277,plain,
% 1.83/2.02 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 1.83/2.02 tff(1278,plain,
% 1.83/2.02 (hskp20 | hskp7 | (~c2_1(a603))),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1277, 101, 919, 907, 1271])).
% 1.83/2.02 tff(1279,plain,
% 1.83/2.02 (hskp7),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1278, 1261, 918])).
% 1.83/2.02 tff(1280,plain,
% 1.83/2.02 (~c3_1(a592)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[736, 1279])).
% 1.83/2.02 tff(1281,plain,
% 1.83/2.02 (~c0_1(a592)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[742, 1279])).
% 1.83/2.02 tff(1282,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1283,plain,
% 1.83/2.02 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1284,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 1.83/2.02 inference(monotonicity,[status(thm)],[1283])).
% 1.83/2.02 tff(1285,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.83/2.02 inference(transitivity,[status(thm)],[1284, 1282])).
% 1.83/2.02 tff(1286,plain,
% 1.83/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 1.83/2.02 inference(quant_inst,[status(thm)],[])).
% 1.83/2.02 tff(1287,plain,
% 1.83/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 1.83/2.02 tff(1288,plain,
% 1.83/2.02 (~c1_1(a592)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1287, 101, 919, 985, 984, 907, 922, 1281, 1280, 240, 918])).
% 1.83/2.02 tff(1289,plain,
% 1.83/2.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1290,plain,
% 1.83/2.02 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1291,plain,
% 1.83/2.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603))))),
% 1.83/2.02 inference(monotonicity,[status(thm)],[1290])).
% 1.83/2.02 tff(1292,plain,
% 1.83/2.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603)))),
% 1.83/2.02 inference(transitivity,[status(thm)],[1291, 1289])).
% 1.83/2.02 tff(1293,plain,
% 1.83/2.02 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 1.83/2.02 inference(quant_inst,[status(thm)],[])).
% 1.83/2.02 tff(1294,plain,
% 1.83/2.02 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.83/2.02 tff(1295,plain,
% 1.83/2.02 (hskp2),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1294, 101, 908, 907, 1281, 1280, 188, 1288, 918])).
% 1.83/2.02 tff(1296,plain,
% 1.83/2.02 (~c3_1(a586)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[206, 1295])).
% 1.83/2.02 tff(1297,plain,
% 1.83/2.02 (c1_1(a586)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[214, 1295])).
% 1.83/2.02 tff(1298,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1299,plain,
% 1.83/2.02 (((~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1300,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599))))),
% 1.83/2.02 inference(monotonicity,[status(thm)],[1299])).
% 1.83/2.02 tff(1301,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.83/2.02 inference(transitivity,[status(thm)],[1300, 1298])).
% 1.83/2.02 tff(1302,plain,
% 1.83/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.83/2.02 inference(quant_inst,[status(thm)],[])).
% 1.83/2.02 tff(1303,plain,
% 1.83/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.83/2.02 tff(1304,plain,
% 1.83/2.02 (c0_1(a586)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1303, 101, 985, 984, 910, 909, 1297, 922, 1296, 240, 1260])).
% 1.83/2.02 tff(1305,plain,
% 1.83/2.02 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.83/2.02 inference(bind,[status(th)],[])).
% 1.83/2.02 tff(1306,plain,
% 1.83/2.02 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.83/2.02 inference(quant_intro,[status(thm)],[1305])).
% 1.83/2.02 tff(1307,plain,
% 1.83/2.02 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1308,plain,
% 1.83/2.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.83/2.02 inference(bind,[status(th)],[])).
% 1.83/2.02 tff(1309,plain,
% 1.83/2.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.83/2.02 inference(quant_intro,[status(thm)],[1308])).
% 1.83/2.02 tff(1310,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.83/2.02 tff(1311,plain,
% 1.83/2.02 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 1.83/2.02 tff(1312,plain,
% 1.83/2.02 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1311, 1307])).
% 1.83/2.02 tff(1313,plain,(
% 1.83/2.02 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.83/2.02 inference(skolemize,[status(sab)],[1312])).
% 1.83/2.02 tff(1314,plain,
% 1.83/2.02 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1313, 1306])).
% 1.83/2.02 tff(1315,plain,
% 1.83/2.02 (((~hskp28) | c1_1(a612)) <=> ((~hskp28) | c1_1(a612))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1316,axiom,((~hskp28) | c1_1(a612)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.83/2.02 tff(1317,plain,
% 1.83/2.02 ((~hskp28) | c1_1(a612)),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 1.83/2.02 tff(1318,plain,
% 1.83/2.02 ((~hskp28) | c1_1(a612)),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1317, 1315])).
% 1.83/2.02 tff(1319,plain,
% 1.83/2.02 ((~hskp28) | c1_1(a612)),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1318, 1315])).
% 1.83/2.02 tff(1320,plain,
% 1.83/2.02 ((~hskp28) | c1_1(a612)),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1319, 1315])).
% 1.83/2.02 tff(1321,plain,
% 1.83/2.02 ((~hskp28) | c1_1(a612)),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1320, 1315])).
% 1.83/2.02 tff(1322,plain,
% 1.83/2.02 (c1_1(a612)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1321, 1180])).
% 1.83/2.02 tff(1323,plain,
% 1.83/2.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1324,plain,
% 1.83/2.02 ((hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))) <=> (hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1325,plain,
% 1.83/2.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))))),
% 1.83/2.02 inference(monotonicity,[status(thm)],[1324])).
% 1.83/2.02 tff(1326,plain,
% 1.83/2.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 1.83/2.02 inference(transitivity,[status(thm)],[1325, 1323])).
% 1.83/2.02 tff(1327,plain,
% 1.83/2.02 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 1.83/2.02 inference(quant_inst,[status(thm)],[])).
% 1.83/2.02 tff(1328,plain,
% 1.83/2.02 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.83/2.02 tff(1329,plain,
% 1.83/2.02 (hskp16 | (~c0_1(a586))),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1328, 101, 1322, 1181, 1297, 1296, 1314, 1189])).
% 1.83/2.02 tff(1330,plain,
% 1.83/2.02 (hskp16),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1329, 1304])).
% 1.83/2.02 tff(1331,plain,
% 1.83/2.02 (~c3_1(a606)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[982, 1330])).
% 1.83/2.02 tff(1332,plain,
% 1.83/2.02 (~c2_1(a606)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1015, 1330])).
% 1.83/2.02 tff(1333,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1334,plain,
% 1.83/2.02 (((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607)))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1335,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607))))),
% 1.83/2.02 inference(monotonicity,[status(thm)],[1334])).
% 1.83/2.02 tff(1336,plain,
% 1.83/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607)))),
% 1.83/2.02 inference(transitivity,[status(thm)],[1335, 1333])).
% 1.83/2.02 tff(1337,plain,
% 1.83/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 1.83/2.02 inference(quant_inst,[status(thm)],[])).
% 1.83/2.02 tff(1338,plain,
% 1.83/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.83/2.02 tff(1339,plain,
% 1.83/2.02 (c0_1(a606)),
% 1.83/2.02 inference(unit_resolution,[status(thm)],[1338, 101, 1236, 1235, 66, 22, 1332, 1331, 1253, 1122, 1243])).
% 1.83/2.02 tff(1340,plain,
% 1.83/2.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.83/2.02 inference(bind,[status(th)],[])).
% 1.83/2.02 tff(1341,plain,
% 1.83/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.83/2.02 inference(quant_intro,[status(thm)],[1340])).
% 1.83/2.02 tff(1342,plain,
% 1.83/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.83/2.02 inference(rewrite,[status(thm)],[])).
% 1.83/2.02 tff(1343,plain,
% 1.83/2.02 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.83/2.02 inference(bind,[status(th)],[])).
% 1.83/2.02 tff(1344,plain,
% 1.83/2.02 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.83/2.02 inference(quant_intro,[status(thm)],[1343])).
% 1.83/2.02 tff(1345,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.83/2.02 tff(1346,plain,
% 1.83/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 1.83/2.02 tff(1347,plain,
% 1.83/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.83/2.02 inference(modus_ponens,[status(thm)],[1346, 1342])).
% 1.83/2.03 tff(1348,plain,(
% 1.83/2.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.83/2.03 inference(skolemize,[status(sab)],[1347])).
% 1.83/2.03 tff(1349,plain,
% 1.83/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1348, 1341])).
% 1.83/2.03 tff(1350,plain,
% 1.83/2.03 (~c2_1(a593)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[510, 1234])).
% 1.83/2.03 tff(1351,plain,
% 1.83/2.03 (((~hskp2) | c2_1(a586)) <=> ((~hskp2) | c2_1(a586))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1352,axiom,((~hskp2) | c2_1(a586)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.83/2.03 tff(1353,plain,
% 1.83/2.03 ((~hskp2) | c2_1(a586)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.83/2.03 tff(1354,plain,
% 1.83/2.03 ((~hskp2) | c2_1(a586)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1353, 1351])).
% 1.83/2.03 tff(1355,plain,
% 1.83/2.03 ((~hskp2) | c2_1(a586)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1354, 1351])).
% 1.83/2.03 tff(1356,plain,
% 1.83/2.03 ((~hskp2) | c2_1(a586)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1355, 1351])).
% 1.83/2.03 tff(1357,plain,
% 1.83/2.03 ((~hskp2) | c2_1(a586)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1356, 1351])).
% 1.83/2.03 tff(1358,plain,
% 1.83/2.03 (c2_1(a586)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1357, 1295])).
% 1.83/2.03 tff(1359,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1360,plain,
% 1.83/2.03 ((hskp9 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1361,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636))))),
% 1.83/2.03 inference(monotonicity,[status(thm)],[1360])).
% 1.83/2.03 tff(1362,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636)))),
% 1.83/2.03 inference(transitivity,[status(thm)],[1361, 1359])).
% 1.83/2.03 tff(1363,plain,
% 1.83/2.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 1.83/2.03 inference(quant_inst,[status(thm)],[])).
% 1.83/2.03 tff(1364,plain,
% 1.83/2.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 1.83/2.03 tff(1365,plain,
% 1.83/2.03 (hskp9),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1364, 101, 1227, 1297, 1358, 1226, 1225, 276, 1304])).
% 1.83/2.03 tff(1366,plain,
% 1.83/2.03 (((~hskp9) | (~c3_1(a595))) <=> ((~hskp9) | (~c3_1(a595)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1367,plain,
% 1.83/2.03 (((~c3_1(a595)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a595)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1368,axiom,((~c3_1(a595)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.83/2.03 tff(1369,plain,
% 1.83/2.03 ((~hskp9) | (~c3_1(a595))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 1.83/2.03 tff(1370,plain,
% 1.83/2.03 ((~hskp9) | (~c3_1(a595))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1369, 1366])).
% 1.83/2.03 tff(1371,plain,
% 1.83/2.03 (~c3_1(a595)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1370, 1365])).
% 1.83/2.03 tff(1372,plain,
% 1.83/2.03 (((~hskp9) | (~c1_1(a595))) <=> ((~hskp9) | (~c1_1(a595)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1373,plain,
% 1.83/2.03 (((~c1_1(a595)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a595)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1374,axiom,((~c1_1(a595)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.83/2.03 tff(1375,plain,
% 1.83/2.03 ((~hskp9) | (~c1_1(a595))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.83/2.03 tff(1376,plain,
% 1.83/2.03 ((~hskp9) | (~c1_1(a595))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1375, 1372])).
% 1.83/2.03 tff(1377,plain,
% 1.83/2.03 (~c1_1(a595)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1376, 1365])).
% 1.83/2.03 tff(1378,plain,
% 1.83/2.03 (((~hskp9) | (~c0_1(a595))) <=> ((~hskp9) | (~c0_1(a595)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1379,plain,
% 1.83/2.03 (((~c0_1(a595)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a595)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1380,axiom,((~c0_1(a595)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.83/2.03 tff(1381,plain,
% 1.83/2.03 ((~hskp9) | (~c0_1(a595))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.83/2.03 tff(1382,plain,
% 1.83/2.03 ((~hskp9) | (~c0_1(a595))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1381, 1378])).
% 1.83/2.03 tff(1383,plain,
% 1.83/2.03 (~c0_1(a595)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1382, 1365])).
% 1.83/2.03 tff(1384,plain,
% 1.83/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1385,plain,
% 1.83/2.03 (((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1386,plain,
% 1.83/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))))),
% 1.83/2.03 inference(monotonicity,[status(thm)],[1385])).
% 1.83/2.03 tff(1387,plain,
% 1.83/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 1.83/2.03 inference(transitivity,[status(thm)],[1386, 1384])).
% 1.83/2.03 tff(1388,plain,
% 1.83/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 1.83/2.03 inference(quant_inst,[status(thm)],[])).
% 1.83/2.03 tff(1389,plain,
% 1.83/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 1.83/2.03 tff(1390,plain,
% 1.83/2.03 ($false),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1389, 101, 1236, 1332, 1331, 1383, 1377, 1371, 1350, 1349, 1243, 1339])).
% 1.83/2.03 tff(1391,plain,(hskp26 | c1_1(a607) | c2_1(a607) | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | (~c3_1(a607)) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 1.83/2.03 tff(1392,plain,
% 1.83/2.03 (hskp26),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1391, 264, 258, 872, 864, 895, 894, 893, 277, 856])).
% 1.83/2.03 tff(1393,plain,
% 1.83/2.03 (c2_1(a583)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[364, 1392])).
% 1.83/2.03 tff(1394,plain,
% 1.83/2.03 (c1_1(a583)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[330, 1392])).
% 1.83/2.03 tff(1395,plain,
% 1.83/2.03 (c0_1(a583)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[338, 1392])).
% 1.83/2.03 tff(1396,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1397,plain,
% 1.83/2.03 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607))) <=> (hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1398,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607))))),
% 1.83/2.03 inference(monotonicity,[status(thm)],[1397])).
% 1.83/2.03 tff(1399,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.03 inference(transitivity,[status(thm)],[1398, 1396])).
% 1.83/2.03 tff(1400,plain,
% 1.83/2.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.03 inference(quant_inst,[status(thm)],[])).
% 1.83/2.03 tff(1401,plain,
% 1.83/2.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 1.83/2.03 tff(1402,plain,
% 1.83/2.03 (hskp9 | c0_1(a607)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1401, 101, 1395, 1394, 1393, 277, 264, 276])).
% 1.83/2.03 tff(1403,plain,
% 1.83/2.03 (hskp9),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1402, 266])).
% 1.83/2.03 tff(1404,plain,
% 1.83/2.03 (~c3_1(a595)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1370, 1403])).
% 1.83/2.03 tff(1405,plain,
% 1.83/2.03 (~c0_1(a595)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1382, 1403])).
% 1.83/2.03 tff(1406,plain,
% 1.83/2.03 (~c1_1(a595)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1376, 1403])).
% 1.83/2.03 tff(1407,plain,
% 1.83/2.03 (hskp6 | c2_1(a603)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[177, 101, 44, 893, 895, 43])).
% 1.83/2.03 tff(1408,plain,
% 1.83/2.03 (c2_1(a603)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1407, 67])).
% 1.83/2.03 tff(1409,plain,
% 1.83/2.03 (hskp28),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1032, 101, 277, 893, 258, 894, 1026, 266, 1408])).
% 1.83/2.03 tff(1410,plain,
% 1.83/2.03 (c3_1(a612)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1040, 1409])).
% 1.83/2.03 tff(1411,plain,
% 1.83/2.03 (c2_1(a612)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1048, 1409])).
% 1.83/2.03 tff(1412,plain,
% 1.83/2.03 (c1_1(a612)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1321, 1409])).
% 1.83/2.03 tff(1413,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1414,plain,
% 1.83/2.03 ((hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1415,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612))))),
% 1.83/2.03 inference(monotonicity,[status(thm)],[1414])).
% 1.83/2.03 tff(1416,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)))),
% 1.83/2.03 inference(transitivity,[status(thm)],[1415, 1413])).
% 1.83/2.03 tff(1417,plain,
% 1.83/2.03 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 1.83/2.03 inference(quant_inst,[status(thm)],[])).
% 1.83/2.03 tff(1418,plain,
% 1.83/2.03 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.83/2.03 tff(1419,plain,
% 1.83/2.03 (hskp10),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1418, 101, 1412, 1411, 1410, 1395, 1394, 1393, 21])).
% 1.83/2.03 tff(1420,plain,
% 1.83/2.03 (~c1_1(a598)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[827, 1419])).
% 1.83/2.03 tff(1421,plain,
% 1.83/2.03 (c0_1(a598)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[808, 1419])).
% 1.83/2.03 tff(1422,plain,
% 1.83/2.03 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1423,plain,
% 1.83/2.03 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598))) <=> (hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1424,plain,
% 1.83/2.03 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598))))),
% 1.83/2.03 inference(monotonicity,[status(thm)],[1423])).
% 1.83/2.03 tff(1425,plain,
% 1.83/2.03 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 1.83/2.03 inference(transitivity,[status(thm)],[1424, 1422])).
% 1.83/2.03 tff(1426,plain,
% 1.83/2.03 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))),
% 1.83/2.03 inference(quant_inst,[status(thm)],[])).
% 1.83/2.03 tff(1427,plain,
% 1.83/2.03 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 1.83/2.03 tff(1428,plain,
% 1.83/2.03 (c2_1(a598)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1427, 101, 44, 67, 1421, 1420, 43])).
% 1.83/2.03 tff(1429,plain,
% 1.83/2.03 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.83/2.03 inference(bind,[status(th)],[])).
% 1.83/2.03 tff(1430,plain,
% 1.83/2.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.83/2.03 inference(quant_intro,[status(thm)],[1429])).
% 1.83/2.03 tff(1431,plain,
% 1.83/2.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1432,plain,
% 1.83/2.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.83/2.03 inference(bind,[status(th)],[])).
% 1.83/2.03 tff(1433,plain,
% 1.83/2.03 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.83/2.03 inference(quant_intro,[status(thm)],[1432])).
% 1.83/2.03 tff(1434,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.83/2.03 tff(1435,plain,
% 1.83/2.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.83/2.03 tff(1436,plain,
% 1.83/2.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1435, 1431])).
% 1.83/2.03 tff(1437,plain,(
% 1.83/2.03 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.83/2.03 inference(skolemize,[status(sab)],[1436])).
% 1.83/2.03 tff(1438,plain,
% 1.83/2.03 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1437, 1430])).
% 1.83/2.03 tff(1439,assumption,(~c3_1(a595)), introduced(assumption)).
% 1.83/2.03 tff(1440,assumption,(~c1_1(a595)), introduced(assumption)).
% 1.83/2.03 tff(1441,assumption,(~c0_1(a595)), introduced(assumption)).
% 1.83/2.03 tff(1442,plain,
% 1.83/2.03 (^[U: $i] : refl((hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.83/2.03 inference(bind,[status(th)],[])).
% 1.83/2.03 tff(1443,plain,
% 1.83/2.03 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.03 inference(quant_intro,[status(thm)],[1442])).
% 1.83/2.03 tff(1444,plain,
% 1.83/2.03 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1445,plain,
% 1.83/2.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp15) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp15) <=> (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.83/2.03 inference(bind,[status(th)],[])).
% 1.83/2.03 tff(1446,plain,
% 1.83/2.03 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp15) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.03 inference(quant_intro,[status(thm)],[1445])).
% 1.83/2.03 tff(1447,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.83/2.03 tff(1448,plain,
% 1.83/2.03 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 1.83/2.03 tff(1449,plain,
% 1.83/2.03 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1448, 1444])).
% 1.83/2.03 tff(1450,plain,(
% 1.83/2.03 ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.03 inference(skolemize,[status(sab)],[1449])).
% 1.83/2.03 tff(1451,plain,
% 1.83/2.03 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1450, 1443])).
% 1.83/2.03 tff(1452,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1453,plain,
% 1.83/2.03 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1454,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603))))),
% 1.83/2.03 inference(monotonicity,[status(thm)],[1453])).
% 1.83/2.03 tff(1455,plain,
% 1.83/2.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603)))),
% 1.83/2.03 inference(transitivity,[status(thm)],[1454, 1452])).
% 1.83/2.03 tff(1456,plain,
% 1.83/2.03 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 1.83/2.03 inference(quant_inst,[status(thm)],[])).
% 1.83/2.03 tff(1457,plain,
% 1.83/2.03 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 1.83/2.03 tff(1458,plain,
% 1.83/2.03 (hskp2 | (~c2_1(a603))),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1457, 101, 895, 894, 1441, 1440, 1439, 188])).
% 1.83/2.03 tff(1459,plain,
% 1.83/2.03 (hskp2),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1458, 1408])).
% 1.83/2.03 tff(1460,plain,
% 1.83/2.03 (~c3_1(a586)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[206, 1459])).
% 1.83/2.03 tff(1461,plain,
% 1.83/2.03 (c2_1(a586)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1357, 1459])).
% 1.83/2.03 tff(1462,plain,
% 1.83/2.03 (c1_1(a586)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[214, 1459])).
% 1.83/2.03 tff(1463,plain,
% 1.83/2.03 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1464,plain,
% 1.83/2.03 ((hskp29 | hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586))) <=> (hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1465,plain,
% 1.83/2.03 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586))))),
% 1.83/2.03 inference(monotonicity,[status(thm)],[1464])).
% 1.83/2.03 tff(1466,plain,
% 1.83/2.03 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.83/2.03 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.83/2.03 tff(1467,plain,
% 1.83/2.03 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.83/2.03 inference(quant_inst,[status(thm)],[])).
% 1.83/2.03 tff(1468,plain,
% 1.83/2.03 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.83/2.03 tff(1469,plain,
% 1.83/2.03 (hskp15),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1468, 251, 101, 1462, 1461, 1460, 1451])).
% 1.83/2.03 tff(1470,plain,
% 1.83/2.03 (((~hskp15) | (~c0_1(a604))) <=> ((~hskp15) | (~c0_1(a604)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1471,plain,
% 1.83/2.03 (((~c0_1(a604)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a604)))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1472,axiom,((~c0_1(a604)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.83/2.03 tff(1473,plain,
% 1.83/2.03 ((~hskp15) | (~c0_1(a604))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 1.83/2.03 tff(1474,plain,
% 1.83/2.03 ((~hskp15) | (~c0_1(a604))),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1473, 1470])).
% 1.83/2.03 tff(1475,plain,
% 1.83/2.03 (~c0_1(a604)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1474, 1469])).
% 1.83/2.03 tff(1476,plain,
% 1.83/2.03 (((~hskp15) | c3_1(a604)) <=> ((~hskp15) | c3_1(a604))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1477,axiom,((~hskp15) | c3_1(a604)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.83/2.03 tff(1478,plain,
% 1.83/2.03 ((~hskp15) | c3_1(a604)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 1.83/2.03 tff(1479,plain,
% 1.83/2.03 ((~hskp15) | c3_1(a604)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1478, 1476])).
% 1.83/2.03 tff(1480,plain,
% 1.83/2.03 ((~hskp15) | c3_1(a604)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1479, 1476])).
% 1.83/2.03 tff(1481,plain,
% 1.83/2.03 ((~hskp15) | c3_1(a604)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1480, 1476])).
% 1.83/2.03 tff(1482,plain,
% 1.83/2.03 ((~hskp15) | c3_1(a604)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1481, 1476])).
% 1.83/2.03 tff(1483,plain,
% 1.83/2.03 (c3_1(a604)),
% 1.83/2.03 inference(unit_resolution,[status(thm)],[1482, 1469])).
% 1.83/2.03 tff(1484,plain,
% 1.83/2.03 (((~hskp15) | c1_1(a604)) <=> ((~hskp15) | c1_1(a604))),
% 1.83/2.03 inference(rewrite,[status(thm)],[])).
% 1.83/2.03 tff(1485,axiom,((~hskp15) | c1_1(a604)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.83/2.03 tff(1486,plain,
% 1.83/2.03 ((~hskp15) | c1_1(a604)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 1.83/2.03 tff(1487,plain,
% 1.83/2.03 ((~hskp15) | c1_1(a604)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1486, 1484])).
% 1.83/2.03 tff(1488,plain,
% 1.83/2.03 ((~hskp15) | c1_1(a604)),
% 1.83/2.03 inference(modus_ponens,[status(thm)],[1487, 1484])).
% 1.83/2.04 tff(1489,plain,
% 1.83/2.04 ((~hskp15) | c1_1(a604)),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1488, 1484])).
% 1.83/2.04 tff(1490,plain,
% 1.83/2.04 ((~hskp15) | c1_1(a604)),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1489, 1484])).
% 1.83/2.04 tff(1491,plain,
% 1.83/2.04 (c1_1(a604)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1490, 1469])).
% 1.83/2.04 tff(1492,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1493,plain,
% 1.83/2.04 ((hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1494,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))))),
% 1.83/2.04 inference(monotonicity,[status(thm)],[1493])).
% 1.83/2.04 tff(1495,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.83/2.04 inference(transitivity,[status(thm)],[1494, 1492])).
% 1.83/2.04 tff(1496,plain,
% 1.83/2.04 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 1.83/2.04 inference(quant_inst,[status(thm)],[])).
% 1.83/2.04 tff(1497,plain,
% 1.83/2.04 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 1.83/2.04 tff(1498,plain,
% 1.83/2.04 (hskp1),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1497, 101, 1491, 1483, 1475, 1441, 1440, 1439, 1438])).
% 1.83/2.04 tff(1499,plain,
% 1.83/2.04 (~c0_1(a585)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1145, 1498])).
% 1.83/2.04 tff(1500,plain,
% 1.83/2.04 (c2_1(a585)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1153, 1498])).
% 1.83/2.04 tff(1501,plain,
% 1.83/2.04 (c1_1(a585)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1161, 1498])).
% 1.83/2.04 tff(1502,plain,
% 1.83/2.04 (c3_1(a598)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[800, 1419])).
% 1.83/2.04 tff(1503,plain,
% 1.83/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1504,plain,
% 1.83/2.04 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1505,plain,
% 1.83/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607))))),
% 1.83/2.04 inference(monotonicity,[status(thm)],[1504])).
% 1.83/2.04 tff(1506,plain,
% 1.83/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 1.83/2.04 inference(transitivity,[status(thm)],[1505, 1503])).
% 1.83/2.04 tff(1507,plain,
% 1.83/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 1.83/2.04 inference(quant_inst,[status(thm)],[])).
% 1.83/2.04 tff(1508,plain,
% 1.83/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1507, 1506])).
% 1.83/2.04 tff(1509,plain,
% 1.83/2.04 ($false),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1508, 101, 277, 1421, 1502, 1501, 1500, 264, 258, 1499, 11, 1428])).
% 1.83/2.04 tff(1510,plain,(hskp6 | hskp22 | c0_1(a595) | c1_1(a595) | c3_1(a595) | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.83/2.04 tff(1511,plain,
% 1.83/2.04 ($false),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1510, 1406, 1405, 44, 67, 1404, 251])).
% 1.83/2.04 tff(1512,plain,(hskp6 | hskp22 | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.83/2.04 tff(1513,plain,
% 1.83/2.04 (hskp6),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1512, 251, 44])).
% 1.83/2.04 tff(1514,plain,
% 1.83/2.04 (~c0_1(a590)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[606, 1513])).
% 1.83/2.04 tff(1515,assumption,(~hskp11), introduced(assumption)).
% 1.83/2.04 tff(1516,plain,
% 1.83/2.04 (^[U: $i] : refl((hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.83/2.04 inference(bind,[status(th)],[])).
% 1.83/2.04 tff(1517,plain,
% 1.83/2.04 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.04 inference(quant_intro,[status(thm)],[1516])).
% 1.83/2.04 tff(1518,plain,
% 1.83/2.04 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1519,plain,
% 1.83/2.04 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp23) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp23) <=> (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.83/2.04 inference(bind,[status(th)],[])).
% 1.83/2.04 tff(1520,plain,
% 1.83/2.04 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp23) <=> ![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.04 inference(quant_intro,[status(thm)],[1519])).
% 1.83/2.04 tff(1521,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.83/2.04 tff(1522,plain,
% 1.83/2.04 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.83/2.04 tff(1523,plain,
% 1.83/2.04 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1522, 1518])).
% 1.83/2.04 tff(1524,plain,(
% 1.83/2.04 ![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.04 inference(skolemize,[status(sab)],[1523])).
% 1.83/2.04 tff(1525,plain,
% 1.83/2.04 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1524, 1517])).
% 1.83/2.04 tff(1526,assumption,(c2_1(a583)), introduced(assumption)).
% 1.83/2.04 tff(1527,assumption,(c1_1(a583)), introduced(assumption)).
% 1.83/2.04 tff(1528,assumption,(c0_1(a583)), introduced(assumption)).
% 1.83/2.04 tff(1529,assumption,(~hskp23), introduced(assumption)).
% 1.83/2.04 tff(1530,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1531,plain,
% 1.83/2.04 ((hskp11 | hskp23 | (~ndr1_0) | c1_1(a587) | (~c3_1(a587)) | (~c0_1(a587))) <=> (hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1532,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a587) | (~c3_1(a587)) | (~c0_1(a587)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587))))),
% 1.83/2.04 inference(monotonicity,[status(thm)],[1531])).
% 1.83/2.04 tff(1533,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a587) | (~c3_1(a587)) | (~c0_1(a587)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587)))),
% 1.83/2.04 inference(transitivity,[status(thm)],[1532, 1530])).
% 1.83/2.04 tff(1534,plain,
% 1.83/2.04 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a587) | (~c3_1(a587)) | (~c0_1(a587)))),
% 1.83/2.04 inference(quant_inst,[status(thm)],[])).
% 1.83/2.04 tff(1535,plain,
% 1.83/2.04 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 1.83/2.04 tff(1536,plain,
% 1.83/2.04 (hskp11 | hskp23 | (~c3_1(a587))),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1535, 101, 910, 906, 1525])).
% 1.83/2.04 tff(1537,plain,
% 1.83/2.04 (~c3_1(a587)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1536, 1529, 1515])).
% 1.83/2.04 tff(1538,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1539,plain,
% 1.83/2.04 ((hskp11 | hskp23 | (~ndr1_0) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1540,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 1.83/2.04 inference(monotonicity,[status(thm)],[1539])).
% 1.83/2.04 tff(1541,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.83/2.04 inference(transitivity,[status(thm)],[1540, 1538])).
% 1.83/2.04 tff(1542,plain,
% 1.83/2.04 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 1.83/2.04 inference(quant_inst,[status(thm)],[])).
% 1.83/2.04 tff(1543,plain,
% 1.83/2.04 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.83/2.04 tff(1544,plain,
% 1.83/2.04 (hskp11 | hskp23 | (~c0_1(a607))),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1543, 101, 303, 66, 1525])).
% 1.83/2.04 tff(1545,plain,
% 1.83/2.04 (~c0_1(a607)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1544, 1529, 1515])).
% 1.83/2.04 tff(1546,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1547,plain,
% 1.83/2.04 ((hskp28 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1548,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607))))),
% 1.83/2.04 inference(monotonicity,[status(thm)],[1547])).
% 1.83/2.04 tff(1549,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607)))),
% 1.83/2.04 inference(transitivity,[status(thm)],[1548, 1546])).
% 1.83/2.04 tff(1550,plain,
% 1.83/2.04 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.83/2.04 inference(quant_inst,[status(thm)],[])).
% 1.83/2.04 tff(1551,plain,
% 1.83/2.04 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 1.83/2.04 tff(1552,plain,
% 1.83/2.04 (hskp28),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1551, 101, 303, 910, 909, 22, 1026, 1545, 1537])).
% 1.83/2.04 tff(1553,plain,
% 1.83/2.04 (c3_1(a612)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1040, 1552])).
% 1.83/2.04 tff(1554,plain,
% 1.83/2.04 (c2_1(a612)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1048, 1552])).
% 1.83/2.04 tff(1555,plain,
% 1.83/2.04 (c1_1(a612)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1321, 1552])).
% 1.83/2.04 tff(1556,plain,
% 1.83/2.04 (hskp10),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1418, 101, 1555, 1554, 1553, 1528, 1527, 1526, 21])).
% 1.83/2.04 tff(1557,plain,
% 1.83/2.04 (~c1_1(a598)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[827, 1556])).
% 1.83/2.04 tff(1558,plain,
% 1.83/2.04 (c3_1(a598)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[800, 1556])).
% 1.83/2.04 tff(1559,plain,
% 1.83/2.04 (c0_1(a598)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[808, 1556])).
% 1.83/2.04 tff(1560,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1561,plain,
% 1.83/2.04 ((hskp11 | hskp23 | (~ndr1_0) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1562,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598))))),
% 1.83/2.04 inference(monotonicity,[status(thm)],[1561])).
% 1.83/2.04 tff(1563,plain,
% 1.83/2.04 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.83/2.04 inference(transitivity,[status(thm)],[1562, 1560])).
% 1.83/2.04 tff(1564,plain,
% 1.83/2.04 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.83/2.04 inference(quant_inst,[status(thm)],[])).
% 1.83/2.04 tff(1565,plain,
% 1.83/2.04 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 1.83/2.04 tff(1566,plain,
% 1.83/2.04 ($false),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1565, 1515, 101, 1529, 1559, 1558, 1557, 1525])).
% 1.83/2.04 tff(1567,plain,(hskp23 | hskp11 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a607)) | (~c0_1(a587)) | (~c2_1(a587)) | c2_1(a607) | c1_1(a587) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.83/2.04 tff(1568,plain,
% 1.83/2.04 (hskp23),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1567, 1515, 1395, 1394, 1393, 277, 872, 864, 258, 856, 264])).
% 1.83/2.04 tff(1569,plain,
% 1.83/2.04 (~c1_1(a636)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[439, 1568])).
% 1.83/2.04 tff(1570,plain,
% 1.83/2.04 (~c0_1(a636)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[445, 1568])).
% 1.83/2.04 tff(1571,plain,
% 1.83/2.04 (c3_1(a636)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[453, 1568])).
% 1.83/2.04 tff(1572,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1573,plain,
% 1.83/2.04 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1574,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636))))),
% 1.83/2.04 inference(monotonicity,[status(thm)],[1573])).
% 1.83/2.04 tff(1575,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)))),
% 1.83/2.04 inference(transitivity,[status(thm)],[1574, 1572])).
% 1.83/2.04 tff(1576,plain,
% 1.83/2.04 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 1.83/2.04 inference(quant_inst,[status(thm)],[])).
% 1.83/2.04 tff(1577,plain,
% 1.83/2.04 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 1.83/2.04 tff(1578,plain,
% 1.83/2.04 (hskp9),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1577, 101, 1395, 1394, 1393, 1571, 1570, 1569, 276])).
% 1.83/2.04 tff(1579,plain,
% 1.83/2.04 (~c3_1(a595)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1370, 1578])).
% 1.83/2.04 tff(1580,plain,
% 1.83/2.04 (~c1_1(a595)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1376, 1578])).
% 1.83/2.04 tff(1581,plain,
% 1.83/2.04 (~c0_1(a595)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1382, 1578])).
% 1.83/2.04 tff(1582,plain,
% 1.83/2.04 (hskp6),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1510, 1581, 44, 1580, 1579, 251])).
% 1.83/2.04 tff(1583,plain,
% 1.83/2.04 (~c0_1(a590)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[606, 1582])).
% 1.83/2.04 tff(1584,plain,
% 1.83/2.04 (c3_1(a590)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[614, 1582])).
% 1.83/2.04 tff(1585,plain,
% 1.83/2.04 (c2_1(a590)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[622, 1582])).
% 1.83/2.04 tff(1586,assumption,(~hskp8), introduced(assumption)).
% 1.83/2.04 tff(1587,plain,
% 1.83/2.04 (hskp8 | hskp6),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[460, 101, 659, 658, 657, 414])).
% 1.83/2.04 tff(1588,plain,
% 1.83/2.04 (hskp6),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1587, 1586])).
% 1.83/2.04 tff(1589,plain,
% 1.83/2.04 (~c0_1(a590)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[606, 1588])).
% 1.83/2.04 tff(1590,plain,
% 1.83/2.04 (c2_1(a590)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[622, 1588])).
% 1.83/2.04 tff(1591,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1592,plain,
% 1.83/2.04 ((hskp8 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636)))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1593,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636))))),
% 1.83/2.04 inference(monotonicity,[status(thm)],[1592])).
% 1.83/2.04 tff(1594,plain,
% 1.83/2.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636)))),
% 1.83/2.04 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.83/2.04 tff(1595,plain,
% 1.83/2.04 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 1.83/2.04 inference(quant_inst,[status(thm)],[])).
% 1.83/2.04 tff(1596,plain,
% 1.83/2.04 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636))),
% 1.83/2.04 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.83/2.04 tff(1597,plain,
% 1.83/2.04 (~c1_1(a590)),
% 1.83/2.04 inference(unit_resolution,[status(thm)],[1596, 101, 1586, 659, 1590, 658, 657, 1589, 1206])).
% 1.83/2.04 tff(1598,plain,
% 1.83/2.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.83/2.04 inference(bind,[status(th)],[])).
% 1.83/2.04 tff(1599,plain,
% 1.83/2.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.04 inference(quant_intro,[status(thm)],[1598])).
% 1.83/2.04 tff(1600,plain,
% 1.83/2.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.04 inference(rewrite,[status(thm)],[])).
% 1.83/2.04 tff(1601,plain,
% 1.83/2.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(1602,plain,
% 1.83/2.05 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[1601])).
% 1.83/2.05 tff(1603,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.83/2.05 tff(1604,plain,
% 1.83/2.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.83/2.05 tff(1605,plain,
% 1.83/2.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1604, 1600])).
% 1.83/2.05 tff(1606,plain,(
% 1.83/2.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.05 inference(skolemize,[status(sab)],[1605])).
% 1.83/2.05 tff(1607,plain,
% 1.83/2.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1606, 1599])).
% 1.83/2.05 tff(1608,plain,
% 1.83/2.05 (c3_1(a590)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[614, 1588])).
% 1.83/2.05 tff(1609,plain,
% 1.83/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1610,plain,
% 1.83/2.05 (((~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1611,plain,
% 1.83/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595)))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[1610])).
% 1.83/2.05 tff(1612,plain,
% 1.83/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595))),
% 1.83/2.05 inference(transitivity,[status(thm)],[1611, 1609])).
% 1.83/2.05 tff(1613,plain,
% 1.83/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(1614,plain,
% 1.83/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595)),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 1.83/2.05 tff(1615,plain,
% 1.83/2.05 (c2_1(a595)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1614, 101, 1590, 1608, 1441, 1439, 1589, 1607, 1597])).
% 1.83/2.05 tff(1616,plain,
% 1.83/2.05 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(1617,plain,
% 1.83/2.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[1616])).
% 1.83/2.05 tff(1618,plain,
% 1.83/2.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1619,plain,
% 1.83/2.05 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(1620,plain,
% 1.83/2.05 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[1619])).
% 1.83/2.05 tff(1621,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.83/2.05 tff(1622,plain,
% 1.83/2.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 1.83/2.05 tff(1623,plain,
% 1.83/2.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1622, 1618])).
% 1.83/2.05 tff(1624,plain,(
% 1.83/2.05 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.83/2.05 inference(skolemize,[status(sab)],[1623])).
% 1.83/2.05 tff(1625,plain,
% 1.83/2.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1624, 1617])).
% 1.83/2.05 tff(1626,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1627,plain,
% 1.83/2.05 ((hskp2 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1628,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595))))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[1627])).
% 1.83/2.05 tff(1629,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 1.83/2.05 inference(transitivity,[status(thm)],[1628, 1626])).
% 1.83/2.05 tff(1630,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(1631,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.83/2.05 tff(1632,plain,
% 1.83/2.05 (hskp2 | (~c2_1(a595))),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1631, 101, 1441, 1440, 1439, 188])).
% 1.83/2.05 tff(1633,plain,
% 1.83/2.05 (hskp2),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1632, 1615])).
% 1.83/2.05 tff(1634,plain,
% 1.83/2.05 (~c3_1(a586)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[206, 1633])).
% 1.83/2.05 tff(1635,plain,
% 1.83/2.05 (c2_1(a586)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1357, 1633])).
% 1.83/2.05 tff(1636,plain,
% 1.83/2.05 (c1_1(a586)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[214, 1633])).
% 1.83/2.05 tff(1637,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1638,plain,
% 1.83/2.05 ((hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1639,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[1638])).
% 1.83/2.05 tff(1640,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 1.83/2.05 inference(transitivity,[status(thm)],[1639, 1637])).
% 1.83/2.05 tff(1641,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(1642,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 1.83/2.05 tff(1643,plain,
% 1.83/2.05 (hskp28),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1642, 101, 1590, 1608, 1636, 1635, 1634, 1625, 1597])).
% 1.83/2.05 tff(1644,plain,
% 1.83/2.05 (c3_1(a612)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1040, 1643])).
% 1.83/2.05 tff(1645,plain,
% 1.83/2.05 (c1_1(a612)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1321, 1643])).
% 1.83/2.05 tff(1646,plain,
% 1.83/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1647,plain,
% 1.83/2.05 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1648,plain,
% 1.83/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[1647])).
% 1.83/2.05 tff(1649,plain,
% 1.83/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.83/2.05 inference(transitivity,[status(thm)],[1648, 1646])).
% 1.83/2.05 tff(1650,plain,
% 1.83/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(1651,plain,
% 1.83/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.83/2.05 tff(1652,plain,
% 1.83/2.05 (~c0_1(a612)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1651, 101, 1645, 1644, 1590, 1608, 1441, 1440, 1589, 65, 1615])).
% 1.83/2.05 tff(1653,plain,
% 1.83/2.05 (c2_1(a612)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1048, 1643])).
% 1.83/2.05 tff(1654,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1655,plain,
% 1.83/2.05 ((hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1656,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636))))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[1655])).
% 1.83/2.05 tff(1657,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636)))),
% 1.83/2.05 inference(transitivity,[status(thm)],[1656, 1654])).
% 1.83/2.05 tff(1658,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(1659,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.83/2.05 tff(1660,plain,
% 1.83/2.05 ($false),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1659, 101, 1586, 1645, 1653, 659, 658, 657, 1206, 1652])).
% 1.83/2.05 tff(1661,plain,(hskp8 | (~c3_1(a636)) | c0_1(a636) | c1_1(a636) | c0_1(a595) | c1_1(a595) | c3_1(a595)), inference(lemma,lemma(discharge,[]))).
% 1.83/2.05 tff(1662,plain,
% 1.83/2.05 (hskp8),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1661, 1571, 1570, 1569, 1581, 1580, 1579])).
% 1.83/2.05 tff(1663,plain,
% 1.83/2.05 (~c2_1(a593)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[510, 1662])).
% 1.83/2.05 tff(1664,plain,
% 1.83/2.05 (^[U: $i] : refl((hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(1665,plain,
% 1.83/2.05 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[1664])).
% 1.83/2.05 tff(1666,plain,
% 1.83/2.05 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1667,plain,
% 1.83/2.05 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp18) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp18) <=> (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(1668,plain,
% 1.83/2.05 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp18) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[1667])).
% 1.83/2.05 tff(1669,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.83/2.05 tff(1670,plain,
% 1.83/2.05 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 1.83/2.05 tff(1671,plain,
% 1.83/2.05 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1670, 1666])).
% 1.83/2.05 tff(1672,plain,(
% 1.83/2.05 ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.05 inference(skolemize,[status(sab)],[1671])).
% 1.83/2.05 tff(1673,plain,
% 1.83/2.05 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1672, 1665])).
% 1.83/2.05 tff(1674,assumption,(~hskp2), introduced(assumption)).
% 1.83/2.05 tff(1675,plain,
% 1.83/2.05 (~c2_1(a595)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1632, 1674])).
% 1.83/2.05 tff(1676,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1677,plain,
% 1.83/2.05 ((hskp2 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1678,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587))))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[1677])).
% 1.83/2.05 tff(1679,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)))),
% 1.83/2.05 inference(transitivity,[status(thm)],[1678, 1676])).
% 1.83/2.05 tff(1680,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(1681,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 1.83/2.05 tff(1682,plain,
% 1.83/2.05 (hskp2 | c3_1(a587)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1681, 101, 909, 1441, 1440, 1439, 906, 188])).
% 1.83/2.05 tff(1683,plain,
% 1.83/2.05 (c3_1(a587)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1682, 1674])).
% 1.83/2.05 tff(1684,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1685,plain,
% 1.83/2.05 ((hskp11 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(1686,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595)))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[1685])).
% 1.83/2.05 tff(1687,plain,
% 1.83/2.05 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595))),
% 1.83/2.05 inference(transitivity,[status(thm)],[1686, 1684])).
% 1.83/2.05 tff(1688,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(1689,plain,
% 1.83/2.05 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595)),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 1.83/2.05 tff(1690,plain,
% 1.83/2.05 ((~c3_1(a587)) | c2_1(a595)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1689, 1515, 101, 910, 909, 1441, 1439, 250])).
% 1.83/2.05 tff(1691,plain,
% 1.83/2.05 ($false),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[1690, 1683, 1675])).
% 1.83/2.06 tff(1692,plain,(hskp2 | hskp11 | (~c0_1(a587)) | (~c2_1(a587)) | c0_1(a595) | c3_1(a595) | c1_1(a595) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 1.83/2.06 tff(1693,plain,
% 1.83/2.06 (hskp2),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1692, 1515, 872, 864, 1581, 1579, 1580, 856])).
% 1.83/2.06 tff(1694,plain,
% 1.83/2.06 (~c3_1(a586)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[206, 1693])).
% 1.83/2.06 tff(1695,plain,
% 1.83/2.06 (c2_1(a586)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1357, 1693])).
% 1.83/2.06 tff(1696,plain,
% 1.83/2.06 (c1_1(a586)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[214, 1693])).
% 1.83/2.06 tff(1697,plain,
% 1.83/2.06 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.83/2.06 inference(rewrite,[status(thm)],[])).
% 1.83/2.06 tff(1698,plain,
% 1.83/2.06 ((hskp29 | hskp18 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586))) <=> (hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.83/2.06 inference(rewrite,[status(thm)],[])).
% 1.83/2.06 tff(1699,plain,
% 1.83/2.06 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586))))),
% 1.83/2.06 inference(monotonicity,[status(thm)],[1698])).
% 1.83/2.06 tff(1700,plain,
% 1.83/2.06 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.83/2.06 inference(transitivity,[status(thm)],[1699, 1697])).
% 1.83/2.06 tff(1701,plain,
% 1.83/2.06 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.83/2.06 inference(quant_inst,[status(thm)],[])).
% 1.83/2.06 tff(1702,plain,
% 1.83/2.06 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586))),
% 1.83/2.06 inference(modus_ponens,[status(thm)],[1701, 1700])).
% 1.83/2.06 tff(1703,plain,
% 1.83/2.06 (hskp18),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1702, 251, 101, 1696, 1695, 1694, 1673])).
% 1.83/2.06 tff(1704,plain,
% 1.83/2.06 (~c2_1(a610)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1087, 1703])).
% 1.83/2.06 tff(1705,plain,
% 1.83/2.06 (~c0_1(a610)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1093, 1703])).
% 1.83/2.06 tff(1706,plain,
% 1.83/2.06 (hskp15),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1468, 251, 101, 1696, 1695, 1694, 1451])).
% 1.83/2.06 tff(1707,plain,
% 1.83/2.06 (~c0_1(a604)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1474, 1706])).
% 1.83/2.06 tff(1708,plain,
% 1.83/2.06 (c3_1(a604)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1482, 1706])).
% 1.83/2.06 tff(1709,plain,
% 1.83/2.06 (c1_1(a604)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1490, 1706])).
% 1.83/2.06 tff(1710,plain,
% 1.83/2.06 (hskp1),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1497, 101, 1709, 1708, 1707, 1581, 1580, 1579, 1438])).
% 1.83/2.06 tff(1711,plain,
% 1.83/2.06 (~c0_1(a585)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1145, 1710])).
% 1.83/2.06 tff(1712,plain,
% 1.83/2.06 (c2_1(a585)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1153, 1710])).
% 1.83/2.06 tff(1713,plain,
% 1.83/2.06 (c1_1(a585)),
% 1.83/2.06 inference(unit_resolution,[status(thm)],[1161, 1710])).
% 1.83/2.06 tff(1714,plain,
% 1.83/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1715,plain,
% 1.92/2.06 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1716,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607))))),
% 1.92/2.06 inference(monotonicity,[status(thm)],[1715])).
% 1.92/2.06 tff(1717,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)))),
% 1.92/2.06 inference(transitivity,[status(thm)],[1716, 1714])).
% 1.92/2.06 tff(1718,plain,
% 1.92/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 1.92/2.06 inference(quant_inst,[status(thm)],[])).
% 1.92/2.06 tff(1719,plain,
% 1.92/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607))),
% 1.92/2.06 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 1.92/2.06 tff(1720,plain,
% 1.92/2.06 (~c3_1(a583)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1719, 101, 1395, 1393, 277, 1713, 1712, 264, 258, 1711, 11])).
% 1.92/2.06 tff(1721,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1722,plain,
% 1.92/2.06 ((hskp16 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604))) <=> (hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1723,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604))))),
% 1.92/2.06 inference(monotonicity,[status(thm)],[1722])).
% 1.92/2.06 tff(1724,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.92/2.06 inference(transitivity,[status(thm)],[1723, 1721])).
% 1.92/2.06 tff(1725,plain,
% 1.92/2.06 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))),
% 1.92/2.06 inference(quant_inst,[status(thm)],[])).
% 1.92/2.06 tff(1726,plain,
% 1.92/2.06 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604))),
% 1.92/2.06 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 1.92/2.06 tff(1727,plain,
% 1.92/2.06 (hskp16),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1726, 101, 1395, 1394, 1709, 1708, 1707, 1314, 1720])).
% 1.92/2.06 tff(1728,plain,
% 1.92/2.06 (c1_1(a606)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[992, 1727])).
% 1.92/2.06 tff(1729,plain,
% 1.92/2.06 (c3_1(a610)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1101, 1703])).
% 1.92/2.06 tff(1730,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1731,plain,
% 1.92/2.06 ((hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1732,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610))))),
% 1.92/2.06 inference(monotonicity,[status(thm)],[1731])).
% 1.92/2.06 tff(1733,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610)))),
% 1.92/2.06 inference(transitivity,[status(thm)],[1732, 1730])).
% 1.92/2.06 tff(1734,plain,
% 1.92/2.06 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 1.92/2.06 inference(quant_inst,[status(thm)],[])).
% 1.92/2.06 tff(1735,plain,
% 1.92/2.06 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610))),
% 1.92/2.06 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.92/2.06 tff(1736,plain,
% 1.92/2.06 (hskp28),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1735, 101, 1395, 1393, 1729, 1705, 1704, 1026, 1720])).
% 1.92/2.06 tff(1737,plain,
% 1.92/2.06 (c3_1(a612)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1040, 1736])).
% 1.92/2.06 tff(1738,plain,
% 1.92/2.06 (c2_1(a612)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1048, 1736])).
% 1.92/2.06 tff(1739,plain,
% 1.92/2.06 (~c0_1(a612)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1188, 101, 1738, 1737, 277, 1713, 1712, 264, 258, 1711, 11])).
% 1.92/2.06 tff(1740,plain,
% 1.92/2.06 (c1_1(a612)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1321, 1736])).
% 1.92/2.06 tff(1741,plain,
% 1.92/2.06 (hskp10),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1418, 101, 1740, 1738, 1737, 1395, 1394, 1393, 21])).
% 1.92/2.06 tff(1742,plain,
% 1.92/2.06 (c3_1(a598)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[800, 1741])).
% 1.92/2.06 tff(1743,plain,
% 1.92/2.06 (~c1_1(a598)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[827, 1741])).
% 1.92/2.06 tff(1744,plain,
% 1.92/2.06 (~c3_1(a606)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[982, 1727])).
% 1.92/2.06 tff(1745,plain,
% 1.92/2.06 (~c2_1(a606)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1015, 1727])).
% 1.92/2.06 tff(1746,plain,
% 1.92/2.06 (c3_1(a593)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[469, 1662])).
% 1.92/2.06 tff(1747,plain,
% 1.92/2.06 (c1_1(a593)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[477, 1662])).
% 1.92/2.06 tff(1748,plain,
% 1.92/2.06 (c0_1(a598)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[808, 1741])).
% 1.92/2.06 tff(1749,assumption,(~hskp27), introduced(assumption)).
% 1.92/2.06 tff(1750,assumption,(~c2_1(a606)), introduced(assumption)).
% 1.92/2.06 tff(1751,assumption,(~c2_1(a610)), introduced(assumption)).
% 1.92/2.06 tff(1752,assumption,(~c0_1(a610)), introduced(assumption)).
% 1.92/2.06 tff(1753,assumption,(c1_1(a606)), introduced(assumption)).
% 1.92/2.06 tff(1754,assumption,(c3_1(a610)), introduced(assumption)).
% 1.92/2.06 tff(1755,plain,
% 1.92/2.06 (hskp27 | (~c0_1(a606))),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1108, 101, 1754, 1753, 1752, 1751, 1750, 495])).
% 1.92/2.06 tff(1756,plain,
% 1.92/2.06 (~c0_1(a606)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1755, 1749])).
% 1.92/2.06 tff(1757,assumption,(~c0_1(a612)), introduced(assumption)).
% 1.92/2.06 tff(1758,assumption,(~c1_1(a598)), introduced(assumption)).
% 1.92/2.06 tff(1759,assumption,(~c3_1(a606)), introduced(assumption)).
% 1.92/2.06 tff(1760,assumption,(c3_1(a612)), introduced(assumption)).
% 1.92/2.06 tff(1761,assumption,(c2_1(a612)), introduced(assumption)).
% 1.92/2.06 tff(1762,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1763,plain,
% 1.92/2.06 (((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1764,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606)))),
% 1.92/2.06 inference(monotonicity,[status(thm)],[1763])).
% 1.92/2.06 tff(1765,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606))),
% 1.92/2.06 inference(transitivity,[status(thm)],[1764, 1762])).
% 1.92/2.06 tff(1766,plain,
% 1.92/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 1.92/2.06 inference(quant_inst,[status(thm)],[])).
% 1.92/2.06 tff(1767,plain,
% 1.92/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606)),
% 1.92/2.06 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 1.92/2.06 tff(1768,plain,
% 1.92/2.06 ((~c2_1(a598)) | c0_1(a606)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1767, 101, 1761, 1760, 812, 1750, 1759, 1758, 1607, 1757])).
% 1.92/2.06 tff(1769,plain,
% 1.92/2.06 (~c2_1(a598)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1768, 1756])).
% 1.92/2.06 tff(1770,assumption,(~c2_1(a593)), introduced(assumption)).
% 1.92/2.06 tff(1771,assumption,(c1_1(a593)), introduced(assumption)).
% 1.92/2.06 tff(1772,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1773,plain,
% 1.92/2.06 ((hskp27 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1774,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610))))),
% 1.92/2.06 inference(monotonicity,[status(thm)],[1773])).
% 1.92/2.06 tff(1775,plain,
% 1.92/2.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610)))),
% 1.92/2.06 inference(transitivity,[status(thm)],[1774, 1772])).
% 1.92/2.06 tff(1776,plain,
% 1.92/2.06 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 1.92/2.06 inference(quant_inst,[status(thm)],[])).
% 1.92/2.06 tff(1777,plain,
% 1.92/2.06 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610))),
% 1.92/2.06 inference(modus_ponens,[status(thm)],[1776, 1775])).
% 1.92/2.06 tff(1778,plain,
% 1.92/2.06 (hskp27 | (~c0_1(a593))),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1777, 101, 1754, 1771, 1752, 1751, 1770, 495])).
% 1.92/2.06 tff(1779,plain,
% 1.92/2.06 (~c0_1(a593)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1778, 1749])).
% 1.92/2.06 tff(1780,assumption,(c3_1(a593)), introduced(assumption)).
% 1.92/2.06 tff(1781,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1782,plain,
% 1.92/2.06 (((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1783,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606)))),
% 1.92/2.06 inference(monotonicity,[status(thm)],[1782])).
% 1.92/2.06 tff(1784,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606))),
% 1.92/2.06 inference(transitivity,[status(thm)],[1783, 1781])).
% 1.92/2.06 tff(1785,plain,
% 1.92/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 1.92/2.06 inference(quant_inst,[status(thm)],[])).
% 1.92/2.06 tff(1786,plain,
% 1.92/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606)),
% 1.92/2.06 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 1.92/2.06 tff(1787,plain,
% 1.92/2.06 ($false),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1786, 101, 813, 1771, 1780, 1750, 1759, 1758, 1253, 1779, 1769, 1756])).
% 1.92/2.06 tff(1788,plain,(hskp27 | (~c0_1(a598)) | (~c1_1(a593)) | (~c3_1(a593)) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~c2_1(a612)) | (~c3_1(a612)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a610)) | (~c1_1(a606)) | c0_1(a610) | c2_1(a610) | c2_1(a593)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.06 tff(1789,plain,
% 1.92/2.06 (hskp27),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1788, 1748, 1747, 1746, 1745, 1744, 1743, 1738, 1737, 1742, 1739, 1729, 1728, 1705, 1704, 1663])).
% 1.92/2.06 tff(1790,plain,
% 1.92/2.06 (c3_1(a611)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[566, 1789])).
% 1.92/2.06 tff(1791,plain,
% 1.92/2.06 (c1_1(a611)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[574, 1789])).
% 1.92/2.06 tff(1792,plain,
% 1.92/2.06 (c0_1(a611)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[582, 1789])).
% 1.92/2.06 tff(1793,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1794,plain,
% 1.92/2.06 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1795,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))))),
% 1.92/2.06 inference(monotonicity,[status(thm)],[1794])).
% 1.92/2.06 tff(1796,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.92/2.06 inference(transitivity,[status(thm)],[1795, 1793])).
% 1.92/2.06 tff(1797,plain,
% 1.92/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 1.92/2.06 inference(quant_inst,[status(thm)],[])).
% 1.92/2.06 tff(1798,plain,
% 1.92/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))),
% 1.92/2.06 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 1.92/2.06 tff(1799,plain,
% 1.92/2.06 (~c2_1(a595)),
% 1.92/2.06 inference(unit_resolution,[status(thm)],[1798, 101, 1792, 1791, 1790, 1585, 1584, 1581, 1580, 1583, 65])).
% 1.92/2.06 tff(1800,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1801,plain,
% 1.92/2.06 (((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598)))),
% 1.92/2.06 inference(rewrite,[status(thm)],[])).
% 1.92/2.06 tff(1802,plain,
% 1.92/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598))))),
% 1.92/2.07 inference(monotonicity,[status(thm)],[1801])).
% 1.92/2.07 tff(1803,plain,
% 1.92/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598)))),
% 1.92/2.07 inference(transitivity,[status(thm)],[1802, 1800])).
% 1.92/2.07 tff(1804,plain,
% 1.92/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 1.92/2.07 inference(quant_inst,[status(thm)],[])).
% 1.92/2.07 tff(1805,plain,
% 1.92/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 1.92/2.07 tff(1806,plain,
% 1.92/2.07 (c2_1(a595) | (~c2_1(a598))),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1805, 101, 1738, 1737, 1742, 1743, 1581, 1579, 1607, 1739])).
% 1.92/2.07 tff(1807,plain,
% 1.92/2.07 (~c2_1(a598)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1806, 1799])).
% 1.92/2.07 tff(1808,plain,
% 1.92/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1809,plain,
% 1.92/2.07 (((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1810,plain,
% 1.92/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604))))),
% 1.92/2.07 inference(monotonicity,[status(thm)],[1809])).
% 1.92/2.07 tff(1811,plain,
% 1.92/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 1.92/2.07 inference(transitivity,[status(thm)],[1810, 1808])).
% 1.92/2.07 tff(1812,plain,
% 1.92/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 1.92/2.07 inference(quant_inst,[status(thm)],[])).
% 1.92/2.07 tff(1813,plain,
% 1.92/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1812, 1811])).
% 1.92/2.07 tff(1814,plain,
% 1.92/2.07 ($false),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1813, 101, 1709, 1708, 1748, 1707, 1743, 1581, 1579, 1253, 1807, 1799])).
% 1.92/2.07 tff(1815,plain,(hskp11 | hskp29 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.92/2.07 tff(1816,plain,
% 1.92/2.07 (hskp11),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1815, 251, 44])).
% 1.92/2.07 tff(1817,plain,
% 1.92/2.07 (~c1_1(a599)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[395, 1816])).
% 1.92/2.07 tff(1818,plain,
% 1.92/2.07 (c2_1(a590)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[622, 1513])).
% 1.92/2.07 tff(1819,plain,
% 1.92/2.07 (c3_1(a599)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[389, 1816])).
% 1.92/2.07 tff(1820,plain,
% 1.92/2.07 (c2_1(a599)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[403, 1816])).
% 1.92/2.07 tff(1821,plain,
% 1.92/2.07 (c3_1(a590)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[614, 1513])).
% 1.92/2.07 tff(1822,assumption,(~hskp9), introduced(assumption)).
% 1.92/2.07 tff(1823,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1824,plain,
% 1.92/2.07 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599))) <=> (hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1825,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599)))),
% 1.92/2.07 inference(monotonicity,[status(thm)],[1824])).
% 1.92/2.07 tff(1826,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599))),
% 1.92/2.07 inference(transitivity,[status(thm)],[1825, 1823])).
% 1.92/2.07 tff(1827,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))),
% 1.92/2.07 inference(quant_inst,[status(thm)],[])).
% 1.92/2.07 tff(1828,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599)),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 1.92/2.07 tff(1829,plain,
% 1.92/2.07 (hskp9 | c0_1(a599)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1828, 101, 1528, 1527, 1526, 426, 425, 276])).
% 1.92/2.07 tff(1830,plain,
% 1.92/2.07 (c0_1(a599)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1829, 1822])).
% 1.92/2.07 tff(1831,plain,
% 1.92/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1832,plain,
% 1.92/2.07 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1833,plain,
% 1.92/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))))),
% 1.92/2.07 inference(monotonicity,[status(thm)],[1832])).
% 1.92/2.07 tff(1834,plain,
% 1.92/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 1.92/2.07 inference(transitivity,[status(thm)],[1833, 1831])).
% 1.92/2.07 tff(1835,plain,
% 1.92/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 1.92/2.07 inference(quant_inst,[status(thm)],[])).
% 1.92/2.07 tff(1836,plain,
% 1.92/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 1.92/2.07 tff(1837,plain,
% 1.92/2.07 ((~c1_1(a590)) | (~c0_1(a599))),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1836, 101, 303, 427, 426, 785, 66, 22, 45, 11])).
% 1.92/2.07 tff(1838,plain,
% 1.92/2.07 (~c1_1(a590)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1837, 1830])).
% 1.92/2.07 tff(1839,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1840,plain,
% 1.92/2.07 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590))) <=> (hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1841,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590)))),
% 1.92/2.07 inference(monotonicity,[status(thm)],[1840])).
% 1.92/2.07 tff(1842,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590))),
% 1.92/2.07 inference(transitivity,[status(thm)],[1841, 1839])).
% 1.92/2.07 tff(1843,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))),
% 1.92/2.07 inference(quant_inst,[status(thm)],[])).
% 1.92/2.07 tff(1844,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590)),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.92/2.07 tff(1845,plain,
% 1.92/2.07 ($false),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1844, 101, 1822, 1528, 1527, 1526, 784, 45, 276, 1838])).
% 1.92/2.07 tff(1846,plain,(hskp9 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a607)) | (~c2_1(a599)) | (~c3_1(a599)) | (~c2_1(a590)) | c1_1(a607) | c2_1(a607) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.07 tff(1847,plain,
% 1.92/2.07 (hskp9),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1846, 1395, 1394, 1393, 1821, 1514, 277, 1820, 1819, 1818, 264, 258, 1817])).
% 1.92/2.07 tff(1848,plain,
% 1.92/2.07 (~c1_1(a595)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1376, 1847])).
% 1.92/2.07 tff(1849,plain,
% 1.92/2.07 (~c0_1(a595)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1382, 1847])).
% 1.92/2.07 tff(1850,assumption,(~hskp28), introduced(assumption)).
% 1.92/2.07 tff(1851,assumption,(~c3_1(a583)), introduced(assumption)).
% 1.92/2.07 tff(1852,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1853,plain,
% 1.92/2.07 ((hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599))) <=> (hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1854,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599))))),
% 1.92/2.07 inference(monotonicity,[status(thm)],[1853])).
% 1.92/2.07 tff(1855,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.92/2.07 inference(transitivity,[status(thm)],[1854, 1852])).
% 1.92/2.07 tff(1856,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.92/2.07 inference(quant_inst,[status(thm)],[])).
% 1.92/2.07 tff(1857,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 1.92/2.07 tff(1858,plain,
% 1.92/2.07 ($false),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1857, 101, 1850, 1527, 1526, 427, 426, 425, 1625, 1851])).
% 1.92/2.07 tff(1859,plain,(c3_1(a583) | hskp28 | (~c1_1(a583)) | (~c2_1(a583)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 1.92/2.07 tff(1860,plain,
% 1.92/2.07 (c3_1(a583)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1859, 1850, 1527, 1526, 427, 426, 425])).
% 1.92/2.07 tff(1861,plain,
% 1.92/2.07 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.92/2.07 inference(bind,[status(th)],[])).
% 1.92/2.07 tff(1862,plain,
% 1.92/2.07 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/2.07 inference(quant_intro,[status(thm)],[1861])).
% 1.92/2.07 tff(1863,plain,
% 1.92/2.07 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1864,plain,
% 1.92/2.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.92/2.07 inference(bind,[status(th)],[])).
% 1.92/2.07 tff(1865,plain,
% 1.92/2.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/2.07 inference(quant_intro,[status(thm)],[1864])).
% 1.92/2.07 tff(1866,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.92/2.07 tff(1867,plain,
% 1.92/2.07 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 1.92/2.07 tff(1868,plain,
% 1.92/2.07 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1867, 1863])).
% 1.92/2.07 tff(1869,plain,(
% 1.92/2.07 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/2.07 inference(skolemize,[status(sab)],[1868])).
% 1.92/2.07 tff(1870,plain,
% 1.92/2.07 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1869, 1862])).
% 1.92/2.07 tff(1871,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1872,plain,
% 1.92/2.07 ((hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c1_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1873,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c1_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 1.92/2.07 inference(monotonicity,[status(thm)],[1872])).
% 1.92/2.07 tff(1874,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c1_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.92/2.07 inference(transitivity,[status(thm)],[1873, 1871])).
% 1.92/2.07 tff(1875,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c1_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 1.92/2.07 inference(quant_inst,[status(thm)],[])).
% 1.92/2.07 tff(1876,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 1.92/2.07 tff(1877,plain,
% 1.92/2.07 (hskp10 | (~c3_1(a583))),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1876, 101, 1528, 1527, 1526, 21])).
% 1.92/2.07 tff(1878,plain,
% 1.92/2.07 (hskp10),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1877, 1860])).
% 1.92/2.07 tff(1879,plain,
% 1.92/2.07 (~c1_1(a598)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[827, 1878])).
% 1.92/2.07 tff(1880,plain,
% 1.92/2.07 (c3_1(a598)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[800, 1878])).
% 1.92/2.07 tff(1881,plain,
% 1.92/2.07 (c0_1(a598)),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[808, 1878])).
% 1.92/2.07 tff(1882,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1883,plain,
% 1.92/2.07 ((hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.92/2.07 inference(rewrite,[status(thm)],[])).
% 1.92/2.07 tff(1884,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598))))),
% 1.92/2.07 inference(monotonicity,[status(thm)],[1883])).
% 1.92/2.07 tff(1885,plain,
% 1.92/2.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.92/2.07 inference(transitivity,[status(thm)],[1884, 1882])).
% 1.92/2.07 tff(1886,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.92/2.07 inference(quant_inst,[status(thm)],[])).
% 1.92/2.07 tff(1887,plain,
% 1.92/2.07 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598))),
% 1.92/2.07 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 1.92/2.07 tff(1888,plain,
% 1.92/2.07 (hskp15),
% 1.92/2.07 inference(unit_resolution,[status(thm)],[1887, 101, 1528, 1527, 1881, 1880, 1879, 1870, 1860])).
% 1.92/2.08 tff(1889,plain,
% 1.92/2.08 (~c0_1(a604)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[1474, 1888])).
% 1.92/2.08 tff(1890,plain,
% 1.92/2.08 (c1_1(a604)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[1490, 1888])).
% 1.92/2.08 tff(1891,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(1892,plain,
% 1.92/2.08 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(1893,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607))))),
% 1.92/2.08 inference(monotonicity,[status(thm)],[1892])).
% 1.92/2.08 tff(1894,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607)))),
% 1.92/2.08 inference(transitivity,[status(thm)],[1893, 1891])).
% 1.92/2.08 tff(1895,plain,
% 1.92/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(1896,plain,
% 1.92/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 1.92/2.08 tff(1897,plain,
% 1.92/2.08 (~c2_1(a604)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[1896, 101, 1528, 1526, 303, 1890, 66, 22, 1889, 11, 1860])).
% 1.92/2.08 tff(1898,plain,
% 1.92/2.08 (c3_1(a604)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[1482, 1888])).
% 1.92/2.08 tff(1899,plain,
% 1.92/2.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(1900,plain,
% 1.92/2.08 ((hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(1901,plain,
% 1.92/2.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604)))),
% 1.92/2.08 inference(monotonicity,[status(thm)],[1900])).
% 1.92/2.08 tff(1902,plain,
% 1.92/2.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604))),
% 1.92/2.08 inference(transitivity,[status(thm)],[1901, 1899])).
% 1.92/2.08 tff(1903,plain,
% 1.92/2.08 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(1904,plain,
% 1.92/2.08 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604)),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.92/2.08 tff(1905,plain,
% 1.92/2.08 (~c2_1(a603)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[1904, 101, 1850, 1898, 919, 1889, 907, 1026, 1897])).
% 1.92/2.08 tff(1906,plain,
% 1.92/2.08 (hskp6 | c2_1(a603)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[177, 101, 44, 919, 908, 43])).
% 1.92/2.08 tff(1907,plain,
% 1.92/2.08 (hskp6),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[1906, 1905])).
% 1.92/2.08 tff(1908,plain,
% 1.92/2.08 (~c0_1(a590)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[606, 1907])).
% 1.92/2.08 tff(1909,plain,
% 1.92/2.08 (c2_1(a590)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[622, 1907])).
% 1.92/2.08 tff(1910,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(1911,plain,
% 1.92/2.08 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(1912,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607))))),
% 1.92/2.08 inference(monotonicity,[status(thm)],[1911])).
% 1.92/2.08 tff(1913,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 1.92/2.08 inference(transitivity,[status(thm)],[1912, 1910])).
% 1.92/2.08 tff(1914,plain,
% 1.92/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(1915,plain,
% 1.92/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.92/2.08 tff(1916,plain,
% 1.92/2.08 (~c1_1(a590)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[1915, 101, 1528, 1526, 303, 1909, 66, 22, 1908, 11, 1860])).
% 1.92/2.08 tff(1917,plain,
% 1.92/2.08 (c3_1(a590)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[614, 1907])).
% 1.92/2.08 tff(1918,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(1919,plain,
% 1.92/2.08 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(1920,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)))),
% 1.92/2.08 inference(monotonicity,[status(thm)],[1919])).
% 1.92/2.08 tff(1921,plain,
% 1.92/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 1.92/2.08 inference(transitivity,[status(thm)],[1920, 1918])).
% 1.92/2.08 tff(1922,plain,
% 1.92/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 1.94/2.08 inference(quant_inst,[status(thm)],[])).
% 1.94/2.08 tff(1923,plain,
% 1.94/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 1.94/2.08 tff(1924,plain,
% 1.94/2.08 ($false),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1923, 101, 1528, 1527, 1909, 1917, 1908, 65, 1860, 1916])).
% 1.94/2.08 tff(1925,plain,(hskp28 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | hskp22 | (~c0_1(a603)) | c1_1(a603) | c3_1(a603) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.08 tff(1926,plain,
% 1.94/2.08 (hskp28),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1925, 1395, 1394, 1393, 277, 264, 258, 44, 893, 895, 894, 1820, 1819, 1817])).
% 1.94/2.08 tff(1927,plain,
% 1.94/2.08 (c1_1(a612)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1321, 1926])).
% 1.94/2.08 tff(1928,plain,
% 1.94/2.08 (c2_1(a612)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1048, 1926])).
% 1.94/2.08 tff(1929,plain,
% 1.94/2.08 (c3_1(a612)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1040, 1926])).
% 1.94/2.08 tff(1930,plain,
% 1.94/2.08 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.94/2.08 inference(bind,[status(th)],[])).
% 1.94/2.08 tff(1931,plain,
% 1.94/2.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.94/2.08 inference(quant_intro,[status(thm)],[1930])).
% 1.94/2.08 tff(1932,plain,
% 1.94/2.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(1933,plain,
% 1.94/2.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.94/2.08 inference(bind,[status(th)],[])).
% 1.94/2.08 tff(1934,plain,
% 1.94/2.08 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.94/2.08 inference(quant_intro,[status(thm)],[1933])).
% 1.94/2.08 tff(1935,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.94/2.08 tff(1936,plain,
% 1.94/2.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 1.94/2.08 tff(1937,plain,
% 1.94/2.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1936, 1932])).
% 1.94/2.08 tff(1938,plain,(
% 1.94/2.08 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.94/2.08 inference(skolemize,[status(sab)],[1937])).
% 1.94/2.08 tff(1939,plain,
% 1.94/2.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1938, 1931])).
% 1.94/2.08 tff(1940,plain,
% 1.94/2.08 (hskp28),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1925, 1528, 1527, 1526, 303, 66, 22, 44, 919, 908, 907, 427, 426, 425])).
% 1.94/2.08 tff(1941,plain,
% 1.94/2.08 (c3_1(a612)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1040, 1940])).
% 1.94/2.08 tff(1942,plain,
% 1.94/2.08 (c2_1(a612)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1048, 1940])).
% 1.94/2.08 tff(1943,plain,
% 1.94/2.08 (c1_1(a612)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1321, 1940])).
% 1.94/2.08 tff(1944,plain,
% 1.94/2.08 (hskp10),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1418, 101, 1943, 1942, 1941, 1528, 1527, 1526, 21])).
% 1.94/2.08 tff(1945,plain,
% 1.94/2.08 (~c1_1(a598)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[827, 1944])).
% 1.94/2.08 tff(1946,plain,
% 1.94/2.08 (c3_1(a598)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[800, 1944])).
% 1.94/2.08 tff(1947,plain,
% 1.94/2.08 (c0_1(a598)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[808, 1944])).
% 1.94/2.08 tff(1948,plain,
% 1.94/2.08 (^[U: $i] : refl((hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.94/2.08 inference(bind,[status(th)],[])).
% 1.94/2.08 tff(1949,plain,
% 1.94/2.08 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.94/2.08 inference(quant_intro,[status(thm)],[1948])).
% 1.94/2.08 tff(1950,plain,
% 1.94/2.08 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(1951,plain,
% 1.94/2.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp8) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp8) <=> (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.94/2.08 inference(bind,[status(th)],[])).
% 1.94/2.08 tff(1952,plain,
% 1.94/2.08 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp8) <=> ![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.94/2.08 inference(quant_intro,[status(thm)],[1951])).
% 1.94/2.08 tff(1953,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.94/2.08 tff(1954,plain,
% 1.94/2.08 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 1.94/2.08 tff(1955,plain,
% 1.94/2.08 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1954, 1950])).
% 1.94/2.08 tff(1956,plain,(
% 1.94/2.08 ![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.94/2.08 inference(skolemize,[status(sab)],[1955])).
% 1.94/2.08 tff(1957,plain,
% 1.94/2.08 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1956, 1949])).
% 1.94/2.08 tff(1958,plain,
% 1.94/2.08 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(1959,plain,
% 1.94/2.08 ((hskp27 | hskp8 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603))) <=> (hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(1960,plain,
% 1.94/2.08 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))))),
% 1.94/2.08 inference(monotonicity,[status(thm)],[1959])).
% 1.94/2.08 tff(1961,plain,
% 1.94/2.08 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.94/2.08 inference(transitivity,[status(thm)],[1960, 1958])).
% 1.94/2.08 tff(1962,plain,
% 1.94/2.08 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.94/2.08 inference(quant_inst,[status(thm)],[])).
% 1.94/2.08 tff(1963,plain,
% 1.94/2.08 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1962, 1961])).
% 1.94/2.08 tff(1964,plain,
% 1.94/2.08 (hskp27 | hskp8 | (~c2_1(a603))),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1963, 101, 919, 907, 1957])).
% 1.94/2.08 tff(1965,plain,
% 1.94/2.08 (~c2_1(a603)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1964, 1749, 1586])).
% 1.94/2.08 tff(1966,plain,
% 1.94/2.08 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(1967,plain,
% 1.94/2.08 ((hskp27 | hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(1968,plain,
% 1.94/2.08 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583))))),
% 1.94/2.08 inference(monotonicity,[status(thm)],[1967])).
% 1.94/2.08 tff(1969,plain,
% 1.94/2.08 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 1.94/2.08 inference(transitivity,[status(thm)],[1968, 1966])).
% 1.94/2.08 tff(1970,plain,
% 1.94/2.08 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))),
% 1.94/2.08 inference(quant_inst,[status(thm)],[])).
% 1.94/2.08 tff(1971,plain,
% 1.94/2.08 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 1.94/2.08 tff(1972,plain,
% 1.94/2.08 (hskp27 | hskp8 | c3_1(a583)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1971, 101, 1528, 1526, 1957])).
% 1.94/2.08 tff(1973,plain,
% 1.94/2.08 (c3_1(a583)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1972, 1749, 1586])).
% 1.94/2.08 tff(1974,plain,
% 1.94/2.08 (hskp6),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[1906, 1965])).
% 1.94/2.08 tff(1975,plain,
% 1.94/2.08 (~c0_1(a590)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[606, 1974])).
% 1.94/2.08 tff(1976,plain,
% 1.94/2.08 (c3_1(a590)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[614, 1974])).
% 1.94/2.08 tff(1977,plain,
% 1.94/2.08 (c2_1(a590)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[622, 1974])).
% 1.94/2.08 tff(1978,plain,
% 1.94/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(1979,plain,
% 1.94/2.08 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(1980,plain,
% 1.94/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599)))),
% 1.94/2.08 inference(monotonicity,[status(thm)],[1979])).
% 1.94/2.09 tff(1981,plain,
% 1.94/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 1.94/2.09 inference(transitivity,[status(thm)],[1980, 1978])).
% 1.94/2.09 tff(1982,plain,
% 1.94/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(1983,plain,
% 1.94/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599)),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 1.94/2.09 tff(1984,plain,
% 1.94/2.09 (c0_1(a599)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1983, 101, 1528, 1527, 427, 1977, 1976, 425, 1975, 65, 1973])).
% 1.94/2.09 tff(1985,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(1986,plain,
% 1.94/2.09 ((hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(1987,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599))))),
% 1.94/2.09 inference(monotonicity,[status(thm)],[1986])).
% 1.94/2.09 tff(1988,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.94/2.09 inference(transitivity,[status(thm)],[1987, 1985])).
% 1.94/2.09 tff(1989,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(1990,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 1.94/2.09 tff(1991,plain,
% 1.94/2.09 (hskp15),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1990, 101, 1528, 1527, 426, 425, 1870, 1973, 1984])).
% 1.94/2.09 tff(1992,plain,
% 1.94/2.09 (~c0_1(a604)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1474, 1991])).
% 1.94/2.09 tff(1993,plain,
% 1.94/2.09 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.94/2.09 inference(bind,[status(th)],[])).
% 1.94/2.09 tff(1994,plain,
% 1.94/2.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.94/2.09 inference(quant_intro,[status(thm)],[1993])).
% 1.94/2.09 tff(1995,plain,
% 1.94/2.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(1996,plain,
% 1.94/2.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.94/2.09 inference(bind,[status(th)],[])).
% 1.94/2.09 tff(1997,plain,
% 1.94/2.09 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.94/2.09 inference(quant_intro,[status(thm)],[1996])).
% 1.94/2.09 tff(1998,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.94/2.09 tff(1999,plain,
% 1.94/2.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 1.94/2.09 tff(2000,plain,
% 1.94/2.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[1999, 1995])).
% 1.94/2.09 tff(2001,plain,(
% 1.94/2.09 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.94/2.09 inference(skolemize,[status(sab)],[2000])).
% 1.94/2.09 tff(2002,plain,
% 1.94/2.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[2001, 1994])).
% 1.94/2.09 tff(2003,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2004,plain,
% 1.94/2.09 ((hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2005,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603))))),
% 1.94/2.09 inference(monotonicity,[status(thm)],[2004])).
% 1.94/2.09 tff(2006,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603)))),
% 1.94/2.09 inference(transitivity,[status(thm)],[2005, 2003])).
% 1.94/2.09 tff(2007,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(2008,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 1.94/2.09 tff(2009,plain,
% 1.94/2.09 (hskp16),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2008, 101, 919, 1977, 1976, 907, 1975, 2002, 1965])).
% 1.94/2.09 tff(2010,plain,
% 1.94/2.09 (~c3_1(a606)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[982, 2009])).
% 1.94/2.09 tff(2011,plain,
% 1.94/2.09 (~c2_1(a606)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1015, 2009])).
% 1.94/2.09 tff(2012,plain,
% 1.94/2.09 (c3_1(a604)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1482, 1991])).
% 1.94/2.09 tff(2013,plain,
% 1.94/2.09 (c1_1(a604)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1490, 1991])).
% 1.94/2.09 tff(2014,plain,
% 1.94/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2015,plain,
% 1.94/2.09 (((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2016,plain,
% 1.94/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606)))),
% 1.94/2.09 inference(monotonicity,[status(thm)],[2015])).
% 1.94/2.09 tff(2017,plain,
% 1.94/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 1.94/2.09 inference(transitivity,[status(thm)],[2016, 2014])).
% 1.94/2.09 tff(2018,plain,
% 1.94/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(2019,plain,
% 1.94/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606)),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 1.94/2.09 tff(2020,plain,
% 1.94/2.09 (c0_1(a606)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2019, 101, 2013, 2012, 919, 2011, 2010, 1992, 908, 1253, 1965])).
% 1.94/2.09 tff(2021,plain,
% 1.94/2.09 (~c2_1(a604)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1896, 101, 1528, 1526, 303, 2013, 66, 22, 1992, 11, 1973])).
% 1.94/2.09 tff(2022,plain,
% 1.94/2.09 (c1_1(a606)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[992, 2009])).
% 1.94/2.09 tff(2023,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2024,plain,
% 1.94/2.09 ((hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2025,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606))))),
% 1.94/2.09 inference(monotonicity,[status(thm)],[2024])).
% 1.94/2.09 tff(2026,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.09 inference(transitivity,[status(thm)],[2025, 2023])).
% 1.94/2.09 tff(2027,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(2028,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[2027, 2026])).
% 1.94/2.09 tff(2029,plain,
% 1.94/2.09 ($false),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2028, 101, 1749, 2022, 2012, 2011, 1992, 495, 2021, 2020])).
% 1.94/2.09 tff(2030,plain,(hskp27 | (~c0_1(a603)) | c1_1(a603) | (~c0_1(a583)) | (~c2_1(a583)) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~c1_1(a583)) | (~c3_1(a599)) | c1_1(a599) | (~c2_1(a599)) | hskp22 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.94/2.09 tff(2031,plain,
% 1.94/2.09 (hskp27),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2030, 1586, 908, 1528, 1526, 303, 66, 22, 907, 1527, 426, 425, 427, 44, 919])).
% 1.94/2.09 tff(2032,plain,
% 1.94/2.09 (c3_1(a611)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[566, 2031])).
% 1.94/2.09 tff(2033,plain,
% 1.94/2.09 (c1_1(a611)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[574, 2031])).
% 1.94/2.09 tff(2034,plain,
% 1.94/2.09 (c0_1(a611)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[582, 2031])).
% 1.94/2.09 tff(2035,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2036,plain,
% 1.94/2.09 ((hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2037,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598))))),
% 1.94/2.09 inference(monotonicity,[status(thm)],[2036])).
% 1.94/2.09 tff(2038,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.94/2.09 inference(transitivity,[status(thm)],[2037, 2035])).
% 1.94/2.09 tff(2039,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(2040,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 1.94/2.09 tff(2041,plain,
% 1.94/2.09 (hskp15),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2040, 101, 2034, 2033, 2032, 1947, 1946, 1945, 1870])).
% 1.94/2.09 tff(2042,plain,
% 1.94/2.09 (~c0_1(a604)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1474, 2041])).
% 1.94/2.09 tff(2043,plain,
% 1.94/2.09 (c3_1(a604)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1482, 2041])).
% 1.94/2.09 tff(2044,plain,
% 1.94/2.09 (c1_1(a604)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1490, 2041])).
% 1.94/2.09 tff(2045,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2046,plain,
% 1.94/2.09 ((hskp8 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604))) <=> (hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2047,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 1.94/2.09 inference(monotonicity,[status(thm)],[2046])).
% 1.94/2.09 tff(2048,plain,
% 1.94/2.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 1.94/2.09 inference(transitivity,[status(thm)],[2047, 2045])).
% 1.94/2.09 tff(2049,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(2050,plain,
% 1.94/2.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 1.94/2.09 tff(2051,plain,
% 1.94/2.09 (~c0_1(a607)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2050, 101, 1586, 303, 2044, 2043, 22, 2042, 1939])).
% 1.94/2.09 tff(2052,plain,
% 1.94/2.09 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2053,plain,
% 1.94/2.09 ((hskp8 | hskp6 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c3_1(a607))) <=> (hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2054,plain,
% 1.94/2.09 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607))))),
% 1.94/2.09 inference(monotonicity,[status(thm)],[2053])).
% 1.94/2.09 tff(2055,plain,
% 1.94/2.09 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 1.94/2.09 inference(transitivity,[status(thm)],[2054, 2052])).
% 1.94/2.09 tff(2056,plain,
% 1.94/2.09 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(2057,plain,
% 1.94/2.09 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.94/2.09 tff(2058,plain,
% 1.94/2.09 (hskp8 | hskp6 | c0_1(a607)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2057, 101, 303, 66, 414])).
% 1.94/2.09 tff(2059,plain,
% 1.94/2.09 (hskp6),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2058, 2051, 1586])).
% 1.94/2.09 tff(2060,plain,
% 1.94/2.09 (~c0_1(a590)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[606, 2059])).
% 1.94/2.09 tff(2061,plain,
% 1.94/2.09 (hskp9 | c0_1(a607)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1401, 101, 1528, 1527, 1526, 303, 66, 276])).
% 1.94/2.09 tff(2062,plain,
% 1.94/2.09 (hskp9),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2061, 2051])).
% 1.94/2.09 tff(2063,plain,
% 1.94/2.09 (~c1_1(a595)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1376, 2062])).
% 1.94/2.09 tff(2064,plain,
% 1.94/2.09 (~c0_1(a595)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1382, 2062])).
% 1.94/2.09 tff(2065,plain,
% 1.94/2.09 (c3_1(a590)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[614, 2059])).
% 1.94/2.09 tff(2066,plain,
% 1.94/2.09 (c2_1(a590)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[622, 2059])).
% 1.94/2.09 tff(2067,plain,
% 1.94/2.09 (~c2_1(a595)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1798, 101, 2034, 2033, 2032, 2066, 2065, 2064, 2063, 2060, 65])).
% 1.94/2.09 tff(2068,plain,
% 1.94/2.09 (~c3_1(a595)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1370, 2062])).
% 1.94/2.09 tff(2069,plain,
% 1.94/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2070,plain,
% 1.94/2.09 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.94/2.09 inference(rewrite,[status(thm)],[])).
% 1.94/2.09 tff(2071,plain,
% 1.94/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599))))),
% 1.94/2.09 inference(monotonicity,[status(thm)],[2070])).
% 1.94/2.09 tff(2072,plain,
% 1.94/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.94/2.09 inference(transitivity,[status(thm)],[2071, 2069])).
% 1.94/2.09 tff(2073,plain,
% 1.94/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(2074,plain,
% 1.94/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599))),
% 1.94/2.09 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 1.94/2.09 tff(2075,plain,
% 1.94/2.09 ($false),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2074, 101, 427, 426, 2066, 2065, 425, 2064, 2068, 2060, 1607, 2067])).
% 1.94/2.09 tff(2076,plain,(hskp8 | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c3_1(a607)) | c1_1(a607) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | c2_1(a607) | c1_1(a603) | c3_1(a603) | hskp22 | (~c0_1(a603))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.09 tff(2077,plain,
% 1.94/2.09 (hskp8),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2076, 1820, 1819, 1817, 277, 264, 1395, 1394, 1393, 258, 895, 894, 44, 893])).
% 1.94/2.09 tff(2078,plain,
% 1.94/2.09 (c1_1(a593)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[477, 2077])).
% 1.94/2.09 tff(2079,plain,
% 1.94/2.09 (~c2_1(a593)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[510, 2077])).
% 1.94/2.09 tff(2080,plain,
% 1.94/2.09 (c3_1(a593)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[469, 2077])).
% 1.94/2.09 tff(2081,assumption,(c1_1(a612)), introduced(assumption)).
% 1.94/2.09 tff(2082,plain,
% 1.94/2.09 (hskp10),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1418, 101, 2081, 1761, 1760, 1528, 1527, 1526, 21])).
% 1.94/2.09 tff(2083,plain,
% 1.94/2.09 (c0_1(a598)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[808, 2082])).
% 1.94/2.09 tff(2084,plain,
% 1.94/2.09 (c3_1(a598)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[800, 2082])).
% 1.94/2.09 tff(2085,plain,
% 1.94/2.09 (~c1_1(a598)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[827, 2082])).
% 1.94/2.09 tff(2086,plain,
% 1.94/2.09 (c2_1(a595)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[2074, 101, 427, 426, 785, 784, 425, 1441, 1439, 45, 1607])).
% 1.94/2.09 tff(2087,plain,
% 1.94/2.09 (hskp2),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1631, 101, 1441, 1440, 1439, 188, 2086])).
% 1.94/2.09 tff(2088,plain,
% 1.94/2.09 (~c3_1(a586)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[206, 2087])).
% 1.94/2.09 tff(2089,plain,
% 1.94/2.09 (c2_1(a586)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1357, 2087])).
% 1.94/2.09 tff(2090,plain,
% 1.94/2.09 (c1_1(a586)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[214, 2087])).
% 1.94/2.09 tff(2091,plain,
% 1.94/2.09 (hskp18),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1702, 251, 101, 2090, 2089, 2088, 1673])).
% 1.94/2.09 tff(2092,plain,
% 1.94/2.09 (~c2_1(a610)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1087, 2091])).
% 1.94/2.09 tff(2093,plain,
% 1.94/2.09 (~c0_1(a610)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[1093, 2091])).
% 1.94/2.09 tff(2094,plain,
% 1.94/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2095,plain,
% 1.94/2.10 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2096,plain,
% 1.94/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595))))),
% 1.94/2.10 inference(monotonicity,[status(thm)],[2095])).
% 1.94/2.10 tff(2097,plain,
% 1.94/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)))),
% 1.94/2.10 inference(transitivity,[status(thm)],[2096, 2094])).
% 1.94/2.10 tff(2098,plain,
% 1.94/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 1.94/2.10 inference(quant_inst,[status(thm)],[])).
% 1.94/2.10 tff(2099,plain,
% 1.94/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 1.94/2.10 tff(2100,plain,
% 1.94/2.10 ((~c0_1(a593)) | (~c2_1(a595))),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2099, 101, 1771, 1780, 785, 784, 1441, 1440, 45, 65])).
% 1.94/2.10 tff(2101,plain,
% 1.94/2.10 (~c0_1(a593)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2100, 2086])).
% 1.94/2.10 tff(2102,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2103,plain,
% 1.94/2.10 ((hskp16 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2104,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595))))),
% 1.94/2.10 inference(monotonicity,[status(thm)],[2103])).
% 1.94/2.10 tff(2105,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595)))),
% 1.94/2.10 inference(transitivity,[status(thm)],[2104, 2102])).
% 1.94/2.10 tff(2106,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 1.94/2.10 inference(quant_inst,[status(thm)],[])).
% 1.94/2.10 tff(2107,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 1.94/2.10 tff(2108,plain,
% 1.94/2.10 (hskp16),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2107, 101, 1771, 1440, 1439, 1770, 932, 2101, 2086])).
% 1.94/2.10 tff(2109,plain,
% 1.94/2.10 (c1_1(a606)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[992, 2108])).
% 1.94/2.10 tff(2110,plain,
% 1.94/2.10 (c3_1(a610)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[1101, 2091])).
% 1.94/2.10 tff(2111,plain,
% 1.94/2.10 ((~c0_1(a612)) | (~c2_1(a595))),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[1651, 101, 2081, 1760, 785, 784, 1441, 1440, 45, 65])).
% 1.94/2.10 tff(2112,plain,
% 1.94/2.10 (~c0_1(a612)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2111, 2086])).
% 1.94/2.10 tff(2113,plain,
% 1.94/2.10 (~c2_1(a606)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[1015, 2108])).
% 1.94/2.10 tff(2114,plain,
% 1.94/2.10 (~c3_1(a606)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[982, 2108])).
% 1.94/2.10 tff(2115,plain,
% 1.94/2.10 ($false),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[1788, 2114, 2113, 1761, 1780, 1770, 1771, 1758, 1749, 1760, 812, 2112, 2110, 2109, 2093, 2092, 813])).
% 1.94/2.10 tff(2116,plain,(c3_1(a595) | (~c2_1(a612)) | (~c3_1(a593)) | c2_1(a593) | (~c1_1(a593)) | c1_1(a598) | hskp27 | (~c3_1(a612)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a595) | hskp29 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a595) | c0_1(a590) | (~c1_1(a612)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.10 tff(2117,plain,
% 1.94/2.10 (c3_1(a595)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2116, 1440, 1780, 1770, 1771, 2085, 1749, 1760, 2084, 2083, 1761, 251, 785, 784, 1441, 45, 2081, 427, 426, 425])).
% 1.94/2.10 tff(2118,plain,
% 1.94/2.10 (~hskp9),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[1370, 2117])).
% 1.94/2.10 tff(2119,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2120,plain,
% 1.94/2.10 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a595) | c0_1(a595) | (~c3_1(a595))) <=> (hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2121,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a595) | c0_1(a595) | (~c3_1(a595)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 1.94/2.10 inference(monotonicity,[status(thm)],[2120])).
% 1.94/2.10 tff(2122,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a595) | c0_1(a595) | (~c3_1(a595)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.94/2.10 inference(transitivity,[status(thm)],[2121, 2119])).
% 1.94/2.10 tff(2123,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a595) | c0_1(a595) | (~c3_1(a595)))),
% 1.94/2.10 inference(quant_inst,[status(thm)],[])).
% 1.94/2.10 tff(2124,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 1.94/2.10 tff(2125,plain,
% 1.94/2.10 (hskp9 | (~c3_1(a595))),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2124, 101, 1528, 1527, 1526, 1441, 1440, 276])).
% 1.94/2.10 tff(2126,plain,
% 1.94/2.10 ($false),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2125, 2118, 2117])).
% 1.94/2.10 tff(2127,plain,(c1_1(a595) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | c0_1(a595) | (~c3_1(a593)) | c2_1(a593) | (~c1_1(a593)) | hskp27 | (~c3_1(a612)) | (~c2_1(a612)) | hskp29 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c1_1(a612)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.10 tff(2128,plain,
% 1.94/2.10 (hskp27),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2127, 1848, 1394, 1393, 1395, 2080, 2079, 2078, 1849, 1929, 1928, 251, 1818, 1821, 1514, 1927, 1820, 1819, 1817])).
% 1.94/2.10 tff(2129,plain,
% 1.94/2.10 (c3_1(a611)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[566, 2128])).
% 1.94/2.10 tff(2130,plain,
% 1.94/2.10 (c1_1(a611)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[574, 2128])).
% 1.94/2.10 tff(2131,plain,
% 1.94/2.10 (c0_1(a611)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[582, 2128])).
% 1.94/2.10 tff(2132,plain,
% 1.94/2.10 (~c2_1(a595)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[1798, 101, 2131, 2130, 2129, 1818, 1821, 1849, 1848, 1514, 65])).
% 1.94/2.10 tff(2133,plain,
% 1.94/2.10 (~c3_1(a595)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[1370, 1847])).
% 1.94/2.10 tff(2134,plain,
% 1.94/2.10 ($false),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2074, 101, 1820, 1819, 1818, 1821, 1817, 1849, 2133, 1514, 1607, 2132])).
% 1.94/2.10 tff(2135,plain,(hskp29 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.94/2.10 tff(2136,plain,
% 1.94/2.10 (hskp29),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2135, 44])).
% 1.94/2.10 tff(2137,plain,
% 1.94/2.10 (((~hskp29) | c3_1(a678)) <=> ((~hskp29) | c3_1(a678))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2138,axiom,((~hskp29) | c3_1(a678)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.94/2.10 tff(2139,plain,
% 1.94/2.10 ((~hskp29) | c3_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 1.94/2.10 tff(2140,plain,
% 1.94/2.10 ((~hskp29) | c3_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2139, 2137])).
% 1.94/2.10 tff(2141,plain,
% 1.94/2.10 ((~hskp29) | c3_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2140, 2137])).
% 1.94/2.10 tff(2142,plain,
% 1.94/2.10 ((~hskp29) | c3_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2141, 2137])).
% 1.94/2.10 tff(2143,plain,
% 1.94/2.10 ((~hskp29) | c3_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2142, 2137])).
% 1.94/2.10 tff(2144,plain,
% 1.94/2.10 (c3_1(a678)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2143, 2136])).
% 1.94/2.10 tff(2145,plain,
% 1.94/2.10 (((~hskp29) | c2_1(a678)) <=> ((~hskp29) | c2_1(a678))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2146,axiom,((~hskp29) | c2_1(a678)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 1.94/2.10 tff(2147,plain,
% 1.94/2.10 ((~hskp29) | c2_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 1.94/2.10 tff(2148,plain,
% 1.94/2.10 ((~hskp29) | c2_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2147, 2145])).
% 1.94/2.10 tff(2149,plain,
% 1.94/2.10 ((~hskp29) | c2_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2148, 2145])).
% 1.94/2.10 tff(2150,plain,
% 1.94/2.10 ((~hskp29) | c2_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2149, 2145])).
% 1.94/2.10 tff(2151,plain,
% 1.94/2.10 ((~hskp29) | c2_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2150, 2145])).
% 1.94/2.10 tff(2152,plain,
% 1.94/2.10 (c2_1(a678)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2151, 2136])).
% 1.94/2.10 tff(2153,plain,
% 1.94/2.10 (((~hskp29) | c0_1(a678)) <=> ((~hskp29) | c0_1(a678))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2154,axiom,((~hskp29) | c0_1(a678)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.94/2.10 tff(2155,plain,
% 1.94/2.10 ((~hskp29) | c0_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 1.94/2.10 tff(2156,plain,
% 1.94/2.10 ((~hskp29) | c0_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2155, 2153])).
% 1.94/2.10 tff(2157,plain,
% 1.94/2.10 ((~hskp29) | c0_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2156, 2153])).
% 1.94/2.10 tff(2158,plain,
% 1.94/2.10 ((~hskp29) | c0_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2157, 2153])).
% 1.94/2.10 tff(2159,plain,
% 1.94/2.10 ((~hskp29) | c0_1(a678)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2158, 2153])).
% 1.94/2.10 tff(2160,plain,
% 1.94/2.10 (c0_1(a678)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2159, 2136])).
% 1.94/2.10 tff(2161,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2162,plain,
% 1.94/2.10 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a607) | c0_1(a607) | c2_1(a607)) <=> (hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2163,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607)))),
% 1.94/2.10 inference(monotonicity,[status(thm)],[2162])).
% 1.94/2.10 tff(2164,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 1.94/2.10 inference(transitivity,[status(thm)],[2163, 2161])).
% 1.94/2.10 tff(2165,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a607) | c0_1(a607) | c2_1(a607))),
% 1.94/2.10 inference(quant_inst,[status(thm)],[])).
% 1.94/2.10 tff(2166,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 1.94/2.10 tff(2167,plain,
% 1.94/2.10 (hskp11 | c0_1(a607)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2166, 101, 2160, 2152, 2144, 33, 22, 250])).
% 1.94/2.10 tff(2168,plain,
% 1.94/2.10 (hskp11),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2167, 109])).
% 1.94/2.10 tff(2169,plain,
% 1.94/2.10 (~c1_1(a599)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[395, 2168])).
% 1.94/2.10 tff(2170,plain,
% 1.94/2.10 (c3_1(a599)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[389, 2168])).
% 1.94/2.10 tff(2171,plain,
% 1.94/2.10 (c2_1(a599)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[403, 2168])).
% 1.94/2.10 tff(2172,plain,
% 1.94/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2173,plain,
% 1.94/2.10 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2174,plain,
% 1.94/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 1.94/2.10 inference(monotonicity,[status(thm)],[2173])).
% 1.94/2.10 tff(2175,plain,
% 1.94/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.94/2.10 inference(transitivity,[status(thm)],[2174, 2172])).
% 1.94/2.10 tff(2176,plain,
% 1.94/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.94/2.10 inference(quant_inst,[status(thm)],[])).
% 1.94/2.10 tff(2177,plain,
% 1.94/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2176, 2175])).
% 1.94/2.10 tff(2178,plain,
% 1.94/2.10 ($false),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2177, 101, 171, 2171, 2170, 215, 194, 2169, 207, 240, 178, 230])).
% 1.94/2.10 tff(2179,plain,(hskp6 | c3_1(a607) | c1_1(a607) | hskp22 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.10 tff(2180,plain,
% 1.94/2.10 (hskp6),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2179, 66, 33, 44, 22])).
% 1.94/2.10 tff(2181,plain,
% 1.94/2.10 (~c0_1(a590)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[606, 2180])).
% 1.94/2.10 tff(2182,plain,
% 1.94/2.10 (c3_1(a590)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[614, 2180])).
% 1.94/2.10 tff(2183,plain,
% 1.94/2.10 (c2_1(a590)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[622, 2180])).
% 1.94/2.10 tff(2184,assumption,(c3_1(a678)), introduced(assumption)).
% 1.94/2.10 tff(2185,assumption,(c2_1(a678)), introduced(assumption)).
% 1.94/2.10 tff(2186,assumption,(c0_1(a678)), introduced(assumption)).
% 1.94/2.10 tff(2187,plain,
% 1.94/2.10 (hskp11 | c0_1(a607)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2166, 101, 2186, 2185, 2184, 33, 22, 250])).
% 1.94/2.10 tff(2188,plain,
% 1.94/2.10 (c0_1(a607)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2187, 1515])).
% 1.94/2.10 tff(2189,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2190,plain,
% 1.94/2.10 ((hskp16 | (~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2191,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607))))),
% 1.94/2.10 inference(monotonicity,[status(thm)],[2190])).
% 1.94/2.10 tff(2192,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607)))),
% 1.94/2.10 inference(transitivity,[status(thm)],[2191, 2189])).
% 1.94/2.10 tff(2193,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 1.94/2.10 inference(quant_inst,[status(thm)],[])).
% 1.94/2.10 tff(2194,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 1.94/2.10 tff(2195,plain,
% 1.94/2.10 (hskp16 | (~c0_1(a607))),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2194, 101, 33, 785, 784, 22, 45, 2002])).
% 1.94/2.10 tff(2196,plain,
% 1.94/2.10 (hskp16),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2195, 2188])).
% 1.94/2.10 tff(2197,plain,
% 1.94/2.10 (~c3_1(a606)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[982, 2196])).
% 1.94/2.10 tff(2198,plain,
% 1.94/2.10 (~c2_1(a606)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[1015, 2196])).
% 1.94/2.10 tff(2199,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2200,plain,
% 1.94/2.10 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2201,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606)))),
% 1.94/2.10 inference(monotonicity,[status(thm)],[2200])).
% 1.94/2.10 tff(2202,plain,
% 1.94/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606))),
% 1.94/2.10 inference(transitivity,[status(thm)],[2201, 2199])).
% 1.94/2.10 tff(2203,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 1.94/2.10 inference(quant_inst,[status(thm)],[])).
% 1.94/2.10 tff(2204,plain,
% 1.94/2.10 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606)),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 1.94/2.10 tff(2205,plain,
% 1.94/2.10 (c0_1(a606)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2204, 1515, 101, 2186, 2185, 2184, 2198, 2197, 250])).
% 1.94/2.10 tff(2206,plain,
% 1.94/2.10 (^[U: $i] : refl((hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.94/2.10 inference(bind,[status(th)],[])).
% 1.94/2.10 tff(2207,plain,
% 1.94/2.10 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(quant_intro,[status(thm)],[2206])).
% 1.94/2.10 tff(2208,plain,
% 1.94/2.10 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2209,plain,
% 1.94/2.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) | hskp11) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.94/2.10 inference(bind,[status(th)],[])).
% 1.94/2.10 tff(2210,plain,
% 1.94/2.10 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) | hskp11) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(quant_intro,[status(thm)],[2209])).
% 1.94/2.10 tff(2211,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 1.94/2.10 tff(2212,plain,
% 1.94/2.10 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 1.94/2.10 tff(2213,plain,
% 1.94/2.10 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2212, 2208])).
% 1.94/2.10 tff(2214,plain,(
% 1.94/2.10 ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(skolemize,[status(sab)],[2213])).
% 1.94/2.10 tff(2215,plain,
% 1.94/2.10 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2214, 2207])).
% 1.94/2.10 tff(2216,plain,
% 1.94/2.10 (c1_1(a606)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[992, 2196])).
% 1.94/2.10 tff(2217,plain,
% 1.94/2.10 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2218,plain,
% 1.94/2.10 ((hskp11 | hskp0 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606))) <=> (hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2219,plain,
% 1.94/2.10 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))))),
% 1.94/2.10 inference(monotonicity,[status(thm)],[2218])).
% 1.94/2.10 tff(2220,plain,
% 1.94/2.10 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.10 inference(transitivity,[status(thm)],[2219, 2217])).
% 1.94/2.10 tff(2221,plain,
% 1.94/2.10 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))),
% 1.94/2.10 inference(quant_inst,[status(thm)],[])).
% 1.94/2.10 tff(2222,plain,
% 1.94/2.10 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))),
% 1.94/2.10 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.94/2.10 tff(2223,plain,
% 1.94/2.10 (hskp0 | (~c0_1(a606))),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2222, 1515, 101, 2216, 2198, 2215])).
% 1.94/2.10 tff(2224,plain,
% 1.94/2.10 (hskp0),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[2223, 2205])).
% 1.94/2.10 tff(2225,plain,
% 1.94/2.10 (~c2_1(a584)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[955, 2224])).
% 1.94/2.10 tff(2226,plain,
% 1.94/2.10 (~c0_1(a584)),
% 1.94/2.10 inference(unit_resolution,[status(thm)],[961, 2224])).
% 1.94/2.10 tff(2227,plain,
% 1.94/2.10 (^[U: $i] : refl((hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.94/2.10 inference(bind,[status(th)],[])).
% 1.94/2.10 tff(2228,plain,
% 1.94/2.10 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(quant_intro,[status(thm)],[2227])).
% 1.94/2.10 tff(2229,plain,
% 1.94/2.10 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.10 inference(rewrite,[status(thm)],[])).
% 1.94/2.10 tff(2230,plain,
% 1.94/2.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp17) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp17) <=> (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.94/2.11 inference(bind,[status(th)],[])).
% 1.94/2.11 tff(2231,plain,
% 1.94/2.11 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp17) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.11 inference(quant_intro,[status(thm)],[2230])).
% 1.94/2.11 tff(2232,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.94/2.11 tff(2233,plain,
% 1.94/2.11 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 1.94/2.11 tff(2234,plain,
% 1.94/2.11 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2233, 2229])).
% 1.94/2.11 tff(2235,plain,(
% 1.94/2.11 ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.11 inference(skolemize,[status(sab)],[2234])).
% 1.94/2.11 tff(2236,plain,
% 1.94/2.11 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2235, 2228])).
% 1.94/2.11 tff(2237,plain,
% 1.94/2.11 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2238,plain,
% 1.94/2.11 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606))) <=> (hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2239,plain,
% 1.94/2.11 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[2238])).
% 1.94/2.11 tff(2240,plain,
% 1.94/2.11 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.94/2.11 inference(transitivity,[status(thm)],[2239, 2237])).
% 1.94/2.11 tff(2241,plain,
% 1.94/2.11 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(2242,plain,
% 1.94/2.11 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.94/2.11 tff(2243,plain,
% 1.94/2.11 (hskp3 | (~c0_1(a606))),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2242, 101, 223, 2216, 2197, 2236])).
% 1.94/2.11 tff(2244,plain,
% 1.94/2.11 (hskp3),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2243, 2205])).
% 1.94/2.11 tff(2245,plain,
% 1.94/2.11 (~c1_1(a587)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[855, 2244])).
% 1.94/2.11 tff(2246,plain,
% 1.94/2.11 (c1_1(a584)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[969, 2224])).
% 1.94/2.11 tff(2247,plain,
% 1.94/2.11 (c2_1(a587)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[863, 2244])).
% 1.94/2.11 tff(2248,plain,
% 1.94/2.11 (c0_1(a587)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[871, 2244])).
% 1.94/2.11 tff(2249,plain,
% 1.94/2.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2250,plain,
% 1.94/2.11 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2251,plain,
% 1.94/2.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587))))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[2250])).
% 1.94/2.11 tff(2252,plain,
% 1.94/2.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587)))),
% 1.94/2.11 inference(transitivity,[status(thm)],[2251, 2249])).
% 1.94/2.11 tff(2253,plain,
% 1.94/2.11 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(2254,plain,
% 1.94/2.11 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 1.94/2.11 tff(2255,plain,
% 1.94/2.11 ($false),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2254, 101, 223, 2248, 2247, 2246, 2245, 2226, 2225, 32])).
% 1.94/2.11 tff(2256,plain,(hskp11 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | c3_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c2_1(a607) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.11 tff(2257,plain,
% 1.94/2.11 (hskp11),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2256, 2183, 2152, 2144, 33, 2160, 2182, 22, 2181])).
% 1.94/2.11 tff(2258,plain,
% 1.94/2.11 (~c1_1(a599)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[395, 2257])).
% 1.94/2.11 tff(2259,plain,
% 1.94/2.11 (c2_1(a599)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[403, 2257])).
% 1.94/2.11 tff(2260,plain,
% 1.94/2.11 (hskp11),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2256, 785, 2185, 2184, 33, 2186, 784, 22, 45])).
% 1.94/2.11 tff(2261,plain,
% 1.94/2.11 (~c1_1(a599)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[395, 2260])).
% 1.94/2.11 tff(2262,plain,
% 1.94/2.11 (c3_1(a599)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[389, 2260])).
% 1.94/2.11 tff(2263,plain,
% 1.94/2.11 (c2_1(a599)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[403, 2260])).
% 1.94/2.11 tff(2264,plain,
% 1.94/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2265,plain,
% 1.94/2.11 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a607) | c0_1(a607) | c2_1(a607)) <=> (c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2266,plain,
% 1.94/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607)))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[2265])).
% 1.94/2.11 tff(2267,plain,
% 1.94/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607))),
% 1.94/2.11 inference(transitivity,[status(thm)],[2266, 2264])).
% 1.94/2.11 tff(2268,plain,
% 1.94/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a607) | c0_1(a607) | c2_1(a607))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(2269,plain,
% 1.94/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607)),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 1.94/2.11 tff(2270,plain,
% 1.94/2.11 (c0_1(a607)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2269, 101, 33, 2263, 2262, 785, 784, 22, 2261, 45, 1607])).
% 1.94/2.11 tff(2271,plain,
% 1.94/2.11 (hskp16),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2195, 2270])).
% 1.94/2.11 tff(2272,plain,
% 1.94/2.11 (~c3_1(a606)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[982, 2271])).
% 1.94/2.11 tff(2273,plain,
% 1.94/2.11 (~c2_1(a606)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[1015, 2271])).
% 1.94/2.11 tff(2274,plain,
% 1.94/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2275,plain,
% 1.94/2.11 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2276,plain,
% 1.94/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606)))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[2275])).
% 1.94/2.11 tff(2277,plain,
% 1.94/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606))),
% 1.94/2.11 inference(transitivity,[status(thm)],[2276, 2274])).
% 1.94/2.11 tff(2278,plain,
% 1.94/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(2279,plain,
% 1.94/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606)),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 1.94/2.11 tff(2280,plain,
% 1.94/2.11 (c0_1(a606)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2279, 101, 2263, 2262, 785, 784, 2273, 2272, 2261, 45, 1607])).
% 1.94/2.11 tff(2281,plain,
% 1.94/2.11 (c1_1(a606)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[992, 2271])).
% 1.94/2.11 tff(2282,plain,
% 1.94/2.11 (hskp3 | (~c0_1(a606))),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2242, 101, 223, 2281, 2272, 2236])).
% 1.94/2.11 tff(2283,plain,
% 1.94/2.11 (hskp3),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2282, 2280])).
% 1.94/2.11 tff(2284,plain,
% 1.94/2.11 (~c1_1(a587)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[855, 2283])).
% 1.94/2.11 tff(2285,plain,
% 1.94/2.11 (c2_1(a587)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[863, 2283])).
% 1.94/2.11 tff(2286,plain,
% 1.94/2.11 (c0_1(a587)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[871, 2283])).
% 1.94/2.11 tff(2287,plain,
% 1.94/2.11 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2288,plain,
% 1.94/2.11 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a607) | c1_1(a607) | c2_1(a607)) <=> (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2289,plain,
% 1.94/2.11 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587))))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[2288])).
% 1.94/2.11 tff(2290,plain,
% 1.94/2.11 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)))),
% 1.94/2.11 inference(transitivity,[status(thm)],[2289, 2287])).
% 1.94/2.11 tff(2291,plain,
% 1.94/2.11 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a607) | c1_1(a607) | c2_1(a607))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(2292,plain,
% 1.94/2.11 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2291, 2290])).
% 1.94/2.11 tff(2293,plain,
% 1.94/2.11 (hskp26),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2292, 101, 33, 2286, 2285, 66, 22, 2284, 905])).
% 1.94/2.11 tff(2294,plain,
% 1.94/2.11 (c2_1(a583)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[364, 2293])).
% 1.94/2.11 tff(2295,plain,
% 1.94/2.11 (c1_1(a583)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[330, 2293])).
% 1.94/2.11 tff(2296,plain,
% 1.94/2.11 (c0_1(a583)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[338, 2293])).
% 1.94/2.11 tff(2297,plain,
% 1.94/2.11 (hskp9 | c0_1(a599)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[1828, 101, 2296, 2295, 2294, 2262, 2261, 276])).
% 1.94/2.11 tff(2298,plain,
% 1.94/2.11 (c0_1(a599)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2297, 1822])).
% 1.94/2.11 tff(2299,plain,
% 1.94/2.11 (^[U: $i] : refl((hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.94/2.11 inference(bind,[status(th)],[])).
% 1.94/2.11 tff(2300,plain,
% 1.94/2.11 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.94/2.11 inference(quant_intro,[status(thm)],[2299])).
% 1.94/2.11 tff(2301,plain,
% 1.94/2.11 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2302,plain,
% 1.94/2.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.94/2.11 inference(bind,[status(th)],[])).
% 1.94/2.11 tff(2303,plain,
% 1.94/2.11 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.94/2.11 inference(quant_intro,[status(thm)],[2302])).
% 1.94/2.11 tff(2304,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.94/2.11 tff(2305,plain,
% 1.94/2.11 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2304, 2303])).
% 1.94/2.11 tff(2306,plain,
% 1.94/2.11 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2305, 2301])).
% 1.94/2.11 tff(2307,plain,(
% 1.94/2.11 ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.94/2.11 inference(skolemize,[status(sab)],[2306])).
% 1.94/2.11 tff(2308,plain,
% 1.94/2.11 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2307, 2300])).
% 1.94/2.11 tff(2309,plain,
% 1.94/2.11 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2310,plain,
% 1.94/2.11 ((hskp25 | hskp9 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606))) <=> (hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2311,plain,
% 1.94/2.11 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606))))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[2310])).
% 1.94/2.11 tff(2312,plain,
% 1.94/2.11 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 1.94/2.11 inference(transitivity,[status(thm)],[2311, 2309])).
% 1.94/2.11 tff(2313,plain,
% 1.94/2.11 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(2314,plain,
% 1.94/2.11 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 1.94/2.11 tff(2315,plain,
% 1.94/2.11 (hskp25 | hskp9),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2314, 101, 2281, 2273, 2272, 2308])).
% 1.94/2.11 tff(2316,plain,
% 1.94/2.11 (hskp25),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2315, 1822])).
% 1.94/2.11 tff(2317,plain,
% 1.94/2.11 (((~hskp25) | c2_1(a651)) <=> ((~hskp25) | c2_1(a651))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2318,axiom,((~hskp25) | c2_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.94/2.11 tff(2319,plain,
% 1.94/2.11 ((~hskp25) | c2_1(a651)),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2318, 2317])).
% 1.94/2.11 tff(2320,plain,
% 1.94/2.11 ((~hskp25) | c2_1(a651)),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2319, 2317])).
% 1.94/2.11 tff(2321,plain,
% 1.94/2.11 ((~hskp25) | c2_1(a651)),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2320, 2317])).
% 1.94/2.11 tff(2322,plain,
% 1.94/2.11 ((~hskp25) | c2_1(a651)),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2321, 2317])).
% 1.94/2.11 tff(2323,plain,
% 1.94/2.11 ((~hskp25) | c2_1(a651)),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2322, 2317])).
% 1.94/2.11 tff(2324,plain,
% 1.94/2.11 (c2_1(a651)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2323, 2316])).
% 1.94/2.11 tff(2325,plain,
% 1.94/2.11 (((~hskp25) | (~c3_1(a651))) <=> ((~hskp25) | (~c3_1(a651)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2326,plain,
% 1.94/2.11 (((~c3_1(a651)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a651)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2327,axiom,((~c3_1(a651)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.94/2.11 tff(2328,plain,
% 1.94/2.11 ((~hskp25) | (~c3_1(a651))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 1.94/2.11 tff(2329,plain,
% 1.94/2.11 ((~hskp25) | (~c3_1(a651))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2328, 2325])).
% 1.94/2.11 tff(2330,plain,
% 1.94/2.11 (~c3_1(a651)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2329, 2316])).
% 1.94/2.11 tff(2331,plain,
% 1.94/2.11 (((~hskp25) | (~c1_1(a651))) <=> ((~hskp25) | (~c1_1(a651)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2332,plain,
% 1.94/2.11 (((~c1_1(a651)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a651)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2333,axiom,((~c1_1(a651)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.94/2.11 tff(2334,plain,
% 1.94/2.11 ((~hskp25) | (~c1_1(a651))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 1.94/2.11 tff(2335,plain,
% 1.94/2.11 ((~hskp25) | (~c1_1(a651))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2334, 2331])).
% 1.94/2.11 tff(2336,plain,
% 1.94/2.11 (~c1_1(a651)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2335, 2316])).
% 1.94/2.11 tff(2337,assumption,(c0_1(a599)), introduced(assumption)).
% 1.94/2.11 tff(2338,assumption,(~c3_1(a651)), introduced(assumption)).
% 1.94/2.11 tff(2339,assumption,(c2_1(a651)), introduced(assumption)).
% 1.94/2.11 tff(2340,assumption,(~c0_1(a604)), introduced(assumption)).
% 1.94/2.11 tff(2341,assumption,(c0_1(a651)), introduced(assumption)).
% 1.94/2.11 tff(2342,plain,
% 1.94/2.11 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2343,plain,
% 1.94/2.11 ((hskp27 | hskp8 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651))) <=> (hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(2344,plain,
% 1.94/2.11 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651))))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[2343])).
% 1.94/2.11 tff(2345,plain,
% 1.94/2.11 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.94/2.11 inference(transitivity,[status(thm)],[2344, 2342])).
% 1.94/2.11 tff(2346,plain,
% 1.94/2.11 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(2347,plain,
% 1.94/2.11 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 1.94/2.11 tff(2348,plain,
% 1.94/2.11 (hskp8 | (~c0_1(a651))),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2347, 101, 1749, 2339, 2338, 1957])).
% 1.94/2.11 tff(2349,plain,
% 1.94/2.11 (hskp8),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[2348, 2341])).
% 1.94/2.11 tff(2350,plain,
% 1.94/2.11 (c3_1(a593)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[469, 2349])).
% 1.94/2.11 tff(2351,assumption,(c0_1(a607)), introduced(assumption)).
% 1.94/2.11 tff(2352,plain,
% 1.94/2.11 (~c2_1(a593)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[510, 2349])).
% 1.94/2.11 tff(2353,plain,
% 1.94/2.11 (c1_1(a593)),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[477, 2349])).
% 1.94/2.11 tff(2354,assumption,(~c3_1(a604)), introduced(assumption)).
% 1.94/2.11 tff(2355,plain,
% 1.94/2.11 (~hskp15),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[1482, 2354])).
% 1.94/2.11 tff(2356,plain,
% 1.94/2.11 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(2357,plain,
% 1.94/2.12 ((hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(2358,plain,
% 1.94/2.12 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599))))),
% 1.94/2.12 inference(monotonicity,[status(thm)],[2357])).
% 1.94/2.12 tff(2359,plain,
% 1.94/2.12 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.94/2.12 inference(transitivity,[status(thm)],[2358, 2356])).
% 1.94/2.12 tff(2360,plain,
% 1.94/2.12 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(2361,plain,
% 1.94/2.12 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[2360, 2359])).
% 1.94/2.12 tff(2362,plain,
% 1.94/2.12 (hskp15 | (~c0_1(a593))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[2361, 101, 426, 1771, 1780, 425, 1870, 2337])).
% 1.94/2.12 tff(2363,plain,
% 1.94/2.12 (~c0_1(a593)),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[2362, 2355])).
% 1.94/2.12 tff(2364,plain,
% 1.94/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(2365,plain,
% 1.94/2.12 (((~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(2366,plain,
% 1.94/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651))))),
% 1.94/2.12 inference(monotonicity,[status(thm)],[2365])).
% 1.94/2.12 tff(2367,plain,
% 1.94/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.94/2.12 inference(transitivity,[status(thm)],[2366, 2364])).
% 1.94/2.12 tff(2368,plain,
% 1.94/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(2369,plain,
% 1.94/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[2368, 2367])).
% 1.94/2.12 tff(2370,plain,
% 1.94/2.12 (~c1_1(a604)),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[2369, 101, 2339, 2354, 427, 426, 2338, 2340, 425, 240, 2341])).
% 1.94/2.12 tff(2371,plain,
% 1.94/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(2372,plain,
% 1.94/2.12 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a604) | c1_1(a604) | c0_1(a604)) <=> (c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(2373,plain,
% 1.94/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))))),
% 1.94/2.12 inference(monotonicity,[status(thm)],[2372])).
% 1.94/2.12 tff(2374,plain,
% 1.94/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 1.94/2.12 inference(transitivity,[status(thm)],[2373, 2371])).
% 1.94/2.12 tff(2375,plain,
% 1.94/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a604) | c1_1(a604) | c0_1(a604))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(2376,plain,
% 1.94/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 1.98/2.12 tff(2377,plain,
% 1.98/2.12 ($false),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2376, 101, 33, 2370, 2354, 1771, 22, 2340, 1770, 1349, 2363, 2351])).
% 1.98/2.12 tff(2378,plain,(c3_1(a604) | c3_1(a607) | (~c1_1(a593)) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~c0_1(a607)) | (~c2_1(a651)) | (~c2_1(a599)) | (~c3_1(a599)) | c3_1(a651) | c1_1(a599) | (~c0_1(a651)) | (~c3_1(a593)) | (~c0_1(a599))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.12 tff(2379,plain,
% 1.98/2.12 (c3_1(a604)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2378, 2353, 33, 22, 2340, 2352, 2351, 2339, 427, 426, 2338, 425, 2341, 2350, 2337])).
% 1.98/2.12 tff(2380,assumption,(c0_1(a606)), introduced(assumption)).
% 1.98/2.12 tff(2381,plain,
% 1.98/2.12 ((~c3_1(a604)) | c2_1(a604)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2028, 101, 1749, 1753, 1750, 2340, 495, 2380])).
% 1.98/2.12 tff(2382,plain,
% 1.98/2.12 (c2_1(a604)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2381, 2379])).
% 1.98/2.12 tff(2383,assumption,(hskp13), introduced(assumption)).
% 1.98/2.12 tff(2384,plain,
% 1.98/2.12 (((~hskp13) | (~c2_1(a601))) <=> ((~hskp13) | (~c2_1(a601)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2385,plain,
% 1.98/2.12 (((~c2_1(a601)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a601)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2386,axiom,((~c2_1(a601)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.98/2.12 tff(2387,plain,
% 1.98/2.12 ((~hskp13) | (~c2_1(a601))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 1.98/2.12 tff(2388,plain,
% 1.98/2.12 ((~hskp13) | (~c2_1(a601))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2387, 2384])).
% 1.98/2.12 tff(2389,plain,
% 1.98/2.12 (~c2_1(a601)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2388, 2383])).
% 1.98/2.12 tff(2390,plain,
% 1.98/2.12 (((~hskp13) | (~c1_1(a601))) <=> ((~hskp13) | (~c1_1(a601)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2391,plain,
% 1.98/2.12 (((~c1_1(a601)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a601)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2392,axiom,((~c1_1(a601)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.98/2.12 tff(2393,plain,
% 1.98/2.12 ((~hskp13) | (~c1_1(a601))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 1.98/2.12 tff(2394,plain,
% 1.98/2.12 ((~hskp13) | (~c1_1(a601))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2393, 2390])).
% 1.98/2.12 tff(2395,plain,
% 1.98/2.12 (~c1_1(a601)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2394, 2383])).
% 1.98/2.12 tff(2396,plain,
% 1.98/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2397,plain,
% 1.98/2.12 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601))) <=> (c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2398,plain,
% 1.98/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606))))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[2397])).
% 1.98/2.12 tff(2399,plain,
% 1.98/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.98/2.12 inference(transitivity,[status(thm)],[2398, 2396])).
% 1.98/2.12 tff(2400,plain,
% 1.98/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))),
% 1.98/2.12 inference(quant_inst,[status(thm)],[])).
% 1.98/2.12 tff(2401,plain,
% 1.98/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 1.98/2.12 tff(2402,plain,
% 1.98/2.12 (~c3_1(a601)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2401, 101, 2186, 2185, 2184, 1753, 1750, 2395, 2389, 1010, 2380])).
% 1.98/2.12 tff(2403,assumption,(c2_1(a604)), introduced(assumption)).
% 1.98/2.12 tff(2404,plain,
% 1.98/2.12 (((~hskp13) | (~c0_1(a601))) <=> ((~hskp13) | (~c0_1(a601)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2405,plain,
% 1.98/2.12 (((~c0_1(a601)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a601)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2406,axiom,((~c0_1(a601)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.98/2.12 tff(2407,plain,
% 1.98/2.12 ((~hskp13) | (~c0_1(a601))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.98/2.12 tff(2408,plain,
% 1.98/2.12 ((~hskp13) | (~c0_1(a601))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2407, 2404])).
% 1.98/2.12 tff(2409,plain,
% 1.98/2.12 (~c0_1(a601)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2408, 2383])).
% 1.98/2.12 tff(2410,assumption,(c3_1(a604)), introduced(assumption)).
% 1.98/2.12 tff(2411,plain,
% 1.98/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2412,plain,
% 1.98/2.12 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a601) | c0_1(a601) | c2_1(a601)) <=> (c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2413,plain,
% 1.98/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a601) | c0_1(a601) | c2_1(a601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604))))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[2412])).
% 1.98/2.12 tff(2414,plain,
% 1.98/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a601) | c0_1(a601) | c2_1(a601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.98/2.12 inference(transitivity,[status(thm)],[2413, 2411])).
% 1.98/2.12 tff(2415,plain,
% 1.98/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a601) | c0_1(a601) | c2_1(a601))),
% 1.98/2.12 inference(quant_inst,[status(thm)],[])).
% 1.98/2.12 tff(2416,plain,
% 1.98/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 1.98/2.12 tff(2417,plain,
% 1.98/2.12 ($false),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2416, 101, 2410, 427, 426, 2340, 2409, 2389, 425, 1607, 2403, 2402])).
% 1.98/2.12 tff(2418,plain,((~hskp13) | (~c3_1(a604)) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | c1_1(a599) | (~c2_1(a604)) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a606)) | c2_1(a606) | (~c0_1(a606))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.12 tff(2419,plain,
% 1.98/2.12 (~hskp13),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2418, 2382, 427, 426, 2340, 425, 2379, 2186, 2185, 2184, 1753, 1750, 2380])).
% 1.98/2.12 tff(2420,plain,
% 1.98/2.12 (^[U: $i] : refl((hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.98/2.12 inference(bind,[status(th)],[])).
% 1.98/2.12 tff(2421,plain,
% 1.98/2.12 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.98/2.12 inference(quant_intro,[status(thm)],[2420])).
% 1.98/2.12 tff(2422,plain,
% 1.98/2.12 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2423,plain,
% 1.98/2.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) | hskp13) <=> ((hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) | hskp13) <=> (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.98/2.12 inference(bind,[status(th)],[])).
% 1.98/2.12 tff(2424,plain,
% 1.98/2.12 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) | hskp13) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.98/2.12 inference(quant_intro,[status(thm)],[2423])).
% 1.98/2.12 tff(2425,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.98/2.12 tff(2426,plain,
% 1.98/2.12 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 1.98/2.12 tff(2427,plain,
% 1.98/2.12 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2426, 2422])).
% 1.98/2.12 tff(2428,plain,(
% 1.98/2.12 ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.98/2.12 inference(skolemize,[status(sab)],[2427])).
% 1.98/2.12 tff(2429,plain,
% 1.98/2.12 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2428, 2421])).
% 1.98/2.12 tff(2430,plain,
% 1.98/2.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2431,plain,
% 1.98/2.12 ((hskp1 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607))) <=> (hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2432,plain,
% 1.98/2.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651))))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[2431])).
% 1.98/2.12 tff(2433,plain,
% 1.98/2.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.98/2.12 inference(transitivity,[status(thm)],[2432, 2430])).
% 1.98/2.12 tff(2434,plain,
% 1.98/2.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))),
% 1.98/2.12 inference(quant_inst,[status(thm)],[])).
% 1.98/2.12 tff(2435,plain,
% 1.98/2.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 1.98/2.12 tff(2436,plain,
% 1.98/2.12 (hskp1 | (~c0_1(a651))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2435, 101, 2339, 2338, 66, 22, 1132, 2351])).
% 1.98/2.12 tff(2437,plain,
% 1.98/2.12 (hskp1),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2436, 2341])).
% 1.98/2.12 tff(2438,plain,
% 1.98/2.12 (~c0_1(a585)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[1145, 2437])).
% 1.98/2.12 tff(2439,plain,
% 1.98/2.12 (c2_1(a585)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[1153, 2437])).
% 1.98/2.12 tff(2440,plain,
% 1.98/2.12 (c1_1(a585)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[1161, 2437])).
% 1.98/2.12 tff(2441,plain,
% 1.98/2.12 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2442,plain,
% 1.98/2.12 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585))) <=> (hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2443,plain,
% 1.98/2.12 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585))))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[2442])).
% 1.98/2.12 tff(2444,plain,
% 1.98/2.12 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)))),
% 1.98/2.12 inference(transitivity,[status(thm)],[2443, 2441])).
% 1.98/2.12 tff(2445,plain,
% 1.98/2.12 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)))),
% 1.98/2.12 inference(quant_inst,[status(thm)],[])).
% 1.98/2.12 tff(2446,plain,
% 1.98/2.12 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 1.98/2.12 tff(2447,plain,
% 1.98/2.12 (hskp19 | hskp13),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2446, 101, 2440, 2439, 2438, 2429])).
% 1.98/2.12 tff(2448,plain,
% 1.98/2.12 (hskp19),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2447, 2419])).
% 1.98/2.12 tff(2449,plain,
% 1.98/2.12 (((~hskp19) | (~c1_1(a617))) <=> ((~hskp19) | (~c1_1(a617)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2450,plain,
% 1.98/2.12 (((~c1_1(a617)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a617)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2451,axiom,((~c1_1(a617)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.98/2.12 tff(2452,plain,
% 1.98/2.12 ((~hskp19) | (~c1_1(a617))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 1.98/2.12 tff(2453,plain,
% 1.98/2.12 ((~hskp19) | (~c1_1(a617))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2452, 2449])).
% 1.98/2.12 tff(2454,plain,
% 1.98/2.12 (~c1_1(a617)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2453, 2448])).
% 1.98/2.12 tff(2455,plain,
% 1.98/2.12 (((~hskp19) | (~c0_1(a617))) <=> ((~hskp19) | (~c0_1(a617)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2456,plain,
% 1.98/2.12 (((~c0_1(a617)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a617)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2457,axiom,((~c0_1(a617)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.98/2.12 tff(2458,plain,
% 1.98/2.12 ((~hskp19) | (~c0_1(a617))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 1.98/2.12 tff(2459,plain,
% 1.98/2.12 ((~hskp19) | (~c0_1(a617))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2458, 2455])).
% 1.98/2.12 tff(2460,plain,
% 1.98/2.12 (~c0_1(a617)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2459, 2448])).
% 1.98/2.12 tff(2461,plain,
% 1.98/2.12 (((~hskp19) | c2_1(a617)) <=> ((~hskp19) | c2_1(a617))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(2462,axiom,((~hskp19) | c2_1(a617)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.98/2.12 tff(2463,plain,
% 1.98/2.12 ((~hskp19) | c2_1(a617)),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 1.98/2.12 tff(2464,plain,
% 1.98/2.12 ((~hskp19) | c2_1(a617)),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2463, 2461])).
% 1.98/2.12 tff(2465,plain,
% 1.98/2.12 ((~hskp19) | c2_1(a617)),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2464, 2461])).
% 1.98/2.12 tff(2466,plain,
% 1.98/2.12 ((~hskp19) | c2_1(a617)),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2465, 2461])).
% 1.98/2.12 tff(2467,plain,
% 1.98/2.12 ((~hskp19) | c2_1(a617)),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[2466, 2461])).
% 1.98/2.12 tff(2468,plain,
% 1.98/2.12 (c2_1(a617)),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[2467, 2448])).
% 1.98/2.12 tff(2469,plain,
% 1.98/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2470,plain,
% 1.98/2.13 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2471,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[2470])).
% 1.98/2.13 tff(2472,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[2471, 2469])).
% 1.98/2.13 tff(2473,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(2474,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 1.98/2.13 tff(2475,plain,
% 1.98/2.13 (~c1_1(a678)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2474, 101, 2186, 2184, 2468, 2379, 2460, 2454, 2340, 65, 2382])).
% 1.98/2.13 tff(2476,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2477,plain,
% 1.98/2.13 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2478,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[2477])).
% 1.98/2.13 tff(2479,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[2478, 2476])).
% 1.98/2.13 tff(2480,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(2481,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 1.98/2.13 tff(2482,plain,
% 1.98/2.13 (~c0_1(a593)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2481, 101, 2468, 2379, 2353, 2350, 2460, 2454, 2340, 65, 2382])).
% 1.98/2.13 tff(2483,plain,
% 1.98/2.13 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2484,plain,
% 1.98/2.13 ((hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2485,plain,
% 1.98/2.13 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[2484])).
% 1.98/2.13 tff(2486,plain,
% 1.98/2.13 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[2485, 2483])).
% 1.98/2.13 tff(2487,plain,
% 1.98/2.13 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(2488,plain,
% 1.98/2.13 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 1.98/2.13 tff(2489,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2488, 101, 223, 2186, 2185, 2353, 2352, 32, 2482, 2475])).
% 1.98/2.13 tff(2490,plain,((~c0_1(a651)) | (~c0_1(a678)) | (~c2_1(a678)) | c0_1(a604) | (~c3_1(a678)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c1_1(a606)) | c2_1(a606) | (~c0_1(a606)) | hskp27 | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | (~c2_1(a651)) | c3_1(a651) | (~c0_1(a599)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(2491,plain,
% 1.98/2.13 (~c0_1(a651)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2490, 2340, 2185, 2186, 2184, 2263, 2262, 2261, 2281, 2273, 2280, 1749, 33, 22, 2270, 2339, 2338, 2337, 66])).
% 1.98/2.13 tff(2492,assumption,(~c1_1(a651)), introduced(assumption)).
% 1.98/2.13 tff(2493,plain,
% 1.98/2.13 (c3_1(a583)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1859, 1850, 425, 1526, 427, 426, 1527])).
% 1.98/2.13 tff(2494,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2495,plain,
% 1.98/2.13 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651))) <=> (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2496,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651)))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[2495])).
% 1.98/2.13 tff(2497,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 1.98/2.13 inference(transitivity,[status(thm)],[2496, 2494])).
% 1.98/2.13 tff(2498,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(2499,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651)),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 1.98/2.13 tff(2500,plain,
% 1.98/2.13 (c0_1(a651)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2499, 101, 1528, 1527, 2339, 785, 784, 2492, 45, 65, 2493])).
% 1.98/2.13 tff(2501,plain,
% 1.98/2.13 (hskp15),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1990, 101, 1528, 1527, 426, 425, 1870, 2493, 2337])).
% 1.98/2.13 tff(2502,plain,
% 1.98/2.13 (~c0_1(a604)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1474, 2501])).
% 1.98/2.13 tff(2503,plain,
% 1.98/2.13 (c3_1(a604)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1482, 2501])).
% 1.98/2.13 tff(2504,plain,
% 1.98/2.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2505,plain,
% 1.98/2.13 ((hskp28 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2506,plain,
% 1.98/2.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[2505])).
% 1.98/2.13 tff(2507,plain,
% 1.98/2.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[2506, 2504])).
% 1.98/2.13 tff(2508,plain,
% 1.98/2.13 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(2509,plain,
% 1.98/2.13 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[2508, 2507])).
% 1.98/2.13 tff(2510,plain,
% 1.98/2.13 (c2_1(a604)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2509, 101, 1850, 2339, 2503, 2338, 2502, 1026, 2500])).
% 1.98/2.13 tff(2511,plain,
% 1.98/2.13 (~hskp13),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2418, 2503, 427, 426, 2502, 425, 2510, 2186, 2185, 2184, 1753, 1750, 2380])).
% 1.98/2.13 tff(2512,plain,
% 1.98/2.13 (c1_1(a604)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1490, 2501])).
% 1.98/2.13 tff(2513,plain,
% 1.98/2.13 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2514,plain,
% 1.98/2.13 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c1_1(a604))) <=> (hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2515,plain,
% 1.98/2.13 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[2514])).
% 1.98/2.13 tff(2516,plain,
% 1.98/2.13 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[2515, 2513])).
% 1.98/2.13 tff(2517,plain,
% 1.98/2.13 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(2518,plain,
% 1.98/2.13 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 1.98/2.13 tff(2519,plain,
% 1.98/2.13 (hskp19 | hskp13),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2518, 101, 2512, 2502, 2429, 2510])).
% 1.98/2.13 tff(2520,plain,
% 1.98/2.13 (hskp19),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2519, 2511])).
% 1.98/2.13 tff(2521,plain,
% 1.98/2.13 (~c1_1(a617)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2453, 2520])).
% 1.98/2.13 tff(2522,plain,
% 1.98/2.13 (~c0_1(a617)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2459, 2520])).
% 1.98/2.13 tff(2523,plain,
% 1.98/2.13 (c2_1(a617)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2467, 2520])).
% 1.98/2.13 tff(2524,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2525,plain,
% 1.98/2.13 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2526,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[2525])).
% 1.98/2.13 tff(2527,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[2526, 2524])).
% 1.98/2.13 tff(2528,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(2529,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 1.98/2.13 tff(2530,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2529, 101, 1528, 1527, 2523, 2503, 2522, 2521, 2502, 65, 2493, 2510])).
% 1.98/2.13 tff(2531,plain,(hskp28 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a606)) | c2_1(a606) | (~c0_1(a606)) | (~c2_1(a651)) | c3_1(a651) | (~c0_1(a599)) | (~c2_1(a590)) | (~c3_1(a590)) | c1_1(a651) | c0_1(a590) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(2532,plain,
% 1.98/2.13 (hskp28),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2531, 2339, 2295, 2263, 2262, 2261, 2186, 2185, 2184, 2281, 2273, 2280, 2296, 2338, 2337, 785, 784, 2492, 45, 2294])).
% 1.98/2.13 tff(2533,plain,
% 1.98/2.13 (c3_1(a612)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1040, 2532])).
% 1.98/2.13 tff(2534,plain,
% 1.98/2.13 (c1_1(a612)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1321, 2532])).
% 1.98/2.13 tff(2535,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2536,plain,
% 1.98/2.13 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651))) <=> (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2537,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651)))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[2536])).
% 1.98/2.13 tff(2538,plain,
% 1.98/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 1.98/2.13 inference(transitivity,[status(thm)],[2537, 2535])).
% 1.98/2.13 tff(2539,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(2540,plain,
% 1.98/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651)),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 1.98/2.13 tff(2541,plain,
% 1.98/2.13 ((~c0_1(a612)) | c0_1(a651)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2540, 101, 2534, 2533, 2339, 785, 784, 2492, 45, 65])).
% 1.98/2.13 tff(2542,plain,
% 1.98/2.13 (~c0_1(a612)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2541, 2491])).
% 1.98/2.13 tff(2543,plain,
% 1.98/2.13 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.98/2.13 inference(bind,[status(th)],[])).
% 1.98/2.13 tff(2544,plain,
% 1.98/2.13 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.98/2.13 inference(quant_intro,[status(thm)],[2543])).
% 1.98/2.13 tff(2545,plain,
% 1.98/2.13 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(2546,plain,
% 1.98/2.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.99/2.14 inference(bind,[status(th)],[])).
% 1.99/2.14 tff(2547,plain,
% 1.99/2.14 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.99/2.14 inference(quant_intro,[status(thm)],[2546])).
% 1.99/2.14 tff(2548,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.99/2.14 tff(2549,plain,
% 1.99/2.14 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 1.99/2.14 tff(2550,plain,
% 1.99/2.14 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2549, 2545])).
% 1.99/2.14 tff(2551,plain,(
% 1.99/2.14 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.99/2.14 inference(skolemize,[status(sab)],[2550])).
% 1.99/2.14 tff(2552,plain,
% 1.99/2.14 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2551, 2544])).
% 1.99/2.14 tff(2553,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2554,plain,
% 1.99/2.14 ((hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a651) | c1_1(a651) | c0_1(a651)) <=> (hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2555,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651)))),
% 1.99/2.14 inference(monotonicity,[status(thm)],[2554])).
% 1.99/2.14 tff(2556,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651))),
% 1.99/2.14 inference(transitivity,[status(thm)],[2555, 2553])).
% 1.99/2.14 tff(2557,plain,
% 1.99/2.14 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a651) | c1_1(a651) | c0_1(a651))),
% 1.99/2.14 inference(quant_inst,[status(thm)],[])).
% 1.99/2.14 tff(2558,plain,
% 1.99/2.14 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651)),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2557, 2556])).
% 1.99/2.14 tff(2559,plain,
% 1.99/2.14 (hskp2 | c0_1(a651)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2558, 101, 2339, 2492, 2338, 188])).
% 1.99/2.14 tff(2560,plain,
% 1.99/2.14 (hskp2),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2559, 2491])).
% 1.99/2.14 tff(2561,plain,
% 1.99/2.14 (~c3_1(a586)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[206, 2560])).
% 1.99/2.14 tff(2562,plain,
% 1.99/2.14 (c2_1(a586)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[1357, 2560])).
% 1.99/2.14 tff(2563,plain,
% 1.99/2.14 (c1_1(a586)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[214, 2560])).
% 1.99/2.14 tff(2564,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2565,plain,
% 1.99/2.14 ((hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))) <=> (hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2566,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))))),
% 1.99/2.14 inference(monotonicity,[status(thm)],[2565])).
% 1.99/2.14 tff(2567,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 1.99/2.14 inference(transitivity,[status(thm)],[2566, 2564])).
% 1.99/2.14 tff(2568,plain,
% 1.99/2.14 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 1.99/2.14 inference(quant_inst,[status(thm)],[])).
% 1.99/2.14 tff(2569,plain,
% 1.99/2.14 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2568, 2567])).
% 1.99/2.14 tff(2570,plain,
% 1.99/2.14 (hskp15),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2569, 101, 2534, 2533, 2563, 2562, 2561, 2552, 2542])).
% 1.99/2.14 tff(2571,plain,
% 1.99/2.14 (c1_1(a604)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[1490, 2570])).
% 1.99/2.14 tff(2572,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2573,plain,
% 1.99/2.14 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a651) | c1_1(a651) | c0_1(a651)) <=> (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2574,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651)))),
% 1.99/2.14 inference(monotonicity,[status(thm)],[2573])).
% 1.99/2.14 tff(2575,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651))),
% 1.99/2.14 inference(transitivity,[status(thm)],[2574, 2572])).
% 1.99/2.14 tff(2576,plain,
% 1.99/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a651) | c1_1(a651) | c0_1(a651))),
% 1.99/2.14 inference(quant_inst,[status(thm)],[])).
% 1.99/2.14 tff(2577,plain,
% 1.99/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651)),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2576, 2575])).
% 1.99/2.14 tff(2578,plain,
% 1.99/2.14 (c2_1(a604) | (~c1_1(a604)) | c0_1(a651)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2577, 101, 33, 2492, 2338, 22, 2340, 1349, 2270])).
% 1.99/2.14 tff(2579,plain,
% 1.99/2.14 (c2_1(a604)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2578, 2571, 2491])).
% 1.99/2.14 tff(2580,plain,
% 1.99/2.14 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.99/2.14 inference(bind,[status(th)],[])).
% 1.99/2.14 tff(2581,plain,
% 1.99/2.14 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.99/2.14 inference(quant_intro,[status(thm)],[2580])).
% 1.99/2.14 tff(2582,plain,
% 1.99/2.14 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2583,plain,
% 1.99/2.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp12) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.99/2.14 inference(bind,[status(th)],[])).
% 1.99/2.14 tff(2584,plain,
% 1.99/2.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.99/2.14 inference(quant_intro,[status(thm)],[2583])).
% 1.99/2.14 tff(2585,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.99/2.14 tff(2586,plain,
% 1.99/2.14 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 1.99/2.14 tff(2587,plain,
% 1.99/2.14 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2586, 2582])).
% 1.99/2.14 tff(2588,plain,(
% 1.99/2.14 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.99/2.14 inference(skolemize,[status(sab)],[2587])).
% 1.99/2.14 tff(2589,plain,
% 1.99/2.14 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2588, 2581])).
% 1.99/2.14 tff(2590,plain,
% 1.99/2.14 (c2_1(a612)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[1048, 2532])).
% 1.99/2.14 tff(2591,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2592,plain,
% 1.99/2.14 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2593,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))))),
% 1.99/2.14 inference(monotonicity,[status(thm)],[2592])).
% 1.99/2.14 tff(2594,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 1.99/2.14 inference(transitivity,[status(thm)],[2593, 2591])).
% 1.99/2.14 tff(2595,plain,
% 1.99/2.14 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 1.99/2.14 inference(quant_inst,[status(thm)],[])).
% 1.99/2.14 tff(2596,plain,
% 1.99/2.14 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 1.99/2.14 tff(2597,plain,
% 1.99/2.14 (hskp12),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2596, 101, 2534, 2590, 2296, 2295, 2294, 2589, 2542])).
% 1.99/2.14 tff(2598,plain,
% 1.99/2.14 (~c3_1(a600)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[675, 2597])).
% 1.99/2.14 tff(2599,plain,
% 1.99/2.14 (c2_1(a600)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[683, 2597])).
% 1.99/2.14 tff(2600,plain,
% 1.99/2.14 (c0_1(a600)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[691, 2597])).
% 1.99/2.14 tff(2601,plain,
% 1.99/2.14 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2602,plain,
% 1.99/2.14 ((hskp27 | hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600))) <=> (hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2603,plain,
% 1.99/2.14 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))))),
% 1.99/2.14 inference(monotonicity,[status(thm)],[2602])).
% 1.99/2.14 tff(2604,plain,
% 1.99/2.14 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 1.99/2.14 inference(transitivity,[status(thm)],[2603, 2601])).
% 1.99/2.14 tff(2605,plain,
% 1.99/2.14 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))),
% 1.99/2.14 inference(quant_inst,[status(thm)],[])).
% 1.99/2.14 tff(2606,plain,
% 1.99/2.14 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 1.99/2.14 tff(2607,plain,
% 1.99/2.14 (hskp8),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2606, 101, 1749, 2600, 2599, 2598, 1957])).
% 1.99/2.14 tff(2608,plain,
% 1.99/2.14 (c3_1(a593)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[469, 2607])).
% 1.99/2.14 tff(2609,plain,
% 1.99/2.14 (c1_1(a593)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[477, 2607])).
% 1.99/2.14 tff(2610,plain,
% 1.99/2.14 (c3_1(a604)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[1482, 2570])).
% 1.99/2.14 tff(2611,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2612,plain,
% 1.99/2.14 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651))) <=> (c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2613,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651)))),
% 1.99/2.14 inference(monotonicity,[status(thm)],[2612])).
% 1.99/2.14 tff(2614,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651))),
% 1.99/2.14 inference(transitivity,[status(thm)],[2613, 2611])).
% 1.99/2.14 tff(2615,plain,
% 1.99/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))),
% 1.99/2.14 inference(quant_inst,[status(thm)],[])).
% 1.99/2.14 tff(2616,plain,
% 1.99/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651)),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 1.99/2.14 tff(2617,plain,
% 1.99/2.14 (~c0_1(a593)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2616, 101, 2339, 2610, 2609, 2608, 2492, 2340, 65, 2491, 2579])).
% 1.99/2.14 tff(2618,plain,
% 1.99/2.14 (~c2_1(a593)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[510, 2607])).
% 1.99/2.14 tff(2619,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2620,plain,
% 1.99/2.14 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a651) | c1_1(a651) | c0_1(a651)) <=> (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2621,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651)))),
% 1.99/2.14 inference(monotonicity,[status(thm)],[2620])).
% 1.99/2.14 tff(2622,plain,
% 1.99/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651))),
% 1.99/2.14 inference(transitivity,[status(thm)],[2621, 2619])).
% 1.99/2.14 tff(2623,plain,
% 1.99/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a651) | c1_1(a651) | c0_1(a651))),
% 1.99/2.14 inference(quant_inst,[status(thm)],[])).
% 1.99/2.14 tff(2624,plain,
% 1.99/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651)),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2623, 2622])).
% 1.99/2.14 tff(2625,plain,
% 1.99/2.14 ($false),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2624, 101, 33, 2609, 2492, 2338, 22, 2618, 1349, 2617, 2270, 2491])).
% 1.99/2.14 tff(2626,plain,(c0_1(a604) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | (~c2_1(a651)) | hskp27 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | (~c0_1(a599)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.14 tff(2627,plain,
% 1.99/2.14 (c0_1(a604)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2626, 2336, 33, 2330, 22, 2324, 1749, 785, 784, 45, 2185, 2186, 2184, 2298, 66])).
% 1.99/2.14 tff(2628,plain,
% 1.99/2.14 (~hskp15),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[1474, 2627])).
% 1.99/2.14 tff(2629,plain,
% 1.99/2.14 (hskp28),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2531, 2324, 2295, 2263, 2262, 2261, 2186, 2185, 2184, 2281, 2273, 2280, 2296, 2330, 2298, 785, 784, 2336, 45, 2294])).
% 1.99/2.14 tff(2630,plain,
% 1.99/2.14 (c3_1(a612)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[1040, 2629])).
% 1.99/2.14 tff(2631,plain,
% 1.99/2.14 (c1_1(a612)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[1321, 2629])).
% 1.99/2.14 tff(2632,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2633,plain,
% 1.99/2.14 ((hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2634,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599))))),
% 1.99/2.14 inference(monotonicity,[status(thm)],[2633])).
% 1.99/2.14 tff(2635,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.99/2.14 inference(transitivity,[status(thm)],[2634, 2632])).
% 1.99/2.14 tff(2636,plain,
% 1.99/2.14 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.99/2.14 inference(quant_inst,[status(thm)],[])).
% 1.99/2.14 tff(2637,plain,
% 1.99/2.14 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599))),
% 1.99/2.14 inference(modus_ponens,[status(thm)],[2636, 2635])).
% 1.99/2.14 tff(2638,plain,
% 1.99/2.14 (hskp15 | (~c0_1(a612))),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2637, 101, 2631, 2630, 2262, 2261, 1870, 2298])).
% 1.99/2.14 tff(2639,plain,
% 1.99/2.14 (~c0_1(a612)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2638, 2628])).
% 1.99/2.14 tff(2640,plain,
% 1.99/2.14 (c2_1(a612)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[1048, 2629])).
% 1.99/2.14 tff(2641,plain,
% 1.99/2.14 (hskp12),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2596, 101, 2631, 2640, 2296, 2295, 2294, 2589, 2639])).
% 1.99/2.14 tff(2642,plain,
% 1.99/2.14 (~c3_1(a600)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[675, 2641])).
% 1.99/2.14 tff(2643,plain,
% 1.99/2.14 (c2_1(a600)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[683, 2641])).
% 1.99/2.14 tff(2644,plain,
% 1.99/2.14 (c0_1(a600)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[691, 2641])).
% 1.99/2.14 tff(2645,plain,
% 1.99/2.14 (hskp8),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2606, 101, 1749, 2644, 2643, 2642, 1957])).
% 1.99/2.14 tff(2646,plain,
% 1.99/2.14 (c3_1(a593)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[469, 2645])).
% 1.99/2.14 tff(2647,plain,
% 1.99/2.14 (c1_1(a593)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[477, 2645])).
% 1.99/2.14 tff(2648,plain,
% 1.99/2.14 (~c0_1(a593)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[2361, 101, 2628, 2262, 2647, 2646, 2261, 1870, 2298])).
% 1.99/2.14 tff(2649,plain,
% 1.99/2.14 (~c2_1(a593)),
% 1.99/2.14 inference(unit_resolution,[status(thm)],[510, 2645])).
% 1.99/2.14 tff(2650,plain,
% 1.99/2.14 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2651,plain,
% 1.99/2.14 ((hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593))) <=> (hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.99/2.14 inference(rewrite,[status(thm)],[])).
% 1.99/2.14 tff(2652,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606))))),
% 1.99/2.15 inference(monotonicity,[status(thm)],[2651])).
% 1.99/2.15 tff(2653,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 1.99/2.15 inference(transitivity,[status(thm)],[2652, 2650])).
% 1.99/2.15 tff(2654,plain,
% 1.99/2.15 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))),
% 1.99/2.15 inference(quant_inst,[status(thm)],[])).
% 1.99/2.15 tff(2655,plain,
% 1.99/2.15 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606))),
% 1.99/2.15 inference(modus_ponens,[status(thm)],[2654, 2653])).
% 1.99/2.15 tff(2656,plain,
% 1.99/2.15 ($false),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2655, 101, 1749, 2281, 2646, 2273, 2649, 495, 2648, 2280])).
% 1.99/2.15 tff(2657,plain,(hskp9 | hskp27 | c3_1(a607) | c2_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.15 tff(2658,plain,
% 1.99/2.15 (hskp9),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2657, 1749, 33, 22, 785, 784, 45, 2185, 2186, 2184, 66])).
% 1.99/2.15 tff(2659,plain,
% 1.99/2.15 (~c3_1(a595)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1370, 2658])).
% 1.99/2.15 tff(2660,plain,
% 1.99/2.15 (~c0_1(a595)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1382, 2658])).
% 1.99/2.15 tff(2661,plain,
% 1.99/2.15 (~c1_1(a595)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1376, 2658])).
% 1.99/2.15 tff(2662,plain,
% 1.99/2.15 (c0_1(a595) | c2_1(a595)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2074, 101, 2263, 2262, 785, 784, 2261, 1439, 45, 1607])).
% 1.99/2.15 tff(2663,plain,
% 1.99/2.15 (c2_1(a595)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2662, 1441])).
% 1.99/2.15 tff(2664,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2665,plain,
% 1.99/2.15 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2666,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))))),
% 1.99/2.15 inference(monotonicity,[status(thm)],[2665])).
% 1.99/2.15 tff(2667,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 1.99/2.15 inference(transitivity,[status(thm)],[2666, 2664])).
% 1.99/2.15 tff(2668,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 1.99/2.15 inference(quant_inst,[status(thm)],[])).
% 1.99/2.15 tff(2669,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))),
% 1.99/2.15 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 1.99/2.15 tff(2670,plain,
% 1.99/2.15 (c0_1(a595) | (~c1_1(a678)) | (~c2_1(a595))),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2669, 101, 2186, 2184, 785, 784, 1440, 45, 65])).
% 1.99/2.15 tff(2671,plain,
% 1.99/2.15 (~c1_1(a678)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2670, 1441, 2663])).
% 1.99/2.15 tff(2672,plain,
% 1.99/2.15 (hskp2 | c0_1(a595) | (~c2_1(a595))),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1631, 101, 1440, 1439, 188])).
% 1.99/2.15 tff(2673,plain,
% 1.99/2.15 (hskp2),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2672, 1441, 2663])).
% 1.99/2.15 tff(2674,plain,
% 1.99/2.15 (~c3_1(a586)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[206, 2673])).
% 1.99/2.15 tff(2675,plain,
% 1.99/2.15 (c2_1(a586)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1357, 2673])).
% 1.99/2.15 tff(2676,plain,
% 1.99/2.15 (c1_1(a586)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[214, 2673])).
% 1.99/2.15 tff(2677,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2678,plain,
% 1.99/2.15 ((hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678))) <=> (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2679,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586))))),
% 1.99/2.15 inference(monotonicity,[status(thm)],[2678])).
% 1.99/2.15 tff(2680,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586)))),
% 1.99/2.15 inference(transitivity,[status(thm)],[2679, 2677])).
% 1.99/2.15 tff(2681,plain,
% 1.99/2.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)))),
% 1.99/2.15 inference(quant_inst,[status(thm)],[])).
% 1.99/2.15 tff(2682,plain,
% 1.99/2.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586))),
% 1.99/2.15 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 1.99/2.15 tff(2683,plain,
% 1.99/2.15 (hskp28),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2682, 101, 2185, 2184, 2676, 2675, 2674, 1625, 2671])).
% 1.99/2.15 tff(2684,plain,
% 1.99/2.15 (c3_1(a612)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1040, 2683])).
% 1.99/2.15 tff(2685,plain,
% 1.99/2.15 (c1_1(a612)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1321, 2683])).
% 1.99/2.15 tff(2686,plain,
% 1.99/2.15 (~c0_1(a612)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1651, 101, 2685, 2684, 785, 784, 1441, 1440, 45, 65, 2663])).
% 1.99/2.15 tff(2687,plain,
% 1.99/2.15 (hskp15),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2569, 101, 2685, 2684, 2676, 2675, 2674, 2552, 2686])).
% 1.99/2.15 tff(2688,plain,
% 1.99/2.15 (~c0_1(a604)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1474, 2687])).
% 1.99/2.15 tff(2689,plain,
% 1.99/2.15 (c1_1(a604)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1490, 2687])).
% 1.99/2.15 tff(2690,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2691,plain,
% 1.99/2.15 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2692,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607))))),
% 1.99/2.15 inference(monotonicity,[status(thm)],[2691])).
% 1.99/2.15 tff(2693,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 1.99/2.15 inference(transitivity,[status(thm)],[2692, 2690])).
% 1.99/2.15 tff(2694,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 1.99/2.15 inference(quant_inst,[status(thm)],[])).
% 1.99/2.15 tff(2695,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607))),
% 1.99/2.15 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 1.99/2.15 tff(2696,plain,
% 1.99/2.15 (c2_1(a604)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2695, 101, 33, 2689, 22, 2688, 1441, 1440, 1439, 1349, 2270])).
% 1.99/2.15 tff(2697,plain,
% 1.99/2.15 (c2_1(a612)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1048, 2683])).
% 1.99/2.15 tff(2698,plain,
% 1.99/2.15 (hskp12),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2596, 101, 2685, 2697, 1528, 1527, 1526, 2589, 2686])).
% 1.99/2.15 tff(2699,plain,
% 1.99/2.15 (~c3_1(a600)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[675, 2698])).
% 1.99/2.15 tff(2700,plain,
% 1.99/2.15 (c2_1(a600)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[683, 2698])).
% 1.99/2.15 tff(2701,plain,
% 1.99/2.15 (c0_1(a600)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[691, 2698])).
% 1.99/2.15 tff(2702,plain,
% 1.99/2.15 (hskp8),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2606, 101, 1749, 2701, 2700, 2699, 1957])).
% 1.99/2.15 tff(2703,plain,
% 1.99/2.15 (c3_1(a593)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[469, 2702])).
% 1.99/2.15 tff(2704,plain,
% 1.99/2.15 (c1_1(a593)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[477, 2702])).
% 1.99/2.15 tff(2705,plain,
% 1.99/2.15 (c3_1(a604)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1482, 2687])).
% 1.99/2.15 tff(2706,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2707,plain,
% 1.99/2.15 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2708,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604))))),
% 1.99/2.15 inference(monotonicity,[status(thm)],[2707])).
% 1.99/2.15 tff(2709,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.99/2.15 inference(transitivity,[status(thm)],[2708, 2706])).
% 1.99/2.15 tff(2710,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 1.99/2.15 inference(quant_inst,[status(thm)],[])).
% 1.99/2.15 tff(2711,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604))),
% 1.99/2.15 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 1.99/2.15 tff(2712,plain,
% 1.99/2.15 (~c0_1(a593)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2711, 101, 2705, 2704, 2703, 2688, 1441, 1440, 65, 2663, 2696])).
% 1.99/2.15 tff(2713,plain,
% 1.99/2.15 (~c2_1(a593)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[510, 2702])).
% 1.99/2.15 tff(2714,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2715,plain,
% 1.99/2.15 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2716,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))))),
% 1.99/2.15 inference(monotonicity,[status(thm)],[2715])).
% 1.99/2.15 tff(2717,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 1.99/2.15 inference(transitivity,[status(thm)],[2716, 2714])).
% 1.99/2.15 tff(2718,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 1.99/2.15 inference(quant_inst,[status(thm)],[])).
% 1.99/2.15 tff(2719,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))),
% 1.99/2.15 inference(modus_ponens,[status(thm)],[2718, 2717])).
% 1.99/2.15 tff(2720,plain,
% 1.99/2.15 ($false),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2719, 101, 33, 2704, 22, 1441, 1440, 1439, 2713, 1349, 2712, 2270])).
% 1.99/2.15 tff(2721,plain,(c0_1(a595) | c3_1(a607) | c2_1(a607) | c1_1(a595) | c3_1(a595) | hskp27 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.15 tff(2722,plain,
% 1.99/2.15 ($false),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2721, 2661, 2660, 22, 33, 2659, 1749, 2296, 2295, 2294, 785, 784, 45, 2185, 2184, 2186])).
% 1.99/2.15 tff(2723,plain,(hskp27 | c2_1(a607) | c3_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.15 tff(2724,plain,
% 1.99/2.15 (hskp27),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2723, 2183, 33, 22, 2182, 2181, 2152, 2144, 2160, 66])).
% 1.99/2.15 tff(2725,plain,
% 1.99/2.15 (c3_1(a611)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[566, 2724])).
% 1.99/2.15 tff(2726,plain,
% 1.99/2.15 (c1_1(a611)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[574, 2724])).
% 1.99/2.15 tff(2727,plain,
% 1.99/2.15 (c0_1(a611)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[582, 2724])).
% 1.99/2.15 tff(2728,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2729,plain,
% 1.99/2.15 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2730,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599)))),
% 1.99/2.15 inference(monotonicity,[status(thm)],[2729])).
% 1.99/2.15 tff(2731,plain,
% 1.99/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 1.99/2.15 inference(transitivity,[status(thm)],[2730, 2728])).
% 1.99/2.15 tff(2732,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 1.99/2.15 inference(quant_inst,[status(thm)],[])).
% 1.99/2.15 tff(2733,plain,
% 1.99/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599)),
% 1.99/2.15 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 1.99/2.15 tff(2734,plain,
% 1.99/2.15 (c0_1(a599)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2733, 101, 2727, 2726, 2725, 2259, 2183, 2182, 2258, 2181, 65])).
% 1.99/2.15 tff(2735,plain,
% 1.99/2.15 (c3_1(a599)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[389, 2257])).
% 1.99/2.15 tff(2736,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2737,plain,
% 1.99/2.15 ((hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2738,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599))))),
% 1.99/2.15 inference(monotonicity,[status(thm)],[2737])).
% 1.99/2.15 tff(2739,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.99/2.15 inference(transitivity,[status(thm)],[2738, 2736])).
% 1.99/2.15 tff(2740,plain,
% 1.99/2.15 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 1.99/2.15 inference(quant_inst,[status(thm)],[])).
% 1.99/2.15 tff(2741,plain,
% 1.99/2.15 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599))),
% 1.99/2.15 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 1.99/2.15 tff(2742,plain,
% 1.99/2.15 (hskp15),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[2741, 101, 2727, 2726, 2725, 2735, 2258, 1870, 2734])).
% 1.99/2.15 tff(2743,plain,
% 1.99/2.15 (~c0_1(a604)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1474, 2742])).
% 1.99/2.15 tff(2744,plain,
% 1.99/2.15 (c1_1(a604)),
% 1.99/2.15 inference(unit_resolution,[status(thm)],[1490, 2742])).
% 1.99/2.15 tff(2745,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2746,plain,
% 1.99/2.15 ((hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.15 inference(rewrite,[status(thm)],[])).
% 1.99/2.15 tff(2747,plain,
% 1.99/2.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604))))),
% 1.99/2.16 inference(monotonicity,[status(thm)],[2746])).
% 1.99/2.16 tff(2748,plain,
% 1.99/2.16 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.16 inference(transitivity,[status(thm)],[2747, 2745])).
% 1.99/2.16 tff(2749,plain,
% 1.99/2.16 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.16 inference(quant_inst,[status(thm)],[])).
% 1.99/2.16 tff(2750,plain,
% 1.99/2.16 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604))),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 1.99/2.16 tff(2751,plain,
% 1.99/2.16 (c2_1(a604)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2750, 101, 223, 2744, 2259, 2743, 2258, 32, 2734])).
% 1.99/2.16 tff(2752,plain,
% 1.99/2.16 (c0_1(a607)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2269, 101, 33, 2259, 2735, 2183, 2182, 22, 2258, 2181, 1607])).
% 1.99/2.16 tff(2753,plain,
% 1.99/2.16 (hskp16 | (~c0_1(a607))),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2194, 101, 33, 2183, 2182, 22, 2181, 2002])).
% 1.99/2.16 tff(2754,plain,
% 1.99/2.16 (hskp16),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2753, 2752])).
% 1.99/2.16 tff(2755,plain,
% 1.99/2.16 (~c3_1(a606)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[982, 2754])).
% 1.99/2.16 tff(2756,plain,
% 1.99/2.16 (~c2_1(a606)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[1015, 2754])).
% 1.99/2.16 tff(2757,plain,
% 1.99/2.16 (c0_1(a606)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2279, 101, 2259, 2735, 2183, 2182, 2756, 2755, 2258, 2181, 1607])).
% 1.99/2.16 tff(2758,plain,
% 1.99/2.16 (c1_1(a606)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[992, 2754])).
% 1.99/2.16 tff(2759,plain,
% 1.99/2.16 (c3_1(a604)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[1482, 2742])).
% 1.99/2.16 tff(2760,plain,
% 1.99/2.16 (~hskp13),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2418, 2751, 2259, 2735, 2743, 2258, 2759, 2160, 2152, 2144, 2758, 2756, 2757])).
% 1.99/2.16 tff(2761,plain,
% 1.99/2.16 (hskp19 | hskp13),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2518, 101, 2744, 2743, 2429, 2751])).
% 1.99/2.16 tff(2762,plain,
% 1.99/2.16 (hskp19),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2761, 2760])).
% 1.99/2.16 tff(2763,plain,
% 1.99/2.16 (~c1_1(a617)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2453, 2762])).
% 1.99/2.16 tff(2764,plain,
% 1.99/2.16 (~c0_1(a617)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2459, 2762])).
% 1.99/2.16 tff(2765,plain,
% 1.99/2.16 (c2_1(a617)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2467, 2762])).
% 1.99/2.16 tff(2766,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2767,plain,
% 1.99/2.16 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2768,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 1.99/2.16 inference(monotonicity,[status(thm)],[2767])).
% 1.99/2.16 tff(2769,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 1.99/2.16 inference(transitivity,[status(thm)],[2768, 2766])).
% 1.99/2.16 tff(2770,plain,
% 1.99/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 1.99/2.16 inference(quant_inst,[status(thm)],[])).
% 1.99/2.16 tff(2771,plain,
% 1.99/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 1.99/2.16 tff(2772,plain,
% 1.99/2.16 ($false),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2771, 101, 2727, 2726, 2725, 2765, 2759, 2764, 2763, 2743, 65, 2751])).
% 1.99/2.16 tff(2773,plain,(c1_1(a607) | c3_1(a607) | c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.99/2.16 tff(2774,plain,
% 1.99/2.16 (c1_1(a607)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2773, 33, 22, 44])).
% 1.99/2.16 tff(2775,plain,
% 1.99/2.16 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2776,plain,
% 1.99/2.16 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2777,plain,
% 1.99/2.16 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 1.99/2.16 inference(monotonicity,[status(thm)],[2776])).
% 1.99/2.16 tff(2778,plain,
% 1.99/2.16 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.16 inference(transitivity,[status(thm)],[2777, 2775])).
% 1.99/2.16 tff(2779,plain,
% 1.99/2.16 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 1.99/2.16 inference(quant_inst,[status(thm)],[])).
% 1.99/2.16 tff(2780,plain,
% 1.99/2.16 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 1.99/2.16 tff(2781,plain,
% 1.99/2.16 (hskp4 | (~c1_1(a607)) | (~c0_1(a607))),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2780, 101, 223, 33, 55])).
% 1.99/2.16 tff(2782,plain,
% 1.99/2.16 (~c0_1(a607)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2781, 139, 2774])).
% 1.99/2.16 tff(2783,plain,
% 1.99/2.16 (hskp14),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[156, 2782, 33, 139])).
% 1.99/2.16 tff(2784,plain,
% 1.99/2.16 (~c1_1(a603)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[162, 2783])).
% 1.99/2.16 tff(2785,plain,
% 1.99/2.16 (c0_1(a603)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[170, 2783])).
% 1.99/2.16 tff(2786,plain,
% 1.99/2.16 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2787,plain,
% 1.99/2.16 ((hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607))) <=> (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2788,plain,
% 1.99/2.16 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607)))),
% 1.99/2.16 inference(monotonicity,[status(thm)],[2787])).
% 1.99/2.16 tff(2789,plain,
% 1.99/2.16 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 1.99/2.16 inference(transitivity,[status(thm)],[2788, 2786])).
% 1.99/2.16 tff(2790,plain,
% 1.99/2.16 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))),
% 1.99/2.16 inference(quant_inst,[status(thm)],[])).
% 1.99/2.16 tff(2791,plain,
% 1.99/2.16 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607)),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 1.99/2.16 tff(2792,plain,
% 1.99/2.16 (~c2_1(a603)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2791, 101, 223, 2785, 2774, 22, 2784, 32, 2782])).
% 1.99/2.16 tff(2793,plain,
% 1.99/2.16 ($false),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[177, 101, 44, 67, 2785, 2784, 43, 2792])).
% 1.99/2.16 tff(2794,plain,(hskp6 | hskp22 | c2_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.16 tff(2795,plain,
% 1.99/2.16 (hskp6),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2794, 33, 22, 44])).
% 1.99/2.16 tff(2796,plain,
% 1.99/2.16 (~c0_1(a590)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[606, 2795])).
% 1.99/2.16 tff(2797,plain,
% 1.99/2.16 (c0_1(a607)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2167, 1515])).
% 1.99/2.16 tff(2798,plain,
% 1.99/2.16 (hskp4),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2781, 2797, 2774])).
% 1.99/2.16 tff(2799,plain,
% 1.99/2.16 (hskp6),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[138, 2798, 44])).
% 1.99/2.16 tff(2800,plain,
% 1.99/2.16 (~c0_1(a590)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[606, 2799])).
% 1.99/2.16 tff(2801,plain,
% 1.99/2.16 (c2_1(a590)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[622, 2799])).
% 1.99/2.16 tff(2802,plain,
% 1.99/2.16 (c3_1(a590)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[614, 2799])).
% 1.99/2.16 tff(2803,plain,
% 1.99/2.16 ($false),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2256, 2802, 2801, 2152, 2144, 33, 2160, 1515, 22, 2800])).
% 1.99/2.16 tff(2804,plain,(hskp11 | c3_1(a607) | c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.99/2.16 tff(2805,plain,
% 1.99/2.16 (hskp11),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2804, 33, 22, 44])).
% 1.99/2.16 tff(2806,plain,
% 1.99/2.16 (~c1_1(a599)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[395, 2805])).
% 1.99/2.16 tff(2807,plain,
% 1.99/2.16 (c3_1(a590)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[614, 2795])).
% 1.99/2.16 tff(2808,plain,
% 1.99/2.16 (c2_1(a590)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[622, 2795])).
% 1.99/2.16 tff(2809,plain,
% 1.99/2.16 (c2_1(a599)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[403, 2805])).
% 1.99/2.16 tff(2810,plain,
% 1.99/2.16 (c3_1(a599)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[389, 2805])).
% 1.99/2.16 tff(2811,plain,
% 1.99/2.16 (c0_1(a607)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2269, 101, 33, 2809, 2810, 2808, 2807, 22, 2806, 2796, 1607])).
% 1.99/2.16 tff(2812,plain,
% 1.99/2.16 (hskp4),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2781, 2811, 2774])).
% 1.99/2.16 tff(2813,plain,
% 1.99/2.16 (~c2_1(a588)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[115, 2812])).
% 1.99/2.16 tff(2814,plain,
% 1.99/2.16 (~c1_1(a588)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[121, 2812])).
% 1.99/2.16 tff(2815,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2816,plain,
% 1.99/2.16 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588))) <=> ((~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2817,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607))))),
% 1.99/2.16 inference(monotonicity,[status(thm)],[2816])).
% 1.99/2.16 tff(2818,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607)))),
% 1.99/2.16 inference(transitivity,[status(thm)],[2817, 2815])).
% 1.99/2.16 tff(2819,plain,
% 1.99/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))),
% 1.99/2.16 inference(quant_inst,[status(thm)],[])).
% 1.99/2.16 tff(2820,plain,
% 1.99/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607))),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 1.99/2.16 tff(2821,plain,
% 1.99/2.16 (~c3_1(a588)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2820, 101, 2160, 2152, 2144, 2774, 22, 2814, 2813, 1010, 2811])).
% 1.99/2.16 tff(2822,plain,
% 1.99/2.16 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2823,plain,
% 1.99/2.16 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2824,plain,
% 1.99/2.16 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 1.99/2.16 inference(monotonicity,[status(thm)],[2823])).
% 1.99/2.16 tff(2825,plain,
% 1.99/2.16 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.16 inference(transitivity,[status(thm)],[2824, 2822])).
% 1.99/2.16 tff(2826,plain,
% 1.99/2.16 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 1.99/2.16 inference(quant_inst,[status(thm)],[])).
% 1.99/2.16 tff(2827,plain,
% 1.99/2.16 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 1.99/2.16 tff(2828,plain,
% 1.99/2.16 (hskp3 | (~c1_1(a607)) | (~c0_1(a607))),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2827, 101, 223, 33, 2236])).
% 1.99/2.16 tff(2829,plain,
% 1.99/2.16 (hskp3),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2828, 2811, 2774])).
% 1.99/2.16 tff(2830,plain,
% 1.99/2.16 (~c1_1(a587)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[855, 2829])).
% 1.99/2.16 tff(2831,plain,
% 1.99/2.16 (c2_1(a587)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[863, 2829])).
% 1.99/2.16 tff(2832,plain,
% 1.99/2.16 (c0_1(a587)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[871, 2829])).
% 1.99/2.16 tff(2833,plain,
% 1.99/2.16 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2834,plain,
% 1.99/2.16 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2835,plain,
% 1.99/2.16 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588)))),
% 1.99/2.16 inference(monotonicity,[status(thm)],[2834])).
% 1.99/2.16 tff(2836,plain,
% 1.99/2.16 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588))),
% 1.99/2.16 inference(transitivity,[status(thm)],[2835, 2833])).
% 1.99/2.16 tff(2837,plain,
% 1.99/2.16 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 1.99/2.16 inference(quant_inst,[status(thm)],[])).
% 1.99/2.16 tff(2838,plain,
% 1.99/2.16 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588)),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 1.99/2.16 tff(2839,plain,
% 1.99/2.16 (hskp26),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2838, 101, 2832, 2831, 2814, 2813, 2830, 905, 2821])).
% 1.99/2.16 tff(2840,plain,
% 1.99/2.16 (c2_1(a583)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[364, 2839])).
% 1.99/2.16 tff(2841,plain,
% 1.99/2.16 (c1_1(a583)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[330, 2839])).
% 1.99/2.16 tff(2842,plain,
% 1.99/2.16 (c0_1(a583)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[338, 2839])).
% 1.99/2.16 tff(2843,plain,
% 1.99/2.16 (hskp16),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2194, 101, 33, 2808, 2807, 22, 2796, 2002, 2811])).
% 1.99/2.16 tff(2844,plain,
% 1.99/2.16 (~c2_1(a606)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[1015, 2843])).
% 1.99/2.16 tff(2845,plain,
% 1.99/2.16 (c1_1(a606)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[992, 2843])).
% 1.99/2.16 tff(2846,plain,
% 1.99/2.16 (~c3_1(a606)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[982, 2843])).
% 1.99/2.16 tff(2847,plain,
% 1.99/2.16 (c0_1(a606)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2279, 101, 2809, 2810, 2808, 2807, 2844, 2846, 2806, 2796, 1607])).
% 1.99/2.16 tff(2848,assumption,(c1_1(a607)), introduced(assumption)).
% 1.99/2.16 tff(2849,assumption,(~hskp17), introduced(assumption)).
% 1.99/2.16 tff(2850,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2851,plain,
% 1.99/2.16 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | c2_1(a604)) <=> (c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2852,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | c2_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604)))),
% 1.99/2.16 inference(monotonicity,[status(thm)],[2851])).
% 1.99/2.16 tff(2853,plain,
% 1.99/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | c2_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604))),
% 1.99/2.16 inference(transitivity,[status(thm)],[2852, 2850])).
% 1.99/2.16 tff(2854,plain,
% 1.99/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | c2_1(a604))),
% 1.99/2.16 inference(quant_inst,[status(thm)],[])).
% 1.99/2.16 tff(2855,plain,
% 1.99/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604)),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 1.99/2.16 tff(2856,plain,
% 1.99/2.16 (c2_1(a604)),
% 1.99/2.16 inference(unit_resolution,[status(thm)],[2855, 101, 2354, 427, 426, 785, 784, 2340, 425, 45, 1607])).
% 1.99/2.16 tff(2857,plain,
% 1.99/2.16 (^[U: $i] : refl((hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.99/2.16 inference(bind,[status(th)],[])).
% 1.99/2.16 tff(2858,plain,
% 1.99/2.16 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.99/2.16 inference(quant_intro,[status(thm)],[2857])).
% 1.99/2.16 tff(2859,plain,
% 1.99/2.16 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.99/2.16 inference(rewrite,[status(thm)],[])).
% 1.99/2.16 tff(2860,plain,
% 1.99/2.16 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp25) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp25) <=> (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.99/2.16 inference(bind,[status(th)],[])).
% 1.99/2.16 tff(2861,plain,
% 1.99/2.16 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp25) <=> ![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.99/2.16 inference(quant_intro,[status(thm)],[2860])).
% 1.99/2.16 tff(2862,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.99/2.16 tff(2863,plain,
% 1.99/2.16 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 1.99/2.16 tff(2864,plain,
% 1.99/2.16 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.99/2.16 inference(modus_ponens,[status(thm)],[2863, 2859])).
% 1.99/2.16 tff(2865,plain,(
% 1.99/2.16 ![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.99/2.16 inference(skolemize,[status(sab)],[2864])).
% 1.99/2.16 tff(2866,plain,
% 1.99/2.16 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2865, 2858])).
% 1.99/2.17 tff(2867,plain,
% 1.99/2.17 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2868,plain,
% 1.99/2.17 ((hskp25 | hskp15 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2869,plain,
% 1.99/2.17 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[2868])).
% 1.99/2.17 tff(2870,plain,
% 1.99/2.17 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 1.99/2.17 inference(transitivity,[status(thm)],[2869, 2867])).
% 1.99/2.17 tff(2871,plain,
% 1.99/2.17 ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(2872,plain,
% 1.99/2.17 ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2871, 2870])).
% 1.99/2.17 tff(2873,plain,
% 1.99/2.17 (hskp25 | hskp15 | (~c1_1(a607)) | (~c0_1(a607))),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2872, 101, 22, 2866])).
% 1.99/2.17 tff(2874,plain,
% 1.99/2.17 (hskp25),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2873, 2355, 2848, 2351])).
% 1.99/2.17 tff(2875,plain,
% 1.99/2.17 (~c3_1(a651)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2329, 2874])).
% 1.99/2.17 tff(2876,plain,
% 1.99/2.17 (~c1_1(a651)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2335, 2874])).
% 1.99/2.17 tff(2877,plain,
% 1.99/2.17 (c2_1(a651)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2323, 2874])).
% 1.99/2.17 tff(2878,plain,
% 1.99/2.17 (~c0_1(a651)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2348, 1586])).
% 1.99/2.17 tff(2879,plain,
% 1.99/2.17 (c3_1(a583)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[1972, 1586, 1749])).
% 1.99/2.17 tff(2880,plain,
% 1.99/2.17 ($false),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2499, 101, 1528, 1527, 2339, 785, 784, 2492, 45, 65, 2879, 2878])).
% 1.99/2.17 tff(2881,plain,(hskp8 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a651)) | (~c2_1(a590)) | (~c3_1(a590)) | c1_1(a651) | c0_1(a590) | hskp27 | c3_1(a651) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.17 tff(2882,plain,
% 1.99/2.17 (hskp8),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2881, 2877, 1527, 1528, 785, 784, 2876, 45, 1749, 2875, 1526])).
% 1.99/2.17 tff(2883,plain,
% 1.99/2.17 (c3_1(a593)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[469, 2882])).
% 1.99/2.17 tff(2884,plain,
% 1.99/2.17 (~c2_1(a593)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[510, 2882])).
% 1.99/2.17 tff(2885,plain,
% 1.99/2.17 (c1_1(a593)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[477, 2882])).
% 1.99/2.17 tff(2886,assumption,(~c1_1(a604)), introduced(assumption)).
% 1.99/2.17 tff(2887,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2888,plain,
% 1.99/2.17 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604))) <=> (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2889,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[2888])).
% 1.99/2.17 tff(2890,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604)))),
% 1.99/2.17 inference(transitivity,[status(thm)],[2889, 2887])).
% 1.99/2.17 tff(2891,plain,
% 1.99/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(2892,plain,
% 1.99/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 1.99/2.17 tff(2893,plain,
% 1.99/2.17 (~c1_1(a678)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2892, 101, 2186, 2184, 2886, 785, 784, 2340, 45, 65, 2403])).
% 1.99/2.17 tff(2894,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2895,plain,
% 1.99/2.17 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604))) <=> (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2896,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[2895])).
% 1.99/2.17 tff(2897,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604)))),
% 1.99/2.17 inference(transitivity,[status(thm)],[2896, 2894])).
% 1.99/2.17 tff(2898,plain,
% 1.99/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(2899,plain,
% 1.99/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 1.99/2.17 tff(2900,plain,
% 1.99/2.17 (~c0_1(a593)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2899, 101, 2886, 1771, 1780, 785, 784, 2340, 45, 65, 2403])).
% 1.99/2.17 tff(2901,plain,
% 1.99/2.17 ($false),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2488, 101, 2849, 2186, 2185, 1771, 1770, 32, 2900, 2893])).
% 1.99/2.17 tff(2902,plain,(c1_1(a604) | hskp17 | (~c0_1(a678)) | (~c2_1(a678)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a593)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a604) | c0_1(a590) | (~c2_1(a604)) | (~c3_1(a678))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.17 tff(2903,plain,
% 1.99/2.17 (c1_1(a604)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2902, 2885, 2186, 2185, 2849, 2884, 2883, 785, 784, 2340, 45, 2856, 2184])).
% 1.99/2.17 tff(2904,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2905,plain,
% 1.99/2.17 ((hskp15 | (~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590))) <=> (hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2906,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[2905])).
% 1.99/2.17 tff(2907,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.17 inference(transitivity,[status(thm)],[2906, 2904])).
% 1.99/2.17 tff(2908,plain,
% 1.99/2.17 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(2909,plain,
% 1.99/2.17 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 1.99/2.17 tff(2910,plain,
% 1.99/2.17 ((~c1_1(a590)) | (~c1_1(a604))),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2909, 101, 2355, 2354, 784, 45, 2552, 2856])).
% 1.99/2.17 tff(2911,plain,
% 1.99/2.17 (~c1_1(a590)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2910, 2903])).
% 1.99/2.17 tff(2912,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2913,plain,
% 1.99/2.17 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2914,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[2913])).
% 1.99/2.17 tff(2915,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.17 inference(transitivity,[status(thm)],[2914, 2912])).
% 1.99/2.17 tff(2916,plain,
% 1.99/2.17 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(2917,plain,
% 1.99/2.17 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2916, 2915])).
% 1.99/2.17 tff(2918,plain,
% 1.99/2.17 (hskp12 | (~c2_1(a604)) | (~c1_1(a604))),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2917, 101, 1528, 1527, 1526, 2340, 2589])).
% 1.99/2.17 tff(2919,plain,
% 1.99/2.17 (hskp12),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2918, 2903, 2856])).
% 1.99/2.17 tff(2920,plain,
% 1.99/2.17 (~c3_1(a600)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[675, 2919])).
% 1.99/2.17 tff(2921,plain,
% 1.99/2.17 (c2_1(a600)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[683, 2919])).
% 1.99/2.17 tff(2922,plain,
% 1.99/2.17 (c0_1(a600)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[691, 2919])).
% 1.99/2.17 tff(2923,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2924,plain,
% 1.99/2.17 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2925,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[2924])).
% 1.99/2.17 tff(2926,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604)))),
% 1.99/2.17 inference(transitivity,[status(thm)],[2925, 2923])).
% 1.99/2.17 tff(2927,plain,
% 1.99/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(2928,plain,
% 1.99/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2927, 2926])).
% 1.99/2.17 tff(2929,plain,
% 1.99/2.17 ($false),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2928, 101, 2903, 2354, 2922, 2921, 785, 784, 2340, 2920, 240, 2911])).
% 1.99/2.17 tff(2930,plain,(c3_1(a604) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a604) | c0_1(a590) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a678)) | (~c2_1(a678)) | hskp17 | (~c3_1(a678)) | hskp27 | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c1_1(a607)) | (~c0_1(a607)) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.17 tff(2931,plain,
% 1.99/2.17 (c3_1(a604)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2930, 1749, 784, 2340, 45, 1528, 1527, 1526, 2186, 2185, 2849, 2184, 785, 427, 426, 425, 2848, 2351, 22])).
% 1.99/2.17 tff(2932,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2933,plain,
% 1.99/2.17 ((hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2934,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[2933])).
% 1.99/2.17 tff(2935,plain,
% 1.99/2.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607)))),
% 1.99/2.17 inference(transitivity,[status(thm)],[2934, 2932])).
% 1.99/2.17 tff(2936,plain,
% 1.99/2.17 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(2937,plain,
% 1.99/2.17 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 1.99/2.17 tff(2938,plain,
% 1.99/2.17 (hskp27 | (~c3_1(a604)) | c2_1(a604)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2937, 101, 2848, 22, 2340, 495, 2351])).
% 1.99/2.17 tff(2939,plain,
% 1.99/2.17 (c2_1(a604)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2938, 2931, 1749])).
% 1.99/2.17 tff(2940,plain,
% 1.99/2.17 (~hskp13),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2418, 2931, 427, 426, 2380, 425, 2340, 2186, 2185, 2184, 1753, 1750, 2939])).
% 1.99/2.17 tff(2941,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2942,plain,
% 1.99/2.17 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(2943,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[2942])).
% 1.99/2.17 tff(2944,plain,
% 1.99/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604)))),
% 1.99/2.17 inference(transitivity,[status(thm)],[2943, 2941])).
% 1.99/2.17 tff(2945,plain,
% 1.99/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(2946,plain,
% 1.99/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[2945, 2944])).
% 1.99/2.17 tff(2947,plain,
% 1.99/2.17 (c0_1(a599)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2946, 101, 1528, 1527, 2410, 427, 2340, 425, 65, 2879, 2403])).
% 1.99/2.17 tff(2948,plain,
% 1.99/2.17 (hskp15),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[1990, 101, 1528, 1527, 426, 425, 1870, 2879, 2947])).
% 1.99/2.17 tff(2949,plain,
% 1.99/2.17 (c1_1(a604)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[1490, 2948])).
% 1.99/2.17 tff(2950,plain,
% 1.99/2.17 (hskp12),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2918, 2949, 2403])).
% 1.99/2.17 tff(2951,plain,
% 1.99/2.17 (~c3_1(a600)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[675, 2950])).
% 1.99/2.17 tff(2952,plain,
% 1.99/2.17 (c2_1(a600)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[683, 2950])).
% 1.99/2.17 tff(2953,plain,
% 1.99/2.17 (c0_1(a600)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[691, 2950])).
% 1.99/2.17 tff(2954,plain,
% 1.99/2.17 ($false),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2606, 101, 1749, 1586, 2953, 2952, 2951, 1957])).
% 1.99/2.17 tff(2955,plain,(hskp8 | hskp27 | (~c2_1(a604)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | c0_1(a604) | (~c3_1(a599)) | c1_1(a599) | (~c3_1(a604)) | (~c2_1(a599))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.17 tff(2956,plain,
% 1.99/2.17 (hskp8),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2955, 1749, 2939, 1528, 1527, 1526, 2340, 426, 425, 2931, 427])).
% 1.99/2.17 tff(2957,plain,
% 1.99/2.17 (c3_1(a593)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[469, 2956])).
% 1.99/2.17 tff(2958,plain,
% 1.99/2.17 (~c2_1(a593)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[510, 2956])).
% 1.99/2.17 tff(2959,plain,
% 1.99/2.17 (c1_1(a593)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[477, 2956])).
% 1.99/2.17 tff(2960,plain,
% 1.99/2.17 (c1_1(a604)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2902, 2959, 2186, 2185, 2849, 2958, 2957, 785, 784, 2340, 45, 2939, 2184])).
% 1.99/2.17 tff(2961,plain,
% 1.99/2.17 (hskp19 | hskp13 | (~c2_1(a604)) | (~c1_1(a604))),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2518, 101, 2340, 2429])).
% 1.99/2.17 tff(2962,plain,
% 1.99/2.17 (hskp19),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2961, 2960, 2940, 2939])).
% 1.99/2.17 tff(2963,plain,
% 1.99/2.17 (~c1_1(a617)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2453, 2962])).
% 1.99/2.17 tff(2964,plain,
% 1.99/2.17 (~c0_1(a617)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2459, 2962])).
% 1.99/2.17 tff(2965,plain,
% 1.99/2.17 (c2_1(a617)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2467, 2962])).
% 1.99/2.17 tff(2966,plain,
% 1.99/2.17 (~c1_1(a678)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2474, 101, 2186, 2184, 2965, 2931, 2964, 2963, 2340, 65, 2939])).
% 1.99/2.17 tff(2967,plain,
% 1.99/2.17 (~c0_1(a593)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2481, 101, 2965, 2931, 2959, 2957, 2964, 2963, 2340, 65, 2939])).
% 1.99/2.17 tff(2968,plain,
% 1.99/2.17 ($false),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[2488, 101, 2849, 2186, 2185, 2959, 2958, 32, 2967, 2966])).
% 1.99/2.18 tff(2969,plain,(hskp27 | hskp17 | (~c0_1(a678)) | (~c2_1(a678)) | c0_1(a604) | (~c3_1(a678)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a599)) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | c2_1(a606) | (~c1_1(a607)) | c2_1(a607) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.18 tff(2970,plain,
% 1.99/2.18 (hskp27),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2969, 2340, 2186, 2185, 2849, 2184, 785, 784, 45, 1528, 1527, 1526, 426, 425, 427, 2380, 1753, 1750, 2848, 22, 2351])).
% 1.99/2.18 tff(2971,plain,
% 1.99/2.18 (c3_1(a611)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[566, 2970])).
% 1.99/2.18 tff(2972,plain,
% 1.99/2.18 (c1_1(a611)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[574, 2970])).
% 1.99/2.18 tff(2973,plain,
% 1.99/2.18 (c0_1(a611)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[582, 2970])).
% 1.99/2.18 tff(2974,plain,
% 1.99/2.18 (c0_1(a599)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2733, 101, 2973, 2972, 2971, 427, 785, 784, 425, 45, 65])).
% 1.99/2.18 tff(2975,plain,
% 1.99/2.18 (hskp15),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2741, 101, 2973, 2972, 2971, 426, 425, 1870, 2974])).
% 1.99/2.18 tff(2976,plain,
% 1.99/2.18 (c1_1(a604)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1490, 2975])).
% 1.99/2.18 tff(2977,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(2978,plain,
% 1.99/2.18 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(2979,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[2978])).
% 1.99/2.18 tff(2980,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.18 inference(transitivity,[status(thm)],[2979, 2977])).
% 1.99/2.18 tff(2981,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(2982,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[2981, 2980])).
% 1.99/2.18 tff(2983,plain,
% 1.99/2.18 (c2_1(a604) | (~c1_1(a604))),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2982, 101, 2849, 910, 909, 2340, 906, 32])).
% 1.99/2.18 tff(2984,plain,
% 1.99/2.18 (c2_1(a604)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2983, 2976])).
% 1.99/2.18 tff(2985,plain,
% 1.99/2.18 (c3_1(a604)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1482, 2975])).
% 1.99/2.18 tff(2986,plain,
% 1.99/2.18 (~hskp13),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2418, 2985, 427, 426, 2380, 425, 2340, 2186, 2185, 2184, 1753, 1750, 2984])).
% 1.99/2.18 tff(2987,plain,
% 1.99/2.18 (hskp19),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2961, 2986, 2976, 2984])).
% 1.99/2.18 tff(2988,plain,
% 1.99/2.18 (~c1_1(a617)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2453, 2987])).
% 1.99/2.18 tff(2989,plain,
% 1.99/2.18 (~c0_1(a617)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2459, 2987])).
% 1.99/2.18 tff(2990,plain,
% 1.99/2.18 (c2_1(a617)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2467, 2987])).
% 1.99/2.18 tff(2991,plain,
% 1.99/2.18 ($false),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2771, 101, 2973, 2972, 2971, 2990, 2985, 2989, 2988, 2340, 65, 2984])).
% 1.99/2.18 tff(2992,plain,(c0_1(a604) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a606)) | c1_1(a599) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a606)) | c2_1(a606) | hskp17 | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a587) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c1_1(a607)) | c2_1(a607) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.18 tff(2993,plain,
% 1.99/2.18 (c0_1(a604)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2992, 2809, 2810, 2847, 2806, 2160, 2152, 2144, 2845, 2844, 223, 2832, 2831, 2830, 2808, 2807, 2796, 2842, 2841, 2840, 2774, 22, 2811])).
% 1.99/2.18 tff(2994,plain,
% 1.99/2.18 (~hskp15),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1474, 2993])).
% 1.99/2.18 tff(2995,plain,
% 1.99/2.18 (hskp4),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2781, 2351, 2848])).
% 1.99/2.18 tff(2996,plain,
% 1.99/2.18 (~c2_1(a588)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[115, 2995])).
% 1.99/2.18 tff(2997,plain,
% 1.99/2.18 (~c1_1(a588)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[121, 2995])).
% 1.99/2.18 tff(2998,plain,
% 1.99/2.18 (~c3_1(a588)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2820, 101, 2186, 2185, 2184, 2848, 22, 2997, 2996, 1010, 2351])).
% 1.99/2.18 tff(2999,plain,
% 1.99/2.18 (hskp3),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2828, 2351, 2848])).
% 1.99/2.18 tff(3000,plain,
% 1.99/2.18 (~c1_1(a587)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[855, 2999])).
% 1.99/2.18 tff(3001,plain,
% 1.99/2.18 (c2_1(a587)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[863, 2999])).
% 1.99/2.18 tff(3002,plain,
% 1.99/2.18 (c0_1(a587)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[871, 2999])).
% 1.99/2.18 tff(3003,plain,
% 1.99/2.18 (hskp26),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2838, 101, 3002, 3001, 2997, 2996, 3000, 905, 2998])).
% 1.99/2.18 tff(3004,plain,
% 1.99/2.18 (c2_1(a583)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[364, 3003])).
% 1.99/2.18 tff(3005,plain,
% 1.99/2.18 (c1_1(a583)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[330, 3003])).
% 1.99/2.18 tff(3006,plain,
% 1.99/2.18 (c0_1(a583)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[338, 3003])).
% 1.99/2.18 tff(3007,assumption,(hskp9), introduced(assumption)).
% 1.99/2.18 tff(3008,plain,
% 1.99/2.18 (~c3_1(a595)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1370, 3007])).
% 1.99/2.18 tff(3009,plain,
% 1.99/2.18 (~c0_1(a595)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1382, 3007])).
% 1.99/2.18 tff(3010,plain,
% 1.99/2.18 (~c1_1(a595)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1376, 3007])).
% 1.99/2.18 tff(3011,plain,
% 1.99/2.18 ($false),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2721, 3010, 3009, 22, 33, 3008, 1749, 1528, 1527, 1526, 785, 784, 45, 2185, 2184, 2186])).
% 1.99/2.18 tff(3012,plain,((~hskp9) | c2_1(a607) | c3_1(a607) | hskp27 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.18 tff(3013,plain,
% 1.99/2.18 (~hskp9),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3012, 1749, 33, 22, 3006, 3005, 3004, 785, 784, 45, 2185, 2184, 2186])).
% 1.99/2.18 tff(3014,plain,
% 1.99/2.18 (hskp9 | c0_1(a599)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1828, 101, 3006, 3005, 3004, 426, 425, 276])).
% 1.99/2.18 tff(3015,plain,
% 1.99/2.18 (c0_1(a599)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3014, 3013])).
% 1.99/2.18 tff(3016,assumption,(~hskp15), introduced(assumption)).
% 1.99/2.18 tff(3017,plain,
% 1.99/2.18 (hskp25),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2873, 3016, 2848, 2351])).
% 1.99/2.18 tff(3018,plain,
% 1.99/2.18 (~c3_1(a651)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2329, 3017])).
% 1.99/2.18 tff(3019,plain,
% 1.99/2.18 (~c1_1(a651)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2335, 3017])).
% 1.99/2.18 tff(3020,plain,
% 1.99/2.18 (c2_1(a651)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2323, 3017])).
% 1.99/2.18 tff(3021,plain,
% 1.99/2.18 (hskp8),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2881, 1749, 3005, 3006, 785, 784, 3020, 45, 3019, 3018, 3004])).
% 1.99/2.18 tff(3022,plain,
% 1.99/2.18 (c3_1(a593)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[469, 3021])).
% 1.99/2.18 tff(3023,plain,
% 1.99/2.18 (c1_1(a593)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[477, 3021])).
% 1.99/2.18 tff(3024,plain,
% 1.99/2.18 ((~c0_1(a593)) | (~c0_1(a599))),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2361, 101, 3016, 426, 3023, 3022, 425, 1870])).
% 1.99/2.18 tff(3025,plain,
% 1.99/2.18 (~c0_1(a593)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3024, 3015])).
% 1.99/2.18 tff(3026,plain,
% 1.99/2.18 (~c2_1(a593)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[510, 3021])).
% 1.99/2.18 tff(3027,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3028,plain,
% 1.99/2.18 ((hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593))) <=> (hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3029,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[3028])).
% 1.99/2.18 tff(3030,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607)))),
% 1.99/2.18 inference(transitivity,[status(thm)],[3029, 3027])).
% 1.99/2.18 tff(3031,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(3032,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[3031, 3030])).
% 1.99/2.18 tff(3033,plain,
% 1.99/2.18 ($false),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3032, 101, 1749, 3022, 2848, 22, 3026, 495, 3025, 2351])).
% 1.99/2.18 tff(3034,plain,(hskp27 | (~c1_1(a607)) | c2_1(a607) | (~c0_1(a607)) | hskp15 | (~c3_1(a599)) | c1_1(a599) | c3_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.18 tff(3035,plain,
% 1.99/2.18 (hskp27),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3034, 2774, 22, 2811, 2994, 2810, 2806, 33, 2808, 2807, 2796, 2152, 2144, 2160])).
% 1.99/2.18 tff(3036,plain,
% 1.99/2.18 (c3_1(a611)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[566, 3035])).
% 1.99/2.18 tff(3037,plain,
% 1.99/2.18 (c1_1(a611)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[574, 3035])).
% 1.99/2.18 tff(3038,plain,
% 1.99/2.18 (c0_1(a611)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[582, 3035])).
% 1.99/2.18 tff(3039,plain,
% 1.99/2.18 (c0_1(a599)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2733, 101, 3038, 3037, 3036, 2809, 2808, 2807, 2806, 2796, 65])).
% 1.99/2.18 tff(3040,plain,
% 1.99/2.18 ($false),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2741, 101, 2994, 3038, 3037, 3036, 2810, 2806, 1870, 3039])).
% 1.99/2.18 tff(3041,plain,(c3_1(a607) | c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.99/2.18 tff(3042,plain,
% 1.99/2.18 (c3_1(a607)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3041, 22, 44])).
% 1.99/2.18 tff(3043,assumption,(~c3_1(a590)), introduced(assumption)).
% 1.99/2.18 tff(3044,plain,
% 1.99/2.18 (~hskp6),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[614, 3043])).
% 1.99/2.18 tff(3045,plain,
% 1.99/2.18 (~hskp4),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[138, 3044, 44])).
% 1.99/2.18 tff(3046,assumption,(~c2_1(a590)), introduced(assumption)).
% 1.99/2.18 tff(3047,plain,
% 1.99/2.18 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3048,plain,
% 1.99/2.18 ((hskp14 | hskp4 | (~ndr1_0) | c2_1(a590) | c0_1(a590) | c3_1(a590)) <=> (hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3049,plain,
% 1.99/2.18 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a590) | c0_1(a590) | c3_1(a590))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0)))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[3048])).
% 1.99/2.18 tff(3050,plain,
% 1.99/2.18 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a590) | c0_1(a590) | c3_1(a590))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0))),
% 1.99/2.18 inference(transitivity,[status(thm)],[3049, 3047])).
% 1.99/2.18 tff(3051,plain,
% 1.99/2.18 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a590) | c0_1(a590) | c3_1(a590))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(3052,plain,
% 1.99/2.18 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0)),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[3051, 3050])).
% 1.99/2.18 tff(3053,plain,
% 1.99/2.18 (hskp14 | hskp4 | c2_1(a590) | c3_1(a590)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3052, 101, 45, 149])).
% 1.99/2.18 tff(3054,plain,
% 1.99/2.18 (hskp14),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3053, 3046, 3045, 3043])).
% 1.99/2.18 tff(3055,plain,
% 1.99/2.18 (~c1_1(a603)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[162, 3054])).
% 1.99/2.18 tff(3056,plain,
% 1.99/2.18 (c0_1(a603)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[170, 3054])).
% 1.99/2.18 tff(3057,plain,
% 1.99/2.18 (c2_1(a603)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[177, 101, 44, 3044, 3056, 3055, 43])).
% 1.99/2.18 tff(3058,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3059,plain,
% 1.99/2.18 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a590) | c0_1(a590) | c2_1(a590)) <=> (hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3060,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a590) | c0_1(a590) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[3059])).
% 1.99/2.18 tff(3061,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a590) | c0_1(a590) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 1.99/2.18 inference(transitivity,[status(thm)],[3060, 3058])).
% 1.99/2.18 tff(3062,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a590) | c0_1(a590) | c2_1(a590))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(3063,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 1.99/2.18 tff(3064,plain,
% 1.99/2.18 (hskp11 | c2_1(a590)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3063, 101, 2160, 2152, 2144, 3043, 45, 250])).
% 1.99/2.18 tff(3065,plain,
% 1.99/2.18 (hskp11),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3064, 3046])).
% 1.99/2.18 tff(3066,plain,
% 1.99/2.18 (~c1_1(a599)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[395, 3065])).
% 1.99/2.18 tff(3067,plain,
% 1.99/2.18 (~c3_1(a603)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[193, 3054])).
% 1.99/2.18 tff(3068,plain,
% 1.99/2.18 (c3_1(a599)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[389, 3065])).
% 1.99/2.18 tff(3069,plain,
% 1.99/2.18 (c2_1(a599)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[403, 3065])).
% 1.99/2.18 tff(3070,plain,
% 1.99/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3071,plain,
% 1.99/2.18 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590))) <=> (c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3072,plain,
% 1.99/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[3071])).
% 1.99/2.18 tff(3073,plain,
% 1.99/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.18 inference(transitivity,[status(thm)],[3072, 3070])).
% 1.99/2.18 tff(3074,plain,
% 1.99/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(3075,plain,
% 1.99/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 1.99/2.18 tff(3076,plain,
% 1.99/2.18 (~c1_1(a590)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3075, 101, 3056, 3069, 3068, 3043, 3067, 3066, 45, 240, 3057])).
% 1.99/2.18 tff(3077,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3078,plain,
% 1.99/2.18 ((hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a590) | c1_1(a590) | c2_1(a590)) <=> (hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3079,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a590) | c1_1(a590) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[3078])).
% 1.99/2.18 tff(3080,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a590) | c1_1(a590) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.18 inference(transitivity,[status(thm)],[3079, 3077])).
% 1.99/2.18 tff(3081,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a590) | c1_1(a590) | c2_1(a590))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(3082,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 1.99/2.18 tff(3083,plain,
% 1.99/2.18 (hskp26),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3082, 101, 3056, 3046, 3043, 3055, 905, 3057, 3076])).
% 1.99/2.18 tff(3084,plain,
% 1.99/2.18 (c2_1(a583)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[364, 3083])).
% 1.99/2.18 tff(3085,plain,
% 1.99/2.18 (c1_1(a583)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[330, 3083])).
% 1.99/2.18 tff(3086,plain,
% 1.99/2.18 (c0_1(a583)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[338, 3083])).
% 1.99/2.18 tff(3087,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3088,plain,
% 1.99/2.18 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a590) | c1_1(a590) | c0_1(a590)) <=> (hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3089,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[3088])).
% 1.99/2.18 tff(3090,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)))),
% 1.99/2.18 inference(transitivity,[status(thm)],[3089, 3087])).
% 1.99/2.18 tff(3091,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a590) | c1_1(a590) | c0_1(a590))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(3092,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[3091, 3090])).
% 1.99/2.18 tff(3093,plain,
% 1.99/2.18 (hskp2),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3092, 101, 3043, 3055, 3067, 45, 188, 3057, 3076])).
% 1.99/2.18 tff(3094,plain,
% 1.99/2.18 (~c3_1(a586)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[206, 3093])).
% 1.99/2.18 tff(3095,plain,
% 1.99/2.18 (c2_1(a586)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1357, 3093])).
% 1.99/2.18 tff(3096,plain,
% 1.99/2.18 (c1_1(a586)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[214, 3093])).
% 1.99/2.18 tff(3097,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3098,plain,
% 1.99/2.18 ((hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599))) <=> (hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3099,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[3098])).
% 1.99/2.18 tff(3100,plain,
% 1.99/2.18 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.99/2.18 inference(transitivity,[status(thm)],[3099, 3097])).
% 1.99/2.18 tff(3101,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(3102,plain,
% 1.99/2.18 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[3101, 3100])).
% 1.99/2.18 tff(3103,plain,
% 1.99/2.18 (hskp28),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3102, 101, 3069, 3068, 3096, 3095, 3066, 3094, 1625])).
% 1.99/2.18 tff(3104,plain,
% 1.99/2.18 (c3_1(a612)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1040, 3103])).
% 1.99/2.18 tff(3105,plain,
% 1.99/2.18 (c2_1(a612)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1048, 3103])).
% 1.99/2.18 tff(3106,plain,
% 1.99/2.18 (c1_1(a612)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1321, 3103])).
% 1.99/2.18 tff(3107,plain,
% 1.99/2.18 (hskp10),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1418, 101, 3106, 3105, 3104, 3086, 3085, 3084, 21])).
% 1.99/2.18 tff(3108,plain,
% 1.99/2.18 (~c1_1(a598)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[827, 3107])).
% 1.99/2.18 tff(3109,plain,
% 1.99/2.18 (c0_1(a598)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[808, 3107])).
% 1.99/2.18 tff(3110,plain,
% 1.99/2.18 (c2_1(a598)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[1427, 101, 44, 3044, 3109, 3108, 43])).
% 1.99/2.18 tff(3111,plain,
% 1.99/2.18 (c0_1(a586)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2177, 101, 3056, 3069, 3068, 3096, 3067, 3066, 3094, 240, 3057])).
% 1.99/2.18 tff(3112,plain,
% 1.99/2.18 (hskp17 | (~c0_1(a586))),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[229, 101, 3045, 3096, 3094, 55])).
% 1.99/2.18 tff(3113,plain,
% 1.99/2.18 (hskp17),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3112, 3111])).
% 1.99/2.18 tff(3114,plain,
% 1.99/2.18 (~c1_1(a607)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[263, 3113])).
% 1.99/2.18 tff(3115,plain,
% 1.99/2.18 (~c0_1(a607)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[108, 3114, 3044])).
% 1.99/2.18 tff(3116,plain,
% 1.99/2.18 (hskp8 | hskp6 | c1_1(a607) | c0_1(a607)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[2057, 101, 3042, 414])).
% 1.99/2.18 tff(3117,plain,
% 1.99/2.18 (hskp8),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[3116, 3114, 3044, 3115])).
% 1.99/2.18 tff(3118,plain,
% 1.99/2.18 (~c2_1(a593)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[510, 3117])).
% 1.99/2.18 tff(3119,plain,
% 1.99/2.18 (c1_1(a593)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[477, 3117])).
% 1.99/2.18 tff(3120,plain,
% 1.99/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3121,plain,
% 1.99/2.18 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(3122,plain,
% 1.99/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607))))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3121])).
% 1.99/2.19 tff(3123,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607)))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3122, 3120])).
% 1.99/2.19 tff(3124,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3125,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607))),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3124, 3123])).
% 1.99/2.19 tff(3126,plain,
% 1.99/2.19 (~c0_1(a593)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3125, 101, 2160, 2152, 2144, 3042, 3119, 3114, 22, 3118, 1010])).
% 1.99/2.19 tff(3127,plain,
% 1.99/2.19 (c3_1(a593)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[469, 3117])).
% 1.99/2.19 tff(3128,plain,
% 1.99/2.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3129,plain,
% 1.99/2.19 ((hskp1 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c3_1(a590) | c1_1(a590) | c0_1(a590)) <=> (hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3130,plain,
% 1.99/2.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c3_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593))))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3129])).
% 1.99/2.19 tff(3131,plain,
% 1.99/2.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c3_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3130, 3128])).
% 1.99/2.19 tff(3132,plain,
% 1.99/2.19 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c3_1(a590) | c1_1(a590) | c0_1(a590))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3133,plain,
% 1.99/2.19 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593))),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3132, 3131])).
% 1.99/2.19 tff(3134,plain,
% 1.99/2.19 (hskp1),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3133, 101, 3119, 3127, 3043, 45, 1438, 3126, 3076])).
% 1.99/2.19 tff(3135,plain,
% 1.99/2.19 (~c0_1(a585)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[1145, 3134])).
% 1.99/2.19 tff(3136,plain,
% 1.99/2.19 (c2_1(a585)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[1153, 3134])).
% 1.99/2.19 tff(3137,plain,
% 1.99/2.19 (c1_1(a585)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[1161, 3134])).
% 1.99/2.19 tff(3138,plain,
% 1.99/2.19 (c3_1(a598)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[800, 3107])).
% 1.99/2.19 tff(3139,plain,
% 1.99/2.19 ($false),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[1508, 101, 3042, 3109, 3138, 3137, 3136, 3114, 22, 3135, 11, 3110])).
% 1.99/2.19 tff(3140,plain,(c2_1(a590) | c2_1(a607) | hskp22 | c3_1(a590) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.19 tff(3141,plain,
% 1.99/2.19 (c2_1(a590)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3140, 3043, 44, 22, 45])).
% 1.99/2.19 tff(3142,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3143,plain,
% 1.99/2.19 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3144,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607))))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3143])).
% 1.99/2.19 tff(3145,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3144, 3142])).
% 1.99/2.19 tff(3146,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3147,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607))),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 1.99/2.19 tff(3148,plain,
% 1.99/2.19 (~c1_1(a590)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3147, 101, 2186, 2185, 2184, 303, 785, 66, 22, 45, 11])).
% 1.99/2.19 tff(3149,plain,
% 1.99/2.19 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3150,plain,
% 1.99/2.19 ((hskp6 | hskp5 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3151,plain,
% 1.99/2.19 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590)))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3150])).
% 1.99/2.19 tff(3152,plain,
% 1.99/2.19 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3151, 3149])).
% 1.99/2.19 tff(3153,plain,
% 1.99/2.19 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3154,plain,
% 1.99/2.19 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590)),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 1.99/2.19 tff(3155,plain,
% 1.99/2.19 (hskp6 | hskp5 | (~c2_1(a590)) | c1_1(a590)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3154, 101, 45, 528])).
% 1.99/2.19 tff(3156,plain,
% 1.99/2.19 (hskp5),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3155, 3148, 67, 785])).
% 1.99/2.19 tff(3157,plain,
% 1.99/2.19 (~c2_1(a589)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[541, 3156])).
% 1.99/2.19 tff(3158,plain,
% 1.99/2.19 (c1_1(a589)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[549, 3156])).
% 1.99/2.19 tff(3159,plain,
% 1.99/2.19 (c0_1(a589)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[557, 3156])).
% 1.99/2.19 tff(3160,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3161,plain,
% 1.99/2.19 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3162,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607))))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3161])).
% 1.99/2.19 tff(3163,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607)))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3162, 3160])).
% 1.99/2.19 tff(3164,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3165,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607))),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 1.99/2.19 tff(3166,plain,
% 1.99/2.19 ($false),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3165, 101, 2186, 2185, 2184, 303, 3159, 3158, 66, 22, 3157, 1010])).
% 1.99/2.19 tff(3167,plain,(c1_1(a607) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c3_1(a607)) | c2_1(a607) | hskp6 | (~c2_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.19 tff(3168,plain,
% 1.99/2.19 (c1_1(a607)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3167, 3044, 2152, 2144, 3042, 22, 2160, 3141, 45])).
% 1.99/2.19 tff(3169,plain,
% 1.99/2.19 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3170,plain,
% 1.99/2.19 ((hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3171,plain,
% 1.99/2.19 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607))))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3170])).
% 1.99/2.19 tff(3172,plain,
% 1.99/2.19 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3171, 3169])).
% 1.99/2.19 tff(3173,plain,
% 1.99/2.19 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3174,plain,
% 1.99/2.19 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607))),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 1.99/2.19 tff(3175,plain,
% 1.99/2.19 (hskp14 | (~c1_1(a607)) | (~c3_1(a607))),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3174, 101, 2160, 2152, 2144, 22, 505])).
% 1.99/2.19 tff(3176,plain,
% 1.99/2.19 (hskp14),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3175, 3168, 3042])).
% 1.99/2.19 tff(3177,plain,
% 1.99/2.19 (~c1_1(a603)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[162, 3176])).
% 1.99/2.19 tff(3178,plain,
% 1.99/2.19 (c0_1(a603)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[170, 3176])).
% 1.99/2.19 tff(3179,plain,
% 1.99/2.19 (c2_1(a603)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[177, 101, 44, 3044, 3178, 3177, 43])).
% 1.99/2.19 tff(3180,plain,
% 1.99/2.19 (~hskp17),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[263, 3168])).
% 1.99/2.19 tff(3181,plain,
% 1.99/2.19 (~c3_1(a603)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[193, 3176])).
% 1.99/2.19 tff(3182,plain,
% 1.99/2.19 (hskp26),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[381, 1515])).
% 1.99/2.19 tff(3183,plain,
% 1.99/2.19 (c0_1(a583)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[338, 3182])).
% 1.99/2.19 tff(3184,plain,
% 1.99/2.19 (c1_1(a583)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[330, 3182])).
% 1.99/2.19 tff(3185,plain,
% 1.99/2.19 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3186,plain,
% 1.99/2.19 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583))) <=> (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3187,plain,
% 1.99/2.19 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583))))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3186])).
% 1.99/2.19 tff(3188,plain,
% 1.99/2.19 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3187, 3185])).
% 1.99/2.19 tff(3189,plain,
% 1.99/2.19 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3190,plain,
% 1.99/2.19 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583))),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 1.99/2.19 tff(3191,plain,
% 1.99/2.19 (c3_1(a583)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3190, 101, 2849, 3045, 3183, 3184, 55])).
% 1.99/2.19 tff(3192,plain,
% 1.99/2.19 (c2_1(a583)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[364, 3182])).
% 1.99/2.19 tff(3193,plain,
% 1.99/2.19 (hskp10),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[1876, 101, 3183, 3184, 3192, 21, 3191])).
% 1.99/2.19 tff(3194,plain,
% 1.99/2.19 (~c1_1(a598)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[827, 3193])).
% 1.99/2.19 tff(3195,plain,
% 1.99/2.19 (c3_1(a598)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[800, 3193])).
% 1.99/2.19 tff(3196,plain,
% 1.99/2.19 (c0_1(a598)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[808, 3193])).
% 1.99/2.19 tff(3197,plain,
% 1.99/2.19 (hskp23),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[1565, 1515, 101, 3196, 3195, 3194, 1525])).
% 1.99/2.19 tff(3198,plain,
% 1.99/2.19 (~c1_1(a636)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[439, 3197])).
% 1.99/2.19 tff(3199,plain,
% 1.99/2.19 (~c0_1(a636)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[445, 3197])).
% 1.99/2.19 tff(3200,plain,
% 1.99/2.19 (c3_1(a636)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[453, 3197])).
% 1.99/2.19 tff(3201,assumption,(c2_1(a636)), introduced(assumption)).
% 1.99/2.19 tff(3202,assumption,(c3_1(a583)), introduced(assumption)).
% 1.99/2.19 tff(3203,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3204,plain,
% 1.99/2.19 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636))) <=> (c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3205,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636))))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3204])).
% 1.99/2.19 tff(3206,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3205, 3203])).
% 1.99/2.19 tff(3207,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3208,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636))),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3207, 3206])).
% 1.99/2.19 tff(3209,plain,
% 1.99/2.19 ($false),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3208, 101, 1528, 1527, 659, 658, 657, 65, 3202, 3201])).
% 1.99/2.19 tff(3210,plain,(c1_1(a636) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | c0_1(a636) | (~c3_1(a583)) | (~c2_1(a636))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.19 tff(3211,plain,
% 1.99/2.19 (~c2_1(a636)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3210, 3200, 3184, 3191, 3199, 3198, 3183])).
% 1.99/2.19 tff(3212,plain,
% 1.99/2.19 (c2_1(a598)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[1427, 101, 44, 3044, 3196, 3194, 43])).
% 1.99/2.19 tff(3213,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3214,plain,
% 1.99/2.19 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590))) <=> (c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3215,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 1.99/2.19 inference(monotonicity,[status(thm)],[3214])).
% 1.99/2.19 tff(3216,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.19 inference(transitivity,[status(thm)],[3215, 3213])).
% 1.99/2.19 tff(3217,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))),
% 1.99/2.19 inference(quant_inst,[status(thm)],[])).
% 1.99/2.19 tff(3218,plain,
% 1.99/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603))),
% 1.99/2.19 inference(modus_ponens,[status(thm)],[3217, 3216])).
% 1.99/2.19 tff(3219,plain,
% 1.99/2.19 (~c1_1(a590)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3218, 101, 919, 3195, 3043, 907, 3194, 45, 240, 3212, 920])).
% 1.99/2.19 tff(3220,plain,
% 1.99/2.19 (hskp5),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[3155, 3219, 3044, 785])).
% 1.99/2.19 tff(3221,plain,
% 1.99/2.19 (~c2_1(a589)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[541, 3220])).
% 1.99/2.19 tff(3222,plain,
% 1.99/2.19 (c1_1(a589)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[549, 3220])).
% 1.99/2.19 tff(3223,plain,
% 1.99/2.19 (c0_1(a589)),
% 1.99/2.19 inference(unit_resolution,[status(thm)],[557, 3220])).
% 1.99/2.19 tff(3224,plain,
% 1.99/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636))),
% 1.99/2.19 inference(rewrite,[status(thm)],[])).
% 1.99/2.19 tff(3225,plain,
% 1.99/2.19 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636))) <=> (c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3226,plain,
% 1.99/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636)))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3225])).
% 1.99/2.20 tff(3227,plain,
% 1.99/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3226, 3224])).
% 1.99/2.20 tff(3228,plain,
% 1.99/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)))),
% 1.99/2.20 inference(quant_inst,[status(thm)],[])).
% 1.99/2.20 tff(3229,plain,
% 1.99/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636)),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 1.99/2.20 tff(3230,plain,
% 1.99/2.20 ($false),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3229, 101, 3200, 3196, 3195, 3223, 3222, 3198, 3221, 1010, 3212, 3211])).
% 1.99/2.20 tff(3231,plain,(hskp11 | (~c2_1(a590)) | c0_1(a590) | (~c0_1(a603)) | c3_1(a590) | c3_1(a603) | (~c2_1(a603)) | hskp22 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.99/2.20 tff(3232,plain,
% 1.99/2.20 (hskp11),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3231, 3141, 45, 3178, 3043, 3181, 3179, 44, 3180])).
% 1.99/2.20 tff(3233,plain,
% 1.99/2.20 (~c1_1(a599)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[395, 3232])).
% 1.99/2.20 tff(3234,plain,
% 1.99/2.20 (c3_1(a599)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[389, 3232])).
% 1.99/2.20 tff(3235,plain,
% 1.99/2.20 (c2_1(a599)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[403, 3232])).
% 1.99/2.20 tff(3236,plain,
% 1.99/2.20 (~c1_1(a590)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3075, 101, 3178, 3235, 3234, 3043, 3181, 3233, 45, 240, 3179])).
% 1.99/2.20 tff(3237,plain,
% 1.99/2.20 (hskp2 | c1_1(a590) | (~c2_1(a603))),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3092, 101, 3043, 3177, 3181, 45, 188])).
% 1.99/2.20 tff(3238,plain,
% 1.99/2.20 (hskp2),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3237, 3236, 3179])).
% 1.99/2.20 tff(3239,plain,
% 1.99/2.20 (~c3_1(a586)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[206, 3238])).
% 1.99/2.20 tff(3240,plain,
% 1.99/2.20 (c1_1(a586)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[214, 3238])).
% 1.99/2.20 tff(3241,plain,
% 1.99/2.20 (~c0_1(a586)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[229, 101, 3180, 3045, 3240, 3239, 55])).
% 1.99/2.20 tff(3242,plain,
% 1.99/2.20 ($false),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[2177, 101, 3178, 3235, 3234, 3240, 3181, 3233, 3239, 240, 3179, 3241])).
% 1.99/2.20 tff(3243,plain,(c3_1(a590) | c0_1(a590) | hskp22 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.20 tff(3244,plain,
% 1.99/2.20 (c3_1(a590)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3243, 45, 44, 22])).
% 1.99/2.20 tff(3245,plain,
% 1.99/2.20 (~hskp6),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[622, 3046])).
% 1.99/2.20 tff(3246,plain,
% 1.99/2.20 (~c0_1(a607)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[108, 66, 67])).
% 1.99/2.20 tff(3247,plain,
% 1.99/2.20 (hskp8),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3116, 66, 67, 3246])).
% 1.99/2.20 tff(3248,plain,
% 1.99/2.20 (~c2_1(a593)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[510, 3247])).
% 1.99/2.20 tff(3249,plain,
% 1.99/2.20 (c3_1(a593)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[469, 3247])).
% 1.99/2.20 tff(3250,plain,
% 1.99/2.20 (c1_1(a593)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[477, 3247])).
% 1.99/2.20 tff(3251,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3252,plain,
% 1.99/2.20 ((hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3253,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593))))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3252])).
% 1.99/2.20 tff(3254,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3253, 3251])).
% 1.99/2.20 tff(3255,plain,
% 1.99/2.20 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 1.99/2.20 inference(quant_inst,[status(thm)],[])).
% 1.99/2.20 tff(3256,plain,
% 1.99/2.20 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593))),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3255, 3254])).
% 1.99/2.20 tff(3257,plain,
% 1.99/2.20 (hskp14),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3256, 101, 2160, 2152, 2144, 3250, 3249, 3248, 505])).
% 1.99/2.20 tff(3258,plain,
% 1.99/2.20 (hskp3),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[311, 3257, 3042, 66, 22])).
% 1.99/2.20 tff(3259,plain,
% 1.99/2.20 (~c1_1(a587)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[855, 3258])).
% 1.99/2.20 tff(3260,plain,
% 1.99/2.20 (~c1_1(a603)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[162, 3257])).
% 1.99/2.20 tff(3261,plain,
% 1.99/2.20 (c0_1(a603)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[170, 3257])).
% 1.99/2.20 tff(3262,plain,
% 1.99/2.20 (~c3_1(a603)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[193, 3257])).
% 1.99/2.20 tff(3263,plain,
% 1.99/2.20 (c0_1(a587)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[871, 3258])).
% 1.99/2.20 tff(3264,plain,
% 1.99/2.20 (c2_1(a587)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[863, 3258])).
% 1.99/2.20 tff(3265,plain,
% 1.99/2.20 ($false),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1391, 3264, 3263, 22, 3042, 660, 66, 3262, 3261, 3260, 3259])).
% 1.99/2.20 tff(3266,plain,(c1_1(a607) | c2_1(a607) | hskp26 | hskp6 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.99/2.20 tff(3267,plain,
% 1.99/2.20 (c1_1(a607)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3266, 660, 22, 3245, 44])).
% 1.99/2.20 tff(3268,plain,
% 1.99/2.20 (hskp14),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3175, 3267, 3042])).
% 1.99/2.20 tff(3269,plain,
% 1.99/2.20 (~c1_1(a603)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[162, 3268])).
% 1.99/2.20 tff(3270,plain,
% 1.99/2.20 (c0_1(a603)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[170, 3268])).
% 1.99/2.20 tff(3271,plain,
% 1.99/2.20 (c2_1(a603)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[177, 101, 44, 3245, 3270, 3269, 43])).
% 1.99/2.20 tff(3272,plain,
% 1.99/2.20 (~hskp17),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[263, 3267])).
% 1.99/2.20 tff(3273,plain,
% 1.99/2.20 (^[U: $i] : refl((hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.99/2.20 inference(bind,[status(th)],[])).
% 1.99/2.20 tff(3274,plain,
% 1.99/2.20 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.99/2.20 inference(quant_intro,[status(thm)],[3273])).
% 1.99/2.20 tff(3275,plain,
% 1.99/2.20 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3276,plain,
% 1.99/2.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp17) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp17) <=> (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.99/2.20 inference(bind,[status(th)],[])).
% 1.99/2.20 tff(3277,plain,
% 1.99/2.20 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp17) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.99/2.20 inference(quant_intro,[status(thm)],[3276])).
% 1.99/2.20 tff(3278,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.99/2.20 tff(3279,plain,
% 1.99/2.20 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3278, 3277])).
% 1.99/2.20 tff(3280,plain,
% 1.99/2.20 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3279, 3275])).
% 1.99/2.20 tff(3281,plain,(
% 1.99/2.20 ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.99/2.20 inference(skolemize,[status(sab)],[3280])).
% 1.99/2.20 tff(3282,plain,
% 1.99/2.20 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3281, 3274])).
% 1.99/2.20 tff(3283,plain,
% 1.99/2.20 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3284,plain,
% 1.99/2.20 ((hskp17 | hskp3 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c1_1(a607))) <=> (hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3285,plain,
% 1.99/2.20 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607))))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3284])).
% 1.99/2.20 tff(3286,plain,
% 1.99/2.20 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607)))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3285, 3283])).
% 1.99/2.20 tff(3287,plain,
% 1.99/2.20 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))),
% 1.99/2.20 inference(quant_inst,[status(thm)],[])).
% 1.99/2.20 tff(3288,plain,
% 1.99/2.20 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607))),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 1.99/2.20 tff(3289,plain,
% 1.99/2.20 (hskp17 | hskp3 | (~c1_1(a607)) | (~c3_1(a607))),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3288, 101, 22, 3282])).
% 1.99/2.20 tff(3290,plain,
% 1.99/2.20 (hskp3),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3289, 3272, 3042, 3267])).
% 1.99/2.20 tff(3291,plain,
% 1.99/2.20 (~c1_1(a587)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[855, 3290])).
% 1.99/2.20 tff(3292,plain,
% 1.99/2.20 (c2_1(a587)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[863, 3290])).
% 1.99/2.20 tff(3293,plain,
% 1.99/2.20 (c0_1(a587)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[871, 3290])).
% 1.99/2.20 tff(3294,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3295,plain,
% 1.99/2.20 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590))) <=> (hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3296,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590))))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3295])).
% 1.99/2.20 tff(3297,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590)))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3296, 3294])).
% 1.99/2.20 tff(3298,plain,
% 1.99/2.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))),
% 1.99/2.20 inference(quant_inst,[status(thm)],[])).
% 1.99/2.20 tff(3299,plain,
% 1.99/2.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590))),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3298, 3297])).
% 1.99/2.20 tff(3300,plain,
% 1.99/2.20 (~c1_1(a590)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3299, 101, 3272, 3046, 3293, 3292, 45, 3291, 32])).
% 1.99/2.20 tff(3301,plain,
% 1.99/2.20 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3302,plain,
% 1.99/2.20 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a590) | c1_1(a590) | c0_1(a590)) <=> (hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3303,plain,
% 1.99/2.20 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590)))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3302])).
% 1.99/2.20 tff(3304,plain,
% 1.99/2.20 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3303, 3301])).
% 1.99/2.20 tff(3305,plain,
% 1.99/2.20 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a590) | c1_1(a590) | c0_1(a590))),
% 1.99/2.20 inference(quant_inst,[status(thm)],[])).
% 1.99/2.20 tff(3306,plain,
% 1.99/2.20 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590)),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3305, 3304])).
% 1.99/2.20 tff(3307,plain,
% 1.99/2.20 (hskp26 | hskp0 | c2_1(a590) | c1_1(a590)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3306, 101, 45, 942])).
% 1.99/2.20 tff(3308,plain,
% 1.99/2.20 (hskp0),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3307, 3300, 3046, 660])).
% 1.99/2.20 tff(3309,plain,
% 1.99/2.20 (~c2_1(a584)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[955, 3308])).
% 1.99/2.20 tff(3310,plain,
% 1.99/2.20 (~c0_1(a584)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[961, 3308])).
% 1.99/2.20 tff(3311,plain,
% 1.99/2.20 (c1_1(a584)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[969, 3308])).
% 1.99/2.20 tff(3312,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3313,plain,
% 1.99/2.20 ((hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3314,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3313])).
% 1.99/2.20 tff(3315,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3314, 3312])).
% 1.99/2.20 tff(3316,plain,
% 1.99/2.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 1.99/2.20 inference(quant_inst,[status(thm)],[])).
% 1.99/2.20 tff(3317,plain,
% 1.99/2.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603))),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3316, 3315])).
% 1.99/2.20 tff(3318,plain,
% 1.99/2.20 ($false),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3317, 101, 3272, 3270, 3311, 3269, 3310, 3309, 32, 3271])).
% 1.99/2.20 tff(3319,plain,(hskp26 | c2_1(a590) | c0_1(a590) | hskp22 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.20 tff(3320,plain,
% 1.99/2.20 (hskp26),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3319, 3046, 45, 44, 22])).
% 1.99/2.20 tff(3321,plain,
% 1.99/2.20 (c2_1(a583)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[364, 3320])).
% 1.99/2.20 tff(3322,plain,
% 1.99/2.20 (c1_1(a583)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[330, 3320])).
% 1.99/2.20 tff(3323,plain,
% 1.99/2.20 (c0_1(a583)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[338, 3320])).
% 1.99/2.20 tff(3324,plain,
% 1.99/2.20 (c2_1(a603)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[177, 101, 44, 67, 3261, 3260, 43])).
% 1.99/2.20 tff(3325,plain,
% 1.99/2.20 (hskp9),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1401, 101, 1528, 1527, 1526, 3042, 66, 276, 3246])).
% 1.99/2.20 tff(3326,plain,
% 1.99/2.20 (~c3_1(a595)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1370, 3325])).
% 1.99/2.20 tff(3327,plain,
% 1.99/2.20 (~c1_1(a595)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1376, 3325])).
% 1.99/2.20 tff(3328,plain,
% 1.99/2.20 (~c0_1(a595)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1382, 3325])).
% 1.99/2.20 tff(3329,plain,
% 1.99/2.20 (hskp2),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1457, 101, 3260, 3262, 3328, 3327, 3326, 188, 3324])).
% 1.99/2.20 tff(3330,plain,
% 1.99/2.20 (~c3_1(a586)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[206, 3329])).
% 1.99/2.20 tff(3331,plain,
% 1.99/2.20 (hskp9),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1401, 101, 3183, 3184, 3192, 3042, 66, 276, 3246])).
% 1.99/2.20 tff(3332,plain,
% 1.99/2.20 (~c3_1(a595)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1370, 3331])).
% 1.99/2.20 tff(3333,plain,
% 1.99/2.20 (~c0_1(a595)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1382, 3331])).
% 1.99/2.20 tff(3334,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3335,plain,
% 1.99/2.20 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3336,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595)))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3335])).
% 1.99/2.20 tff(3337,plain,
% 1.99/2.20 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3336, 3334])).
% 1.99/2.20 tff(3338,plain,
% 1.99/2.20 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 1.99/2.20 inference(quant_inst,[status(thm)],[])).
% 1.99/2.20 tff(3339,plain,
% 1.99/2.20 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595)),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3338, 3337])).
% 1.99/2.20 tff(3340,plain,
% 1.99/2.20 (c2_1(a595)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3339, 1515, 101, 2160, 2152, 2144, 3333, 3332, 250])).
% 1.99/2.20 tff(3341,plain,
% 1.99/2.20 (~c1_1(a595)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1376, 3331])).
% 1.99/2.20 tff(3342,plain,
% 1.99/2.20 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3343,plain,
% 1.99/2.20 ((hskp6 | hskp5 | (~ndr1_0) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3344,plain,
% 1.99/2.20 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595))))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3343])).
% 1.99/2.20 tff(3345,plain,
% 1.99/2.20 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3344, 3342])).
% 1.99/2.20 tff(3346,plain,
% 1.99/2.20 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 1.99/2.20 inference(quant_inst,[status(thm)],[])).
% 1.99/2.20 tff(3347,plain,
% 1.99/2.20 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595))),
% 1.99/2.20 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 1.99/2.20 tff(3348,plain,
% 1.99/2.20 (hskp5 | (~c2_1(a595))),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3347, 101, 67, 3333, 3341, 528])).
% 1.99/2.20 tff(3349,plain,
% 1.99/2.20 (hskp5),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3348, 3340])).
% 1.99/2.20 tff(3350,plain,
% 1.99/2.20 (~c2_1(a589)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[541, 3349])).
% 1.99/2.20 tff(3351,plain,
% 1.99/2.20 (c1_1(a589)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[549, 3349])).
% 1.99/2.20 tff(3352,plain,
% 1.99/2.20 (c0_1(a589)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[557, 3349])).
% 1.99/2.20 tff(3353,plain,
% 1.99/2.20 ($false),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3165, 101, 2160, 2152, 2144, 3042, 3352, 3351, 66, 22, 3350, 1010])).
% 1.99/2.20 tff(3354,plain,(c1_1(a607) | c2_1(a607) | hskp6 | hskp11 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.99/2.20 tff(3355,plain,
% 1.99/2.20 (c1_1(a607)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3354, 1515, 67, 22, 44])).
% 1.99/2.20 tff(3356,plain,
% 1.99/2.20 (~hskp17),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[263, 3355])).
% 1.99/2.20 tff(3357,plain,
% 1.99/2.20 (hskp17 | c3_1(a583)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3190, 101, 139, 3183, 3184, 55])).
% 1.99/2.20 tff(3358,plain,
% 1.99/2.20 (c3_1(a583)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3357, 3356])).
% 1.99/2.20 tff(3359,plain,
% 1.99/2.20 (hskp10 | (~c3_1(a583))),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1876, 101, 3183, 3184, 3192, 21])).
% 1.99/2.20 tff(3360,plain,
% 1.99/2.20 (hskp10),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3359, 3358])).
% 1.99/2.20 tff(3361,plain,
% 1.99/2.20 (~c1_1(a598)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[827, 3360])).
% 1.99/2.20 tff(3362,plain,
% 1.99/2.20 (c3_1(a598)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[800, 3360])).
% 1.99/2.20 tff(3363,plain,
% 1.99/2.20 (c0_1(a598)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[808, 3360])).
% 1.99/2.20 tff(3364,plain,
% 1.99/2.20 (hskp23),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1565, 1515, 101, 3363, 3362, 3361, 1525])).
% 1.99/2.20 tff(3365,plain,
% 1.99/2.20 (~c1_1(a636)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[439, 3364])).
% 1.99/2.20 tff(3366,plain,
% 1.99/2.20 (~c0_1(a636)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[445, 3364])).
% 1.99/2.20 tff(3367,plain,
% 1.99/2.20 (c3_1(a636)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[453, 3364])).
% 1.99/2.20 tff(3368,plain,
% 1.99/2.20 (~c2_1(a636)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[3210, 3367, 3184, 3358, 3366, 3365, 3183])).
% 1.99/2.20 tff(3369,plain,
% 1.99/2.20 (c2_1(a598)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1427, 101, 44, 67, 3363, 3361, 43])).
% 1.99/2.20 tff(3370,plain,
% 1.99/2.20 (hskp15),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1887, 101, 3183, 3184, 3363, 3362, 3361, 1870, 3358])).
% 1.99/2.20 tff(3371,plain,
% 1.99/2.20 (~c0_1(a604)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1474, 3370])).
% 1.99/2.20 tff(3372,plain,
% 1.99/2.20 (c1_1(a604)),
% 1.99/2.20 inference(unit_resolution,[status(thm)],[1490, 3370])).
% 1.99/2.20 tff(3373,plain,
% 1.99/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3374,plain,
% 1.99/2.20 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 1.99/2.20 inference(rewrite,[status(thm)],[])).
% 1.99/2.20 tff(3375,plain,
% 1.99/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636)))),
% 1.99/2.20 inference(monotonicity,[status(thm)],[3374])).
% 1.99/2.20 tff(3376,plain,
% 1.99/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 1.99/2.20 inference(transitivity,[status(thm)],[3375, 3373])).
% 1.99/2.20 tff(3377,plain,
% 1.99/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 1.99/2.21 inference(quant_inst,[status(thm)],[])).
% 1.99/2.21 tff(3378,plain,
% 1.99/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636)),
% 1.99/2.21 inference(modus_ponens,[status(thm)],[3377, 3376])).
% 1.99/2.21 tff(3379,plain,
% 1.99/2.21 (~c2_1(a604)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3378, 101, 3367, 3372, 3363, 3362, 3365, 3371, 11, 3369, 3368])).
% 1.99/2.21 tff(3380,plain,
% 1.99/2.21 (hskp14),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3175, 3355, 3042])).
% 1.99/2.21 tff(3381,plain,
% 1.99/2.21 (~c1_1(a603)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[162, 3380])).
% 1.99/2.21 tff(3382,plain,
% 1.99/2.21 (c0_1(a603)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[170, 3380])).
% 1.99/2.21 tff(3383,plain,
% 1.99/2.21 (c2_1(a603)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[177, 101, 44, 67, 3382, 3381, 43])).
% 1.99/2.21 tff(3384,plain,
% 1.99/2.21 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3385,plain,
% 1.99/2.21 ((hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3386,plain,
% 1.99/2.21 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604))))),
% 1.99/2.21 inference(monotonicity,[status(thm)],[3385])).
% 1.99/2.21 tff(3387,plain,
% 1.99/2.21 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.21 inference(transitivity,[status(thm)],[3386, 3384])).
% 1.99/2.21 tff(3388,plain,
% 1.99/2.21 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 1.99/2.21 inference(quant_inst,[status(thm)],[])).
% 1.99/2.21 tff(3389,plain,
% 1.99/2.21 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604))),
% 1.99/2.21 inference(modus_ponens,[status(thm)],[3388, 3387])).
% 1.99/2.21 tff(3390,plain,
% 1.99/2.21 ($false),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3389, 101, 3356, 3372, 3382, 3371, 3381, 32, 3383, 3379])).
% 1.99/2.21 tff(3391,plain,(hskp11 | hskp22 | hskp6 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 1.99/2.21 tff(3392,plain,
% 1.99/2.21 (hskp11),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3391, 67, 44, 22])).
% 1.99/2.21 tff(3393,plain,
% 1.99/2.21 (~c1_1(a599)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[395, 3392])).
% 1.99/2.21 tff(3394,plain,
% 1.99/2.21 (c1_1(a586)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[214, 3329])).
% 1.99/2.21 tff(3395,plain,
% 1.99/2.21 (c3_1(a599)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[389, 3392])).
% 1.99/2.21 tff(3396,plain,
% 1.99/2.21 (c2_1(a599)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[403, 3392])).
% 1.99/2.21 tff(3397,plain,
% 1.99/2.21 (c0_1(a586)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[2177, 101, 3261, 3396, 3395, 3394, 3262, 3393, 3330, 240, 3324])).
% 1.99/2.21 tff(3398,plain,
% 1.99/2.21 (~c0_1(a593)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3125, 101, 2160, 2152, 2144, 3042, 3250, 66, 22, 3248, 1010])).
% 1.99/2.21 tff(3399,plain,
% 1.99/2.21 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3400,plain,
% 1.99/2.21 ((hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3401,plain,
% 1.99/2.21 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603))))),
% 1.99/2.21 inference(monotonicity,[status(thm)],[3400])).
% 1.99/2.21 tff(3402,plain,
% 1.99/2.21 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603)))),
% 1.99/2.21 inference(transitivity,[status(thm)],[3401, 3399])).
% 1.99/2.21 tff(3403,plain,
% 1.99/2.21 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 1.99/2.21 inference(quant_inst,[status(thm)],[])).
% 1.99/2.21 tff(3404,plain,
% 1.99/2.21 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603))),
% 1.99/2.21 inference(modus_ponens,[status(thm)],[3403, 3402])).
% 1.99/2.21 tff(3405,plain,
% 1.99/2.21 (hskp16 | (~c2_1(a603))),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3404, 101, 3250, 3260, 3262, 3248, 932, 3398])).
% 1.99/2.21 tff(3406,plain,
% 1.99/2.21 (hskp16),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3405, 3324])).
% 1.99/2.21 tff(3407,plain,
% 1.99/2.21 (~c2_1(a606)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[1015, 3406])).
% 1.99/2.21 tff(3408,plain,
% 1.99/2.21 (c1_1(a606)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[992, 3406])).
% 1.99/2.21 tff(3409,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3410,plain,
% 1.99/2.21 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3411,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))))),
% 1.99/2.21 inference(monotonicity,[status(thm)],[3410])).
% 1.99/2.21 tff(3412,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 1.99/2.21 inference(transitivity,[status(thm)],[3411, 3409])).
% 1.99/2.21 tff(3413,plain,
% 1.99/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 1.99/2.21 inference(quant_inst,[status(thm)],[])).
% 1.99/2.21 tff(3414,plain,
% 1.99/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))),
% 1.99/2.21 inference(modus_ponens,[status(thm)],[3413, 3412])).
% 1.99/2.21 tff(3415,plain,
% 1.99/2.21 (~c0_1(a606)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3414, 101, 2160, 2152, 2144, 3042, 3408, 66, 22, 3407, 1010])).
% 1.99/2.21 tff(3416,plain,
% 1.99/2.21 (~c3_1(a606)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[982, 3406])).
% 1.99/2.21 tff(3417,plain,
% 1.99/2.21 (c2_1(a586)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[1357, 3329])).
% 1.99/2.21 tff(3418,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3419,plain,
% 1.99/2.21 (((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3420,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606))))),
% 1.99/2.21 inference(monotonicity,[status(thm)],[3419])).
% 1.99/2.21 tff(3421,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606)))),
% 1.99/2.21 inference(transitivity,[status(thm)],[3420, 3418])).
% 1.99/2.21 tff(3422,plain,
% 1.99/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 1.99/2.21 inference(quant_inst,[status(thm)],[])).
% 1.99/2.21 tff(3423,plain,
% 1.99/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606))),
% 1.99/2.21 inference(modus_ponens,[status(thm)],[3422, 3421])).
% 1.99/2.21 tff(3424,plain,
% 1.99/2.21 ($false),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3423, 101, 3408, 3396, 3395, 3417, 3416, 3393, 3330, 240, 3415, 3397])).
% 1.99/2.21 tff(3425,plain,(c1_1(a607) | c2_1(a607) | hskp22 | hskp6 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 1.99/2.21 tff(3426,plain,
% 1.99/2.21 (c1_1(a607)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3425, 3245, 44, 22, 3323, 3322, 3321])).
% 1.99/2.21 tff(3427,plain,
% 1.99/2.21 (~hskp17),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[263, 3426])).
% 1.99/2.21 tff(3428,plain,
% 1.99/2.21 (hskp3),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3289, 3427, 3042, 3426])).
% 1.99/2.21 tff(3429,plain,
% 1.99/2.21 (~c1_1(a587)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[855, 3428])).
% 1.99/2.21 tff(3430,plain,
% 1.99/2.21 (c2_1(a587)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[863, 3428])).
% 1.99/2.21 tff(3431,plain,
% 1.99/2.21 (c0_1(a587)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[871, 3428])).
% 1.99/2.21 tff(3432,plain,
% 1.99/2.21 (~c1_1(a590)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3299, 101, 3427, 3046, 3431, 3430, 45, 3429, 32])).
% 1.99/2.21 tff(3433,plain,
% 1.99/2.21 (~hskp4),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[138, 3245, 44])).
% 1.99/2.21 tff(3434,plain,
% 1.99/2.21 (hskp17 | c3_1(a583)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3190, 101, 3433, 3323, 3322, 55])).
% 1.99/2.21 tff(3435,plain,
% 1.99/2.21 (c3_1(a583)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3434, 3427])).
% 1.99/2.21 tff(3436,plain,
% 1.99/2.21 (hskp10 | (~c3_1(a583))),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[1876, 101, 3323, 3322, 3321, 21])).
% 1.99/2.21 tff(3437,plain,
% 1.99/2.21 (hskp10),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[3436, 3435])).
% 1.99/2.21 tff(3438,plain,
% 1.99/2.21 (~c1_1(a598)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[827, 3437])).
% 1.99/2.21 tff(3439,plain,
% 1.99/2.21 (c0_1(a598)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[808, 3437])).
% 1.99/2.21 tff(3440,plain,
% 1.99/2.21 (c2_1(a598)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[1427, 101, 44, 3245, 3439, 3438, 43])).
% 1.99/2.21 tff(3441,plain,
% 1.99/2.21 (c3_1(a598)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[800, 3437])).
% 1.99/2.21 tff(3442,plain,
% 1.99/2.21 (hskp15),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[1887, 101, 3323, 3322, 3439, 3441, 3438, 1870, 3435])).
% 1.99/2.21 tff(3443,plain,
% 1.99/2.21 (~c0_1(a604)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[1474, 3442])).
% 1.99/2.21 tff(3444,plain,
% 1.99/2.21 (c1_1(a604)),
% 1.99/2.21 inference(unit_resolution,[status(thm)],[1490, 3442])).
% 1.99/2.21 tff(3445,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3446,plain,
% 1.99/2.21 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a590) | c2_1(a590) | (~c3_1(a590)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.21 inference(rewrite,[status(thm)],[])).
% 1.99/2.21 tff(3447,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a590) | c2_1(a590) | (~c3_1(a590)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 1.99/2.21 inference(monotonicity,[status(thm)],[3446])).
% 1.99/2.21 tff(3448,plain,
% 1.99/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a590) | c2_1(a590) | (~c3_1(a590)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 1.99/2.21 inference(transitivity,[status(thm)],[3447, 3445])).
% 2.07/2.21 tff(3449,plain,
% 2.07/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a590) | c2_1(a590) | (~c3_1(a590)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 2.07/2.21 inference(quant_inst,[status(thm)],[])).
% 2.07/2.21 tff(3450,plain,
% 2.07/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604))),
% 2.07/2.21 inference(modus_ponens,[status(thm)],[3449, 3448])).
% 2.07/2.21 tff(3451,plain,
% 2.07/2.21 (~c2_1(a604)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[3450, 101, 3444, 3439, 3441, 3046, 3244, 3443, 11, 3440, 3432])).
% 2.07/2.21 tff(3452,plain,
% 2.07/2.21 (hskp14),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[3175, 3426, 3042])).
% 2.07/2.21 tff(3453,plain,
% 2.07/2.21 (~c1_1(a603)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[162, 3452])).
% 2.07/2.21 tff(3454,plain,
% 2.07/2.21 (c0_1(a603)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[170, 3452])).
% 2.07/2.21 tff(3455,plain,
% 2.07/2.21 (c2_1(a603)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[177, 101, 44, 3245, 3454, 3453, 43])).
% 2.07/2.21 tff(3456,plain,
% 2.07/2.21 ($false),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[3389, 101, 3427, 3444, 3454, 3443, 3453, 32, 3455, 3451])).
% 2.07/2.21 tff(3457,plain,(c2_1(a590) | hskp22 | c0_1(a590) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.21 tff(3458,plain,
% 2.07/2.21 (c2_1(a590)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[3457, 45, 44, 22])).
% 2.07/2.21 tff(3459,plain,
% 2.07/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 2.07/2.21 inference(rewrite,[status(thm)],[])).
% 2.07/2.21 tff(3460,plain,
% 2.07/2.21 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 2.07/2.21 inference(rewrite,[status(thm)],[])).
% 2.07/2.21 tff(3461,plain,
% 2.07/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)))),
% 2.07/2.21 inference(monotonicity,[status(thm)],[3460])).
% 2.07/2.21 tff(3462,plain,
% 2.07/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 2.07/2.21 inference(transitivity,[status(thm)],[3461, 3459])).
% 2.07/2.21 tff(3463,plain,
% 2.07/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 2.07/2.21 inference(quant_inst,[status(thm)],[])).
% 2.07/2.21 tff(3464,plain,
% 2.07/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)),
% 2.07/2.21 inference(modus_ponens,[status(thm)],[3463, 3462])).
% 2.07/2.21 tff(3465,plain,
% 2.07/2.21 (~c1_1(a678)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[3464, 101, 2186, 2184, 785, 784, 45, 65, 3148])).
% 2.07/2.21 tff(3466,assumption,(~hskp0), introduced(assumption)).
% 2.07/2.21 tff(3467,plain,
% 2.07/2.21 (hskp26 | hskp0 | c1_1(a607) | c0_1(a607)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[948, 101, 22, 942])).
% 2.07/2.21 tff(3468,plain,
% 2.07/2.21 (c0_1(a607)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[3467, 3466, 66, 660])).
% 2.07/2.21 tff(3469,plain,
% 2.07/2.21 (hskp23),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[1223, 3468])).
% 2.07/2.21 tff(3470,plain,
% 2.07/2.21 (~c1_1(a636)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[439, 3469])).
% 2.07/2.21 tff(3471,plain,
% 2.07/2.21 (~c0_1(a636)),
% 2.07/2.21 inference(unit_resolution,[status(thm)],[445, 3469])).
% 2.07/2.21 tff(3472,plain,
% 2.07/2.21 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636))),
% 2.07/2.21 inference(rewrite,[status(thm)],[])).
% 2.07/2.21 tff(3473,plain,
% 2.07/2.21 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a636) | c1_1(a636) | c0_1(a636)) <=> (hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636))),
% 2.07/2.21 inference(rewrite,[status(thm)],[])).
% 2.07/2.21 tff(3474,plain,
% 2.07/2.21 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a636) | c1_1(a636) | c0_1(a636))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636)))),
% 2.07/2.22 inference(monotonicity,[status(thm)],[3473])).
% 2.07/2.22 tff(3475,plain,
% 2.07/2.22 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a636) | c1_1(a636) | c0_1(a636))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636))),
% 2.07/2.22 inference(transitivity,[status(thm)],[3474, 3472])).
% 2.07/2.22 tff(3476,plain,
% 2.07/2.22 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a636) | c1_1(a636) | c0_1(a636))),
% 2.07/2.22 inference(quant_inst,[status(thm)],[])).
% 2.07/2.22 tff(3477,plain,
% 2.07/2.22 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636)),
% 2.07/2.22 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 2.07/2.22 tff(3478,plain,
% 2.07/2.22 (c2_1(a636)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3477, 660, 101, 3466, 3471, 3470, 942])).
% 2.07/2.22 tff(3479,plain,
% 2.07/2.22 (hskp26 | hskp28 | (~c0_1(a607)) | (~c3_1(a607))),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1178, 101, 22, 1172])).
% 2.07/2.22 tff(3480,plain,
% 2.07/2.22 (hskp28),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3479, 3468, 303, 660])).
% 2.07/2.22 tff(3481,plain,
% 2.07/2.22 (c3_1(a612)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1040, 3480])).
% 2.07/2.22 tff(3482,plain,
% 2.07/2.22 (c1_1(a612)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1321, 3480])).
% 2.07/2.22 tff(3483,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3484,plain,
% 2.07/2.22 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636))) <=> (c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3485,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636))))),
% 2.07/2.22 inference(monotonicity,[status(thm)],[3484])).
% 2.07/2.22 tff(3486,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636)))),
% 2.07/2.22 inference(transitivity,[status(thm)],[3485, 3483])).
% 2.07/2.22 tff(3487,plain,
% 2.07/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))),
% 2.07/2.22 inference(quant_inst,[status(thm)],[])).
% 2.07/2.22 tff(3488,plain,
% 2.07/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636))),
% 2.07/2.22 inference(modus_ponens,[status(thm)],[3487, 3486])).
% 2.07/2.22 tff(3489,plain,
% 2.07/2.22 (~c0_1(a612)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3488, 101, 3482, 3481, 785, 784, 3471, 3470, 45, 65, 3478])).
% 2.07/2.22 tff(3490,plain,
% 2.07/2.22 (c2_1(a612)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1048, 3480])).
% 2.07/2.22 tff(3491,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3492,plain,
% 2.07/2.22 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3493,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607))))),
% 2.07/2.22 inference(monotonicity,[status(thm)],[3492])).
% 2.07/2.22 tff(3494,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 2.07/2.22 inference(transitivity,[status(thm)],[3493, 3491])).
% 2.07/2.22 tff(3495,plain,
% 2.07/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.07/2.22 inference(quant_inst,[status(thm)],[])).
% 2.07/2.22 tff(3496,plain,
% 2.07/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607))),
% 2.07/2.22 inference(modus_ponens,[status(thm)],[3495, 3494])).
% 2.07/2.22 tff(3497,plain,
% 2.07/2.22 ($false),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3496, 101, 2186, 2185, 2184, 3482, 3490, 303, 66, 22, 11, 3489])).
% 2.07/2.22 tff(3498,plain,(hskp0 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.07/2.22 tff(3499,plain,
% 2.07/2.22 (hskp0),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3498, 660, 2185, 2184, 303, 66, 22, 785, 784, 45, 2186])).
% 2.07/2.22 tff(3500,plain,
% 2.07/2.22 (~c2_1(a584)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[955, 3499])).
% 2.07/2.22 tff(3501,plain,
% 2.07/2.22 (~c0_1(a584)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[961, 3499])).
% 2.07/2.22 tff(3502,assumption,(~c3_1(a584)), introduced(assumption)).
% 2.07/2.22 tff(3503,assumption,(~c2_1(a584)), introduced(assumption)).
% 2.07/2.22 tff(3504,assumption,(~c0_1(a584)), introduced(assumption)).
% 2.07/2.22 tff(3505,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3506,plain,
% 2.07/2.22 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a584) | c0_1(a584) | c2_1(a584)) <=> (c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3507,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a584) | c0_1(a584) | c2_1(a584))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599))))),
% 2.07/2.22 inference(monotonicity,[status(thm)],[3506])).
% 2.07/2.22 tff(3508,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a584) | c0_1(a584) | c2_1(a584))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 2.07/2.22 inference(transitivity,[status(thm)],[3507, 3505])).
% 2.07/2.22 tff(3509,plain,
% 2.07/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a584) | c0_1(a584) | c2_1(a584))),
% 2.07/2.22 inference(quant_inst,[status(thm)],[])).
% 2.07/2.22 tff(3510,plain,
% 2.07/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599))),
% 2.07/2.22 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 2.07/2.22 tff(3511,plain,
% 2.07/2.22 ($false),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3510, 101, 427, 426, 785, 784, 425, 45, 3504, 3503, 1607, 3502])).
% 2.07/2.22 tff(3512,plain,(c3_1(a584) | (~c2_1(a599)) | (~c3_1(a599)) | (~c2_1(a590)) | (~c3_1(a590)) | c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.22 tff(3513,plain,
% 2.07/2.22 (c3_1(a584)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3512, 985, 984, 785, 784, 922, 45, 3501, 3500])).
% 2.07/2.22 tff(3514,plain,
% 2.07/2.22 (c1_1(a584)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[969, 3499])).
% 2.07/2.22 tff(3515,plain,
% 2.07/2.22 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3516,plain,
% 2.07/2.22 ((hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a584) | (~c1_1(a584)) | (~c3_1(a584))) <=> (hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3517,plain,
% 2.07/2.22 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a584) | (~c1_1(a584)) | (~c3_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))))),
% 2.07/2.22 inference(monotonicity,[status(thm)],[3516])).
% 2.07/2.22 tff(3518,plain,
% 2.07/2.22 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a584) | (~c1_1(a584)) | (~c3_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 2.07/2.22 inference(transitivity,[status(thm)],[3517, 3515])).
% 2.07/2.22 tff(3519,plain,
% 2.07/2.22 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a584) | (~c1_1(a584)) | (~c3_1(a584)))),
% 2.07/2.22 inference(quant_inst,[status(thm)],[])).
% 2.07/2.22 tff(3520,plain,
% 2.07/2.22 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))),
% 2.07/2.22 inference(modus_ponens,[status(thm)],[3519, 3518])).
% 2.07/2.22 tff(3521,plain,
% 2.07/2.22 (hskp14 | (~c3_1(a584))),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3520, 101, 2186, 2185, 2184, 3514, 3500, 505])).
% 2.07/2.22 tff(3522,plain,
% 2.07/2.22 (hskp14),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3521, 3513])).
% 2.07/2.22 tff(3523,plain,
% 2.07/2.22 (hskp3),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[311, 3522, 303, 66, 22])).
% 2.07/2.22 tff(3524,plain,
% 2.07/2.22 (~c1_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[855, 3523])).
% 2.07/2.22 tff(3525,plain,
% 2.07/2.22 (~c1_1(a603)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[162, 3522])).
% 2.07/2.22 tff(3526,plain,
% 2.07/2.22 (c0_1(a603)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[170, 3522])).
% 2.07/2.22 tff(3527,plain,
% 2.07/2.22 (~c3_1(a603)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[193, 3522])).
% 2.07/2.22 tff(3528,plain,
% 2.07/2.22 (c0_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[871, 3523])).
% 2.07/2.22 tff(3529,plain,
% 2.07/2.22 (c2_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[863, 3523])).
% 2.07/2.22 tff(3530,plain,
% 2.07/2.22 ($false),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1391, 3529, 3528, 22, 303, 66, 660, 3527, 3526, 3525, 3524])).
% 2.07/2.22 tff(3531,plain,(hskp26 | c2_1(a607) | (~c3_1(a607)) | c1_1(a607) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.22 tff(3532,plain,
% 2.07/2.22 (hskp26),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3531, 66, 303, 22, 2186, 2185, 2184, 785, 784, 45])).
% 2.07/2.22 tff(3533,plain,
% 2.07/2.22 (c2_1(a583)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[364, 3532])).
% 2.07/2.22 tff(3534,plain,
% 2.07/2.22 (c1_1(a583)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[330, 3532])).
% 2.07/2.22 tff(3535,plain,
% 2.07/2.22 (c0_1(a583)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[338, 3532])).
% 2.07/2.22 tff(3536,plain,
% 2.07/2.22 (hskp9),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1844, 101, 3535, 3534, 3533, 784, 45, 276, 3148])).
% 2.07/2.22 tff(3537,plain,
% 2.07/2.22 (~c3_1(a595)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1370, 3536])).
% 2.07/2.22 tff(3538,plain,
% 2.07/2.22 (~c0_1(a595)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1382, 3536])).
% 2.07/2.22 tff(3539,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3540,plain,
% 2.07/2.22 (((~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3541,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595)))),
% 2.07/2.22 inference(monotonicity,[status(thm)],[3540])).
% 2.07/2.22 tff(3542,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595))),
% 2.07/2.22 inference(transitivity,[status(thm)],[3541, 3539])).
% 2.07/2.22 tff(3543,plain,
% 2.07/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 2.07/2.22 inference(quant_inst,[status(thm)],[])).
% 2.07/2.22 tff(3544,plain,
% 2.07/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595)),
% 2.07/2.22 inference(modus_ponens,[status(thm)],[3543, 3542])).
% 2.07/2.22 tff(3545,plain,
% 2.07/2.22 (c2_1(a595)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3544, 101, 2185, 2184, 785, 784, 3538, 3537, 45, 1607, 3465])).
% 2.07/2.22 tff(3546,plain,
% 2.07/2.22 (~c1_1(a595)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1376, 3536])).
% 2.07/2.22 tff(3547,plain,
% 2.07/2.22 (hskp2 | (~c2_1(a595))),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1631, 101, 3538, 3546, 3537, 188])).
% 2.07/2.22 tff(3548,plain,
% 2.07/2.22 (hskp2),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3547, 3545])).
% 2.07/2.22 tff(3549,plain,
% 2.07/2.22 (~c3_1(a586)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[206, 3548])).
% 2.07/2.22 tff(3550,plain,
% 2.07/2.22 (c2_1(a586)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1357, 3548])).
% 2.07/2.22 tff(3551,plain,
% 2.07/2.22 (c1_1(a586)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[214, 3548])).
% 2.07/2.22 tff(3552,plain,
% 2.07/2.22 (hskp28),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[2682, 101, 2185, 2184, 3551, 3550, 3549, 1625, 3465])).
% 2.07/2.22 tff(3553,plain,
% 2.07/2.22 (c3_1(a612)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1040, 3552])).
% 2.07/2.22 tff(3554,plain,
% 2.07/2.22 (c1_1(a612)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1321, 3552])).
% 2.07/2.22 tff(3555,plain,
% 2.07/2.22 (~c0_1(a612)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1651, 101, 3554, 3553, 785, 784, 3538, 3546, 45, 65, 3545])).
% 2.07/2.22 tff(3556,plain,
% 2.07/2.22 (c2_1(a612)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[1048, 3552])).
% 2.07/2.22 tff(3557,plain,
% 2.07/2.22 ($false),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3496, 101, 2186, 2185, 2184, 3554, 3556, 303, 66, 22, 11, 3555])).
% 2.07/2.22 tff(3558,plain,(c1_1(a607) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c3_1(a607)) | c2_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.22 tff(3559,plain,
% 2.07/2.22 (c1_1(a607)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3558, 3458, 2152, 2144, 3042, 22, 2160, 3244, 45])).
% 2.07/2.22 tff(3560,plain,
% 2.07/2.22 (~hskp17),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[263, 3559])).
% 2.07/2.22 tff(3561,plain,
% 2.07/2.22 (hskp3),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3289, 3559, 3042, 3560])).
% 2.07/2.22 tff(3562,plain,
% 2.07/2.22 (~c1_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[855, 3561])).
% 2.07/2.22 tff(3563,plain,
% 2.07/2.22 (c2_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[863, 3561])).
% 2.07/2.22 tff(3564,plain,
% 2.07/2.22 (c0_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[871, 3561])).
% 2.07/2.22 tff(3565,plain,
% 2.07/2.22 (~hskp17),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[263, 2848])).
% 2.07/2.22 tff(3566,plain,
% 2.07/2.22 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3567,plain,
% 2.07/2.22 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607))) <=> (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3568,plain,
% 2.07/2.22 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607)))),
% 2.07/2.22 inference(monotonicity,[status(thm)],[3567])).
% 2.07/2.22 tff(3569,plain,
% 2.07/2.22 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607))),
% 2.07/2.22 inference(transitivity,[status(thm)],[3568, 3566])).
% 2.07/2.22 tff(3570,plain,
% 2.07/2.22 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))),
% 2.07/2.22 inference(quant_inst,[status(thm)],[])).
% 2.07/2.22 tff(3571,plain,
% 2.07/2.22 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607)),
% 2.07/2.22 inference(modus_ponens,[status(thm)],[3570, 3569])).
% 2.07/2.22 tff(3572,plain,
% 2.07/2.22 ($false),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3571, 101, 3565, 910, 909, 2848, 22, 906, 32, 1])).
% 2.07/2.22 tff(3573,plain,(c0_1(a607) | (~c0_1(a587)) | (~c2_1(a587)) | (~c1_1(a607)) | c2_1(a607) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.22 tff(3574,plain,
% 2.07/2.22 (c0_1(a607)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3573, 3564, 3563, 3559, 22, 3562])).
% 2.07/2.22 tff(3575,plain,
% 2.07/2.22 (hskp14),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3175, 3559, 3042])).
% 2.07/2.22 tff(3576,plain,
% 2.07/2.22 (~c3_1(a603)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[193, 3575])).
% 2.07/2.22 tff(3577,plain,
% 2.07/2.22 (~c1_1(a603)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[162, 3575])).
% 2.07/2.22 tff(3578,plain,
% 2.07/2.22 (c0_1(a603)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[170, 3575])).
% 2.07/2.22 tff(3579,plain,
% 2.07/2.22 (hskp3),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3289, 2848, 303, 3565])).
% 2.07/2.22 tff(3580,plain,
% 2.07/2.22 (~c1_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[855, 3579])).
% 2.07/2.22 tff(3581,plain,
% 2.07/2.22 (c2_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[863, 3579])).
% 2.07/2.22 tff(3582,plain,
% 2.07/2.22 (c0_1(a587)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[871, 3579])).
% 2.07/2.22 tff(3583,plain,
% 2.07/2.22 (hskp26 | c2_1(a603)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[916, 101, 3582, 3581, 908, 907, 3580, 905])).
% 2.07/2.22 tff(3584,plain,
% 2.07/2.22 (c2_1(a603)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3583, 660])).
% 2.07/2.22 tff(3585,plain,
% 2.07/2.22 ($false),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[2791, 101, 3565, 919, 2848, 22, 908, 32, 1, 920])).
% 2.07/2.22 tff(3586,plain,(c0_1(a607) | (~c0_1(a603)) | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~c2_1(a603))), inference(lemma,lemma(discharge,[]))).
% 2.07/2.22 tff(3587,plain,
% 2.07/2.22 (c0_1(a607)),
% 2.07/2.22 inference(unit_resolution,[status(thm)],[3586, 3584, 2848, 22, 908, 919])).
% 2.07/2.22 tff(3588,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3589,plain,
% 2.07/2.22 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> ((~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.22 inference(rewrite,[status(thm)],[])).
% 2.07/2.22 tff(3590,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.07/2.22 inference(monotonicity,[status(thm)],[3589])).
% 2.07/2.22 tff(3591,plain,
% 2.07/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3590, 3588])).
% 2.07/2.23 tff(3592,plain,
% 2.07/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3593,plain,
% 2.07/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3592, 3591])).
% 2.07/2.23 tff(3594,plain,
% 2.07/2.23 (c0_1(a599) | (~c0_1(a607))),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3593, 101, 303, 985, 785, 784, 2848, 922, 45, 65])).
% 2.07/2.23 tff(3595,plain,
% 2.07/2.23 (c0_1(a599)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3594, 3587])).
% 2.07/2.23 tff(3596,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3597,plain,
% 2.07/2.23 ((hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3598,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.07/2.23 inference(monotonicity,[status(thm)],[3597])).
% 2.07/2.23 tff(3599,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3598, 3596])).
% 2.07/2.23 tff(3600,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3601,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3600, 3599])).
% 2.07/2.23 tff(3602,plain,
% 2.07/2.23 (hskp15 | (~c0_1(a599)) | (~c0_1(a607))),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3601, 101, 303, 984, 2848, 922, 1870])).
% 2.07/2.23 tff(3603,plain,
% 2.07/2.23 (hskp15),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3602, 3587, 3595])).
% 2.07/2.23 tff(3604,plain,
% 2.07/2.23 (~c0_1(a604)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[1474, 3603])).
% 2.07/2.23 tff(3605,plain,
% 2.07/2.23 (c1_1(a604)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[1490, 3603])).
% 2.07/2.23 tff(3606,plain,
% 2.07/2.23 (c2_1(a604)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3389, 101, 3565, 3605, 919, 3604, 908, 32, 3584])).
% 2.07/2.23 tff(3607,plain,
% 2.07/2.23 (c3_1(a604)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[1482, 3603])).
% 2.07/2.23 tff(3608,assumption,(hskp19), introduced(assumption)).
% 2.07/2.23 tff(3609,plain,
% 2.07/2.23 (~c1_1(a617)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[2453, 3608])).
% 2.07/2.23 tff(3610,plain,
% 2.07/2.23 (~c0_1(a617)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[2459, 3608])).
% 2.07/2.23 tff(3611,plain,
% 2.07/2.23 (c2_1(a617)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[2467, 3608])).
% 2.07/2.23 tff(3612,plain,
% 2.07/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3613,plain,
% 2.07/2.23 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3614,plain,
% 2.07/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617))))),
% 2.07/2.23 inference(monotonicity,[status(thm)],[3613])).
% 2.07/2.23 tff(3615,plain,
% 2.07/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3614, 3612])).
% 2.07/2.23 tff(3616,plain,
% 2.07/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3617,plain,
% 2.07/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3616, 3615])).
% 2.07/2.23 tff(3618,plain,
% 2.07/2.23 ($false),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3617, 101, 3611, 303, 2410, 3610, 3609, 2848, 2340, 65, 2351, 2403])).
% 2.07/2.23 tff(3619,plain,((~hskp19) | (~c3_1(a607)) | (~c3_1(a604)) | (~c1_1(a607)) | c0_1(a604) | (~c0_1(a607)) | (~c2_1(a604))), inference(lemma,lemma(discharge,[]))).
% 2.07/2.23 tff(3620,plain,
% 2.07/2.23 (~hskp19),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3619, 3607, 303, 2848, 3604, 3587, 3606])).
% 2.07/2.23 tff(3621,plain,
% 2.07/2.23 (^[U: $i] : refl((hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 2.07/2.23 inference(bind,[status(th)],[])).
% 2.07/2.23 tff(3622,plain,
% 2.07/2.23 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/2.23 inference(quant_intro,[status(thm)],[3621])).
% 2.07/2.23 tff(3623,plain,
% 2.07/2.23 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3624,plain,
% 2.07/2.23 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp20) <=> ((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.07/2.23 inference(bind,[status(th)],[])).
% 2.07/2.23 tff(3625,plain,
% 2.07/2.23 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp20) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/2.23 inference(quant_intro,[status(thm)],[3624])).
% 2.07/2.23 tff(3626,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 2.07/2.23 tff(3627,plain,
% 2.07/2.23 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3626, 3625])).
% 2.07/2.23 tff(3628,plain,
% 2.07/2.23 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3627, 3623])).
% 2.07/2.23 tff(3629,plain,(
% 2.07/2.23 ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/2.23 inference(skolemize,[status(sab)],[3628])).
% 2.07/2.23 tff(3630,plain,
% 2.07/2.23 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3629, 3622])).
% 2.07/2.23 tff(3631,plain,
% 2.07/2.23 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3632,plain,
% 2.07/2.23 ((hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3633,plain,
% 2.07/2.23 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.07/2.23 inference(monotonicity,[status(thm)],[3632])).
% 2.07/2.23 tff(3634,plain,
% 2.07/2.23 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3633, 3631])).
% 2.07/2.23 tff(3635,plain,
% 2.07/2.23 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3636,plain,
% 2.07/2.23 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3635, 3634])).
% 2.07/2.23 tff(3637,plain,
% 2.07/2.23 (hskp20 | hskp19 | (~c1_1(a607)) | (~c0_1(a607))),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3636, 101, 303, 3630])).
% 2.07/2.23 tff(3638,plain,
% 2.07/2.23 (hskp20),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3637, 3620, 2848, 3587])).
% 2.07/2.23 tff(3639,plain,
% 2.07/2.23 (~c3_1(a623)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[643, 3638])).
% 2.07/2.23 tff(3640,plain,
% 2.07/2.23 (~c2_1(a623)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[649, 3638])).
% 2.07/2.23 tff(3641,plain,
% 2.07/2.23 (~c1_1(a623)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[655, 3638])).
% 2.07/2.23 tff(3642,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3643,plain,
% 2.07/2.23 ((hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a623) | c1_1(a623) | c2_1(a623)) <=> (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3644,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))))),
% 2.07/2.23 inference(monotonicity,[status(thm)],[3643])).
% 2.07/2.23 tff(3645,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3644, 3642])).
% 2.07/2.23 tff(3646,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a623) | c1_1(a623) | c2_1(a623))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3647,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3646, 3645])).
% 2.07/2.23 tff(3648,plain,
% 2.07/2.23 ($false),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3647, 660, 101, 919, 3641, 3640, 3639, 908, 905, 3584])).
% 2.07/2.23 tff(3649,plain,(hskp26 | (~c0_1(a603)) | c1_1(a603) | (~c1_1(a607)) | (~c3_1(a607)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | c2_1(a607) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.23 tff(3650,plain,
% 2.07/2.23 (hskp26),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3649, 3578, 3577, 3559, 3042, 3458, 3244, 45, 22, 3576])).
% 2.07/2.23 tff(3651,plain,
% 2.07/2.23 (c2_1(a583)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[364, 3650])).
% 2.07/2.23 tff(3652,plain,
% 2.07/2.23 (c1_1(a583)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[330, 3650])).
% 2.07/2.23 tff(3653,plain,
% 2.07/2.23 (c0_1(a583)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[338, 3650])).
% 2.07/2.23 tff(3654,assumption,(hskp0), introduced(assumption)).
% 2.07/2.23 tff(3655,assumption,(~c1_1(a678)), introduced(assumption)).
% 2.07/2.23 tff(3656,plain,
% 2.07/2.23 (~c2_1(a584)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[955, 3654])).
% 2.07/2.23 tff(3657,plain,
% 2.07/2.23 (~c0_1(a584)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[961, 3654])).
% 2.07/2.23 tff(3658,plain,
% 2.07/2.23 (c1_1(a584)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[969, 3654])).
% 2.07/2.23 tff(3659,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3660,plain,
% 2.07/2.23 ((hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3661,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678))))),
% 2.07/2.23 inference(monotonicity,[status(thm)],[3660])).
% 2.07/2.23 tff(3662,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3661, 3659])).
% 2.07/2.23 tff(3663,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3664,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3663, 3662])).
% 2.07/2.23 tff(3665,plain,
% 2.07/2.23 ($false),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3664, 101, 2849, 2186, 2185, 3658, 3657, 3656, 32, 3655])).
% 2.07/2.23 tff(3666,plain,((~hskp0) | hskp17 | (~c0_1(a678)) | (~c2_1(a678)) | c1_1(a678)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.23 tff(3667,plain,
% 2.07/2.23 (c1_1(a678)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3666, 3654, 2186, 2185, 3565])).
% 2.07/2.23 tff(3668,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3669,plain,
% 2.07/2.23 ((hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3670,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 2.07/2.23 inference(monotonicity,[status(thm)],[3669])).
% 2.07/2.23 tff(3671,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3670, 3668])).
% 2.07/2.23 tff(3672,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3673,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3672, 3671])).
% 2.07/2.23 tff(3674,plain,
% 2.07/2.23 (hskp10 | (~c1_1(a678))),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3673, 101, 2185, 2184, 1528, 1527, 1526, 21])).
% 2.07/2.23 tff(3675,plain,
% 2.07/2.23 (hskp10),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3674, 3667])).
% 2.07/2.23 tff(3676,plain,
% 2.07/2.23 (~c1_1(a598)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[827, 3675])).
% 2.07/2.23 tff(3677,plain,
% 2.07/2.23 (c3_1(a598)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[800, 3675])).
% 2.07/2.23 tff(3678,plain,
% 2.07/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3679,plain,
% 2.07/2.23 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598))) <=> ((~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3680,plain,
% 2.07/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607))))),
% 2.07/2.23 inference(monotonicity,[status(thm)],[3679])).
% 2.07/2.23 tff(3681,plain,
% 2.07/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3680, 3678])).
% 2.07/2.23 tff(3682,plain,
% 2.07/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3683,plain,
% 2.07/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607))),
% 2.07/2.23 inference(modus_ponens,[status(thm)],[3682, 3681])).
% 2.07/2.23 tff(3684,plain,
% 2.07/2.23 (c2_1(a598)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[3683, 101, 2186, 2185, 2184, 3677, 2848, 22, 3676, 1010, 2351])).
% 2.07/2.23 tff(3685,plain,
% 2.07/2.23 (c0_1(a598)),
% 2.07/2.23 inference(unit_resolution,[status(thm)],[808, 3675])).
% 2.07/2.23 tff(3686,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3687,plain,
% 2.07/2.23 ((hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 2.07/2.23 inference(rewrite,[status(thm)],[])).
% 2.07/2.23 tff(3688,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598))))),
% 2.07/2.23 inference(monotonicity,[status(thm)],[3687])).
% 2.07/2.23 tff(3689,plain,
% 2.07/2.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 2.07/2.23 inference(transitivity,[status(thm)],[3688, 3686])).
% 2.07/2.23 tff(3690,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 2.07/2.23 inference(quant_inst,[status(thm)],[])).
% 2.07/2.23 tff(3691,plain,
% 2.07/2.23 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3690, 3689])).
% 2.07/2.24 tff(3692,plain,
% 2.07/2.24 ($false),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3691, 101, 3565, 3685, 3658, 3676, 3657, 3656, 32, 3684])).
% 2.07/2.24 tff(3693,plain,((~hskp0) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a607)) | c2_1(a607) | (~c0_1(a607)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 2.07/2.24 tff(3694,plain,
% 2.07/2.24 (~hskp0),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3693, 3559, 2152, 2144, 2160, 22, 3574, 3653, 3652, 3651])).
% 2.07/2.24 tff(3695,plain,
% 2.07/2.24 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3696,plain,
% 2.07/2.24 ((hskp11 | hskp0 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3697,plain,
% 2.07/2.24 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3696])).
% 2.07/2.24 tff(3698,plain,
% 2.07/2.24 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3697, 3695])).
% 2.07/2.24 tff(3699,plain,
% 2.07/2.24 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.07/2.24 inference(quant_inst,[status(thm)],[])).
% 2.07/2.24 tff(3700,plain,
% 2.07/2.24 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3699, 3698])).
% 2.07/2.24 tff(3701,plain,
% 2.07/2.24 (hskp11 | hskp0 | (~c1_1(a607)) | (~c0_1(a607))),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3700, 101, 22, 2215])).
% 2.07/2.24 tff(3702,plain,
% 2.07/2.24 (hskp11),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3701, 3694, 3559, 3574])).
% 2.07/2.24 tff(3703,plain,
% 2.07/2.24 (~c1_1(a599)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[395, 3702])).
% 2.07/2.24 tff(3704,plain,
% 2.07/2.24 (c2_1(a599)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[403, 3702])).
% 2.07/2.24 tff(3705,plain,
% 2.07/2.24 (c0_1(a599)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3593, 101, 3042, 3704, 3458, 3244, 3559, 3703, 45, 65, 3574])).
% 2.07/2.24 tff(3706,plain,
% 2.07/2.24 (c3_1(a599)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[389, 3702])).
% 2.07/2.24 tff(3707,plain,
% 2.07/2.24 (hskp15),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3601, 101, 3042, 3706, 3559, 3703, 1870, 3574, 3705])).
% 2.07/2.24 tff(3708,plain,
% 2.07/2.24 (c3_1(a604)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[1482, 3707])).
% 2.07/2.24 tff(3709,plain,
% 2.07/2.24 (~c0_1(a604)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[1474, 3707])).
% 2.07/2.24 tff(3710,plain,
% 2.07/2.24 (c1_1(a604)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[1490, 3707])).
% 2.07/2.24 tff(3711,plain,
% 2.07/2.24 (c2_1(a604)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[2750, 101, 3560, 3710, 3704, 3709, 3703, 32, 3705])).
% 2.07/2.24 tff(3712,assumption,(~c1_1(a590)), introduced(assumption)).
% 2.07/2.24 tff(3713,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3714,plain,
% 2.07/2.24 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> ((~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3715,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3714])).
% 2.07/2.24 tff(3716,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3715, 3713])).
% 2.07/2.24 tff(3717,plain,
% 2.07/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 2.07/2.24 inference(quant_inst,[status(thm)],[])).
% 2.07/2.24 tff(3718,plain,
% 2.07/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3717, 3716])).
% 2.07/2.24 tff(3719,plain,
% 2.07/2.24 ($false),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3718, 101, 303, 2410, 785, 2848, 2340, 45, 65, 2351, 2403, 3712])).
% 2.07/2.24 tff(3720,plain,(c1_1(a590) | (~c3_1(a607)) | (~c3_1(a604)) | (~c2_1(a590)) | (~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~c0_1(a607)) | (~c2_1(a604))), inference(lemma,lemma(discharge,[]))).
% 2.07/2.24 tff(3721,plain,
% 2.07/2.24 (c1_1(a590)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3720, 3711, 3042, 3458, 3559, 3709, 45, 3574, 3708])).
% 2.07/2.24 tff(3722,plain,
% 2.07/2.24 (~hskp19),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3619, 3711, 3042, 3559, 3709, 3574, 3708])).
% 2.07/2.24 tff(3723,plain,
% 2.07/2.24 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3724,plain,
% 2.07/2.24 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590))) <=> (hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3725,plain,
% 2.07/2.24 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590))))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3724])).
% 2.07/2.24 tff(3726,plain,
% 2.07/2.24 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3725, 3723])).
% 2.07/2.24 tff(3727,plain,
% 2.07/2.24 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.07/2.24 inference(quant_inst,[status(thm)],[])).
% 2.07/2.24 tff(3728,plain,
% 2.07/2.24 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3727, 3726])).
% 2.07/2.24 tff(3729,plain,
% 2.07/2.24 (hskp19 | hskp13 | (~c2_1(a590)) | (~c1_1(a590))),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3728, 101, 45, 2429])).
% 2.07/2.24 tff(3730,plain,
% 2.07/2.24 (hskp13),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3729, 3722, 3458, 3721])).
% 2.07/2.24 tff(3731,plain,
% 2.07/2.24 (~c2_1(a601)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[2388, 3730])).
% 2.07/2.24 tff(3732,plain,
% 2.07/2.24 (~c1_1(a601)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[2394, 3730])).
% 2.07/2.24 tff(3733,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3734,plain,
% 2.07/2.24 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601))) <=> ((~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3735,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607))))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3734])).
% 2.07/2.24 tff(3736,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607)))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3735, 3733])).
% 2.07/2.24 tff(3737,plain,
% 2.07/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))),
% 2.07/2.24 inference(quant_inst,[status(thm)],[])).
% 2.07/2.24 tff(3738,plain,
% 2.07/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3737, 3736])).
% 2.07/2.24 tff(3739,plain,
% 2.07/2.24 (~c3_1(a601)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3738, 101, 2160, 2152, 2144, 3559, 22, 3732, 3731, 1010, 3574])).
% 2.07/2.24 tff(3740,plain,
% 2.07/2.24 (~c0_1(a601)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[2408, 3730])).
% 2.07/2.24 tff(3741,plain,
% 2.07/2.24 ($false),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[2416, 101, 3708, 3704, 3706, 3709, 3740, 3731, 3703, 1607, 3711, 3739])).
% 2.07/2.24 tff(3742,plain,(c0_1(a590) | c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.07/2.24 tff(3743,plain,
% 2.07/2.24 (c0_1(a590)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3742, 22, 44])).
% 2.07/2.24 tff(3744,plain,
% 2.07/2.24 (~hskp6),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[606, 3743])).
% 2.07/2.24 tff(3745,plain,
% 2.07/2.24 (hskp26),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3266, 66, 22, 3744, 44])).
% 2.07/2.24 tff(3746,plain,
% 2.07/2.24 (c2_1(a583)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[364, 3745])).
% 2.07/2.24 tff(3747,plain,
% 2.07/2.24 (c0_1(a583)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[338, 3745])).
% 2.07/2.24 tff(3748,plain,
% 2.07/2.24 (c1_1(a583)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[330, 3745])).
% 2.07/2.24 tff(3749,plain,
% 2.07/2.24 ($false),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3425, 3748, 3747, 44, 22, 3744, 66, 3746])).
% 2.07/2.24 tff(3750,plain,(c1_1(a607) | hskp22 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.24 tff(3751,plain,
% 2.07/2.24 (c1_1(a607)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3750, 22, 44])).
% 2.07/2.24 tff(3752,plain,
% 2.07/2.24 (~hskp17),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[263, 3751])).
% 2.07/2.24 tff(3753,plain,
% 2.07/2.24 (hskp3),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3289, 3751, 3042, 3752])).
% 2.07/2.24 tff(3754,plain,
% 2.07/2.24 (~c1_1(a587)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[855, 3753])).
% 2.07/2.24 tff(3755,plain,
% 2.07/2.24 (c0_1(a587)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[871, 3753])).
% 2.07/2.24 tff(3756,plain,
% 2.07/2.24 (c2_1(a587)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[863, 3753])).
% 2.07/2.24 tff(3757,plain,
% 2.07/2.24 (c0_1(a607)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3573, 3756, 3755, 3751, 22, 3754])).
% 2.07/2.24 tff(3758,plain,
% 2.07/2.24 (hskp11),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3391, 3744, 44, 22])).
% 2.07/2.24 tff(3759,plain,
% 2.07/2.24 (~c1_1(a599)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[395, 3758])).
% 2.07/2.24 tff(3760,plain,
% 2.07/2.24 (c3_1(a599)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[389, 3758])).
% 2.07/2.24 tff(3761,plain,
% 2.07/2.24 (c2_1(a599)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[403, 3758])).
% 2.07/2.24 tff(3762,assumption,(~c0_1(a599)), introduced(assumption)).
% 2.07/2.24 tff(3763,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3764,plain,
% 2.07/2.24 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> ((~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3765,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3764])).
% 2.07/2.24 tff(3766,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3765, 3763])).
% 2.07/2.24 tff(3767,plain,
% 2.07/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 2.07/2.24 inference(quant_inst,[status(thm)],[])).
% 2.07/2.24 tff(3768,plain,
% 2.07/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3767, 3766])).
% 2.07/2.24 tff(3769,plain,
% 2.07/2.24 ($false),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3768, 101, 303, 427, 426, 2848, 425, 65, 2351, 3762])).
% 2.07/2.24 tff(3770,plain,(c0_1(a599) | (~c3_1(a607)) | (~c2_1(a599)) | (~c3_1(a599)) | (~c1_1(a607)) | c1_1(a599) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 2.07/2.24 tff(3771,plain,
% 2.07/2.24 (c0_1(a599)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3770, 3042, 3761, 3760, 3751, 3759, 3757])).
% 2.07/2.24 tff(3772,plain,
% 2.07/2.24 (hskp15 | (~c1_1(a607)) | (~c0_1(a599)) | (~c0_1(a607))),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3601, 101, 3042, 3760, 3759, 1870])).
% 2.07/2.24 tff(3773,plain,
% 2.07/2.24 (hskp15),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3772, 3771, 3751, 3757])).
% 2.07/2.24 tff(3774,plain,
% 2.07/2.24 (c3_1(a604)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[1482, 3773])).
% 2.07/2.24 tff(3775,plain,
% 2.07/2.24 (~c0_1(a604)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[1474, 3773])).
% 2.07/2.24 tff(3776,plain,
% 2.07/2.24 (hskp14),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3175, 3751, 3042])).
% 2.07/2.24 tff(3777,plain,
% 2.07/2.24 (~c1_1(a603)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[162, 3776])).
% 2.07/2.24 tff(3778,plain,
% 2.07/2.24 (c0_1(a603)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[170, 3776])).
% 2.07/2.24 tff(3779,plain,
% 2.07/2.24 (c2_1(a603)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[177, 101, 44, 3744, 3778, 3777, 43])).
% 2.07/2.24 tff(3780,plain,
% 2.07/2.24 (c1_1(a604)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[1490, 3773])).
% 2.07/2.24 tff(3781,plain,
% 2.07/2.24 (c2_1(a604)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3389, 101, 3752, 3780, 3778, 3775, 3777, 32, 3779])).
% 2.07/2.24 tff(3782,plain,
% 2.07/2.24 (~hskp19),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3619, 3781, 3042, 3751, 3775, 3757, 3774])).
% 2.07/2.24 tff(3783,plain,
% 2.07/2.24 (hskp20 | hskp19 | (~c1_1(a607)) | (~c0_1(a607))),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3636, 101, 3042, 3630])).
% 2.07/2.24 tff(3784,plain,
% 2.07/2.24 (hskp20),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3783, 3782, 3751, 3757])).
% 2.07/2.24 tff(3785,plain,
% 2.07/2.24 (~c2_1(a623)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[649, 3784])).
% 2.07/2.24 tff(3786,plain,
% 2.07/2.24 (~c1_1(a623)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[655, 3784])).
% 2.07/2.24 tff(3787,plain,
% 2.07/2.24 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3788,plain,
% 2.07/2.24 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a623) | c1_1(a623) | (~c0_1(a623))) <=> (hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3789,plain,
% 2.07/2.24 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a623) | c1_1(a623) | (~c0_1(a623)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623))))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3788])).
% 2.07/2.24 tff(3790,plain,
% 2.07/2.24 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a623) | c1_1(a623) | (~c0_1(a623)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623)))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3789, 3787])).
% 2.07/2.24 tff(3791,plain,
% 2.07/2.24 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a623) | c1_1(a623) | (~c0_1(a623)))),
% 2.07/2.24 inference(quant_inst,[status(thm)],[])).
% 2.07/2.24 tff(3792,plain,
% 2.07/2.24 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3791, 3790])).
% 2.07/2.24 tff(3793,plain,
% 2.07/2.24 (~c0_1(a623)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3792, 101, 44, 3744, 3786, 3785, 43])).
% 2.07/2.24 tff(3794,plain,
% 2.07/2.24 (~hskp4),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[138, 3744, 44])).
% 2.07/2.24 tff(3795,plain,
% 2.07/2.24 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3796,plain,
% 2.07/2.24 ((hskp10 | hskp4 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a604))) <=> (hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3797,plain,
% 2.07/2.24 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a604)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604))))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3796])).
% 2.07/2.24 tff(3798,plain,
% 2.07/2.24 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a604)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3797, 3795])).
% 2.07/2.24 tff(3799,plain,
% 2.07/2.24 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a604)))),
% 2.07/2.24 inference(quant_inst,[status(thm)],[])).
% 2.07/2.24 tff(3800,plain,
% 2.07/2.24 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3799, 3798])).
% 2.07/2.24 tff(3801,plain,
% 2.07/2.24 (hskp10),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3800, 101, 3794, 3774, 3775, 783, 3781])).
% 2.07/2.24 tff(3802,plain,
% 2.07/2.24 (~c1_1(a598)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[827, 3801])).
% 2.07/2.24 tff(3803,plain,
% 2.07/2.24 (c3_1(a598)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[800, 3801])).
% 2.07/2.24 tff(3804,plain,
% 2.07/2.24 (c2_1(a598)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3683, 101, 2160, 2152, 2144, 3803, 3751, 22, 3802, 1010, 3757])).
% 2.07/2.24 tff(3805,plain,
% 2.07/2.24 (~c3_1(a623)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[643, 3784])).
% 2.07/2.24 tff(3806,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3807,plain,
% 2.07/2.24 (((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3808,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623)))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3807])).
% 2.07/2.24 tff(3809,plain,
% 2.07/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3808, 3806])).
% 2.07/2.24 tff(3810,plain,
% 2.07/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 2.07/2.24 inference(quant_inst,[status(thm)],[])).
% 2.07/2.24 tff(3811,plain,
% 2.07/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623)),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 2.07/2.24 tff(3812,plain,
% 2.07/2.24 ($false),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3811, 101, 3774, 3803, 3785, 3805, 3775, 3802, 1607, 3804, 3781, 3793])).
% 2.07/2.24 tff(3813,plain,(c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.07/2.24 tff(3814,plain,
% 2.07/2.24 (hskp22),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3813, 22])).
% 2.07/2.24 tff(3815,plain,
% 2.07/2.24 (((~hskp22) | c1_1(a633)) <=> ((~hskp22) | c1_1(a633))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3816,axiom,((~hskp22) | c1_1(a633)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 2.07/2.24 tff(3817,plain,
% 2.07/2.24 ((~hskp22) | c1_1(a633)),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3816, 3815])).
% 2.07/2.24 tff(3818,plain,
% 2.07/2.24 ((~hskp22) | c1_1(a633)),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3817, 3815])).
% 2.07/2.24 tff(3819,plain,
% 2.07/2.24 ((~hskp22) | c1_1(a633)),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3818, 3815])).
% 2.07/2.24 tff(3820,plain,
% 2.07/2.24 ((~hskp22) | c1_1(a633)),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3819, 3815])).
% 2.07/2.24 tff(3821,plain,
% 2.07/2.24 ((~hskp22) | c1_1(a633)),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3820, 3815])).
% 2.07/2.24 tff(3822,plain,
% 2.07/2.24 (c1_1(a633)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3821, 3814])).
% 2.07/2.24 tff(3823,plain,
% 2.07/2.24 (((~hskp22) | (~c0_1(a633))) <=> ((~hskp22) | (~c0_1(a633)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3824,plain,
% 2.07/2.24 (((~c0_1(a633)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a633)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3825,axiom,((~c0_1(a633)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 2.07/2.24 tff(3826,plain,
% 2.07/2.24 ((~hskp22) | (~c0_1(a633))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3825, 3824])).
% 2.07/2.24 tff(3827,plain,
% 2.07/2.24 ((~hskp22) | (~c0_1(a633))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3826, 3823])).
% 2.07/2.24 tff(3828,plain,
% 2.07/2.24 (~c0_1(a633)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3827, 3814])).
% 2.07/2.24 tff(3829,plain,
% 2.07/2.24 (((~hskp22) | (~c3_1(a633))) <=> ((~hskp22) | (~c3_1(a633)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3830,plain,
% 2.07/2.24 (((~c3_1(a633)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a633)))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3831,axiom,((~c3_1(a633)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 2.07/2.24 tff(3832,plain,
% 2.07/2.24 ((~hskp22) | (~c3_1(a633))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3831, 3830])).
% 2.07/2.24 tff(3833,plain,
% 2.07/2.24 ((~hskp22) | (~c3_1(a633))),
% 2.07/2.24 inference(modus_ponens,[status(thm)],[3832, 3829])).
% 2.07/2.24 tff(3834,plain,
% 2.07/2.24 (~c3_1(a633)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3833, 3814])).
% 2.07/2.24 tff(3835,plain,
% 2.07/2.24 (hskp22),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3750, 22, 66])).
% 2.07/2.24 tff(3836,plain,
% 2.07/2.24 (c1_1(a633)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3821, 3835])).
% 2.07/2.24 tff(3837,plain,
% 2.07/2.24 (~c3_1(a633)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3833, 3835])).
% 2.07/2.24 tff(3838,plain,
% 2.07/2.24 (~c0_1(a633)),
% 2.07/2.24 inference(unit_resolution,[status(thm)],[3827, 3835])).
% 2.07/2.24 tff(3839,assumption,(~c3_1(a633)), introduced(assumption)).
% 2.07/2.24 tff(3840,assumption,(~c0_1(a633)), introduced(assumption)).
% 2.07/2.24 tff(3841,plain,
% 2.07/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3842,plain,
% 2.07/2.24 ((hskp11 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633))),
% 2.07/2.24 inference(rewrite,[status(thm)],[])).
% 2.07/2.24 tff(3843,plain,
% 2.07/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633)))),
% 2.07/2.24 inference(monotonicity,[status(thm)],[3842])).
% 2.07/2.24 tff(3844,plain,
% 2.07/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633))),
% 2.07/2.24 inference(transitivity,[status(thm)],[3843, 3841])).
% 2.07/2.24 tff(3845,plain,
% 2.07/2.24 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3846,plain,
% 2.07/2.25 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633)),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3845, 3844])).
% 2.07/2.25 tff(3847,plain,
% 2.07/2.25 ((~c3_1(a583)) | c2_1(a633)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3846, 1515, 101, 3183, 3192, 3840, 3839, 250])).
% 2.07/2.25 tff(3848,plain,
% 2.07/2.25 (c2_1(a633)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3847, 3202])).
% 2.07/2.25 tff(3849,plain,
% 2.07/2.25 (hskp10),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3359, 3202])).
% 2.07/2.25 tff(3850,plain,
% 2.07/2.25 (~c1_1(a598)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[827, 3849])).
% 2.07/2.25 tff(3851,assumption,(c1_1(a633)), introduced(assumption)).
% 2.07/2.25 tff(3852,plain,
% 2.07/2.25 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3853,plain,
% 2.07/2.25 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3854,plain,
% 2.07/2.25 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3853])).
% 2.07/2.25 tff(3855,plain,
% 2.07/2.25 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3854, 3852])).
% 2.07/2.25 tff(3856,plain,
% 2.07/2.25 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3857,plain,
% 2.07/2.25 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3856, 3855])).
% 2.07/2.25 tff(3858,plain,
% 2.07/2.25 (hskp12 | (~c2_1(a633))),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3857, 101, 3183, 3184, 3192, 3851, 3840, 2589])).
% 2.07/2.25 tff(3859,plain,
% 2.07/2.25 (hskp12),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3858, 3848])).
% 2.07/2.25 tff(3860,plain,
% 2.07/2.25 (~c3_1(a600)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[675, 3859])).
% 2.07/2.25 tff(3861,plain,
% 2.07/2.25 (c3_1(a598)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[800, 3849])).
% 2.07/2.25 tff(3862,plain,
% 2.07/2.25 (c2_1(a600)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[683, 3859])).
% 2.07/2.25 tff(3863,plain,
% 2.07/2.25 (c0_1(a600)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[691, 3859])).
% 2.07/2.25 tff(3864,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3865,plain,
% 2.07/2.25 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3866,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633))))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3865])).
% 2.07/2.25 tff(3867,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3866, 3864])).
% 2.07/2.25 tff(3868,plain,
% 2.07/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3869,plain,
% 2.07/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633))),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3868, 3867])).
% 2.07/2.25 tff(3870,plain,
% 2.07/2.25 (~c2_1(a598)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3869, 101, 3851, 3863, 3862, 3861, 3840, 3839, 3860, 3850, 240])).
% 2.07/2.25 tff(3871,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3872,plain,
% 2.07/2.25 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3873,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3872])).
% 2.07/2.25 tff(3874,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3873, 3871])).
% 2.07/2.25 tff(3875,plain,
% 2.07/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3876,plain,
% 2.07/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3875, 3874])).
% 2.07/2.25 tff(3877,plain,
% 2.07/2.25 ($false),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3876, 101, 3183, 3192, 3851, 3861, 3840, 3850, 11, 3870, 3202, 3848])).
% 2.07/2.25 tff(3878,plain,((~c3_1(a583)) | (~c1_1(a633)) | c0_1(a633) | c3_1(a633) | hskp11), inference(lemma,lemma(discharge,[]))).
% 2.07/2.25 tff(3879,plain,
% 2.07/2.25 (~c3_1(a583)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3878, 1515, 3838, 3837, 3836])).
% 2.07/2.25 tff(3880,plain,
% 2.07/2.25 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3881,plain,
% 2.07/2.25 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583))) <=> (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3882,plain,
% 2.07/2.25 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583))))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3881])).
% 2.07/2.25 tff(3883,plain,
% 2.07/2.25 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3882, 3880])).
% 2.07/2.25 tff(3884,plain,
% 2.07/2.25 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3885,plain,
% 2.07/2.25 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583))),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3884, 3883])).
% 2.07/2.25 tff(3886,plain,
% 2.07/2.25 (hskp3 | c3_1(a583)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3885, 101, 223, 3183, 3184, 2236])).
% 2.07/2.25 tff(3887,plain,
% 2.07/2.25 (hskp3),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3886, 3879])).
% 2.07/2.25 tff(3888,plain,
% 2.07/2.25 (~c1_1(a587)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[855, 3887])).
% 2.07/2.25 tff(3889,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3890,plain,
% 2.07/2.25 ((hskp29 | hskp18 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583))) <=> (hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3891,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3890])).
% 2.07/2.25 tff(3892,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3891, 3889])).
% 2.07/2.25 tff(3893,plain,
% 2.07/2.25 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3894,plain,
% 2.07/2.25 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3893, 3892])).
% 2.07/2.25 tff(3895,plain,
% 2.07/2.25 (hskp18 | c3_1(a583)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3894, 251, 101, 3184, 3192, 1673])).
% 2.07/2.25 tff(3896,plain,
% 2.07/2.25 (hskp18),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3895, 3879])).
% 2.07/2.25 tff(3897,plain,
% 2.07/2.25 (~c2_1(a610)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[1087, 3896])).
% 2.07/2.25 tff(3898,plain,
% 2.07/2.25 (~c0_1(a610)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[1093, 3896])).
% 2.07/2.25 tff(3899,plain,
% 2.07/2.25 (c2_1(a587)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[863, 3887])).
% 2.07/2.25 tff(3900,plain,
% 2.07/2.25 (c0_1(a587)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[871, 3887])).
% 2.07/2.25 tff(3901,plain,
% 2.07/2.25 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3902,plain,
% 2.07/2.25 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610))) <=> (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3903,plain,
% 2.07/2.25 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610))))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3902])).
% 2.07/2.25 tff(3904,plain,
% 2.07/2.25 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610)))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3903, 3901])).
% 2.07/2.25 tff(3905,plain,
% 2.07/2.25 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3906,plain,
% 2.07/2.25 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610))),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 2.07/2.25 tff(3907,plain,
% 2.07/2.25 (~c1_1(a610)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3906, 101, 223, 3900, 3899, 3898, 3897, 3888, 32])).
% 2.07/2.25 tff(3908,plain,
% 2.07/2.25 (hskp4 | c3_1(a583)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3190, 101, 223, 3183, 3184, 55])).
% 2.07/2.25 tff(3909,plain,
% 2.07/2.25 (hskp4),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3908, 3879])).
% 2.07/2.25 tff(3910,plain,
% 2.07/2.25 (~c2_1(a588)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[115, 3909])).
% 2.07/2.25 tff(3911,plain,
% 2.07/2.25 (~c1_1(a588)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[121, 3909])).
% 2.07/2.25 tff(3912,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3913,plain,
% 2.07/2.25 ((hskp29 | hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633))) <=> (hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3914,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3913])).
% 2.07/2.25 tff(3915,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3914, 3912])).
% 2.07/2.25 tff(3916,plain,
% 2.07/2.25 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3917,plain,
% 2.07/2.25 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3916, 3915])).
% 2.07/2.25 tff(3918,plain,
% 2.07/2.25 (hskp29 | hskp15 | (~c2_1(a633))),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3917, 101, 3851, 3839, 1451])).
% 2.07/2.25 tff(3919,plain,
% 2.07/2.25 (~c2_1(a633)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3918, 3016, 251])).
% 2.07/2.25 tff(3920,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3921,plain,
% 2.07/2.25 ((hskp29 | hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583))) <=> (hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3922,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3921])).
% 2.07/2.25 tff(3923,plain,
% 2.07/2.25 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3922, 3920])).
% 2.07/2.25 tff(3924,plain,
% 2.07/2.25 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3925,plain,
% 2.07/2.25 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3924, 3923])).
% 2.07/2.25 tff(3926,plain,
% 2.07/2.25 (hskp15 | c3_1(a583)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3925, 251, 101, 3184, 3192, 1451])).
% 2.07/2.25 tff(3927,plain,
% 2.07/2.25 (c3_1(a583)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3926, 3016])).
% 2.07/2.25 tff(3928,plain,
% 2.07/2.25 ($false),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3847, 3927, 3919])).
% 2.07/2.25 tff(3929,plain,(hskp15 | hskp11 | c0_1(a633) | c3_1(a633) | hskp29 | (~c1_1(a633))), inference(lemma,lemma(discharge,[]))).
% 2.07/2.25 tff(3930,plain,
% 2.07/2.25 (hskp15),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3929, 1515, 3838, 3837, 251, 3836])).
% 2.07/2.25 tff(3931,plain,
% 2.07/2.25 (~c0_1(a604)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[1474, 3930])).
% 2.07/2.25 tff(3932,plain,
% 2.07/2.25 (c0_1(a588)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[129, 3909])).
% 2.07/2.25 tff(3933,plain,
% 2.07/2.25 (c3_1(a604)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[1482, 3930])).
% 2.07/2.25 tff(3934,plain,
% 2.07/2.25 (c1_1(a604)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[1490, 3930])).
% 2.07/2.25 tff(3935,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3936,plain,
% 2.07/2.25 (((~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a607) | c0_1(a607) | c2_1(a607)) <=> (c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607))),
% 2.07/2.25 inference(rewrite,[status(thm)],[])).
% 2.07/2.25 tff(3937,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607)))),
% 2.07/2.25 inference(monotonicity,[status(thm)],[3936])).
% 2.07/2.25 tff(3938,plain,
% 2.07/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607))),
% 2.07/2.25 inference(transitivity,[status(thm)],[3937, 3935])).
% 2.07/2.25 tff(3939,plain,
% 2.07/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a607) | c0_1(a607) | c2_1(a607))),
% 2.07/2.25 inference(quant_inst,[status(thm)],[])).
% 2.07/2.25 tff(3940,plain,
% 2.07/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607)),
% 2.07/2.25 inference(modus_ponens,[status(thm)],[3939, 3938])).
% 2.07/2.25 tff(3941,plain,
% 2.07/2.25 (c0_1(a607)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[3940, 101, 33, 3934, 3933, 3932, 22, 3931, 3911, 3910, 1253])).
% 2.07/2.25 tff(3942,plain,
% 2.07/2.25 (hskp16),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[1726, 101, 3183, 3184, 3934, 3933, 3931, 1314, 3879])).
% 2.07/2.25 tff(3943,plain,
% 2.07/2.25 (~c3_1(a606)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[982, 3942])).
% 2.07/2.25 tff(3944,plain,
% 2.07/2.25 (~c2_1(a606)),
% 2.07/2.25 inference(unit_resolution,[status(thm)],[1015, 3942])).
% 2.07/2.26 tff(3945,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3946,plain,
% 2.07/2.26 (((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3947,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607))))),
% 2.07/2.26 inference(monotonicity,[status(thm)],[3946])).
% 2.07/2.26 tff(3948,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607)))),
% 2.07/2.26 inference(transitivity,[status(thm)],[3947, 3945])).
% 2.07/2.26 tff(3949,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 2.07/2.26 inference(quant_inst,[status(thm)],[])).
% 2.07/2.26 tff(3950,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607))),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[3949, 3948])).
% 2.07/2.26 tff(3951,plain,
% 2.07/2.26 (c0_1(a606)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[3950, 101, 3934, 3933, 66, 22, 3944, 3943, 3931, 1253, 3941])).
% 2.07/2.26 tff(3952,plain,
% 2.07/2.26 (c1_1(a606)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[992, 3942])).
% 2.07/2.26 tff(3953,plain,
% 2.07/2.26 (c3_1(a610)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1101, 3896])).
% 2.07/2.26 tff(3954,plain,
% 2.07/2.26 (hskp28),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1735, 101, 3183, 3192, 3953, 3898, 3897, 1026, 3879])).
% 2.07/2.26 tff(3955,plain,
% 2.07/2.26 (c3_1(a612)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1040, 3954])).
% 2.07/2.26 tff(3956,plain,
% 2.07/2.26 (c2_1(a612)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1048, 3954])).
% 2.07/2.26 tff(3957,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3958,plain,
% 2.07/2.26 (((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3959,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610))))),
% 2.07/2.26 inference(monotonicity,[status(thm)],[3958])).
% 2.07/2.26 tff(3960,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 2.07/2.26 inference(transitivity,[status(thm)],[3959, 3957])).
% 2.07/2.26 tff(3961,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 2.07/2.26 inference(quant_inst,[status(thm)],[])).
% 2.07/2.26 tff(3962,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610))),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[3961, 3960])).
% 2.07/2.26 tff(3963,plain,
% 2.07/2.26 (~c0_1(a612)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[3962, 101, 3956, 3955, 3953, 3952, 3897, 3944, 1010, 3951, 3907])).
% 2.07/2.26 tff(3964,plain,
% 2.07/2.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3965,plain,
% 2.07/2.26 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a610) | c0_1(a610) | (~c3_1(a610))) <=> (hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3966,plain,
% 2.07/2.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610))))),
% 2.07/2.26 inference(monotonicity,[status(thm)],[3965])).
% 2.07/2.26 tff(3967,plain,
% 2.07/2.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610)))),
% 2.07/2.26 inference(transitivity,[status(thm)],[3966, 3964])).
% 2.07/2.26 tff(3968,plain,
% 2.07/2.26 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))),
% 2.07/2.26 inference(quant_inst,[status(thm)],[])).
% 2.07/2.26 tff(3969,plain,
% 2.07/2.26 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610))),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 2.07/2.26 tff(3970,plain,
% 2.07/2.26 (hskp9),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[3969, 101, 3183, 3184, 3192, 3953, 3898, 276, 3907])).
% 2.07/2.26 tff(3971,plain,
% 2.07/2.26 (~c1_1(a595)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1376, 3970])).
% 2.07/2.26 tff(3972,plain,
% 2.07/2.26 (~c0_1(a595)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1382, 3970])).
% 2.07/2.26 tff(3973,plain,
% 2.07/2.26 (hskp27),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1108, 101, 3953, 3952, 3898, 3897, 3944, 495, 3951])).
% 2.07/2.26 tff(3974,plain,
% 2.07/2.26 (c3_1(a611)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[566, 3973])).
% 2.07/2.26 tff(3975,plain,
% 2.07/2.26 (c1_1(a611)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[574, 3973])).
% 2.07/2.26 tff(3976,plain,
% 2.07/2.26 (c0_1(a611)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[582, 3973])).
% 2.07/2.26 tff(3977,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3978,plain,
% 2.07/2.26 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3979,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595))))),
% 2.07/2.26 inference(monotonicity,[status(thm)],[3978])).
% 2.07/2.26 tff(3980,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595)))),
% 2.07/2.26 inference(transitivity,[status(thm)],[3979, 3977])).
% 2.07/2.26 tff(3981,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 2.07/2.26 inference(quant_inst,[status(thm)],[])).
% 2.07/2.26 tff(3982,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595))),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[3981, 3980])).
% 2.07/2.26 tff(3983,plain,
% 2.07/2.26 (~c2_1(a595)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[3982, 101, 3956, 3955, 3976, 3975, 3974, 3972, 3971, 65, 3963])).
% 2.07/2.26 tff(3984,plain,
% 2.07/2.26 (~c3_1(a595)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1370, 3970])).
% 2.07/2.26 tff(3985,plain,
% 2.07/2.26 (c1_1(a612)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[1321, 3954])).
% 2.07/2.26 tff(3986,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3987,plain,
% 2.07/2.26 (((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3988,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607))))),
% 2.07/2.26 inference(monotonicity,[status(thm)],[3987])).
% 2.07/2.26 tff(3989,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607)))),
% 2.07/2.26 inference(transitivity,[status(thm)],[3988, 3986])).
% 2.07/2.26 tff(3990,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 2.07/2.26 inference(quant_inst,[status(thm)],[])).
% 2.07/2.26 tff(3991,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607))),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[3990, 3989])).
% 2.07/2.26 tff(3992,plain,
% 2.07/2.26 ($false),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[3991, 101, 3985, 3955, 66, 22, 3972, 3984, 1253, 3941, 3963, 3983])).
% 2.07/2.26 tff(3993,plain,(hskp11 | c1_1(a607) | c2_1(a607) | c3_1(a607) | hskp29), inference(lemma,lemma(discharge,[]))).
% 2.07/2.26 tff(3994,plain,
% 2.07/2.26 (hskp11),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[3993, 251, 22, 33, 66])).
% 2.07/2.26 tff(3995,plain,
% 2.07/2.26 (~c1_1(a599)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[395, 3994])).
% 2.07/2.26 tff(3996,plain,
% 2.07/2.26 ((hskp29 | hskp17 | hskp7) <=> (hskp29 | hskp17 | hskp7)),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3997,plain,
% 2.07/2.26 (((hskp29 | hskp7) | hskp17) <=> (hskp29 | hskp17 | hskp7)),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(3998,axiom,((hskp29 | hskp7) | hskp17), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 2.07/2.26 tff(3999,plain,
% 2.07/2.26 (hskp29 | hskp17 | hskp7),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[3998, 3997])).
% 2.07/2.26 tff(4000,plain,
% 2.07/2.26 (hskp29 | hskp17 | hskp7),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[3999, 3996])).
% 2.07/2.26 tff(4001,plain,
% 2.07/2.26 (hskp29 | hskp17 | hskp7),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[4000, 3996])).
% 2.07/2.26 tff(4002,plain,
% 2.07/2.26 (hskp29 | hskp17 | hskp7),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[4001, 3996])).
% 2.07/2.26 tff(4003,plain,
% 2.07/2.26 (hskp29 | hskp17 | hskp7),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[4002, 3996])).
% 2.07/2.26 tff(4004,plain,
% 2.07/2.26 (hskp7),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[4003, 251, 223])).
% 2.07/2.26 tff(4005,plain,
% 2.07/2.26 (~c3_1(a592)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[736, 4004])).
% 2.07/2.26 tff(4006,plain,
% 2.07/2.26 (~c0_1(a592)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[742, 4004])).
% 2.07/2.26 tff(4007,plain,
% 2.07/2.26 (c2_1(a592)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[750, 4004])).
% 2.07/2.26 tff(4008,plain,
% 2.07/2.26 (c3_1(a599)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[389, 3994])).
% 2.07/2.26 tff(4009,plain,
% 2.07/2.26 (c2_1(a599)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[403, 3994])).
% 2.07/2.26 tff(4010,plain,
% 2.07/2.26 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(4011,plain,
% 2.07/2.26 ((hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633))) <=> (hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(4012,plain,
% 2.07/2.26 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633))))),
% 2.07/2.26 inference(monotonicity,[status(thm)],[4011])).
% 2.07/2.26 tff(4013,plain,
% 2.07/2.26 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633)))),
% 2.07/2.26 inference(transitivity,[status(thm)],[4012, 4010])).
% 2.07/2.26 tff(4014,plain,
% 2.07/2.26 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))),
% 2.07/2.26 inference(quant_inst,[status(thm)],[])).
% 2.07/2.26 tff(4015,plain,
% 2.07/2.26 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633))),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[4014, 4013])).
% 2.07/2.26 tff(4016,plain,
% 2.07/2.26 ((~c0_1(a599)) | c2_1(a633)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[4015, 101, 223, 3851, 427, 3840, 425, 32])).
% 2.07/2.26 tff(4017,plain,
% 2.07/2.26 (~c0_1(a599)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[4016, 3919])).
% 2.07/2.26 tff(4018,plain,
% 2.07/2.26 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(4019,plain,
% 2.07/2.26 ((hskp29 | hskp15 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592))) <=> (hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(4020,plain,
% 2.07/2.26 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592))))),
% 2.07/2.26 inference(monotonicity,[status(thm)],[4019])).
% 2.07/2.26 tff(4021,plain,
% 2.07/2.26 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)))),
% 2.07/2.26 inference(transitivity,[status(thm)],[4020, 4018])).
% 2.07/2.26 tff(4022,plain,
% 2.07/2.26 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)))),
% 2.07/2.26 inference(quant_inst,[status(thm)],[])).
% 2.07/2.26 tff(4023,plain,
% 2.07/2.26 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592))),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[4022, 4021])).
% 2.07/2.26 tff(4024,plain,
% 2.07/2.26 (hskp15 | (~c1_1(a592))),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[4023, 251, 101, 4007, 4005, 1451])).
% 2.07/2.26 tff(4025,plain,
% 2.07/2.26 (~c1_1(a592)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[4024, 3016])).
% 2.07/2.26 tff(4026,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(4027,plain,
% 2.07/2.26 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 2.07/2.26 inference(rewrite,[status(thm)],[])).
% 2.07/2.26 tff(4028,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633))))),
% 2.07/2.26 inference(monotonicity,[status(thm)],[4027])).
% 2.07/2.26 tff(4029,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 2.07/2.26 inference(transitivity,[status(thm)],[4028, 4026])).
% 2.07/2.26 tff(4030,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 2.07/2.26 inference(quant_inst,[status(thm)],[])).
% 2.07/2.26 tff(4031,plain,
% 2.07/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633))),
% 2.07/2.26 inference(modus_ponens,[status(thm)],[4030, 4029])).
% 2.07/2.26 tff(4032,plain,
% 2.07/2.26 (c1_1(a592) | (~c0_1(a607)) | c2_1(a633)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[4031, 101, 3851, 33, 3840, 22, 4006, 4005, 1349])).
% 2.07/2.26 tff(4033,plain,
% 2.07/2.26 (~c0_1(a607)),
% 2.07/2.26 inference(unit_resolution,[status(thm)],[4032, 4025, 3919])).
% 2.07/2.26 tff(4034,plain,
% 2.07/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4035,plain,
% 2.07/2.27 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | c2_1(a607)) <=> (c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4036,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607)))),
% 2.07/2.27 inference(monotonicity,[status(thm)],[4035])).
% 2.07/2.27 tff(4037,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607))),
% 2.07/2.27 inference(transitivity,[status(thm)],[4036, 4034])).
% 2.07/2.27 tff(4038,plain,
% 2.07/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | c2_1(a607))),
% 2.07/2.27 inference(quant_inst,[status(thm)],[])).
% 2.07/2.27 tff(4039,plain,
% 2.07/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607)),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4038, 4037])).
% 2.07/2.27 tff(4040,plain,
% 2.07/2.27 ($false),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4039, 101, 33, 427, 426, 22, 425, 1607, 4033, 4017])).
% 2.07/2.27 tff(4041,plain,(hskp15 | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | c2_1(a607) | c1_1(a599) | (~c1_1(a633)) | c0_1(a633) | hskp29 | c3_1(a633)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.27 tff(4042,plain,
% 2.07/2.27 (hskp15),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4041, 4009, 33, 4008, 22, 3995, 3836, 3838, 251, 3837])).
% 2.07/2.27 tff(4043,plain,
% 2.07/2.27 (~c0_1(a604)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[1474, 4042])).
% 2.07/2.27 tff(4044,plain,
% 2.07/2.27 (c3_1(a604)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[1482, 4042])).
% 2.07/2.27 tff(4045,plain,
% 2.07/2.27 (c1_1(a604)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[1490, 4042])).
% 2.07/2.27 tff(4046,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4047,plain,
% 2.07/2.27 ((hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4048,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607))))),
% 2.07/2.27 inference(monotonicity,[status(thm)],[4047])).
% 2.07/2.27 tff(4049,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607)))),
% 2.07/2.27 inference(transitivity,[status(thm)],[4048, 4046])).
% 2.07/2.27 tff(4050,plain,
% 2.07/2.27 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 2.07/2.27 inference(quant_inst,[status(thm)],[])).
% 2.07/2.27 tff(4051,plain,
% 2.07/2.27 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607))),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4050, 4049])).
% 2.07/2.27 tff(4052,plain,
% 2.07/2.27 (hskp14 | (~c0_1(a607))),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4051, 101, 764, 66, 22, 773, 763, 287])).
% 2.07/2.27 tff(4053,plain,
% 2.07/2.27 (~c0_1(a607)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4052, 340])).
% 2.07/2.27 tff(4054,plain,
% 2.07/2.27 (hskp4),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[156, 4053, 33, 340])).
% 2.07/2.27 tff(4055,plain,
% 2.07/2.27 (~c2_1(a588)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[115, 4054])).
% 2.07/2.27 tff(4056,plain,
% 2.07/2.27 (~c1_1(a588)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[121, 4054])).
% 2.07/2.27 tff(4057,plain,
% 2.07/2.27 (c0_1(a588)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[129, 4054])).
% 2.07/2.27 tff(4058,assumption,(c1_1(a604)), introduced(assumption)).
% 2.07/2.27 tff(4059,plain,
% 2.07/2.27 ($false),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[3940, 101, 33, 4058, 2410, 4057, 22, 2340, 4056, 4055, 1253, 4053])).
% 2.07/2.27 tff(4060,plain,(hskp14 | c3_1(a607) | (~c1_1(a604)) | (~c3_1(a604)) | c2_1(a607) | c0_1(a604) | (~c2_1(a592)) | c1_1(a607) | c0_1(a592) | c3_1(a592)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.27 tff(4061,plain,
% 2.07/2.27 (hskp14),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4060, 4045, 33, 4044, 22, 4043, 4007, 66, 4006, 4005])).
% 2.07/2.27 tff(4062,plain,
% 2.07/2.27 (~c3_1(a603)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[193, 4061])).
% 2.07/2.27 tff(4063,plain,
% 2.07/2.27 (c0_1(a603)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[170, 4061])).
% 2.07/2.27 tff(4064,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4065,plain,
% 2.07/2.27 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4066,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633))))),
% 2.07/2.27 inference(monotonicity,[status(thm)],[4065])).
% 2.07/2.27 tff(4067,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633)))),
% 2.07/2.27 inference(transitivity,[status(thm)],[4066, 4064])).
% 2.07/2.27 tff(4068,plain,
% 2.07/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.07/2.27 inference(quant_inst,[status(thm)],[])).
% 2.07/2.27 tff(4069,plain,
% 2.07/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633))),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4068, 4067])).
% 2.07/2.27 tff(4070,plain,
% 2.07/2.27 (~c2_1(a603)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4069, 101, 3836, 4063, 4009, 4008, 3838, 3837, 4062, 3995, 240])).
% 2.07/2.27 tff(4071,plain,
% 2.07/2.27 (~c1_1(a603)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[162, 4061])).
% 2.07/2.27 tff(4072,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4073,plain,
% 2.07/2.27 (((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4074,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633)))),
% 2.07/2.27 inference(monotonicity,[status(thm)],[4073])).
% 2.07/2.27 tff(4075,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633))),
% 2.07/2.27 inference(transitivity,[status(thm)],[4074, 4072])).
% 2.07/2.27 tff(4076,plain,
% 2.07/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 2.07/2.27 inference(quant_inst,[status(thm)],[])).
% 2.07/2.27 tff(4077,plain,
% 2.07/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633)),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4076, 4075])).
% 2.07/2.27 tff(4078,plain,
% 2.07/2.27 (c2_1(a633)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4077, 101, 4045, 4044, 4063, 3838, 3837, 4043, 4071, 1253, 4070])).
% 2.07/2.27 tff(4079,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4080,plain,
% 2.07/2.27 ((hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607)) <=> (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4081,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599))))),
% 2.07/2.27 inference(monotonicity,[status(thm)],[4080])).
% 2.07/2.27 tff(4082,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)))),
% 2.07/2.27 inference(transitivity,[status(thm)],[4081, 4079])).
% 2.07/2.27 tff(4083,plain,
% 2.07/2.27 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))),
% 2.07/2.27 inference(quant_inst,[status(thm)],[])).
% 2.07/2.27 tff(4084,plain,
% 2.07/2.27 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599))),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4083, 4082])).
% 2.07/2.27 tff(4085,plain,
% 2.07/2.27 (hskp26 | (~c0_1(a599))),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4084, 101, 33, 427, 66, 22, 425, 905])).
% 2.07/2.27 tff(4086,plain,
% 2.07/2.27 (~c0_1(a599)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4085, 660])).
% 2.07/2.27 tff(4087,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4088,plain,
% 2.07/2.27 ((hskp26 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607)) <=> (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4089,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599)))),
% 2.07/2.27 inference(monotonicity,[status(thm)],[4088])).
% 2.07/2.27 tff(4090,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599))),
% 2.07/2.27 inference(transitivity,[status(thm)],[4089, 4087])).
% 2.07/2.27 tff(4091,plain,
% 2.07/2.27 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))),
% 2.07/2.27 inference(quant_inst,[status(thm)],[])).
% 2.07/2.27 tff(4092,plain,
% 2.07/2.27 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599)),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4091, 4090])).
% 2.07/2.27 tff(4093,plain,
% 2.07/2.27 (hskp26 | c0_1(a599)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4092, 101, 33, 426, 66, 22, 425, 637])).
% 2.07/2.27 tff(4094,plain,
% 2.07/2.27 ($false),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4093, 4086, 660])).
% 2.07/2.27 tff(4095,plain,(hskp26 | c3_1(a607) | (~c3_1(a599)) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~c2_1(a599))), inference(lemma,lemma(discharge,[]))).
% 2.07/2.27 tff(4096,plain,
% 2.07/2.27 (hskp26),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4095, 4008, 33, 66, 22, 3995, 4009])).
% 2.07/2.27 tff(4097,plain,
% 2.07/2.27 (c2_1(a583)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[364, 4096])).
% 2.07/2.27 tff(4098,plain,
% 2.07/2.27 (c1_1(a583)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[330, 4096])).
% 2.07/2.27 tff(4099,plain,
% 2.07/2.27 (c0_1(a583)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[338, 4096])).
% 2.07/2.27 tff(4100,plain,
% 2.07/2.27 (hskp12),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[3857, 101, 4099, 4098, 4097, 3836, 3838, 2589, 4078])).
% 2.07/2.27 tff(4101,plain,
% 2.07/2.27 (~c3_1(a600)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[675, 4100])).
% 2.07/2.27 tff(4102,plain,
% 2.07/2.27 (c2_1(a600)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[683, 4100])).
% 2.07/2.27 tff(4103,plain,
% 2.07/2.27 (c0_1(a600)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[691, 4100])).
% 2.07/2.27 tff(4104,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4105,plain,
% 2.07/2.27 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4106,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633))))),
% 2.07/2.27 inference(monotonicity,[status(thm)],[4105])).
% 2.07/2.27 tff(4107,plain,
% 2.07/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 2.07/2.27 inference(transitivity,[status(thm)],[4106, 4104])).
% 2.07/2.27 tff(4108,plain,
% 2.07/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.07/2.27 inference(quant_inst,[status(thm)],[])).
% 2.07/2.27 tff(4109,plain,
% 2.07/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633))),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4108, 4107])).
% 2.07/2.27 tff(4110,plain,
% 2.07/2.27 ($false),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4109, 101, 3836, 4103, 4102, 4009, 4008, 3838, 3837, 4101, 3995, 240])).
% 2.07/2.27 tff(4111,plain,(hskp29 | c3_1(a607) | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.27 tff(4112,plain,
% 2.07/2.27 (hskp29),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4111, 33, 66, 22])).
% 2.07/2.27 tff(4113,plain,
% 2.07/2.27 (c3_1(a678)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[2143, 4112])).
% 2.07/2.27 tff(4114,plain,
% 2.07/2.27 (c2_1(a678)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[2151, 4112])).
% 2.07/2.27 tff(4115,plain,
% 2.07/2.27 (c0_1(a678)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[2159, 4112])).
% 2.07/2.27 tff(4116,plain,
% 2.07/2.27 (hskp11 | c0_1(a607)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[2166, 101, 4115, 4114, 4113, 33, 22, 250])).
% 2.07/2.27 tff(4117,plain,
% 2.07/2.27 (c0_1(a607)),
% 2.07/2.27 inference(unit_resolution,[status(thm)],[4116, 1515])).
% 2.07/2.27 tff(4118,plain,
% 2.07/2.27 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 2.07/2.27 inference(bind,[status(th)],[])).
% 2.07/2.27 tff(4119,plain,
% 2.07/2.27 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.07/2.27 inference(quant_intro,[status(thm)],[4118])).
% 2.07/2.27 tff(4120,plain,
% 2.07/2.27 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.27 tff(4121,plain,
% 2.07/2.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 2.07/2.27 inference(bind,[status(th)],[])).
% 2.07/2.27 tff(4122,plain,
% 2.07/2.27 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.07/2.27 inference(quant_intro,[status(thm)],[4121])).
% 2.07/2.27 tff(4123,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 2.07/2.27 tff(4124,plain,
% 2.07/2.27 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4123, 4122])).
% 2.07/2.27 tff(4125,plain,
% 2.07/2.27 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4124, 4120])).
% 2.07/2.27 tff(4126,plain,(
% 2.07/2.27 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.07/2.27 inference(skolemize,[status(sab)],[4125])).
% 2.07/2.27 tff(4127,plain,
% 2.07/2.27 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.07/2.27 inference(modus_ponens,[status(thm)],[4126, 4119])).
% 2.07/2.27 tff(4128,plain,
% 2.07/2.27 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607)))),
% 2.07/2.27 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4129,plain,
% 2.07/2.28 ((hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c3_1(a607) | c2_1(a607) | (~c0_1(a607))) <=> (hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4130,plain,
% 2.07/2.28 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607))))),
% 2.07/2.28 inference(monotonicity,[status(thm)],[4129])).
% 2.07/2.28 tff(4131,plain,
% 2.07/2.28 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607)))),
% 2.07/2.28 inference(transitivity,[status(thm)],[4130, 4128])).
% 2.07/2.28 tff(4132,plain,
% 2.07/2.28 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)))),
% 2.07/2.28 inference(quant_inst,[status(thm)],[])).
% 2.07/2.28 tff(4133,plain,
% 2.07/2.28 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607))),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 2.07/2.28 tff(4134,plain,
% 2.07/2.28 (hskp8),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4133, 101, 3183, 3192, 33, 22, 4127, 4117, 3879])).
% 2.07/2.28 tff(4135,plain,
% 2.07/2.28 (~c2_1(a593)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[510, 4134])).
% 2.07/2.28 tff(4136,plain,
% 2.07/2.28 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4137,plain,
% 2.07/2.28 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4138,plain,
% 2.07/2.28 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633)))),
% 2.07/2.28 inference(monotonicity,[status(thm)],[4137])).
% 2.07/2.28 tff(4139,plain,
% 2.07/2.28 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633))),
% 2.07/2.28 inference(transitivity,[status(thm)],[4138, 4136])).
% 2.07/2.28 tff(4140,plain,
% 2.07/2.28 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 2.07/2.28 inference(quant_inst,[status(thm)],[])).
% 2.07/2.28 tff(4141,plain,
% 2.07/2.28 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633)),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4140, 4139])).
% 2.07/2.28 tff(4142,plain,
% 2.07/2.28 (hskp11 | c2_1(a633)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4141, 101, 4115, 4114, 4113, 3838, 3837, 250])).
% 2.07/2.28 tff(4143,plain,
% 2.07/2.28 (c2_1(a633)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4142, 1515])).
% 2.07/2.28 tff(4144,plain,
% 2.07/2.28 (c3_1(a593)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[469, 4134])).
% 2.07/2.28 tff(4145,plain,
% 2.07/2.28 (c1_1(a593)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[477, 4134])).
% 2.07/2.28 tff(4146,assumption,(c2_1(a633)), introduced(assumption)).
% 2.07/2.28 tff(4147,plain,
% 2.07/2.28 (^[U: $i] : refl((hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.07/2.28 inference(bind,[status(th)],[])).
% 2.07/2.28 tff(4148,plain,
% 2.07/2.28 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/2.28 inference(quant_intro,[status(thm)],[4147])).
% 2.07/2.28 tff(4149,plain,
% 2.07/2.28 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4150,plain,
% 2.07/2.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp11) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp11) <=> (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.07/2.28 inference(bind,[status(th)],[])).
% 2.07/2.28 tff(4151,plain,
% 2.07/2.28 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp11) <=> ![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/2.28 inference(quant_intro,[status(thm)],[4150])).
% 2.07/2.28 tff(4152,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 2.07/2.28 tff(4153,plain,
% 2.07/2.28 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4152, 4151])).
% 2.07/2.28 tff(4154,plain,
% 2.07/2.28 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4153, 4149])).
% 2.07/2.28 tff(4155,plain,(
% 2.07/2.28 ![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/2.28 inference(skolemize,[status(sab)],[4154])).
% 2.07/2.28 tff(4156,plain,
% 2.07/2.28 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4155, 4148])).
% 2.07/2.28 tff(4157,plain,
% 2.07/2.28 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4158,plain,
% 2.07/2.28 ((hskp11 | hskp15 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c0_1(a593))) <=> (hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4159,plain,
% 2.07/2.28 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593))))),
% 2.07/2.28 inference(monotonicity,[status(thm)],[4158])).
% 2.07/2.28 tff(4160,plain,
% 2.07/2.28 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)))),
% 2.07/2.28 inference(transitivity,[status(thm)],[4159, 4157])).
% 2.07/2.28 tff(4161,plain,
% 2.07/2.28 ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c0_1(a593)))),
% 2.07/2.28 inference(quant_inst,[status(thm)],[])).
% 2.07/2.28 tff(4162,plain,
% 2.07/2.28 ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593))),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 2.07/2.28 tff(4163,plain,
% 2.07/2.28 (hskp15 | (~c0_1(a593))),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4162, 1515, 101, 1780, 1770, 4156])).
% 2.07/2.28 tff(4164,plain,
% 2.07/2.28 (~c0_1(a593)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4163, 3016])).
% 2.07/2.28 tff(4165,plain,
% 2.07/2.28 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4166,plain,
% 2.07/2.28 ((hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4167,plain,
% 2.07/2.28 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.07/2.28 inference(monotonicity,[status(thm)],[4166])).
% 2.07/2.28 tff(4168,plain,
% 2.07/2.28 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.28 inference(transitivity,[status(thm)],[4167, 4165])).
% 2.07/2.28 tff(4169,plain,
% 2.07/2.28 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 2.07/2.28 inference(quant_inst,[status(thm)],[])).
% 2.07/2.28 tff(4170,plain,
% 2.07/2.28 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4169, 4168])).
% 2.07/2.28 tff(4171,plain,
% 2.07/2.28 ($false),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4170, 101, 3016, 3851, 1771, 1780, 3839, 2552, 4164, 4146])).
% 2.07/2.28 tff(4172,plain,(hskp15 | (~c1_1(a633)) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a633) | (~c2_1(a633)) | hskp11 | c2_1(a593)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.28 tff(4173,plain,
% 2.07/2.28 (hskp15),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4172, 4145, 3836, 4144, 3837, 4143, 1515, 4135])).
% 2.07/2.28 tff(4174,plain,
% 2.07/2.28 (~c0_1(a604)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1474, 4173])).
% 2.07/2.28 tff(4175,plain,
% 2.07/2.28 (c3_1(a604)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1482, 4173])).
% 2.07/2.28 tff(4176,plain,
% 2.07/2.28 (c1_1(a604)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1490, 4173])).
% 2.07/2.28 tff(4177,plain,
% 2.07/2.28 (hskp16),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1726, 101, 3183, 3184, 4176, 4175, 4174, 1314, 3879])).
% 2.07/2.28 tff(4178,plain,
% 2.07/2.28 (~c3_1(a606)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[982, 4177])).
% 2.07/2.28 tff(4179,plain,
% 2.07/2.28 (~c2_1(a606)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1015, 4177])).
% 2.07/2.28 tff(4180,plain,
% 2.07/2.28 (c0_1(a606)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[3950, 101, 4176, 4175, 66, 22, 4179, 4178, 4174, 1253, 4117])).
% 2.07/2.28 tff(4181,plain,
% 2.07/2.28 (c1_1(a606)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[992, 4177])).
% 2.07/2.28 tff(4182,plain,
% 2.07/2.28 (hskp0 | (~c0_1(a606))),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[2222, 1515, 101, 4181, 4179, 2215])).
% 2.07/2.28 tff(4183,plain,
% 2.07/2.28 (hskp0),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4182, 4180])).
% 2.07/2.28 tff(4184,plain,
% 2.07/2.28 (~c2_1(a584)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[955, 4183])).
% 2.07/2.28 tff(4185,plain,
% 2.07/2.28 (~c0_1(a584)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[961, 4183])).
% 2.07/2.28 tff(4186,plain,
% 2.07/2.28 (hskp3),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[3885, 101, 223, 3183, 3184, 2236, 3879])).
% 2.07/2.28 tff(4187,plain,
% 2.07/2.28 (~c1_1(a587)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[855, 4186])).
% 2.07/2.28 tff(4188,plain,
% 2.07/2.28 (c1_1(a584)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[969, 4183])).
% 2.07/2.28 tff(4189,plain,
% 2.07/2.28 (c2_1(a587)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[863, 4186])).
% 2.07/2.28 tff(4190,plain,
% 2.07/2.28 (c0_1(a587)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[871, 4186])).
% 2.07/2.28 tff(4191,plain,
% 2.07/2.28 ($false),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[2254, 101, 223, 4190, 4189, 4188, 4187, 4185, 4184, 32])).
% 2.07/2.28 tff(4192,plain,(hskp11 | c1_1(a607) | c2_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.28 tff(4193,plain,
% 2.07/2.28 (hskp11),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4192, 33, 22, 66])).
% 2.07/2.28 tff(4194,plain,
% 2.07/2.28 (~c1_1(a599)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[395, 4193])).
% 2.07/2.28 tff(4195,plain,
% 2.07/2.28 (c3_1(a599)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[389, 4193])).
% 2.07/2.28 tff(4196,plain,
% 2.07/2.28 (c2_1(a599)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[403, 4193])).
% 2.07/2.28 tff(4197,plain,
% 2.07/2.28 ($false),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4109, 101, 3851, 692, 684, 427, 426, 3840, 3839, 676, 425, 240])).
% 2.07/2.28 tff(4198,plain,((~hskp12) | (~c1_1(a633)) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a633) | c3_1(a633) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.28 tff(4199,plain,
% 2.07/2.28 (~hskp12),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4198, 4196, 3836, 4195, 3838, 3837, 4194])).
% 2.07/2.28 tff(4200,plain,
% 2.07/2.28 (hskp26),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4095, 4195, 33, 66, 22, 4194, 4196])).
% 2.07/2.28 tff(4201,plain,
% 2.07/2.28 (c2_1(a583)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[364, 4200])).
% 2.07/2.28 tff(4202,plain,
% 2.07/2.28 (c1_1(a583)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[330, 4200])).
% 2.07/2.28 tff(4203,plain,
% 2.07/2.28 (c0_1(a583)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[338, 4200])).
% 2.07/2.28 tff(4204,plain,
% 2.07/2.28 (hskp12 | (~c2_1(a633))),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[3857, 101, 4203, 4202, 4201, 3836, 3838, 2589])).
% 2.07/2.28 tff(4205,plain,
% 2.07/2.28 (~c2_1(a633)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4204, 4199])).
% 2.07/2.28 tff(4206,plain,
% 2.07/2.28 ((~c0_1(a599)) | c2_1(a633)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4015, 101, 223, 3836, 4196, 3838, 4194, 32])).
% 2.07/2.28 tff(4207,plain,
% 2.07/2.28 (~c0_1(a599)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4206, 4205])).
% 2.07/2.28 tff(4208,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4209,plain,
% 2.07/2.28 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4210,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633))))),
% 2.07/2.28 inference(monotonicity,[status(thm)],[4209])).
% 2.07/2.28 tff(4211,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 2.07/2.28 inference(transitivity,[status(thm)],[4210, 4208])).
% 2.07/2.28 tff(4212,plain,
% 2.07/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.07/2.28 inference(quant_inst,[status(thm)],[])).
% 2.07/2.28 tff(4213,plain,
% 2.07/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633))),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4212, 4211])).
% 2.07/2.28 tff(4214,plain,
% 2.07/2.28 ($false),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4213, 101, 1528, 1526, 3851, 427, 426, 3840, 3839, 425, 240, 1851])).
% 2.07/2.28 tff(4215,plain,(c3_1(a583) | (~c0_1(a583)) | (~c2_1(a583)) | (~c1_1(a633)) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a633) | c3_1(a633) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.28 tff(4216,plain,
% 2.07/2.28 (c3_1(a583)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4215, 4203, 4201, 3836, 4196, 4195, 3838, 3837, 4194])).
% 2.07/2.28 tff(4217,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4218,plain,
% 2.07/2.28 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4219,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)))),
% 2.07/2.28 inference(monotonicity,[status(thm)],[4218])).
% 2.07/2.28 tff(4220,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.07/2.28 inference(transitivity,[status(thm)],[4219, 4217])).
% 2.07/2.28 tff(4221,plain,
% 2.07/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 2.07/2.28 inference(quant_inst,[status(thm)],[])).
% 2.07/2.28 tff(4222,plain,
% 2.07/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4221, 4220])).
% 2.07/2.28 tff(4223,plain,
% 2.07/2.28 ($false),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4222, 101, 4203, 4202, 4196, 4195, 4194, 65, 4216, 4207])).
% 2.07/2.28 tff(4224,plain,(c3_1(a607) | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.28 tff(4225,plain,
% 2.07/2.28 (c3_1(a607)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4224, 22, 66])).
% 2.07/2.28 tff(4226,assumption,(hskp29), introduced(assumption)).
% 2.07/2.28 tff(4227,plain,
% 2.07/2.28 (c3_1(a678)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[2143, 4226])).
% 2.07/2.28 tff(4228,plain,
% 2.07/2.28 (c2_1(a678)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[2151, 4226])).
% 2.07/2.28 tff(4229,plain,
% 2.07/2.28 (c0_1(a678)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[2159, 4226])).
% 2.07/2.28 tff(4230,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4231,plain,
% 2.07/2.28 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.28 inference(rewrite,[status(thm)],[])).
% 2.07/2.28 tff(4232,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.07/2.28 inference(monotonicity,[status(thm)],[4231])).
% 2.07/2.28 tff(4233,plain,
% 2.07/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.07/2.28 inference(transitivity,[status(thm)],[4232, 4230])).
% 2.07/2.28 tff(4234,plain,
% 2.07/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 2.07/2.28 inference(quant_inst,[status(thm)],[])).
% 2.07/2.28 tff(4235,plain,
% 2.07/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.07/2.28 inference(modus_ponens,[status(thm)],[4234, 4233])).
% 2.07/2.28 tff(4236,plain,
% 2.07/2.28 (~c2_1(a633)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4235, 101, 4229, 4228, 4227, 3836, 4225, 3838, 66, 22, 11])).
% 2.07/2.28 tff(4237,plain,
% 2.07/2.28 ($false),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4141, 1515, 101, 4229, 4228, 4227, 3838, 3837, 250, 4236])).
% 2.07/2.28 tff(4238,plain,((~hskp29) | hskp11 | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.07/2.28 tff(4239,plain,
% 2.07/2.28 (~hskp29),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4238, 1515, 66, 22])).
% 2.07/2.28 tff(4240,plain,
% 2.07/2.28 (hskp29 | hskp18),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[3894, 101, 3184, 3192, 1673, 3879])).
% 2.07/2.28 tff(4241,plain,
% 2.07/2.28 (hskp18),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[4240, 4239])).
% 2.07/2.28 tff(4242,plain,
% 2.07/2.28 (~c2_1(a610)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1087, 4241])).
% 2.07/2.28 tff(4243,plain,
% 2.07/2.28 (~c0_1(a610)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1093, 4241])).
% 2.07/2.28 tff(4244,plain,
% 2.07/2.28 (c3_1(a610)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1101, 4241])).
% 2.07/2.28 tff(4245,plain,
% 2.07/2.28 (hskp28),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1735, 101, 3183, 3192, 4244, 4243, 4242, 1026, 3879])).
% 2.07/2.28 tff(4246,plain,
% 2.07/2.28 (c3_1(a612)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1040, 4245])).
% 2.07/2.28 tff(4247,plain,
% 2.07/2.28 (c2_1(a612)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1048, 4245])).
% 2.07/2.28 tff(4248,plain,
% 2.07/2.28 (c1_1(a612)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1321, 4245])).
% 2.07/2.28 tff(4249,plain,
% 2.07/2.28 (hskp10),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[1418, 101, 4248, 4247, 4246, 3183, 3184, 3192, 21])).
% 2.07/2.28 tff(4250,plain,
% 2.07/2.28 (~c1_1(a598)),
% 2.07/2.28 inference(unit_resolution,[status(thm)],[827, 4249])).
% 2.07/2.28 tff(4251,plain,
% 2.07/2.28 (c3_1(a598)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[800, 4249])).
% 2.07/2.29 tff(4252,plain,
% 2.07/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633)))),
% 2.07/2.29 inference(rewrite,[status(thm)],[])).
% 2.07/2.29 tff(4253,plain,
% 2.07/2.29 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633)))),
% 2.07/2.29 inference(rewrite,[status(thm)],[])).
% 2.07/2.29 tff(4254,plain,
% 2.07/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633))))),
% 2.07/2.29 inference(monotonicity,[status(thm)],[4253])).
% 2.07/2.29 tff(4255,plain,
% 2.07/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633)))),
% 2.07/2.29 inference(transitivity,[status(thm)],[4254, 4252])).
% 2.07/2.29 tff(4256,plain,
% 2.07/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.07/2.29 inference(quant_inst,[status(thm)],[])).
% 2.07/2.29 tff(4257,plain,
% 2.07/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633))),
% 2.07/2.29 inference(modus_ponens,[status(thm)],[4256, 4255])).
% 2.07/2.29 tff(4258,plain,
% 2.07/2.29 (~c2_1(a598)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[4257, 101, 3183, 3192, 3836, 4251, 3838, 3837, 4250, 240, 3879])).
% 2.07/2.29 tff(4259,plain,
% 2.07/2.29 (c0_1(a598)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[808, 4249])).
% 2.07/2.29 tff(4260,plain,
% 2.07/2.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598)))),
% 2.07/2.29 inference(rewrite,[status(thm)],[])).
% 2.07/2.29 tff(4261,plain,
% 2.07/2.29 ((hskp1 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c0_1(a598))) <=> (hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598)))),
% 2.07/2.29 inference(rewrite,[status(thm)],[])).
% 2.07/2.29 tff(4262,plain,
% 2.07/2.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598))))),
% 2.07/2.29 inference(monotonicity,[status(thm)],[4261])).
% 2.07/2.29 tff(4263,plain,
% 2.07/2.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598)))),
% 2.07/2.29 inference(transitivity,[status(thm)],[4262, 4260])).
% 2.07/2.29 tff(4264,plain,
% 2.07/2.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c0_1(a598)))),
% 2.07/2.29 inference(quant_inst,[status(thm)],[])).
% 2.07/2.29 tff(4265,plain,
% 2.07/2.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598))),
% 2.07/2.29 inference(modus_ponens,[status(thm)],[4264, 4263])).
% 2.07/2.29 tff(4266,plain,
% 2.07/2.29 (hskp1),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[4265, 101, 3183, 3192, 4259, 4250, 1132, 4258, 3879])).
% 2.07/2.29 tff(4267,plain,
% 2.07/2.29 (~c0_1(a585)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1145, 4266])).
% 2.07/2.29 tff(4268,plain,
% 2.07/2.29 (c2_1(a585)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1153, 4266])).
% 2.07/2.29 tff(4269,plain,
% 2.07/2.29 (c1_1(a585)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1161, 4266])).
% 2.07/2.29 tff(4270,plain,
% 2.07/2.29 (~c0_1(a612)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1188, 101, 4247, 4246, 4225, 4269, 4268, 66, 22, 4267, 11])).
% 2.07/2.29 tff(4271,plain,
% 2.07/2.29 (hskp23),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1565, 1515, 101, 4259, 4251, 4250, 1525])).
% 2.07/2.29 tff(4272,plain,
% 2.07/2.29 (~c1_1(a636)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[439, 4271])).
% 2.07/2.29 tff(4273,plain,
% 2.07/2.29 (~c0_1(a636)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[445, 4271])).
% 2.07/2.29 tff(4274,plain,
% 2.07/2.29 (c3_1(a636)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[453, 4271])).
% 2.07/2.29 tff(4275,plain,
% 2.07/2.29 (hskp9),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1577, 101, 3183, 3184, 3192, 4274, 4273, 4272, 276])).
% 2.07/2.29 tff(4276,plain,
% 2.07/2.29 (~c1_1(a595)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1376, 4275])).
% 2.07/2.29 tff(4277,plain,
% 2.07/2.29 (~c0_1(a595)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1382, 4275])).
% 2.07/2.29 tff(4278,plain,
% 2.07/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 2.07/2.29 inference(rewrite,[status(thm)],[])).
% 2.07/2.29 tff(4279,plain,
% 2.07/2.29 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 2.07/2.29 inference(rewrite,[status(thm)],[])).
% 2.07/2.29 tff(4280,plain,
% 2.07/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636))))),
% 2.07/2.29 inference(monotonicity,[status(thm)],[4279])).
% 2.07/2.29 tff(4281,plain,
% 2.07/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 2.07/2.29 inference(transitivity,[status(thm)],[4280, 4278])).
% 2.07/2.29 tff(4282,plain,
% 2.07/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.07/2.29 inference(quant_inst,[status(thm)],[])).
% 2.07/2.29 tff(4283,plain,
% 2.07/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636))),
% 2.07/2.29 inference(modus_ponens,[status(thm)],[4282, 4281])).
% 2.07/2.29 tff(4284,plain,
% 2.07/2.29 (~c2_1(a636)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[4283, 101, 3183, 3192, 4274, 3836, 4272, 3838, 3837, 240, 3879])).
% 2.07/2.29 tff(4285,plain,
% 2.07/2.29 (hskp15),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[3929, 4239, 3838, 3837, 1515, 3836])).
% 2.07/2.29 tff(4286,plain,
% 2.07/2.29 (~c0_1(a604)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1474, 4285])).
% 2.07/2.29 tff(4287,plain,
% 2.07/2.29 (c3_1(a604)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1482, 4285])).
% 2.07/2.29 tff(4288,plain,
% 2.07/2.29 (c1_1(a604)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1490, 4285])).
% 2.07/2.29 tff(4289,plain,
% 2.07/2.29 (hskp16),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1726, 101, 3183, 3184, 4288, 4287, 4286, 1314, 3879])).
% 2.07/2.29 tff(4290,plain,
% 2.07/2.29 (~c3_1(a606)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[982, 4289])).
% 2.07/2.29 tff(4291,plain,
% 2.07/2.29 (~c2_1(a606)),
% 2.07/2.29 inference(unit_resolution,[status(thm)],[1015, 4289])).
% 2.07/2.29 tff(4292,plain,
% 2.07/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 2.07/2.29 inference(rewrite,[status(thm)],[])).
% 2.07/2.29 tff(4293,plain,
% 2.07/2.29 (((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 2.07/2.29 inference(rewrite,[status(thm)],[])).
% 2.07/2.29 tff(4294,plain,
% 2.07/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606)))),
% 2.15/2.29 inference(monotonicity,[status(thm)],[4293])).
% 2.15/2.29 tff(4295,plain,
% 2.15/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 2.15/2.29 inference(transitivity,[status(thm)],[4294, 4292])).
% 2.15/2.29 tff(4296,plain,
% 2.15/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 2.15/2.29 inference(quant_inst,[status(thm)],[])).
% 2.15/2.29 tff(4297,plain,
% 2.15/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606)),
% 2.15/2.29 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 2.15/2.29 tff(4298,plain,
% 2.15/2.29 (c0_1(a606)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4297, 101, 4288, 4287, 4259, 4291, 4290, 4286, 4250, 1253, 4258])).
% 2.15/2.29 tff(4299,plain,
% 2.15/2.29 (c1_1(a606)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[992, 4289])).
% 2.15/2.29 tff(4300,plain,
% 2.15/2.29 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636))),
% 2.15/2.29 inference(rewrite,[status(thm)],[])).
% 2.15/2.29 tff(4301,plain,
% 2.15/2.29 ((hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a636) | c2_1(a636) | (~c3_1(a636))) <=> (hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636))),
% 2.15/2.29 inference(rewrite,[status(thm)],[])).
% 2.15/2.29 tff(4302,plain,
% 2.15/2.29 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a636) | c2_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636)))),
% 2.15/2.29 inference(monotonicity,[status(thm)],[4301])).
% 2.15/2.29 tff(4303,plain,
% 2.15/2.29 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a636) | c2_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636))),
% 2.15/2.29 inference(transitivity,[status(thm)],[4302, 4300])).
% 2.15/2.29 tff(4304,plain,
% 2.15/2.29 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a636) | c2_1(a636) | (~c3_1(a636)))),
% 2.15/2.29 inference(quant_inst,[status(thm)],[])).
% 2.15/2.29 tff(4305,plain,
% 2.15/2.29 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636)),
% 2.15/2.29 inference(modus_ponens,[status(thm)],[4304, 4303])).
% 2.15/2.29 tff(4306,plain,
% 2.15/2.29 (hskp27),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4305, 101, 4274, 4299, 4273, 4291, 495, 4298, 4284])).
% 2.15/2.29 tff(4307,plain,
% 2.15/2.29 (c3_1(a611)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[566, 4306])).
% 2.15/2.29 tff(4308,plain,
% 2.15/2.29 (c1_1(a611)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[574, 4306])).
% 2.15/2.29 tff(4309,plain,
% 2.15/2.29 (c0_1(a611)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[582, 4306])).
% 2.15/2.29 tff(4310,plain,
% 2.15/2.29 (~c2_1(a595)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[3982, 101, 4247, 4246, 4309, 4308, 4307, 4277, 4276, 65, 4270])).
% 2.15/2.29 tff(4311,plain,
% 2.15/2.29 (~c3_1(a595)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[1370, 4275])).
% 2.15/2.29 tff(4312,plain,
% 2.15/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)))),
% 2.15/2.29 inference(rewrite,[status(thm)],[])).
% 2.15/2.29 tff(4313,plain,
% 2.15/2.29 (((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)))),
% 2.15/2.29 inference(rewrite,[status(thm)],[])).
% 2.15/2.29 tff(4314,plain,
% 2.15/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598))))),
% 2.15/2.29 inference(monotonicity,[status(thm)],[4313])).
% 2.15/2.29 tff(4315,plain,
% 2.15/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)))),
% 2.15/2.29 inference(transitivity,[status(thm)],[4314, 4312])).
% 2.15/2.29 tff(4316,plain,
% 2.15/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 2.15/2.29 inference(quant_inst,[status(thm)],[])).
% 2.15/2.29 tff(4317,plain,
% 2.15/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598))),
% 2.15/2.29 inference(modus_ponens,[status(thm)],[4316, 4315])).
% 2.15/2.29 tff(4318,plain,
% 2.15/2.29 ($false),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4317, 101, 4248, 4246, 4259, 4250, 4277, 4311, 1253, 4258, 4270, 4310])).
% 2.15/2.29 tff(4319,plain,(hskp11 | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.29 tff(4320,plain,
% 2.15/2.29 (hskp11),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4319, 22, 66])).
% 2.15/2.29 tff(4321,plain,
% 2.15/2.29 (~c1_1(a599)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[395, 4320])).
% 2.15/2.29 tff(4322,plain,
% 2.15/2.29 (c2_1(a599)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[403, 4320])).
% 2.15/2.29 tff(4323,plain,
% 2.15/2.29 (c3_1(a599)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[389, 4320])).
% 2.15/2.29 tff(4324,plain,
% 2.15/2.29 (hskp3),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[311, 299, 4225, 66, 22])).
% 2.15/2.29 tff(4325,plain,
% 2.15/2.29 (~c1_1(a587)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[855, 4324])).
% 2.15/2.29 tff(4326,plain,
% 2.15/2.29 (c0_1(a587)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[871, 4324])).
% 2.15/2.29 tff(4327,plain,
% 2.15/2.29 (c2_1(a587)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[863, 4324])).
% 2.15/2.29 tff(4328,plain,
% 2.15/2.29 ($false),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[1391, 4327, 4326, 66, 22, 4225, 660, 302, 300, 301, 4325])).
% 2.15/2.29 tff(4329,plain,((~hskp14) | c1_1(a607) | c2_1(a607) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.15/2.29 tff(4330,plain,
% 2.15/2.29 (~hskp14),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4329, 660, 22, 66])).
% 2.15/2.29 tff(4331,plain,
% 2.15/2.29 (~hskp12),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4198, 4323, 3836, 4322, 3838, 3837, 4321])).
% 2.15/2.29 tff(4332,plain,
% 2.15/2.29 (hskp8),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[712, 660, 4331])).
% 2.15/2.29 tff(4333,plain,
% 2.15/2.29 (~c2_1(a593)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[510, 4332])).
% 2.15/2.29 tff(4334,plain,
% 2.15/2.29 (c3_1(a593)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[469, 4332])).
% 2.15/2.29 tff(4335,plain,
% 2.15/2.29 (c1_1(a593)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[477, 4332])).
% 2.15/2.29 tff(4336,plain,
% 2.15/2.29 (hskp14 | (~c0_1(a599))),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[517, 101, 4322, 4323, 4335, 4334, 4333, 505])).
% 2.15/2.29 tff(4337,plain,
% 2.15/2.29 (~c0_1(a599)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4336, 4330])).
% 2.15/2.29 tff(4338,assumption,(~c2_1(a633)), introduced(assumption)).
% 2.15/2.29 tff(4339,plain,
% 2.15/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633))),
% 2.15/2.29 inference(rewrite,[status(thm)],[])).
% 2.15/2.29 tff(4340,plain,
% 2.15/2.29 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633))),
% 2.15/2.29 inference(rewrite,[status(thm)],[])).
% 2.15/2.29 tff(4341,plain,
% 2.15/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633)))),
% 2.15/2.29 inference(monotonicity,[status(thm)],[4340])).
% 2.15/2.29 tff(4342,plain,
% 2.15/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633))),
% 2.15/2.29 inference(transitivity,[status(thm)],[4341, 4339])).
% 2.15/2.29 tff(4343,plain,
% 2.15/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 2.15/2.29 inference(quant_inst,[status(thm)],[])).
% 2.15/2.29 tff(4344,plain,
% 2.15/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633)),
% 2.15/2.29 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 2.15/2.29 tff(4345,plain,
% 2.15/2.29 ($false),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4344, 101, 427, 426, 3840, 3839, 425, 1607, 3762, 4338])).
% 2.15/2.29 tff(4346,plain,(c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c2_1(a633)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.29 tff(4347,plain,
% 2.15/2.29 (c2_1(a633)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4346, 4337, 4323, 3838, 3837, 4321, 4322])).
% 2.15/2.29 tff(4348,plain,
% 2.15/2.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.29 inference(rewrite,[status(thm)],[])).
% 2.15/2.29 tff(4349,plain,
% 2.15/2.29 ((hskp28 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599))) <=> (hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.29 inference(rewrite,[status(thm)],[])).
% 2.15/2.29 tff(4350,plain,
% 2.15/2.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.15/2.29 inference(monotonicity,[status(thm)],[4349])).
% 2.15/2.29 tff(4351,plain,
% 2.15/2.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.29 inference(transitivity,[status(thm)],[4350, 4348])).
% 2.15/2.29 tff(4352,plain,
% 2.15/2.29 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))),
% 2.15/2.29 inference(quant_inst,[status(thm)],[])).
% 2.15/2.29 tff(4353,plain,
% 2.15/2.29 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.15/2.29 inference(modus_ponens,[status(thm)],[4352, 4351])).
% 2.15/2.29 tff(4354,plain,
% 2.15/2.29 (hskp28 | (~c2_1(a633))),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4353, 101, 3836, 4322, 4323, 3837, 4321, 1625])).
% 2.15/2.29 tff(4355,plain,
% 2.15/2.29 (hskp28),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[4354, 4347])).
% 2.15/2.29 tff(4356,plain,
% 2.15/2.29 (c3_1(a612)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[1040, 4355])).
% 2.15/2.29 tff(4357,plain,
% 2.15/2.29 (c1_1(a612)),
% 2.15/2.29 inference(unit_resolution,[status(thm)],[1321, 4355])).
% 2.15/2.29 tff(4358,plain,
% 2.15/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4359,plain,
% 2.15/2.30 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4360,plain,
% 2.15/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4359])).
% 2.15/2.30 tff(4361,plain,
% 2.15/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4360, 4358])).
% 2.15/2.30 tff(4362,plain,
% 2.15/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4363,plain,
% 2.15/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4362, 4361])).
% 2.15/2.30 tff(4364,plain,
% 2.15/2.30 (~c0_1(a612)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4363, 101, 4357, 4356, 4322, 4323, 4321, 65, 4337])).
% 2.15/2.30 tff(4365,plain,
% 2.15/2.30 (hskp23 | hskp14),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[433, 101, 4322, 4323, 4321, 424])).
% 2.15/2.30 tff(4366,plain,
% 2.15/2.30 (hskp23),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4365, 4330])).
% 2.15/2.30 tff(4367,plain,
% 2.15/2.30 (c3_1(a636)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[453, 4366])).
% 2.15/2.30 tff(4368,plain,
% 2.15/2.30 (~c0_1(a636)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[445, 4366])).
% 2.15/2.30 tff(4369,plain,
% 2.15/2.30 (~c1_1(a636)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[439, 4366])).
% 2.15/2.30 tff(4370,plain,
% 2.15/2.30 (~hskp20),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[668, 4369, 660, 4368, 4367])).
% 2.15/2.30 tff(4371,plain,
% 2.15/2.30 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4372,plain,
% 2.15/2.30 ((hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c1_1(a612))) <=> (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4373,plain,
% 2.15/2.30 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c1_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4372])).
% 2.15/2.30 tff(4374,plain,
% 2.15/2.30 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c1_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4373, 4371])).
% 2.15/2.30 tff(4375,plain,
% 2.15/2.30 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c1_1(a612)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4376,plain,
% 2.15/2.30 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4375, 4374])).
% 2.15/2.30 tff(4377,plain,
% 2.15/2.30 (hskp7),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4376, 101, 4370, 4357, 4356, 726, 4364])).
% 2.15/2.30 tff(4378,plain,
% 2.15/2.30 (~c0_1(a592)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[742, 4377])).
% 2.15/2.30 tff(4379,plain,
% 2.15/2.30 (c2_1(a592)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[750, 4377])).
% 2.15/2.30 tff(4380,plain,
% 2.15/2.30 (~c3_1(a592)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[736, 4377])).
% 2.15/2.30 tff(4381,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4382,plain,
% 2.15/2.30 ((hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4383,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4382])).
% 2.15/2.30 tff(4384,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633)))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4383, 4381])).
% 2.15/2.30 tff(4385,plain,
% 2.15/2.30 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4386,plain,
% 2.15/2.30 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4385, 4384])).
% 2.15/2.30 tff(4387,plain,
% 2.15/2.30 (hskp14 | (~c0_1(a607)) | (~c2_1(a633))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4386, 101, 3838, 3837, 66, 22, 287])).
% 2.15/2.30 tff(4388,plain,
% 2.15/2.30 (~c0_1(a607)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4387, 4347, 4330])).
% 2.15/2.30 tff(4389,plain,
% 2.15/2.30 (hskp26 | hskp0 | c2_1(a607) | c0_1(a607)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[948, 101, 66, 942])).
% 2.15/2.30 tff(4390,plain,
% 2.15/2.30 (hskp0),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4389, 4388, 22, 660])).
% 2.15/2.30 tff(4391,plain,
% 2.15/2.30 (~c2_1(a584)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[955, 4390])).
% 2.15/2.30 tff(4392,plain,
% 2.15/2.30 (~c0_1(a584)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[961, 4390])).
% 2.15/2.30 tff(4393,plain,
% 2.15/2.30 (c1_1(a584)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[969, 4390])).
% 2.15/2.30 tff(4394,plain,
% 2.15/2.30 (hskp14 | (~c0_1(a599))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[517, 101, 4322, 4323, 1771, 1780, 1770, 505])).
% 2.15/2.30 tff(4395,plain,
% 2.15/2.30 (~c0_1(a599)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4394, 340])).
% 2.15/2.30 tff(4396,plain,
% 2.15/2.30 (c2_1(a633)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4346, 4395, 4323, 3838, 3837, 4321, 4322])).
% 2.15/2.30 tff(4397,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4398,plain,
% 2.15/2.30 ((hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4399,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4398])).
% 2.15/2.30 tff(4400,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633)))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4399, 4397])).
% 2.15/2.30 tff(4401,plain,
% 2.15/2.30 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4402,plain,
% 2.15/2.30 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4401, 4400])).
% 2.15/2.30 tff(4403,plain,
% 2.15/2.30 ($false),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4402, 101, 340, 130, 3840, 3839, 122, 116, 287, 4146])).
% 2.15/2.30 tff(4404,plain,((~hskp4) | hskp14 | c0_1(a633) | c3_1(a633) | (~c2_1(a633))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.30 tff(4405,plain,
% 2.15/2.30 (~hskp4),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4404, 340, 3838, 3837, 4396])).
% 2.15/2.30 tff(4406,plain,
% 2.15/2.30 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4407,plain,
% 2.15/2.30 ((hskp10 | hskp4 | (~ndr1_0) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599))) <=> (hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4408,plain,
% 2.15/2.30 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4407])).
% 2.15/2.30 tff(4409,plain,
% 2.15/2.30 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4408, 4406])).
% 2.15/2.30 tff(4410,plain,
% 2.15/2.30 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4411,plain,
% 2.15/2.30 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4410, 4409])).
% 2.15/2.30 tff(4412,plain,
% 2.15/2.30 (hskp10 | hskp4 | c0_1(a599)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4411, 101, 4322, 4323, 783])).
% 2.15/2.30 tff(4413,plain,
% 2.15/2.30 (hskp10),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4412, 4405, 4395])).
% 2.15/2.30 tff(4414,plain,
% 2.15/2.30 (c0_1(a598)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[808, 4413])).
% 2.15/2.30 tff(4415,plain,
% 2.15/2.30 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4416,plain,
% 2.15/2.30 ((hskp29 | hskp18 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633))) <=> (hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4417,plain,
% 2.15/2.30 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4416])).
% 2.15/2.30 tff(4418,plain,
% 2.15/2.30 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4417, 4415])).
% 2.15/2.30 tff(4419,plain,
% 2.15/2.30 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4420,plain,
% 2.15/2.30 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4419, 4418])).
% 2.15/2.30 tff(4421,plain,
% 2.15/2.30 (hskp29 | hskp18 | (~c2_1(a633))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4420, 101, 3836, 3837, 1673])).
% 2.15/2.30 tff(4422,plain,
% 2.15/2.30 (hskp18),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4421, 251, 4396])).
% 2.15/2.30 tff(4423,plain,
% 2.15/2.30 (~c2_1(a610)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1087, 4422])).
% 2.15/2.30 tff(4424,plain,
% 2.15/2.30 (~c0_1(a610)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1093, 4422])).
% 2.15/2.30 tff(4425,plain,
% 2.15/2.30 (hskp6),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[600, 251, 340, 4321, 4323, 4322])).
% 2.15/2.30 tff(4426,plain,
% 2.15/2.30 (~c0_1(a590)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[606, 4425])).
% 2.15/2.30 tff(4427,plain,
% 2.15/2.30 (c3_1(a590)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[614, 4425])).
% 2.15/2.30 tff(4428,plain,
% 2.15/2.30 (c2_1(a590)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[622, 4425])).
% 2.15/2.30 tff(4429,plain,
% 2.15/2.30 (hskp3),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[837, 4428, 4225, 763, 764, 66, 22, 773, 4405, 4427, 4426])).
% 2.15/2.30 tff(4430,plain,
% 2.15/2.30 (c2_1(a587)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[863, 4429])).
% 2.15/2.30 tff(4431,plain,
% 2.15/2.30 (c0_1(a587)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[871, 4429])).
% 2.15/2.30 tff(4432,plain,
% 2.15/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4433,plain,
% 2.15/2.30 (((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4434,plain,
% 2.15/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4433])).
% 2.15/2.30 tff(4435,plain,
% 2.15/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4434, 4432])).
% 2.15/2.30 tff(4436,plain,
% 2.15/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4437,plain,
% 2.15/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4436, 4435])).
% 2.15/2.30 tff(4438,plain,
% 2.15/2.30 (~c3_1(a587)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4437, 101, 3836, 4225, 4431, 4430, 3838, 66, 22, 11, 4396])).
% 2.15/2.30 tff(4439,plain,
% 2.15/2.30 (~c1_1(a587)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[855, 4429])).
% 2.15/2.30 tff(4440,assumption,(c1_1(a584)), introduced(assumption)).
% 2.15/2.30 tff(4441,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4442,plain,
% 2.15/2.30 ((hskp16 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4443,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4442])).
% 2.15/2.30 tff(4444,plain,
% 2.15/2.30 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587)))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4443, 4441])).
% 2.15/2.30 tff(4445,plain,
% 2.15/2.30 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4446,plain,
% 2.15/2.30 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4445, 4444])).
% 2.15/2.30 tff(4447,plain,
% 2.15/2.30 (hskp16),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4446, 101, 4430, 4440, 4439, 3504, 3503, 932, 4438])).
% 2.15/2.30 tff(4448,plain,
% 2.15/2.30 (c1_1(a606)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[992, 4447])).
% 2.15/2.30 tff(4449,plain,
% 2.15/2.30 (c3_1(a610)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1101, 4422])).
% 2.15/2.30 tff(4450,plain,
% 2.15/2.30 (hskp28),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4354, 4396])).
% 2.15/2.30 tff(4451,plain,
% 2.15/2.30 (c3_1(a612)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1040, 4450])).
% 2.15/2.30 tff(4452,plain,
% 2.15/2.30 (c1_1(a612)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1321, 4450])).
% 2.15/2.30 tff(4453,plain,
% 2.15/2.30 (~c0_1(a612)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4363, 101, 4452, 4451, 4322, 4323, 4321, 65, 4395])).
% 2.15/2.30 tff(4454,plain,
% 2.15/2.30 (c3_1(a598)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[800, 4413])).
% 2.15/2.30 tff(4455,plain,
% 2.15/2.30 (~c1_1(a598)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[827, 4413])).
% 2.15/2.30 tff(4456,plain,
% 2.15/2.30 (~hskp27),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[591, 251, 340])).
% 2.15/2.30 tff(4457,plain,
% 2.15/2.30 (c2_1(a612)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1048, 4450])).
% 2.15/2.30 tff(4458,plain,
% 2.15/2.30 (~c2_1(a606)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1015, 4447])).
% 2.15/2.30 tff(4459,plain,
% 2.15/2.30 (~c3_1(a606)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[982, 4447])).
% 2.15/2.30 tff(4460,plain,
% 2.15/2.30 ($false),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1788, 4459, 4458, 1771, 4457, 4456, 1770, 1780, 4455, 4451, 4454, 4453, 4449, 4448, 4424, 4423, 4414])).
% 2.15/2.30 tff(4461,plain,(hskp29 | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a584)) | c0_1(a584) | c2_1(a584) | c1_1(a607) | c2_1(a607) | c3_1(a592) | (~c2_1(a592)) | c0_1(a592) | hskp14), inference(lemma,lemma(discharge,[]))).
% 2.15/2.30 tff(4462,plain,
% 2.15/2.30 (hskp29),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4461, 4335, 4333, 4334, 4393, 4392, 4391, 66, 22, 4380, 4379, 4378, 4330])).
% 2.15/2.30 tff(4463,plain,
% 2.15/2.30 (c3_1(a678)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[2143, 4462])).
% 2.15/2.30 tff(4464,plain,
% 2.15/2.30 (c2_1(a678)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[2151, 4462])).
% 2.15/2.30 tff(4465,plain,
% 2.15/2.30 (c0_1(a678)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[2159, 4462])).
% 2.15/2.30 tff(4466,plain,
% 2.15/2.30 ($false),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4235, 101, 4465, 4464, 4463, 3836, 4225, 3838, 66, 22, 11, 4347])).
% 2.15/2.30 tff(4467,plain,(hskp26 | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.30 tff(4468,plain,
% 2.15/2.30 (hskp26),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4467, 22, 66])).
% 2.15/2.30 tff(4469,plain,
% 2.15/2.30 (c0_1(a583)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[338, 4468])).
% 2.15/2.30 tff(4470,plain,
% 2.15/2.30 (c2_1(a583)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[364, 4468])).
% 2.15/2.30 tff(4471,plain,
% 2.15/2.30 (c3_1(a583)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4215, 4470, 4322, 3836, 4323, 4469, 3838, 3837, 4321])).
% 2.15/2.30 tff(4472,plain,
% 2.15/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4473,plain,
% 2.15/2.30 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4474,plain,
% 2.15/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4473])).
% 2.15/2.30 tff(4475,plain,
% 2.15/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4474, 4472])).
% 2.15/2.30 tff(4476,plain,
% 2.15/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4477,plain,
% 2.15/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4476, 4475])).
% 2.15/2.31 tff(4478,plain,
% 2.15/2.31 (~c2_1(a633)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4477, 101, 4469, 4470, 3836, 4225, 3838, 66, 22, 11, 4471])).
% 2.15/2.31 tff(4479,plain,
% 2.15/2.31 (c1_1(a583)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[330, 4468])).
% 2.15/2.31 tff(4480,plain,
% 2.15/2.31 (hskp10),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1877, 3202])).
% 2.15/2.31 tff(4481,plain,
% 2.15/2.31 (~c1_1(a598)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[827, 4480])).
% 2.15/2.31 tff(4482,plain,
% 2.15/2.31 (c3_1(a598)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[800, 4480])).
% 2.15/2.31 tff(4483,plain,
% 2.15/2.31 (c0_1(a598)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[808, 4480])).
% 2.15/2.31 tff(4484,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1887, 101, 3016, 1528, 1527, 4483, 4482, 4481, 1870, 3202])).
% 2.15/2.31 tff(4485,plain,((~c3_1(a583)) | hskp15 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4486,plain,
% 2.15/2.31 (hskp15),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4485, 4471, 4469, 4479, 4470])).
% 2.15/2.31 tff(4487,plain,
% 2.15/2.31 (~c0_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1474, 4486])).
% 2.15/2.31 tff(4488,plain,
% 2.15/2.31 (c3_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1482, 4486])).
% 2.15/2.31 tff(4489,plain,
% 2.15/2.31 (c1_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1490, 4486])).
% 2.15/2.31 tff(4490,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4491,plain,
% 2.15/2.31 (((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4492,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633)))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4491])).
% 2.15/2.31 tff(4493,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4492, 4490])).
% 2.15/2.31 tff(4494,plain,
% 2.15/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4495,plain,
% 2.15/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633)),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4494, 4493])).
% 2.15/2.31 tff(4496,plain,
% 2.15/2.31 ((~c0_1(a607)) | c2_1(a633)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4495, 101, 4489, 4488, 3838, 3837, 66, 22, 4487, 1253])).
% 2.15/2.31 tff(4497,plain,
% 2.15/2.31 (~c0_1(a607)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4496, 4478])).
% 2.15/2.31 tff(4498,plain,
% 2.15/2.31 (hskp9 | c0_1(a607)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1401, 101, 4469, 4479, 4470, 4225, 66, 276])).
% 2.15/2.31 tff(4499,plain,
% 2.15/2.31 (hskp9),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4498, 4497])).
% 2.15/2.31 tff(4500,plain,
% 2.15/2.31 (~c3_1(a595)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1370, 4499])).
% 2.15/2.31 tff(4501,plain,
% 2.15/2.31 (~c1_1(a595)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1376, 4499])).
% 2.15/2.31 tff(4502,plain,
% 2.15/2.31 (~c0_1(a595)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1382, 4499])).
% 2.15/2.31 tff(4503,plain,
% 2.15/2.31 (hskp1),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1497, 101, 4489, 4488, 4487, 4502, 4501, 4500, 1438])).
% 2.15/2.31 tff(4504,plain,
% 2.15/2.31 (~c0_1(a585)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1145, 4503])).
% 2.15/2.31 tff(4505,plain,
% 2.15/2.31 (c2_1(a585)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1153, 4503])).
% 2.15/2.31 tff(4506,plain,
% 2.15/2.31 (c1_1(a585)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1161, 4503])).
% 2.15/2.31 tff(4507,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1719, 101, 4469, 4470, 4225, 4506, 4505, 66, 22, 4504, 11, 4471])).
% 2.15/2.31 tff(4508,plain,(c2_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4509,plain,
% 2.15/2.31 (c2_1(a607)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4508, 66])).
% 2.15/2.31 tff(4510,plain,
% 2.15/2.31 (~hskp17),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[257, 4509])).
% 2.15/2.31 tff(4511,assumption,(~c1_1(a633)), introduced(assumption)).
% 2.15/2.31 tff(4512,plain,
% 2.15/2.31 (~hskp22),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[3821, 4511])).
% 2.15/2.31 tff(4513,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4514,plain,
% 2.15/2.31 ((hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a633) | c1_1(a633) | c0_1(a633)) <=> (hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4515,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0)))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4514])).
% 2.15/2.31 tff(4516,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4515, 4513])).
% 2.15/2.31 tff(4517,plain,
% 2.15/2.31 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a633) | c1_1(a633) | c0_1(a633))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4518,plain,
% 2.15/2.31 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0)),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4517, 4516])).
% 2.15/2.31 tff(4519,plain,
% 2.15/2.31 (hskp2 | c1_1(a633) | c0_1(a633)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4518, 101, 33, 3839, 66, 4509, 188])).
% 2.15/2.31 tff(4520,plain,
% 2.15/2.31 (hskp2),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4519, 4511, 3840])).
% 2.15/2.31 tff(4521,plain,
% 2.15/2.31 (~c3_1(a586)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[206, 4520])).
% 2.15/2.31 tff(4522,plain,
% 2.15/2.31 (hskp29),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[2135, 4512])).
% 2.15/2.31 tff(4523,plain,
% 2.15/2.31 (c3_1(a678)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[2143, 4522])).
% 2.15/2.31 tff(4524,plain,
% 2.15/2.31 (c2_1(a678)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[2151, 4522])).
% 2.15/2.31 tff(4525,plain,
% 2.15/2.31 (c0_1(a678)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[2159, 4522])).
% 2.15/2.31 tff(4526,plain,
% 2.15/2.31 (hskp11 | c2_1(a633)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4141, 101, 4525, 4524, 4523, 3840, 3839, 250])).
% 2.15/2.31 tff(4527,plain,
% 2.15/2.31 (c2_1(a633)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4526, 1515])).
% 2.15/2.31 tff(4528,plain,
% 2.15/2.31 (~c3_1(a583)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4485, 3016, 3183, 3184, 3192])).
% 2.15/2.31 tff(4529,plain,
% 2.15/2.31 (hskp4 | c3_1(a583)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[3190, 101, 2849, 3183, 3184, 55])).
% 2.15/2.31 tff(4530,plain,
% 2.15/2.31 (hskp4),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4529, 4528])).
% 2.15/2.31 tff(4531,plain,
% 2.15/2.31 (hskp6),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[138, 4530, 4512])).
% 2.15/2.31 tff(4532,plain,
% 2.15/2.31 (~c0_1(a590)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[606, 4531])).
% 2.15/2.31 tff(4533,plain,
% 2.15/2.31 (c3_1(a590)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[614, 4531])).
% 2.15/2.31 tff(4534,plain,
% 2.15/2.31 (c2_1(a590)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[622, 4531])).
% 2.15/2.31 tff(4535,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4536,plain,
% 2.15/2.31 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4537,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4536])).
% 2.15/2.31 tff(4538,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4537, 4535])).
% 2.15/2.31 tff(4539,plain,
% 2.15/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4540,plain,
% 2.15/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4539, 4538])).
% 2.15/2.31 tff(4541,plain,
% 2.15/2.31 (~c1_1(a678)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4540, 101, 4525, 4523, 4511, 4534, 4533, 3840, 4532, 65, 4146])).
% 2.15/2.31 tff(4542,plain,
% 2.15/2.31 (~c2_1(a588)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[115, 4530])).
% 2.15/2.31 tff(4543,plain,
% 2.15/2.31 (c0_1(a588)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[129, 4530])).
% 2.15/2.31 tff(4544,plain,
% 2.15/2.31 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4545,plain,
% 2.15/2.31 ((hskp11 | hskp15 | (~ndr1_0) | c2_1(a588) | (~c3_1(a588)) | (~c0_1(a588))) <=> (hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4546,plain,
% 2.15/2.31 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a588) | (~c3_1(a588)) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4545])).
% 2.15/2.31 tff(4547,plain,
% 2.15/2.31 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a588) | (~c3_1(a588)) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588)))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4546, 4544])).
% 2.15/2.31 tff(4548,plain,
% 2.15/2.31 ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a588) | (~c3_1(a588)) | (~c0_1(a588)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4549,plain,
% 2.15/2.31 ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4548, 4547])).
% 2.15/2.31 tff(4550,plain,
% 2.15/2.31 (~c3_1(a588)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4549, 1515, 101, 3016, 4543, 4542, 4156])).
% 2.15/2.31 tff(4551,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4552,plain,
% 2.15/2.31 ((hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4553,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4552])).
% 2.15/2.31 tff(4554,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590)))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4553, 4551])).
% 2.15/2.31 tff(4555,plain,
% 2.15/2.31 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4556,plain,
% 2.15/2.31 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 2.15/2.31 tff(4557,plain,
% 2.15/2.31 (hskp16),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4556, 101, 4534, 4533, 4543, 4532, 4542, 2002, 4550])).
% 2.15/2.31 tff(4558,plain,
% 2.15/2.31 (~c3_1(a606)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[982, 4557])).
% 2.15/2.31 tff(4559,plain,
% 2.15/2.31 (c1_1(a606)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[992, 4557])).
% 2.15/2.31 tff(4560,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4561,plain,
% 2.15/2.31 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4562,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4561])).
% 2.15/2.31 tff(4563,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4562, 4560])).
% 2.15/2.31 tff(4564,plain,
% 2.15/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4565,plain,
% 2.15/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4564, 4563])).
% 2.15/2.31 tff(4566,plain,
% 2.15/2.31 (c0_1(a606)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4565, 101, 4524, 4523, 3183, 3192, 4559, 4558, 240, 4528, 4541])).
% 2.15/2.31 tff(4567,plain,
% 2.15/2.31 (~c2_1(a606)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1015, 4557])).
% 2.15/2.31 tff(4568,plain,
% 2.15/2.31 (~hskp0),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[3666, 4541, 2849, 4524, 4525])).
% 2.15/2.31 tff(4569,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[2222, 1515, 101, 4568, 4559, 4567, 2215, 4566])).
% 2.15/2.31 tff(4570,plain,(hskp15 | hskp11 | hskp17 | c1_1(a633) | c0_1(a633) | (~c2_1(a633))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4571,plain,
% 2.15/2.31 (hskp15),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4570, 1515, 2849, 4511, 3840, 4527])).
% 2.15/2.31 tff(4572,plain,
% 2.15/2.31 (~c0_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1474, 4571])).
% 2.15/2.31 tff(4573,plain,
% 2.15/2.31 (c3_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1482, 4571])).
% 2.15/2.31 tff(4574,plain,
% 2.15/2.31 (c1_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1490, 4571])).
% 2.15/2.31 tff(4575,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4576,plain,
% 2.15/2.31 ((hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633)) <=> (hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4577,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4576])).
% 2.15/2.31 tff(4578,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4577, 4575])).
% 2.15/2.31 tff(4579,plain,
% 2.15/2.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4580,plain,
% 2.15/2.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4579, 4578])).
% 2.15/2.31 tff(4581,plain,
% 2.15/2.31 (hskp1),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4580, 101, 4511, 4574, 4573, 3840, 3839, 4572, 1438])).
% 2.15/2.31 tff(4582,plain,
% 2.15/2.31 (~c0_1(a585)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1145, 4581])).
% 2.15/2.31 tff(4583,plain,
% 2.15/2.31 (c2_1(a585)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1153, 4581])).
% 2.15/2.31 tff(4584,plain,
% 2.15/2.31 (c1_1(a585)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1161, 4581])).
% 2.15/2.31 tff(4585,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4586,plain,
% 2.15/2.31 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4587,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4586])).
% 2.15/2.31 tff(4588,plain,
% 2.15/2.31 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4587, 4585])).
% 2.15/2.31 tff(4589,plain,
% 2.15/2.31 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4590,plain,
% 2.15/2.31 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 2.15/2.31 tff(4591,plain,
% 2.15/2.31 (hskp12),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4590, 101, 3183, 3184, 3192, 4584, 4583, 4582, 2589])).
% 2.15/2.31 tff(4592,plain,
% 2.15/2.31 (~c3_1(a600)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[675, 4591])).
% 2.15/2.31 tff(4593,plain,
% 2.15/2.31 (c2_1(a600)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[683, 4591])).
% 2.15/2.31 tff(4594,plain,
% 2.15/2.31 (c0_1(a600)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[691, 4591])).
% 2.15/2.31 tff(4595,plain,
% 2.15/2.31 (hskp4),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4529, 1851])).
% 2.15/2.31 tff(4596,plain,
% 2.15/2.31 (hskp6),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[138, 4595, 4512])).
% 2.15/2.31 tff(4597,plain,
% 2.15/2.31 (~c0_1(a590)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[606, 4596])).
% 2.15/2.31 tff(4598,plain,
% 2.15/2.31 (c3_1(a590)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[614, 4596])).
% 2.15/2.31 tff(4599,plain,
% 2.15/2.31 (c2_1(a590)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[622, 4596])).
% 2.15/2.31 tff(4600,plain,
% 2.15/2.31 (~c1_1(a678)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4540, 101, 4525, 4523, 4511, 4599, 4598, 3840, 4597, 65, 4146])).
% 2.15/2.31 tff(4601,assumption,(~c3_1(a600)), introduced(assumption)).
% 2.15/2.31 tff(4602,plain,
% 2.15/2.31 (hskp15),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4570, 1515, 2849, 4511, 3840, 4146])).
% 2.15/2.31 tff(4603,plain,
% 2.15/2.31 (~c0_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1474, 4602])).
% 2.15/2.31 tff(4604,plain,
% 2.15/2.31 (c3_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1482, 4602])).
% 2.15/2.31 tff(4605,plain,
% 2.15/2.31 (c1_1(a604)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1490, 4602])).
% 2.15/2.31 tff(4606,plain,
% 2.15/2.31 (hskp16),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1726, 101, 3183, 3184, 4605, 4604, 4603, 1314, 1851])).
% 2.15/2.31 tff(4607,plain,
% 2.15/2.31 (~c3_1(a606)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[982, 4606])).
% 2.15/2.31 tff(4608,assumption,(c2_1(a600)), introduced(assumption)).
% 2.15/2.31 tff(4609,assumption,(c0_1(a600)), introduced(assumption)).
% 2.15/2.31 tff(4610,plain,
% 2.15/2.31 (c1_1(a606)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[992, 4606])).
% 2.15/2.31 tff(4611,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4612,plain,
% 2.15/2.31 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4613,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4612])).
% 2.15/2.31 tff(4614,plain,
% 2.15/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4613, 4611])).
% 2.15/2.31 tff(4615,plain,
% 2.15/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4616,plain,
% 2.15/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4615, 4614])).
% 2.15/2.31 tff(4617,plain,
% 2.15/2.31 (c0_1(a606)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4616, 101, 4524, 4523, 4610, 4609, 4608, 4607, 4601, 240, 4600])).
% 2.15/2.32 tff(4618,plain,
% 2.15/2.32 (~c2_1(a606)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[1015, 4606])).
% 2.15/2.32 tff(4619,plain,
% 2.15/2.32 (~hskp0),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3666, 4600, 2849, 4524, 4525])).
% 2.15/2.32 tff(4620,plain,
% 2.15/2.32 ($false),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[2222, 1515, 101, 4619, 4610, 4618, 2215, 4617])).
% 2.15/2.32 tff(4621,plain,(c3_1(a583) | hskp11 | (~c0_1(a600)) | (~c2_1(a600)) | c3_1(a600) | hskp17 | c1_1(a633) | c0_1(a633) | (~c2_1(a633))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.32 tff(4622,plain,
% 2.15/2.32 (c3_1(a583)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4621, 1515, 4594, 4593, 4592, 2849, 4511, 3840, 4527])).
% 2.15/2.32 tff(4623,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4624,plain,
% 2.15/2.32 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4625,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[4624])).
% 2.15/2.32 tff(4626,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633)))),
% 2.15/2.32 inference(transitivity,[status(thm)],[4625, 4623])).
% 2.15/2.32 tff(4627,plain,
% 2.15/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(4628,plain,
% 2.15/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4627, 4626])).
% 2.15/2.32 tff(4629,plain,
% 2.15/2.32 (~c2_1(a604)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4628, 101, 3183, 3184, 4511, 4573, 3840, 4572, 65, 4622, 4527])).
% 2.15/2.32 tff(4630,plain,
% 2.15/2.32 (hskp10),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3359, 4622])).
% 2.15/2.32 tff(4631,plain,
% 2.15/2.32 (~c1_1(a598)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[827, 4630])).
% 2.15/2.32 tff(4632,plain,
% 2.15/2.32 (c3_1(a598)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[800, 4630])).
% 2.15/2.32 tff(4633,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4634,plain,
% 2.15/2.32 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4635,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598)))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[4634])).
% 2.15/2.32 tff(4636,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598))),
% 2.15/2.32 inference(transitivity,[status(thm)],[4635, 4633])).
% 2.15/2.32 tff(4637,plain,
% 2.15/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(4638,plain,
% 2.15/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4637, 4636])).
% 2.15/2.32 tff(4639,plain,
% 2.15/2.32 (c2_1(a598)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4638, 101, 4525, 4524, 4523, 4632, 4584, 4583, 4631, 4582, 11])).
% 2.15/2.32 tff(4640,plain,
% 2.15/2.32 (c0_1(a598)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[808, 4630])).
% 2.15/2.32 tff(4641,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4642,plain,
% 2.15/2.32 ((hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4643,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[4642])).
% 2.15/2.32 tff(4644,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604)))),
% 2.15/2.32 inference(transitivity,[status(thm)],[4643, 4641])).
% 2.15/2.32 tff(4645,plain,
% 2.15/2.32 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(4646,plain,
% 2.15/2.32 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4645, 4644])).
% 2.15/2.32 tff(4647,plain,
% 2.15/2.32 ($false),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4646, 101, 2849, 4574, 4640, 4572, 4631, 32, 4639, 4629])).
% 2.15/2.32 tff(4648,plain,(hskp11 | hskp17 | c1_1(a633) | c0_1(a633) | c3_1(a633)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.32 tff(4649,plain,
% 2.15/2.32 (hskp11),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4648, 4511, 4510, 3840, 3839])).
% 2.15/2.32 tff(4650,plain,
% 2.15/2.32 (~c1_1(a599)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[395, 4649])).
% 2.15/2.32 tff(4651,plain,
% 2.15/2.32 (c1_1(a586)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[214, 4520])).
% 2.15/2.32 tff(4652,plain,
% 2.15/2.32 (c3_1(a599)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[389, 4649])).
% 2.15/2.32 tff(4653,plain,
% 2.15/2.32 (c2_1(a599)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[403, 4649])).
% 2.15/2.32 tff(4654,plain,
% 2.15/2.32 (c2_1(a586)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[1357, 4520])).
% 2.15/2.32 tff(4655,plain,
% 2.15/2.32 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4656,plain,
% 2.15/2.32 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607))) <=> (hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4657,plain,
% 2.15/2.32 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0)))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[4656])).
% 2.15/2.32 tff(4658,plain,
% 2.15/2.32 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 2.15/2.32 inference(transitivity,[status(thm)],[4657, 4655])).
% 2.15/2.32 tff(4659,plain,
% 2.15/2.32 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(4660,plain,
% 2.15/2.32 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4659, 4658])).
% 2.15/2.32 tff(4661,plain,
% 2.15/2.32 (hskp4 | hskp3 | c3_1(a607) | (~c2_1(a607))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4660, 101, 66, 762])).
% 2.15/2.32 tff(4662,plain,
% 2.15/2.32 (hskp3),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4661, 752, 4509, 33])).
% 2.15/2.32 tff(4663,plain,
% 2.15/2.32 (~c1_1(a587)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[855, 4662])).
% 2.15/2.32 tff(4664,assumption,(~c3_1(a586)), introduced(assumption)).
% 2.15/2.32 tff(4665,assumption,(c1_1(a586)), introduced(assumption)).
% 2.15/2.32 tff(4666,plain,
% 2.15/2.32 (hskp4 | (~c0_1(a586))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[229, 101, 4510, 4665, 4664, 55])).
% 2.15/2.32 tff(4667,plain,
% 2.15/2.32 (~c0_1(a586)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4666, 752])).
% 2.15/2.32 tff(4668,plain,
% 2.15/2.32 (c2_1(a587)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[863, 4662])).
% 2.15/2.32 tff(4669,plain,
% 2.15/2.32 (c0_1(a587)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[871, 4662])).
% 2.15/2.32 tff(4670,assumption,(~c0_1(a586)), introduced(assumption)).
% 2.15/2.32 tff(4671,plain,
% 2.15/2.32 (~c2_1(a603)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[2177, 101, 302, 427, 426, 4665, 300, 425, 4664, 240, 4670])).
% 2.15/2.32 tff(4672,plain,
% 2.15/2.32 ($false),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[916, 660, 101, 910, 909, 301, 300, 906, 905, 4671])).
% 2.15/2.32 tff(4673,plain,((~hskp14) | hskp26 | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a587) | (~c2_1(a599)) | (~c3_1(a599)) | (~c1_1(a586)) | c1_1(a599) | c3_1(a586) | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.32 tff(4674,plain,
% 2.15/2.32 (~hskp14),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4673, 4669, 660, 4668, 4663, 427, 426, 4665, 425, 4664, 4667])).
% 2.15/2.32 tff(4675,plain,
% 2.15/2.32 (~hskp12),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[700, 4674, 44])).
% 2.15/2.32 tff(4676,assumption,(c2_1(a586)), introduced(assumption)).
% 2.15/2.32 tff(4677,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4678,plain,
% 2.15/2.32 ((hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4679,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586)))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[4678])).
% 2.15/2.32 tff(4680,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586))),
% 2.15/2.32 inference(transitivity,[status(thm)],[4679, 4677])).
% 2.15/2.32 tff(4681,plain,
% 2.15/2.32 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(4682,plain,
% 2.15/2.32 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4681, 4680])).
% 2.15/2.32 tff(4683,plain,
% 2.15/2.32 (hskp12 | (~c1_1(a678))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4682, 101, 2160, 2152, 4665, 4676, 2589, 4667])).
% 2.15/2.32 tff(4684,plain,
% 2.15/2.32 (~c1_1(a678)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4683, 4675])).
% 2.15/2.32 tff(4685,plain,
% 2.15/2.32 (~hskp0),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3666, 4684, 4510, 2152, 2160])).
% 2.15/2.32 tff(4686,plain,
% 2.15/2.32 ((hskp21 | hskp14 | hskp0) <=> (hskp21 | hskp14 | hskp0)),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4687,plain,
% 2.15/2.32 (((hskp14 | hskp21) | hskp0) <=> (hskp21 | hskp14 | hskp0)),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4688,axiom,((hskp14 | hskp21) | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 2.15/2.32 tff(4689,plain,
% 2.15/2.32 (hskp21 | hskp14 | hskp0),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4688, 4687])).
% 2.15/2.32 tff(4690,plain,
% 2.15/2.32 (hskp21 | hskp14 | hskp0),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4689, 4686])).
% 2.15/2.32 tff(4691,plain,
% 2.15/2.32 (hskp21 | hskp14 | hskp0),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4690, 4686])).
% 2.15/2.32 tff(4692,plain,
% 2.15/2.32 (hskp21 | hskp14 | hskp0),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4691, 4686])).
% 2.15/2.32 tff(4693,plain,
% 2.15/2.32 (hskp21 | hskp14 | hskp0),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4692, 4686])).
% 2.15/2.32 tff(4694,plain,
% 2.15/2.32 (hskp21),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4693, 4685, 4674])).
% 2.15/2.32 tff(4695,plain,
% 2.15/2.32 (((~hskp21) | (~c3_1(a629))) <=> ((~hskp21) | (~c3_1(a629)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4696,plain,
% 2.15/2.32 (((~c3_1(a629)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a629)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4697,axiom,((~c3_1(a629)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 2.15/2.32 tff(4698,plain,
% 2.15/2.32 ((~hskp21) | (~c3_1(a629))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4697, 4696])).
% 2.15/2.32 tff(4699,plain,
% 2.15/2.32 ((~hskp21) | (~c3_1(a629))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4698, 4695])).
% 2.15/2.32 tff(4700,plain,
% 2.15/2.32 (~c3_1(a629)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4699, 4694])).
% 2.15/2.32 tff(4701,plain,
% 2.15/2.32 (((~hskp21) | (~c2_1(a629))) <=> ((~hskp21) | (~c2_1(a629)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4702,plain,
% 2.15/2.32 (((~c2_1(a629)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a629)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4703,axiom,((~c2_1(a629)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 2.15/2.32 tff(4704,plain,
% 2.15/2.32 ((~hskp21) | (~c2_1(a629))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4703, 4702])).
% 2.15/2.32 tff(4705,plain,
% 2.15/2.32 ((~hskp21) | (~c2_1(a629))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4704, 4701])).
% 2.15/2.32 tff(4706,plain,
% 2.15/2.32 (~c2_1(a629)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4705, 4694])).
% 2.15/2.32 tff(4707,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4708,plain,
% 2.15/2.32 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c1_1(a629) | c2_1(a629)) <=> (hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4709,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c1_1(a629) | c2_1(a629))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629)))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[4708])).
% 2.15/2.32 tff(4710,plain,
% 2.15/2.32 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c1_1(a629) | c2_1(a629))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629))),
% 2.15/2.32 inference(transitivity,[status(thm)],[4709, 4707])).
% 2.15/2.32 tff(4711,plain,
% 2.15/2.32 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c1_1(a629) | c2_1(a629))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(4712,plain,
% 2.15/2.32 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4711, 4710])).
% 2.15/2.32 tff(4713,plain,
% 2.15/2.32 (c1_1(a629)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4712, 660, 101, 4669, 4668, 4706, 4700, 4663, 905])).
% 2.15/2.32 tff(4714,plain,
% 2.15/2.32 (((~hskp21) | c0_1(a629)) <=> ((~hskp21) | c0_1(a629))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4715,axiom,((~hskp21) | c0_1(a629)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 2.15/2.32 tff(4716,plain,
% 2.15/2.32 ((~hskp21) | c0_1(a629)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4715, 4714])).
% 2.15/2.32 tff(4717,plain,
% 2.15/2.32 ((~hskp21) | c0_1(a629)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4716, 4714])).
% 2.15/2.32 tff(4718,plain,
% 2.15/2.32 ((~hskp21) | c0_1(a629)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4717, 4714])).
% 2.15/2.32 tff(4719,plain,
% 2.15/2.32 ((~hskp21) | c0_1(a629)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4718, 4714])).
% 2.15/2.32 tff(4720,plain,
% 2.15/2.32 ((~hskp21) | c0_1(a629)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4719, 4714])).
% 2.15/2.32 tff(4721,plain,
% 2.15/2.32 (c0_1(a629)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4720, 4694])).
% 2.15/2.32 tff(4722,plain,
% 2.15/2.32 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4723,plain,
% 2.15/2.32 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a629) | (~c1_1(a629)) | (~c0_1(a629))) <=> (hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4724,plain,
% 2.15/2.32 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a629) | (~c1_1(a629)) | (~c0_1(a629)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[4723])).
% 2.15/2.32 tff(4725,plain,
% 2.15/2.32 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a629) | (~c1_1(a629)) | (~c0_1(a629)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629)))),
% 2.15/2.32 inference(transitivity,[status(thm)],[4724, 4722])).
% 2.15/2.32 tff(4726,plain,
% 2.15/2.32 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a629) | (~c1_1(a629)) | (~c0_1(a629)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(4727,plain,
% 2.15/2.32 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4726, 4725])).
% 2.15/2.32 tff(4728,plain,
% 2.15/2.32 ($false),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4727, 101, 4510, 752, 4721, 4700, 55, 4713])).
% 2.15/2.32 tff(4729,plain,(hskp4 | hskp26 | (~c1_1(a586)) | (~c2_1(a586)) | hskp22 | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c3_1(a586) | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.32 tff(4730,plain,
% 2.15/2.32 (hskp4),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4729, 660, 4651, 4654, 4512, 4653, 4652, 4650, 4521, 33, 66])).
% 2.15/2.32 tff(4731,plain,
% 2.15/2.32 (hskp6),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[138, 4730, 4512])).
% 2.15/2.32 tff(4732,plain,
% 2.15/2.32 (~c0_1(a590)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[606, 4731])).
% 2.15/2.32 tff(4733,plain,
% 2.15/2.32 (c3_1(a590)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[614, 4731])).
% 2.15/2.32 tff(4734,plain,
% 2.15/2.32 (c2_1(a590)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[622, 4731])).
% 2.15/2.32 tff(4735,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4736,plain,
% 2.15/2.32 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(4737,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633)))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[4736])).
% 2.15/2.32 tff(4738,plain,
% 2.15/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 2.15/2.32 inference(transitivity,[status(thm)],[4737, 4735])).
% 2.15/2.32 tff(4739,plain,
% 2.15/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(4740,plain,
% 2.15/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[4739, 4738])).
% 2.15/2.32 tff(4741,plain,
% 2.15/2.32 (c2_1(a633)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4740, 101, 4653, 4652, 4734, 4733, 3840, 3839, 4650, 4732, 1607])).
% 2.15/2.33 tff(4742,plain,
% 2.15/2.33 (hskp28),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[3102, 101, 4653, 4652, 4651, 4654, 4650, 4521, 1625])).
% 2.15/2.33 tff(4743,plain,
% 2.15/2.33 (c3_1(a612)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1040, 4742])).
% 2.15/2.33 tff(4744,plain,
% 2.15/2.33 (c1_1(a612)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1321, 4742])).
% 2.15/2.33 tff(4745,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4746,plain,
% 2.15/2.33 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4747,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[4746])).
% 2.15/2.33 tff(4748,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 2.15/2.33 inference(transitivity,[status(thm)],[4747, 4745])).
% 2.15/2.33 tff(4749,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(4750,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[4749, 4748])).
% 2.15/2.33 tff(4751,plain,
% 2.15/2.33 ((~c0_1(a612)) | (~c2_1(a633))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4750, 101, 4744, 4743, 4511, 4734, 4733, 3840, 4732, 65])).
% 2.15/2.33 tff(4752,plain,
% 2.15/2.33 (~c0_1(a612)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4751, 4741])).
% 2.15/2.33 tff(4753,plain,
% 2.15/2.33 (~c2_1(a588)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[115, 4730])).
% 2.15/2.33 tff(4754,plain,
% 2.15/2.33 (~c1_1(a588)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[121, 4730])).
% 2.15/2.33 tff(4755,plain,
% 2.15/2.33 (c2_1(a612)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1048, 4742])).
% 2.15/2.33 tff(4756,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4757,plain,
% 2.15/2.33 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4758,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[4757])).
% 2.15/2.33 tff(4759,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.15/2.33 inference(transitivity,[status(thm)],[4758, 4756])).
% 2.15/2.33 tff(4760,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(4761,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[4760, 4759])).
% 2.15/2.33 tff(4762,plain,
% 2.15/2.33 (~c3_1(a588)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4761, 101, 4525, 4524, 4523, 4744, 4755, 4754, 4753, 11, 4752])).
% 2.15/2.33 tff(4763,plain,
% 2.15/2.33 ((~c1_1(a678)) | (~c2_1(a633))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4540, 101, 4525, 4523, 4511, 4734, 4733, 3840, 4732, 65])).
% 2.15/2.33 tff(4764,plain,
% 2.15/2.33 (~c1_1(a678)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4763, 4741])).
% 2.15/2.33 tff(4765,plain,
% 2.15/2.33 (c0_1(a588)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[129, 4730])).
% 2.15/2.33 tff(4766,plain,
% 2.15/2.33 (hskp14),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4402, 101, 4765, 3840, 3839, 4754, 4753, 287, 4741])).
% 2.15/2.33 tff(4767,plain,
% 2.15/2.33 (~c3_1(a603)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[193, 4766])).
% 2.15/2.33 tff(4768,plain,
% 2.15/2.33 (~c1_1(a603)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[162, 4766])).
% 2.15/2.33 tff(4769,plain,
% 2.15/2.33 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4770,plain,
% 2.15/2.33 ((hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4771,plain,
% 2.15/2.33 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603)))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[4770])).
% 2.15/2.33 tff(4772,plain,
% 2.15/2.33 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603))),
% 2.15/2.33 inference(transitivity,[status(thm)],[4771, 4769])).
% 2.15/2.33 tff(4773,plain,
% 2.15/2.33 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(4774,plain,
% 2.15/2.33 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603)),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[4773, 4772])).
% 2.15/2.33 tff(4775,plain,
% 2.15/2.33 (c2_1(a603)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4774, 660, 101, 4525, 4524, 4768, 4767, 905, 4764])).
% 2.15/2.33 tff(4776,plain,
% 2.15/2.33 (c0_1(a603)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[170, 4766])).
% 2.15/2.33 tff(4777,plain,
% 2.15/2.33 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4778,plain,
% 2.15/2.33 ((hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4779,plain,
% 2.15/2.33 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[4778])).
% 2.15/2.33 tff(4780,plain,
% 2.15/2.33 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.15/2.33 inference(transitivity,[status(thm)],[4779, 4777])).
% 2.15/2.33 tff(4781,plain,
% 2.15/2.33 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(4782,plain,
% 2.15/2.33 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[4781, 4780])).
% 2.15/2.33 tff(4783,plain,
% 2.15/2.33 ($false),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4782, 660, 101, 4776, 4768, 4754, 4753, 905, 4775, 4762])).
% 2.15/2.33 tff(4784,plain,(hskp26 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.33 tff(4785,plain,
% 2.15/2.33 (hskp26),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4784, 4511, 3840, 3839, 33, 66])).
% 2.15/2.33 tff(4786,plain,
% 2.15/2.33 (c1_1(a583)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[330, 4785])).
% 2.15/2.33 tff(4787,plain,
% 2.15/2.33 (c0_1(a583)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[338, 4785])).
% 2.15/2.33 tff(4788,plain,
% 2.15/2.33 (hskp3 | c3_1(a583)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[3885, 101, 4510, 1528, 1527, 2236])).
% 2.15/2.33 tff(4789,plain,
% 2.15/2.33 (c3_1(a583)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4788, 288])).
% 2.15/2.33 tff(4790,plain,
% 2.15/2.33 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4791,plain,
% 2.15/2.33 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586))) <=> (hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4792,plain,
% 2.15/2.33 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[4791])).
% 2.15/2.33 tff(4793,plain,
% 2.15/2.33 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 2.15/2.33 inference(transitivity,[status(thm)],[4792, 4790])).
% 2.15/2.33 tff(4794,plain,
% 2.15/2.33 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(4795,plain,
% 2.15/2.33 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[4794, 4793])).
% 2.15/2.33 tff(4796,plain,
% 2.15/2.33 (hskp3 | (~c0_1(a586))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4795, 101, 4510, 4665, 4664, 2236])).
% 2.15/2.33 tff(4797,plain,
% 2.15/2.33 (~c0_1(a586)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4796, 288])).
% 2.15/2.33 tff(4798,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4799,plain,
% 2.15/2.33 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4800,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[4799])).
% 2.15/2.33 tff(4801,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 2.15/2.33 inference(transitivity,[status(thm)],[4800, 4798])).
% 2.15/2.33 tff(4802,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(4803,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[4802, 4801])).
% 2.15/2.33 tff(4804,plain,
% 2.15/2.33 (c0_1(a586) | (~c0_1(a607))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4803, 101, 33, 427, 426, 4665, 4509, 425, 4664, 240])).
% 2.15/2.33 tff(4805,plain,
% 2.15/2.33 (~c0_1(a607)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4804, 4797])).
% 2.15/2.33 tff(4806,plain,
% 2.15/2.33 (hskp4),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4661, 288, 4509, 33])).
% 2.15/2.33 tff(4807,plain,
% 2.15/2.33 (hskp6),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[138, 4806, 44])).
% 2.15/2.33 tff(4808,plain,
% 2.15/2.33 (~c0_1(a590)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[606, 4807])).
% 2.15/2.33 tff(4809,plain,
% 2.15/2.33 (c3_1(a590)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[614, 4807])).
% 2.15/2.33 tff(4810,plain,
% 2.15/2.33 (c2_1(a590)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[622, 4807])).
% 2.15/2.33 tff(4811,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4812,plain,
% 2.15/2.33 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4813,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[4812])).
% 2.15/2.33 tff(4814,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.15/2.33 inference(transitivity,[status(thm)],[4813, 4811])).
% 2.15/2.33 tff(4815,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(4816,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 2.15/2.33 tff(4817,plain,
% 2.15/2.33 ($false),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4816, 101, 1528, 1527, 4810, 4809, 66, 4509, 4808, 65, 4805, 4789])).
% 2.15/2.33 tff(4818,plain,(hskp3 | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a607) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | (~c1_1(a586)) | c1_1(a599) | c3_1(a586) | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.15/2.33 tff(4819,plain,
% 2.15/2.33 (hskp3),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4818, 4787, 4786, 66, 33, 4653, 4652, 4651, 4650, 4521, 4512])).
% 2.15/2.33 tff(4820,plain,
% 2.15/2.33 (~c1_1(a587)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[855, 4819])).
% 2.15/2.33 tff(4821,plain,
% 2.15/2.33 (c2_1(a583)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[364, 4785])).
% 2.15/2.33 tff(4822,plain,
% 2.15/2.33 (hskp4 | c3_1(a583)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[3190, 101, 4510, 1528, 1527, 55])).
% 2.15/2.33 tff(4823,plain,
% 2.15/2.33 (c3_1(a583)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4822, 752])).
% 2.15/2.33 tff(4824,plain,
% 2.15/2.33 (~c0_1(a607)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4804, 4667])).
% 2.15/2.33 tff(4825,plain,
% 2.15/2.33 (hskp15),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4485, 4823, 1528, 1527, 1526])).
% 2.15/2.33 tff(4826,plain,
% 2.15/2.33 (~c0_1(a604)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1474, 4825])).
% 2.15/2.33 tff(4827,plain,
% 2.15/2.33 (c3_1(a604)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1482, 4825])).
% 2.15/2.33 tff(4828,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4829,plain,
% 2.15/2.33 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4830,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607)))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[4829])).
% 2.15/2.33 tff(4831,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607))),
% 2.15/2.33 inference(transitivity,[status(thm)],[4830, 4828])).
% 2.15/2.33 tff(4832,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(4833,plain,
% 2.15/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607)),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[4832, 4831])).
% 2.15/2.33 tff(4834,plain,
% 2.15/2.33 (~c2_1(a604)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4833, 101, 1528, 1527, 4827, 66, 4509, 4826, 65, 4824, 4823])).
% 2.15/2.33 tff(4835,plain,
% 2.15/2.33 (hskp28),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[3102, 101, 427, 426, 4665, 4676, 425, 4664, 1625])).
% 2.15/2.33 tff(4836,plain,
% 2.15/2.33 (c3_1(a612)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1040, 4835])).
% 2.15/2.33 tff(4837,plain,
% 2.15/2.33 (c2_1(a612)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1048, 4835])).
% 2.15/2.33 tff(4838,plain,
% 2.15/2.33 (c1_1(a612)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1321, 4835])).
% 2.15/2.33 tff(4839,plain,
% 2.15/2.33 (hskp10),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1418, 101, 4838, 4837, 4836, 1528, 1527, 1526, 21])).
% 2.15/2.33 tff(4840,plain,
% 2.15/2.33 (~c1_1(a598)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[827, 4839])).
% 2.15/2.33 tff(4841,plain,
% 2.15/2.33 (c3_1(a598)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[800, 4839])).
% 2.15/2.33 tff(4842,plain,
% 2.15/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(4843,plain,
% 2.15/2.33 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4844,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598)))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[4843])).
% 2.15/2.34 tff(4845,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598))),
% 2.15/2.34 inference(transitivity,[status(thm)],[4844, 4842])).
% 2.15/2.34 tff(4846,plain,
% 2.15/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(4847,plain,
% 2.15/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598)),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[4846, 4845])).
% 2.15/2.34 tff(4848,plain,
% 2.15/2.34 (c2_1(a598)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4847, 101, 2186, 2185, 2184, 4841, 4665, 4676, 4840, 11, 4667])).
% 2.15/2.34 tff(4849,plain,
% 2.15/2.34 (c0_1(a598)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[808, 4839])).
% 2.15/2.34 tff(4850,plain,
% 2.15/2.34 (c1_1(a604)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1490, 4825])).
% 2.15/2.34 tff(4851,plain,
% 2.15/2.34 ($false),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4646, 101, 4510, 4850, 4849, 4826, 4840, 32, 4848, 4834])).
% 2.15/2.34 tff(4852,plain,(hskp4 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a586)) | (~c2_1(a586)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a607) | (~c2_1(a583)) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.34 tff(4853,plain,
% 2.15/2.34 (hskp4),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4852, 4525, 4524, 4523, 4651, 4654, 4787, 4786, 66, 4821, 33, 4653, 4652, 4650, 4521])).
% 2.15/2.34 tff(4854,plain,
% 2.15/2.34 (hskp6),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[138, 4853, 4512])).
% 2.15/2.34 tff(4855,plain,
% 2.15/2.34 (~c0_1(a590)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[606, 4854])).
% 2.15/2.34 tff(4856,plain,
% 2.15/2.34 (c3_1(a590)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[614, 4854])).
% 2.15/2.34 tff(4857,plain,
% 2.15/2.34 (c2_1(a590)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[622, 4854])).
% 2.15/2.34 tff(4858,plain,
% 2.15/2.34 (c2_1(a633)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4740, 101, 4653, 4652, 4857, 4856, 3840, 3839, 4650, 4855, 1607])).
% 2.15/2.34 tff(4859,plain,
% 2.15/2.34 ((~c0_1(a612)) | (~c2_1(a633))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4750, 101, 4744, 4743, 4511, 4857, 4856, 3840, 4855, 65])).
% 2.15/2.34 tff(4860,plain,
% 2.15/2.34 (~c0_1(a612)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4859, 4858])).
% 2.15/2.34 tff(4861,plain,
% 2.15/2.34 (~c2_1(a588)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[115, 4853])).
% 2.15/2.34 tff(4862,plain,
% 2.15/2.34 (~c1_1(a588)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[121, 4853])).
% 2.15/2.34 tff(4863,plain,
% 2.15/2.34 (~c3_1(a588)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4761, 101, 4525, 4524, 4523, 4744, 4755, 4862, 4861, 11, 4860])).
% 2.15/2.34 tff(4864,plain,
% 2.15/2.34 (c0_1(a588)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[129, 4853])).
% 2.15/2.34 tff(4865,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4866,plain,
% 2.15/2.34 ((hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612))) <=> (hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4867,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[4866])).
% 2.15/2.34 tff(4868,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))),
% 2.15/2.34 inference(transitivity,[status(thm)],[4867, 4865])).
% 2.15/2.34 tff(4869,plain,
% 2.15/2.34 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(4870,plain,
% 2.15/2.34 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[4869, 4868])).
% 2.15/2.34 tff(4871,plain,
% 2.15/2.34 (hskp16),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4870, 101, 4755, 4743, 4864, 4861, 2002, 4860, 4863])).
% 2.15/2.34 tff(4872,plain,
% 2.15/2.34 (~c2_1(a606)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1015, 4871])).
% 2.15/2.34 tff(4873,plain,
% 2.15/2.34 (c2_1(a587)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[863, 4819])).
% 2.15/2.34 tff(4874,plain,
% 2.15/2.34 (c0_1(a587)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[871, 4819])).
% 2.15/2.34 tff(4875,plain,
% 2.15/2.34 (c1_1(a606)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[992, 4871])).
% 2.15/2.34 tff(4876,assumption,(~c0_1(a606)), introduced(assumption)).
% 2.15/2.34 tff(4877,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4878,plain,
% 2.15/2.34 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | c2_1(a606) | (~c1_1(a606))) <=> (hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4879,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | c2_1(a606) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[4878])).
% 2.15/2.34 tff(4880,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | c2_1(a606) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606)))),
% 2.15/2.34 inference(transitivity,[status(thm)],[4879, 4877])).
% 2.15/2.34 tff(4881,plain,
% 2.15/2.34 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | c2_1(a606) | (~c1_1(a606)))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(4882,plain,
% 2.15/2.34 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[4881, 4880])).
% 2.15/2.34 tff(4883,plain,
% 2.15/2.34 ($false),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4882, 101, 2849, 1753, 910, 909, 1750, 906, 32, 4876])).
% 2.15/2.34 tff(4884,plain,(c0_1(a606) | hskp17 | (~c1_1(a606)) | (~c0_1(a587)) | (~c2_1(a587)) | c2_1(a606) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.34 tff(4885,plain,
% 2.15/2.34 (c0_1(a606)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4884, 4875, 4510, 4874, 4873, 4872, 4820])).
% 2.15/2.34 tff(4886,plain,
% 2.15/2.34 (hskp15),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2569, 101, 4744, 4743, 4651, 4654, 4521, 2552, 4860])).
% 2.15/2.34 tff(4887,plain,
% 2.15/2.34 (~c0_1(a604)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1474, 4886])).
% 2.15/2.34 tff(4888,plain,
% 2.15/2.34 (~c3_1(a606)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[982, 4871])).
% 2.15/2.34 tff(4889,plain,
% 2.15/2.34 (c1_1(a604)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1490, 4886])).
% 2.15/2.34 tff(4890,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4891,plain,
% 2.15/2.34 (((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633)) <=> (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4892,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[4891])).
% 2.15/2.34 tff(4893,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606)))),
% 2.15/2.34 inference(transitivity,[status(thm)],[4892, 4890])).
% 2.15/2.34 tff(4894,plain,
% 2.15/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(4895,plain,
% 2.15/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[4894, 4893])).
% 2.15/2.34 tff(4896,plain,
% 2.15/2.34 (c2_1(a604)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4895, 101, 4511, 4889, 3840, 3839, 4872, 4888, 4887, 1349, 4885])).
% 2.15/2.34 tff(4897,plain,
% 2.15/2.34 (c3_1(a604)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1482, 4886])).
% 2.15/2.34 tff(4898,plain,
% 2.15/2.34 (~hskp13),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2418, 4896, 4653, 4652, 4887, 4650, 4885, 4525, 4524, 4523, 4875, 4872, 4897])).
% 2.15/2.34 tff(4899,plain,
% 2.15/2.34 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4900,plain,
% 2.15/2.34 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612))) <=> (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4901,plain,
% 2.15/2.34 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[4900])).
% 2.15/2.34 tff(4902,plain,
% 2.15/2.34 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.15/2.34 inference(transitivity,[status(thm)],[4901, 4899])).
% 2.15/2.34 tff(4903,plain,
% 2.15/2.34 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(4904,plain,
% 2.15/2.34 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[4903, 4902])).
% 2.15/2.34 tff(4905,plain,
% 2.15/2.34 (hskp19 | hskp13 | c0_1(a612)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4904, 101, 4744, 4755, 2429])).
% 2.15/2.34 tff(4906,plain,
% 2.15/2.34 (hskp19),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4905, 4898, 4860])).
% 2.15/2.34 tff(4907,plain,
% 2.15/2.34 (~c1_1(a617)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2453, 4906])).
% 2.15/2.34 tff(4908,plain,
% 2.15/2.34 (~c0_1(a617)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2459, 4906])).
% 2.15/2.34 tff(4909,plain,
% 2.15/2.34 (hskp12),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2596, 101, 4744, 4755, 4787, 4786, 4821, 2589, 4860])).
% 2.15/2.34 tff(4910,plain,
% 2.15/2.34 (~c3_1(a600)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[675, 4909])).
% 2.15/2.34 tff(4911,plain,
% 2.15/2.34 (c2_1(a600)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[683, 4909])).
% 2.15/2.34 tff(4912,plain,
% 2.15/2.34 (c0_1(a600)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[691, 4909])).
% 2.15/2.34 tff(4913,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4914,plain,
% 2.15/2.34 ((hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4915,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[4914])).
% 2.15/2.34 tff(4916,plain,
% 2.15/2.34 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.15/2.34 inference(transitivity,[status(thm)],[4915, 4913])).
% 2.15/2.34 tff(4917,plain,
% 2.15/2.34 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(4918,plain,
% 2.15/2.34 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[4917, 4916])).
% 2.15/2.34 tff(4919,plain,
% 2.15/2.34 (hskp8),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4918, 101, 4912, 4911, 4864, 4910, 4861, 4127, 4863])).
% 2.15/2.34 tff(4920,plain,
% 2.15/2.34 (c3_1(a593)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[469, 4919])).
% 2.15/2.34 tff(4921,plain,
% 2.15/2.34 (c1_1(a593)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[477, 4919])).
% 2.15/2.34 tff(4922,plain,
% 2.15/2.34 (c2_1(a617)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2467, 4906])).
% 2.15/2.34 tff(4923,plain,
% 2.15/2.34 (~c0_1(a593)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2481, 101, 4922, 4897, 4921, 4920, 4908, 4907, 4887, 65, 4896])).
% 2.15/2.34 tff(4924,plain,
% 2.15/2.34 (~c2_1(a593)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[510, 4919])).
% 2.15/2.34 tff(4925,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4926,plain,
% 2.15/2.34 (((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a633) | c1_1(a633) | c0_1(a633)) <=> (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4927,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[4926])).
% 2.15/2.34 tff(4928,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 2.15/2.34 inference(transitivity,[status(thm)],[4927, 4925])).
% 2.15/2.34 tff(4929,plain,
% 2.15/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a633) | c1_1(a633) | c0_1(a633))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(4930,plain,
% 2.15/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[4929, 4928])).
% 2.15/2.34 tff(4931,plain,
% 2.15/2.34 ($false),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4930, 101, 4511, 4921, 3840, 3839, 4872, 4888, 4924, 1349, 4923, 4885])).
% 2.15/2.34 tff(4932,plain,(c1_1(a633) | c0_1(a633) | c3_1(a633) | c1_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.34 tff(4933,plain,
% 2.15/2.34 (c1_1(a633)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[4932, 3840, 3839, 66, 33])).
% 2.15/2.34 tff(4934,plain,
% 2.15/2.34 (~c3_1(a583)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[3878, 1515, 3840, 3839, 3851])).
% 2.15/2.34 tff(4935,plain,
% 2.15/2.34 (hskp3),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[3885, 101, 2849, 3183, 3184, 2236, 4934])).
% 2.15/2.34 tff(4936,plain,
% 2.15/2.34 (~c1_1(a587)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[855, 4935])).
% 2.15/2.34 tff(4937,plain,
% 2.15/2.34 (c2_1(a587)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[863, 4935])).
% 2.15/2.34 tff(4938,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4939,plain,
% 2.15/2.34 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a587) | (~c3_1(a587)) | (~c2_1(a587)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(4940,plain,
% 2.15/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a587) | (~c3_1(a587)) | (~c2_1(a587)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[4939])).
% 2.15/2.35 tff(4941,plain,
% 2.15/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a587) | (~c3_1(a587)) | (~c2_1(a587)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[4940, 4938])).
% 2.15/2.35 tff(4942,plain,
% 2.15/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a587) | (~c3_1(a587)) | (~c2_1(a587)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(4943,plain,
% 2.15/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[4942, 4941])).
% 2.15/2.35 tff(4944,plain,
% 2.15/2.35 (~c3_1(a587)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4943, 101, 3183, 3192, 3851, 4937, 3840, 3839, 4936, 240, 4934])).
% 2.15/2.35 tff(4945,plain,
% 2.15/2.35 (^[U: $i] : refl((hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 2.15/2.35 inference(bind,[status(th)],[])).
% 2.15/2.35 tff(4946,plain,
% 2.15/2.35 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.15/2.35 inference(quant_intro,[status(thm)],[4945])).
% 2.15/2.35 tff(4947,plain,
% 2.15/2.35 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(4948,plain,
% 2.15/2.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp11) <=> ((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp11))), rewrite(((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp11) <=> (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 2.15/2.35 inference(bind,[status(th)],[])).
% 2.15/2.35 tff(4949,plain,
% 2.15/2.35 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp11) <=> ![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.15/2.35 inference(quant_intro,[status(thm)],[4948])).
% 2.15/2.35 tff(4950,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 2.15/2.35 tff(4951,plain,
% 2.15/2.35 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[4950, 4949])).
% 2.15/2.35 tff(4952,plain,
% 2.15/2.35 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[4951, 4947])).
% 2.15/2.35 tff(4953,plain,(
% 2.15/2.35 ![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.15/2.35 inference(skolemize,[status(sab)],[4952])).
% 2.15/2.35 tff(4954,plain,
% 2.15/2.35 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[4953, 4946])).
% 2.15/2.35 tff(4955,plain,
% 2.15/2.35 (hskp4),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[3190, 101, 2849, 3183, 3184, 55, 4934])).
% 2.15/2.35 tff(4956,plain,
% 2.15/2.35 (~c2_1(a588)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[115, 4955])).
% 2.15/2.35 tff(4957,plain,
% 2.15/2.35 (~c1_1(a588)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[121, 4955])).
% 2.15/2.35 tff(4958,plain,
% 2.15/2.35 (c0_1(a588)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[129, 4955])).
% 2.15/2.35 tff(4959,plain,
% 2.15/2.35 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(4960,plain,
% 2.15/2.35 ((hskp11 | hskp21 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588))) <=> (hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(4961,plain,
% 2.15/2.35 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[4960])).
% 2.15/2.35 tff(4962,plain,
% 2.15/2.35 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[4961, 4959])).
% 2.15/2.35 tff(4963,plain,
% 2.15/2.35 ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(4964,plain,
% 2.15/2.35 ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[4963, 4962])).
% 2.15/2.35 tff(4965,plain,
% 2.15/2.35 (hskp21),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4964, 1515, 101, 4958, 4957, 4956, 4954])).
% 2.15/2.35 tff(4966,plain,
% 2.15/2.35 (~c3_1(a629)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4699, 4965])).
% 2.15/2.35 tff(4967,plain,
% 2.15/2.35 (~c2_1(a629)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4705, 4965])).
% 2.15/2.35 tff(4968,plain,
% 2.15/2.35 (c0_1(a587)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[871, 4935])).
% 2.15/2.35 tff(4969,plain,
% 2.15/2.35 (c0_1(a629)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4720, 4965])).
% 2.15/2.35 tff(4970,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(4971,plain,
% 2.15/2.35 ((hskp8 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629))) <=> (hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(4972,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[4971])).
% 2.15/2.35 tff(4973,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[4972, 4970])).
% 2.15/2.35 tff(4974,plain,
% 2.15/2.35 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(4975,plain,
% 2.15/2.35 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[4974, 4973])).
% 2.15/2.35 tff(4976,plain,
% 2.15/2.35 (hskp8),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4975, 101, 4969, 4968, 4937, 4967, 4966, 4127, 4944])).
% 2.15/2.35 tff(4977,plain,
% 2.15/2.35 (~c2_1(a593)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[510, 4976])).
% 2.15/2.35 tff(4978,plain,
% 2.15/2.35 (c3_1(a593)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[469, 4976])).
% 2.15/2.35 tff(4979,plain,
% 2.15/2.35 (c1_1(a593)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[477, 4976])).
% 2.15/2.35 tff(4980,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(4981,plain,
% 2.15/2.35 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633))) <=> (hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(4982,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[4981])).
% 2.15/2.35 tff(4983,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[4982, 4980])).
% 2.15/2.35 tff(4984,plain,
% 2.15/2.35 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(4985,plain,
% 2.15/2.35 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[4984, 4983])).
% 2.15/2.35 tff(4986,plain,
% 2.15/2.35 (c2_1(a633)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4985, 101, 2849, 3851, 4968, 4937, 3840, 4936, 32])).
% 2.15/2.35 tff(4987,plain,
% 2.15/2.35 (hskp15),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4172, 4977, 1515, 4978, 3839, 4986, 4979, 3851])).
% 2.15/2.35 tff(4988,plain,
% 2.15/2.35 (~c0_1(a604)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1474, 4987])).
% 2.15/2.35 tff(4989,plain,
% 2.15/2.35 (c3_1(a604)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1482, 4987])).
% 2.15/2.35 tff(4990,plain,
% 2.15/2.35 (c1_1(a604)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1490, 4987])).
% 2.15/2.35 tff(4991,plain,
% 2.15/2.35 (hskp16),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1726, 101, 3183, 3184, 4990, 4989, 4988, 1314, 4934])).
% 2.15/2.35 tff(4992,plain,
% 2.15/2.35 (~c2_1(a606)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1015, 4991])).
% 2.15/2.35 tff(4993,plain,
% 2.15/2.35 (c1_1(a606)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[992, 4991])).
% 2.15/2.35 tff(4994,plain,
% 2.15/2.35 (c0_1(a606)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4884, 4993, 2849, 4968, 4937, 4992, 4936])).
% 2.15/2.35 tff(4995,plain,
% 2.15/2.35 (hskp0),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[2222, 1515, 101, 4993, 4992, 2215, 4994])).
% 2.15/2.35 tff(4996,plain,
% 2.15/2.35 (~c2_1(a584)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[955, 4995])).
% 2.15/2.35 tff(4997,plain,
% 2.15/2.35 (c1_1(a584)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[969, 4995])).
% 2.15/2.35 tff(4998,plain,
% 2.15/2.35 (~c0_1(a584)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[961, 4995])).
% 2.15/2.35 tff(4999,plain,
% 2.15/2.35 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5000,plain,
% 2.15/2.35 ((hskp17 | hskp3 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a593))) <=> (hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5001,plain,
% 2.15/2.35 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5000])).
% 2.15/2.35 tff(5002,plain,
% 2.15/2.35 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5001, 4999])).
% 2.15/2.35 tff(5003,plain,
% 2.15/2.35 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5004,plain,
% 2.15/2.35 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5003, 5002])).
% 2.15/2.35 tff(5005,plain,
% 2.15/2.35 (hskp17 | hskp3),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5004, 101, 1771, 1780, 1770, 3282])).
% 2.15/2.35 tff(5006,plain,
% 2.15/2.35 (hskp3),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5005, 2849])).
% 2.15/2.35 tff(5007,plain,
% 2.15/2.35 (~c1_1(a587)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[855, 5006])).
% 2.15/2.35 tff(5008,plain,
% 2.15/2.35 (c2_1(a587)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[863, 5006])).
% 2.15/2.35 tff(5009,plain,
% 2.15/2.35 (c0_1(a587)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[871, 5006])).
% 2.15/2.35 tff(5010,plain,
% 2.15/2.35 ($false),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[2254, 101, 2849, 5009, 5008, 4440, 5007, 3504, 3503, 32])).
% 2.15/2.35 tff(5011,plain,(hskp17 | (~c1_1(a584)) | c0_1(a584) | c2_1(a584) | (~c1_1(a593)) | (~c3_1(a593)) | c2_1(a593)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.35 tff(5012,plain,
% 2.15/2.35 ($false),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5011, 4998, 4997, 2849, 4996, 4979, 4978, 4977])).
% 2.15/2.35 tff(5013,plain,(hskp11 | hskp17 | c3_1(a633) | (~c1_1(a633)) | c0_1(a633)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.35 tff(5014,plain,
% 2.15/2.35 (hskp11),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5013, 4933, 3839, 4510, 3840])).
% 2.15/2.35 tff(5015,plain,
% 2.15/2.35 (~c1_1(a599)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[395, 5014])).
% 2.15/2.35 tff(5016,plain,
% 2.15/2.35 (c3_1(a599)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[389, 5014])).
% 2.15/2.35 tff(5017,plain,
% 2.15/2.35 (c2_1(a599)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[403, 5014])).
% 2.15/2.35 tff(5018,plain,
% 2.15/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5019,plain,
% 2.15/2.35 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5020,plain,
% 2.15/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5019])).
% 2.15/2.35 tff(5021,plain,
% 2.15/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5020, 5018])).
% 2.15/2.35 tff(5022,plain,
% 2.15/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5023,plain,
% 2.15/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5022, 5021])).
% 2.15/2.35 tff(5024,plain,
% 2.15/2.35 (~c0_1(a607)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5023, 101, 4933, 33, 5017, 5016, 3840, 3839, 4509, 5015, 240])).
% 2.15/2.35 tff(5025,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5026,plain,
% 2.15/2.35 ((hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a607) | c1_1(a607) | c0_1(a607)) <=> (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5027,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5026])).
% 2.15/2.35 tff(5028,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5027, 5025])).
% 2.15/2.35 tff(5029,plain,
% 2.15/2.35 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a607) | c1_1(a607) | c0_1(a607))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5030,plain,
% 2.15/2.35 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5029, 5028])).
% 2.15/2.35 tff(5031,plain,
% 2.15/2.35 (hskp2 | c0_1(a607)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5030, 101, 33, 66, 4509, 188])).
% 2.15/2.35 tff(5032,plain,
% 2.15/2.35 (hskp2),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5031, 5024])).
% 2.15/2.35 tff(5033,plain,
% 2.15/2.35 (~c3_1(a586)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[206, 5032])).
% 2.15/2.35 tff(5034,plain,
% 2.15/2.35 (c2_1(a586)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1357, 5032])).
% 2.15/2.35 tff(5035,plain,
% 2.15/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5036,plain,
% 2.15/2.35 (((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5037,plain,
% 2.15/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5036])).
% 2.15/2.35 tff(5038,plain,
% 2.15/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5037, 5035])).
% 2.15/2.35 tff(5039,plain,
% 2.15/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5040,plain,
% 2.15/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5039, 5038])).
% 2.15/2.35 tff(5041,plain,
% 2.15/2.35 (~c0_1(a586)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5040, 101, 4933, 5017, 5016, 5034, 3840, 3839, 5015, 5033, 240])).
% 2.15/2.35 tff(5042,plain,
% 2.15/2.35 (c1_1(a586)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[214, 5032])).
% 2.15/2.35 tff(5043,plain,
% 2.15/2.35 (hskp28),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[3102, 101, 5017, 5016, 5042, 5034, 5015, 5033, 1625])).
% 2.15/2.35 tff(5044,plain,
% 2.15/2.35 (c2_1(a612)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1048, 5043])).
% 2.15/2.35 tff(5045,plain,
% 2.15/2.35 (c1_1(a612)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1321, 5043])).
% 2.15/2.35 tff(5046,plain,
% 2.15/2.35 (~hskp12),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4198, 5016, 4933, 5017, 3840, 3839, 5015])).
% 2.15/2.35 tff(5047,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5048,plain,
% 2.15/2.35 ((hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5049,plain,
% 2.15/2.35 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5048])).
% 2.15/2.36 tff(5050,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5049, 5047])).
% 2.15/2.36 tff(5051,plain,
% 2.15/2.36 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5052,plain,
% 2.15/2.36 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5051, 5050])).
% 2.15/2.36 tff(5053,plain,
% 2.15/2.36 (~c0_1(a612)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5052, 101, 5046, 5045, 5044, 5042, 5034, 2589, 5041])).
% 2.15/2.36 tff(5054,plain,
% 2.15/2.36 (c3_1(a612)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1040, 5043])).
% 2.15/2.36 tff(5055,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5056,plain,
% 2.15/2.36 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5057,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633)))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5056])).
% 2.15/2.36 tff(5058,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5057, 5055])).
% 2.15/2.36 tff(5059,plain,
% 2.15/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5060,plain,
% 2.15/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633)),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5059, 5058])).
% 2.15/2.36 tff(5061,plain,
% 2.15/2.36 (c2_1(a633)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5060, 101, 5044, 5054, 5017, 5016, 3840, 3839, 5015, 1607, 5053])).
% 2.15/2.36 tff(5062,assumption,(hskp8), introduced(assumption)).
% 2.15/2.36 tff(5063,plain,
% 2.15/2.36 (c3_1(a593)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[469, 5062])).
% 2.15/2.36 tff(5064,plain,
% 2.15/2.36 (c1_1(a593)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[477, 5062])).
% 2.15/2.36 tff(5065,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5066,plain,
% 2.15/2.36 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5067,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607)))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5066])).
% 2.15/2.36 tff(5068,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5067, 5065])).
% 2.15/2.36 tff(5069,plain,
% 2.15/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5070,plain,
% 2.15/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607)),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5069, 5068])).
% 2.15/2.36 tff(5071,plain,
% 2.15/2.36 (~c0_1(a593)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5070, 101, 1761, 1760, 5064, 5063, 66, 4509, 65, 1, 1757])).
% 2.15/2.36 tff(5072,plain,
% 2.15/2.36 (~c2_1(a593)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[510, 5062])).
% 2.15/2.36 tff(5073,plain,
% 2.15/2.36 (hskp3),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5004, 101, 4510, 5064, 5063, 5072, 3282])).
% 2.15/2.36 tff(5074,plain,
% 2.15/2.36 (~c1_1(a587)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[855, 5073])).
% 2.15/2.36 tff(5075,plain,
% 2.15/2.36 (c2_1(a587)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[863, 5073])).
% 2.15/2.36 tff(5076,plain,
% 2.15/2.36 (c0_1(a587)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[871, 5073])).
% 2.15/2.36 tff(5077,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5078,plain,
% 2.15/2.36 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5079,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5078])).
% 2.15/2.36 tff(5080,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5079, 5077])).
% 2.15/2.36 tff(5081,plain,
% 2.15/2.36 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5082,plain,
% 2.15/2.36 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5081, 5080])).
% 2.15/2.36 tff(5083,plain,
% 2.15/2.36 ($false),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5082, 101, 4510, 5064, 5076, 5075, 5072, 5074, 32, 5071])).
% 2.15/2.36 tff(5084,plain,((~hskp8) | (~c2_1(a612)) | (~c3_1(a612)) | c1_1(a607) | c0_1(a607) | c0_1(a612)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.36 tff(5085,plain,
% 2.15/2.36 (~hskp8),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5084, 5044, 5054, 66, 5024, 5053])).
% 2.15/2.36 tff(5086,plain,
% 2.15/2.36 (hskp26),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[712, 5085, 5046])).
% 2.15/2.36 tff(5087,plain,
% 2.15/2.36 (c2_1(a583)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[364, 5086])).
% 2.15/2.36 tff(5088,plain,
% 2.15/2.36 (c1_1(a583)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[330, 5086])).
% 2.15/2.36 tff(5089,plain,
% 2.15/2.36 (c0_1(a583)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[338, 5086])).
% 2.15/2.36 tff(5090,plain,
% 2.15/2.36 ($false),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[3857, 101, 5046, 5089, 5088, 5087, 4933, 3840, 2589, 5061])).
% 2.15/2.36 tff(5091,plain,(c0_1(a633) | c1_1(a607) | c3_1(a633) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.36 tff(5092,plain,
% 2.15/2.36 (c0_1(a633)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5091, 3839, 66, 33])).
% 2.15/2.36 tff(5093,plain,
% 2.15/2.36 (~hskp22),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[3827, 5092])).
% 2.15/2.36 tff(5094,plain,
% 2.15/2.36 (hskp2),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5031, 1])).
% 2.15/2.36 tff(5095,plain,
% 2.15/2.36 (~c3_1(a586)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[206, 5094])).
% 2.15/2.36 tff(5096,plain,
% 2.15/2.36 (hskp4 | c3_1(a583)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[3190, 101, 4510, 3183, 3184, 55])).
% 2.15/2.36 tff(5097,plain,
% 2.15/2.36 (c3_1(a583)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5096, 752])).
% 2.15/2.36 tff(5098,plain,
% 2.15/2.36 (hskp10),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[3359, 5097])).
% 2.15/2.36 tff(5099,plain,
% 2.15/2.36 (~c1_1(a598)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[827, 5098])).
% 2.15/2.36 tff(5100,plain,
% 2.15/2.36 (c3_1(a598)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[800, 5098])).
% 2.15/2.36 tff(5101,plain,
% 2.15/2.36 (c0_1(a598)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[808, 5098])).
% 2.15/2.36 tff(5102,plain,
% 2.15/2.36 (hskp23),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1565, 1515, 101, 5101, 5100, 5099, 1525])).
% 2.15/2.36 tff(5103,plain,
% 2.15/2.36 (~c1_1(a636)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[439, 5102])).
% 2.15/2.36 tff(5104,plain,
% 2.15/2.36 (~c0_1(a636)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[445, 5102])).
% 2.15/2.36 tff(5105,plain,
% 2.15/2.36 (c3_1(a636)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[453, 5102])).
% 2.15/2.36 tff(5106,plain,
% 2.15/2.36 (~c2_1(a636)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[3210, 5105, 3184, 5097, 5104, 5103, 3183])).
% 2.15/2.36 tff(5107,plain,
% 2.15/2.36 (hskp15),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[4485, 5097, 3183, 3184, 3192])).
% 2.15/2.36 tff(5108,plain,
% 2.15/2.36 (~c0_1(a604)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1474, 5107])).
% 2.15/2.36 tff(5109,plain,
% 2.15/2.36 (c1_1(a604)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1490, 5107])).
% 2.15/2.36 tff(5110,plain,
% 2.15/2.36 (c2_1(a604)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[2982, 101, 4510, 5109, 4669, 4668, 5108, 4663, 32])).
% 2.15/2.36 tff(5111,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5112,plain,
% 2.15/2.36 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5113,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5112])).
% 2.15/2.36 tff(5114,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5113, 5111])).
% 2.15/2.36 tff(5115,plain,
% 2.15/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5116,plain,
% 2.15/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5115, 5114])).
% 2.15/2.36 tff(5117,plain,
% 2.15/2.36 (c2_1(a598) | (~c2_1(a604))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5116, 101, 2186, 2185, 2184, 5109, 5100, 5108, 5099, 11])).
% 2.15/2.36 tff(5118,plain,
% 2.15/2.36 (c2_1(a598)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5117, 5110])).
% 2.15/2.36 tff(5119,plain,
% 2.15/2.36 ($false),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[3378, 101, 5105, 5109, 5101, 5100, 5103, 5108, 11, 5118, 5110, 5106])).
% 2.15/2.36 tff(5120,plain,(hskp4 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | hskp11 | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.36 tff(5121,plain,
% 2.15/2.36 (hskp4),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5120, 1515, 2152, 2144, 2160, 33, 66])).
% 2.15/2.36 tff(5122,plain,
% 2.15/2.36 (hskp6),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[138, 5121, 44])).
% 2.15/2.36 tff(5123,plain,
% 2.15/2.36 (~c0_1(a590)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[606, 5122])).
% 2.15/2.36 tff(5124,plain,
% 2.15/2.36 (~c2_1(a588)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[115, 5121])).
% 2.15/2.36 tff(5125,plain,
% 2.15/2.36 (~c1_1(a588)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[121, 5121])).
% 2.15/2.36 tff(5126,plain,
% 2.15/2.36 (c0_1(a588)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[129, 5121])).
% 2.15/2.36 tff(5127,plain,
% 2.15/2.36 (hskp21),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[4964, 1515, 101, 5126, 5125, 5124, 4954])).
% 2.15/2.36 tff(5128,plain,
% 2.15/2.36 (~c3_1(a629)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[4699, 5127])).
% 2.15/2.36 tff(5129,plain,
% 2.15/2.36 (~c2_1(a629)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[4705, 5127])).
% 2.15/2.36 tff(5130,plain,
% 2.15/2.36 (c3_1(a590)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[614, 5122])).
% 2.15/2.36 tff(5131,plain,
% 2.15/2.36 (c2_1(a590)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[622, 5122])).
% 2.15/2.36 tff(5132,plain,
% 2.15/2.36 (c0_1(a629)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[4720, 5127])).
% 2.15/2.36 tff(5133,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5134,plain,
% 2.15/2.36 ((hskp16 | (~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5135,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5134])).
% 2.15/2.36 tff(5136,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5135, 5133])).
% 2.15/2.36 tff(5137,plain,
% 2.15/2.36 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5138,plain,
% 2.15/2.36 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5137, 5136])).
% 2.15/2.36 tff(5139,plain,
% 2.15/2.36 (hskp16),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5138, 101, 5132, 5131, 5130, 5129, 5128, 5123, 2002])).
% 2.15/2.36 tff(5140,plain,
% 2.15/2.36 (~c3_1(a606)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[982, 5139])).
% 2.15/2.36 tff(5141,plain,
% 2.15/2.36 (~c2_1(a606)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1015, 5139])).
% 2.15/2.36 tff(5142,plain,
% 2.15/2.36 (c0_1(a606)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[2204, 1515, 101, 2160, 2152, 2144, 5141, 5140, 250])).
% 2.15/2.36 tff(5143,plain,
% 2.15/2.36 (c1_1(a606)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[992, 5139])).
% 2.15/2.36 tff(5144,plain,
% 2.15/2.36 (hskp0 | (~c0_1(a606))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[2222, 1515, 101, 5143, 5141, 2215])).
% 2.15/2.36 tff(5145,plain,
% 2.15/2.36 (hskp0),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5144, 5142])).
% 2.15/2.36 tff(5146,plain,
% 2.15/2.36 (c1_1(a678)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[3666, 5145, 4510, 2152, 2160])).
% 2.15/2.36 tff(5147,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5148,plain,
% 2.15/2.36 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5149,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5148])).
% 2.15/2.36 tff(5150,plain,
% 2.15/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5149, 5147])).
% 2.15/2.36 tff(5151,plain,
% 2.15/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5152,plain,
% 2.15/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5151, 5150])).
% 2.15/2.36 tff(5153,plain,
% 2.15/2.36 ((~c1_1(a678)) | c0_1(a607)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5152, 101, 2160, 2144, 5131, 5130, 66, 4509, 5123, 65])).
% 2.15/2.36 tff(5154,plain,
% 2.15/2.36 (c0_1(a607)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5153, 5146])).
% 2.15/2.36 tff(5155,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5156,plain,
% 2.15/2.36 ((hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629))) <=> (hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5157,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5156])).
% 2.15/2.36 tff(5158,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5157, 5155])).
% 2.15/2.36 tff(5159,plain,
% 2.15/2.36 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5160,plain,
% 2.15/2.36 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5159, 5158])).
% 2.15/2.36 tff(5161,plain,
% 2.15/2.36 (hskp8 | (~c0_1(a607))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5160, 101, 5132, 33, 5129, 5128, 4509, 4127])).
% 2.15/2.36 tff(5162,plain,
% 2.15/2.36 (hskp8),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5161, 5154])).
% 2.15/2.36 tff(5163,plain,
% 2.15/2.36 (~c2_1(a593)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[510, 5162])).
% 2.15/2.36 tff(5164,plain,
% 2.15/2.36 (~c0_1(a584)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[961, 5145])).
% 2.15/2.36 tff(5165,plain,
% 2.15/2.36 (c1_1(a584)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[969, 5145])).
% 2.15/2.36 tff(5166,plain,
% 2.15/2.36 (~c2_1(a584)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[955, 5145])).
% 2.15/2.36 tff(5167,plain,
% 2.15/2.36 (c1_1(a593)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[477, 5162])).
% 2.15/2.36 tff(5168,plain,
% 2.15/2.36 (c3_1(a593)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[469, 5162])).
% 2.15/2.36 tff(5169,plain,
% 2.15/2.36 ($false),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5011, 5168, 5167, 4510, 5166, 5165, 5164, 5163])).
% 2.15/2.36 tff(5170,plain,(hskp11 | c3_1(a607) | c1_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.15/2.36 tff(5171,plain,
% 2.15/2.36 (hskp11),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5170, 5093, 66, 33])).
% 2.15/2.36 tff(5172,plain,
% 2.15/2.36 (~c1_1(a599)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[395, 5171])).
% 2.15/2.36 tff(5173,plain,
% 2.15/2.36 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5174,plain,
% 2.15/2.36 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633))) <=> (hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5175,plain,
% 2.15/2.36 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5174])).
% 2.15/2.36 tff(5176,plain,
% 2.15/2.36 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5175, 5173])).
% 2.15/2.36 tff(5177,plain,
% 2.15/2.36 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5178,plain,
% 2.15/2.36 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5177, 5176])).
% 2.15/2.36 tff(5179,plain,
% 2.15/2.36 (hskp4 | (~c0_1(a633)) | (~c1_1(a633))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5178, 101, 4510, 3839, 55])).
% 2.15/2.36 tff(5180,plain,
% 2.15/2.36 (~c1_1(a633)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5179, 752, 5092])).
% 2.15/2.36 tff(5181,plain,
% 2.15/2.36 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5182,plain,
% 2.15/2.37 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a633) | c1_1(a633) | c2_1(a633)) <=> (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5183,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633)))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5182])).
% 2.15/2.37 tff(5184,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5183, 5181])).
% 2.15/2.37 tff(5185,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a633) | c1_1(a633) | c2_1(a633))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5186,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633)),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5185, 5184])).
% 2.15/2.37 tff(5187,plain,
% 2.15/2.37 (c2_1(a633)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5186, 660, 101, 5180, 4669, 4668, 3839, 4663, 905])).
% 2.15/2.37 tff(5188,assumption,(hskp2), introduced(assumption)).
% 2.15/2.37 tff(5189,plain,
% 2.15/2.37 (~c3_1(a586)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[206, 5188])).
% 2.15/2.37 tff(5190,plain,
% 2.15/2.37 (hskp11),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5170, 44, 66, 33])).
% 2.15/2.37 tff(5191,plain,
% 2.15/2.37 (~c1_1(a599)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[395, 5190])).
% 2.15/2.37 tff(5192,plain,
% 2.15/2.37 (c3_1(a599)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[389, 5190])).
% 2.15/2.37 tff(5193,plain,
% 2.15/2.37 (c2_1(a599)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[403, 5190])).
% 2.15/2.37 tff(5194,plain,
% 2.15/2.37 (c1_1(a586)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[214, 5188])).
% 2.15/2.37 tff(5195,plain,
% 2.15/2.37 (c2_1(a586)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[1357, 5188])).
% 2.15/2.37 tff(5196,plain,
% 2.15/2.37 ($false),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[4729, 5195, 5194, 44, 752, 660, 5193, 5192, 5191, 5189, 33, 66])).
% 2.15/2.37 tff(5197,plain,((~hskp2) | hskp22 | hskp4 | hskp26 | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.37 tff(5198,plain,
% 2.15/2.37 (~hskp2),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5197, 752, 5093, 660, 33, 66])).
% 2.15/2.37 tff(5199,plain,
% 2.15/2.37 (c0_1(a607)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5031, 5198])).
% 2.15/2.37 tff(5200,plain,
% 2.15/2.37 (c3_1(a599)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[389, 5171])).
% 2.15/2.37 tff(5201,plain,
% 2.15/2.37 (c2_1(a599)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[403, 5171])).
% 2.15/2.37 tff(5202,assumption,(hskp7), introduced(assumption)).
% 2.15/2.37 tff(5203,plain,
% 2.15/2.37 (~c3_1(a592)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[736, 5202])).
% 2.15/2.37 tff(5204,plain,
% 2.15/2.37 (~c0_1(a592)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[742, 5202])).
% 2.15/2.37 tff(5205,assumption,(c2_1(a607)), introduced(assumption)).
% 2.15/2.37 tff(5206,plain,
% 2.15/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5207,plain,
% 2.15/2.37 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5208,plain,
% 2.15/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5207])).
% 2.15/2.37 tff(5209,plain,
% 2.15/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5208, 5206])).
% 2.15/2.37 tff(5210,plain,
% 2.15/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5211,plain,
% 2.15/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5210, 5209])).
% 2.15/2.37 tff(5212,plain,
% 2.15/2.37 (~c1_1(a592)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5211, 101, 33, 427, 426, 5205, 425, 5204, 5203, 240, 2351])).
% 2.15/2.37 tff(5213,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5214,plain,
% 2.15/2.37 ((hskp2 | (~ndr1_0) | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5215,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5214])).
% 2.15/2.37 tff(5216,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633)))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5215, 5213])).
% 2.15/2.37 tff(5217,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5218,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5217, 5216])).
% 2.15/2.37 tff(5219,plain,
% 2.15/2.37 ($false),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5218, 101, 1674, 4511, 3839, 5204, 5203, 188, 5212, 4146])).
% 2.15/2.37 tff(5220,plain,((~hskp7) | hskp2 | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | (~c2_1(a607)) | c1_1(a599) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.37 tff(5221,plain,
% 2.15/2.37 (~hskp7),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5220, 5198, 5180, 3839, 5187, 33, 5201, 5200, 4509, 5172, 5199])).
% 2.15/2.37 tff(5222,plain,
% 2.15/2.37 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5223,plain,
% 2.15/2.37 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607))) <=> (hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5224,plain,
% 2.15/2.37 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5223])).
% 2.15/2.37 tff(5225,plain,
% 2.15/2.37 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5224, 5222])).
% 2.15/2.37 tff(5226,plain,
% 2.15/2.37 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5227,plain,
% 2.15/2.37 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5226, 5225])).
% 2.15/2.37 tff(5228,plain,
% 2.15/2.37 (hskp20 | hskp7 | c3_1(a607) | (~c0_1(a607))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5227, 101, 4509, 1271])).
% 2.15/2.37 tff(5229,plain,
% 2.15/2.37 (hskp20),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5228, 5221, 33, 5199])).
% 2.15/2.37 tff(5230,plain,
% 2.15/2.37 (~c3_1(a623)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[643, 5229])).
% 2.15/2.37 tff(5231,plain,
% 2.15/2.37 (~c2_1(a623)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[649, 5229])).
% 2.15/2.37 tff(5232,plain,
% 2.15/2.37 (~c1_1(a623)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[655, 5229])).
% 2.15/2.37 tff(5233,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5234,plain,
% 2.15/2.37 ((hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a623) | c1_1(a623) | c2_1(a623)) <=> (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5235,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5234])).
% 2.15/2.37 tff(5236,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633)))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5235, 5233])).
% 2.15/2.37 tff(5237,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a623) | c1_1(a623) | c2_1(a623))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5238,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5237, 5236])).
% 2.15/2.37 tff(5239,plain,
% 2.15/2.37 ($false),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5238, 660, 101, 5180, 5092, 5232, 5231, 5230, 905, 5187])).
% 2.15/2.37 tff(5240,plain,(hskp4 | hskp26 | c3_1(a607) | c3_1(a633) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.37 tff(5241,plain,
% 2.15/2.37 (hskp4),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5240, 660, 33, 3839, 66])).
% 2.15/2.37 tff(5242,plain,
% 2.15/2.37 (~c2_1(a588)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[115, 5241])).
% 2.15/2.37 tff(5243,plain,
% 2.15/2.37 (~c1_1(a588)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[121, 5241])).
% 2.15/2.37 tff(5244,plain,
% 2.15/2.37 (c0_1(a588)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[129, 5241])).
% 2.15/2.37 tff(5245,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5246,plain,
% 2.15/2.37 ((hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5247,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607)))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5246])).
% 2.15/2.37 tff(5248,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5247, 5245])).
% 2.15/2.37 tff(5249,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5250,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607)),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5249, 5248])).
% 2.15/2.37 tff(5251,plain,
% 2.15/2.37 (hskp14 | c0_1(a607)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5250, 101, 33, 5244, 4509, 5243, 5242, 287])).
% 2.15/2.37 tff(5252,plain,
% 2.15/2.37 (hskp14),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5251, 1])).
% 2.15/2.37 tff(5253,plain,
% 2.15/2.37 (hskp6),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[138, 5241, 5093])).
% 2.15/2.37 tff(5254,plain,
% 2.15/2.37 (~c0_1(a590)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[606, 5253])).
% 2.15/2.37 tff(5255,plain,
% 2.15/2.37 (c3_1(a590)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[614, 5253])).
% 2.15/2.37 tff(5256,plain,
% 2.15/2.37 (c2_1(a590)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[622, 5253])).
% 2.15/2.37 tff(5257,plain,
% 2.15/2.37 (hskp29),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[2135, 5093])).
% 2.15/2.37 tff(5258,plain,
% 2.15/2.37 (c3_1(a678)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[2143, 5257])).
% 2.15/2.37 tff(5259,plain,
% 2.15/2.37 (c0_1(a678)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[2159, 5257])).
% 2.15/2.37 tff(5260,plain,
% 2.15/2.37 ((~c1_1(a678)) | c0_1(a607)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5152, 101, 5259, 5258, 5256, 5255, 66, 4509, 5254, 65])).
% 2.15/2.37 tff(5261,plain,
% 2.15/2.37 (~c1_1(a678)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5260, 1])).
% 2.15/2.37 tff(5262,plain,
% 2.15/2.37 (c2_1(a678)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[2151, 5257])).
% 2.15/2.37 tff(5263,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5264,plain,
% 2.15/2.37 ((hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c1_1(a633) | c2_1(a633)) <=> (hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5265,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633)))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5264])).
% 2.15/2.37 tff(5266,plain,
% 2.15/2.37 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5265, 5263])).
% 2.15/2.37 tff(5267,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c1_1(a633) | c2_1(a633))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5268,plain,
% 2.15/2.37 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633)),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5267, 5266])).
% 2.15/2.37 tff(5269,plain,
% 2.15/2.37 (c2_1(a633)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5268, 660, 101, 5259, 5262, 4511, 3839, 905, 5261])).
% 2.15/2.37 tff(5270,plain,
% 2.15/2.37 (c1_1(a586)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[214, 5094])).
% 2.15/2.37 tff(5271,plain,
% 2.15/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)))),
% 2.23/2.37 inference(rewrite,[status(thm)],[])).
% 2.23/2.37 tff(5272,plain,
% 2.23/2.37 (((~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> ((~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)))),
% 2.23/2.37 inference(rewrite,[status(thm)],[])).
% 2.23/2.37 tff(5273,plain,
% 2.23/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633))))),
% 2.23/2.37 inference(monotonicity,[status(thm)],[5272])).
% 2.23/2.37 tff(5274,plain,
% 2.23/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)))),
% 2.23/2.37 inference(transitivity,[status(thm)],[5273, 5271])).
% 2.23/2.37 tff(5275,plain,
% 2.23/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 2.23/2.37 inference(quant_inst,[status(thm)],[])).
% 2.23/2.37 tff(5276,plain,
% 2.23/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633))),
% 2.23/2.37 inference(modus_ponens,[status(thm)],[5275, 5274])).
% 2.23/2.37 tff(5277,plain,
% 2.23/2.37 (c0_1(a586)),
% 2.23/2.37 inference(unit_resolution,[status(thm)],[5276, 101, 5201, 5200, 5270, 5092, 3839, 5172, 5095, 240, 5269])).
% 2.23/2.37 tff(5278,plain,
% 2.23/2.37 (c2_1(a586)),
% 2.23/2.37 inference(unit_resolution,[status(thm)],[1357, 5094])).
% 2.23/2.37 tff(5279,plain,
% 2.23/2.37 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588)))),
% 2.23/2.37 inference(rewrite,[status(thm)],[])).
% 2.23/2.37 tff(5280,plain,
% 2.23/2.37 ((hskp1 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588)))),
% 2.23/2.37 inference(rewrite,[status(thm)],[])).
% 2.23/2.37 tff(5281,plain,
% 2.23/2.37 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588))))),
% 2.23/2.37 inference(monotonicity,[status(thm)],[5280])).
% 2.23/2.37 tff(5282,plain,
% 2.23/2.37 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588)))),
% 2.23/2.37 inference(transitivity,[status(thm)],[5281, 5279])).
% 2.23/2.37 tff(5283,plain,
% 2.23/2.37 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 2.23/2.37 inference(quant_inst,[status(thm)],[])).
% 2.23/2.37 tff(5284,plain,
% 2.23/2.37 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588))),
% 2.23/2.37 inference(modus_ponens,[status(thm)],[5283, 5282])).
% 2.23/2.37 tff(5285,plain,
% 2.23/2.37 (hskp1),
% 2.23/2.37 inference(unit_resolution,[status(thm)],[5284, 101, 5244, 5278, 5243, 5242, 5095, 1132, 5277])).
% 2.23/2.37 tff(5286,plain,
% 2.23/2.37 (~c0_1(a585)),
% 2.23/2.37 inference(unit_resolution,[status(thm)],[1145, 5285])).
% 2.23/2.37 tff(5287,plain,
% 2.23/2.37 (c2_1(a585)),
% 2.23/2.37 inference(unit_resolution,[status(thm)],[1153, 5285])).
% 2.23/2.37 tff(5288,plain,
% 2.23/2.37 (c1_1(a585)),
% 2.23/2.37 inference(unit_resolution,[status(thm)],[1161, 5285])).
% 2.23/2.37 tff(5289,plain,
% 2.23/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588)))),
% 2.23/2.37 inference(rewrite,[status(thm)],[])).
% 2.23/2.37 tff(5290,plain,
% 2.23/2.37 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588)))),
% 2.23/2.37 inference(rewrite,[status(thm)],[])).
% 2.23/2.37 tff(5291,plain,
% 2.23/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588))))),
% 2.23/2.37 inference(monotonicity,[status(thm)],[5290])).
% 2.23/2.37 tff(5292,plain,
% 2.23/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588)))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5291, 5289])).
% 2.23/2.38 tff(5293,plain,
% 2.23/2.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5294,plain,
% 2.23/2.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588))),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5293, 5292])).
% 2.23/2.38 tff(5295,plain,
% 2.23/2.38 (~c3_1(a588)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5294, 101, 5259, 5262, 5258, 5288, 5287, 5243, 5242, 5286, 11])).
% 2.23/2.38 tff(5296,plain,
% 2.23/2.38 (hskp28),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[2682, 101, 5262, 5258, 5270, 5278, 5095, 1625, 5261])).
% 2.23/2.38 tff(5297,plain,
% 2.23/2.38 (c3_1(a612)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1040, 5296])).
% 2.23/2.38 tff(5298,plain,
% 2.23/2.38 (c2_1(a612)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1048, 5296])).
% 2.23/2.38 tff(5299,plain,
% 2.23/2.38 (c1_1(a612)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1321, 5296])).
% 2.23/2.38 tff(5300,plain,
% 2.23/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5301,plain,
% 2.23/2.38 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5302,plain,
% 2.23/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)))),
% 2.23/2.38 inference(monotonicity,[status(thm)],[5301])).
% 2.23/2.38 tff(5303,plain,
% 2.23/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5302, 5300])).
% 2.23/2.38 tff(5304,plain,
% 2.23/2.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5305,plain,
% 2.23/2.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5304, 5303])).
% 2.23/2.38 tff(5306,plain,
% 2.23/2.38 (~c0_1(a612)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5305, 101, 5299, 5297, 5256, 5255, 66, 4509, 5254, 65, 1])).
% 2.23/2.38 tff(5307,plain,
% 2.23/2.38 (~hskp8),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5084, 5306, 1, 66, 5298, 5297])).
% 2.23/2.38 tff(5308,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5309,plain,
% 2.23/2.38 ((hskp8 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5310,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633))))),
% 2.23/2.38 inference(monotonicity,[status(thm)],[5309])).
% 2.23/2.38 tff(5311,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633)))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5310, 5308])).
% 2.23/2.38 tff(5312,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5313,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633))),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5312, 5311])).
% 2.23/2.38 tff(5314,plain,
% 2.23/2.38 ($false),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5313, 101, 5307, 5244, 5092, 3839, 5242, 4127, 5269, 5295])).
% 2.23/2.38 tff(5315,plain,(c0_1(a607) | c3_1(a633) | c1_1(a607) | hskp26 | c1_1(a633) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.38 tff(5316,plain,
% 2.23/2.38 (c0_1(a607)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5315, 4511, 66, 660, 3839, 33])).
% 2.23/2.38 tff(5317,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5318,plain,
% 2.23/2.38 ((hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5319,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607))))),
% 2.23/2.38 inference(monotonicity,[status(thm)],[5318])).
% 2.23/2.38 tff(5320,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607)))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5319, 5317])).
% 2.23/2.38 tff(5321,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5322,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607))),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5321, 5320])).
% 2.23/2.38 tff(5323,plain,
% 2.23/2.38 (hskp1 | (~c0_1(a607))),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5322, 101, 33, 5244, 4509, 5243, 5242, 1132])).
% 2.23/2.38 tff(5324,plain,
% 2.23/2.38 (hskp1),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5323, 5316])).
% 2.23/2.38 tff(5325,plain,
% 2.23/2.38 (~c0_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1145, 5324])).
% 2.23/2.38 tff(5326,plain,
% 2.23/2.38 (c2_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1153, 5324])).
% 2.23/2.38 tff(5327,plain,
% 2.23/2.38 (c1_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1161, 5324])).
% 2.23/2.38 tff(5328,plain,
% 2.23/2.38 (~c3_1(a588)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5294, 101, 5259, 5262, 5258, 5327, 5326, 5243, 5242, 5325, 11])).
% 2.23/2.38 tff(5329,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5330,plain,
% 2.23/2.38 ((hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a633) | c1_1(a633) | c2_1(a633)) <=> (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5331,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633)))),
% 2.23/2.38 inference(monotonicity,[status(thm)],[5330])).
% 2.23/2.38 tff(5332,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5331, 5329])).
% 2.23/2.38 tff(5333,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a633) | c1_1(a633) | c2_1(a633))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5334,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633)),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5333, 5332])).
% 2.23/2.38 tff(5335,plain,
% 2.23/2.38 (hskp26 | c1_1(a633) | (~c0_1(a607)) | c2_1(a633)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5334, 101, 3839, 66, 4509, 905])).
% 2.23/2.38 tff(5336,plain,
% 2.23/2.38 (c2_1(a633)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5335, 5316, 660, 4511])).
% 2.23/2.38 tff(5337,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5338,plain,
% 2.23/2.38 ((hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5339,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633))))),
% 2.23/2.38 inference(monotonicity,[status(thm)],[5338])).
% 2.23/2.38 tff(5340,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633)))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5339, 5337])).
% 2.23/2.38 tff(5341,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5342,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633))),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5341, 5340])).
% 2.23/2.38 tff(5343,plain,
% 2.23/2.38 ($false),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5342, 660, 101, 4511, 5092, 5243, 5242, 905, 5336, 5328])).
% 2.23/2.38 tff(5344,plain,(c1_1(a633) | hskp26 | c3_1(a607) | c3_1(a633) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.38 tff(5345,plain,
% 2.23/2.38 (c1_1(a633)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5344, 660, 33, 3839, 66])).
% 2.23/2.38 tff(5346,plain,
% 2.23/2.38 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5347,plain,
% 2.23/2.38 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633))) <=> (hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5348,plain,
% 2.23/2.38 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633))))),
% 2.23/2.38 inference(monotonicity,[status(thm)],[5347])).
% 2.23/2.38 tff(5349,plain,
% 2.23/2.38 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5348, 5346])).
% 2.23/2.38 tff(5350,plain,
% 2.23/2.38 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5351,plain,
% 2.23/2.38 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633))),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 2.23/2.38 tff(5352,plain,
% 2.23/2.38 (hskp3 | (~c0_1(a633)) | (~c1_1(a633))),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5351, 101, 4510, 3839, 2236])).
% 2.23/2.38 tff(5353,plain,
% 2.23/2.38 (hskp3),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5352, 5345, 5092])).
% 2.23/2.38 tff(5354,plain,
% 2.23/2.38 (c0_1(a587)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[871, 5353])).
% 2.23/2.38 tff(5355,plain,
% 2.23/2.38 (~c1_1(a587)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[855, 5353])).
% 2.23/2.38 tff(5356,plain,
% 2.23/2.38 (c2_1(a587)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[863, 5353])).
% 2.23/2.38 tff(5357,plain,
% 2.23/2.38 (c0_1(a586)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[4673, 5270, 5201, 5356, 5355, 5354, 5200, 5252, 5172, 5095, 660])).
% 2.23/2.38 tff(5358,plain,
% 2.23/2.38 (hskp1),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5284, 101, 5244, 5278, 5243, 5242, 5095, 1132, 5357])).
% 2.23/2.38 tff(5359,plain,
% 2.23/2.38 (~c0_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1145, 5358])).
% 2.23/2.38 tff(5360,plain,
% 2.23/2.38 (c2_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1153, 5358])).
% 2.23/2.38 tff(5361,plain,
% 2.23/2.38 (c1_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1161, 5358])).
% 2.23/2.38 tff(5362,plain,
% 2.23/2.38 (~c3_1(a588)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5294, 101, 5259, 5262, 5258, 5361, 5360, 5243, 5242, 5359, 11])).
% 2.23/2.38 tff(5363,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5364,plain,
% 2.23/2.38 ((hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a633) | c2_1(a633) | (~c0_1(a633))) <=> (hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5365,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a633) | c2_1(a633) | (~c0_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633)))),
% 2.23/2.38 inference(monotonicity,[status(thm)],[5364])).
% 2.23/2.38 tff(5366,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a633) | c2_1(a633) | (~c0_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5365, 5363])).
% 2.23/2.38 tff(5367,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a633) | c2_1(a633) | (~c0_1(a633)))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5368,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633)),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 2.23/2.38 tff(5369,plain,
% 2.23/2.38 (hskp8 | c2_1(a633)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5368, 101, 5278, 5092, 3839, 5095, 4127, 5357])).
% 2.23/2.38 tff(5370,plain,
% 2.23/2.38 (c2_1(a633)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5369, 5307])).
% 2.23/2.38 tff(5371,plain,
% 2.23/2.38 ($false),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5313, 101, 5307, 5244, 5092, 3839, 5242, 4127, 5370, 5362])).
% 2.23/2.38 tff(5372,plain,(c0_1(a607) | c3_1(a633) | c1_1(a607) | hskp26 | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.38 tff(5373,plain,
% 2.23/2.38 (c0_1(a607)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5372, 660, 66, 3839, 33])).
% 2.23/2.38 tff(5374,plain,
% 2.23/2.38 (hskp1),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5323, 5373])).
% 2.23/2.38 tff(5375,plain,
% 2.23/2.38 (~c0_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1145, 5374])).
% 2.23/2.38 tff(5376,plain,
% 2.23/2.38 (c2_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1153, 5374])).
% 2.23/2.38 tff(5377,plain,
% 2.23/2.38 (c1_1(a585)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1161, 5374])).
% 2.23/2.38 tff(5378,plain,
% 2.23/2.38 (~c3_1(a588)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5294, 101, 5259, 5262, 5258, 5377, 5376, 5243, 5242, 5375, 11])).
% 2.23/2.38 tff(5379,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5380,plain,
% 2.23/2.38 ((hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5381,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607))))),
% 2.23/2.38 inference(monotonicity,[status(thm)],[5380])).
% 2.23/2.38 tff(5382,plain,
% 2.23/2.38 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607)))),
% 2.23/2.38 inference(transitivity,[status(thm)],[5381, 5379])).
% 2.23/2.38 tff(5383,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 2.23/2.38 inference(quant_inst,[status(thm)],[])).
% 2.23/2.38 tff(5384,plain,
% 2.23/2.38 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607))),
% 2.23/2.38 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 2.23/2.38 tff(5385,plain,
% 2.23/2.38 ($false),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5384, 660, 101, 66, 4509, 5243, 5242, 905, 5373, 5378])).
% 2.23/2.38 tff(5386,plain,(hskp26 | c1_1(a607) | c3_1(a607) | c3_1(a633)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.38 tff(5387,plain,
% 2.23/2.38 (hskp26),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5386, 3839, 33, 66])).
% 2.23/2.38 tff(5388,plain,
% 2.23/2.38 (c2_1(a583)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[364, 5387])).
% 2.23/2.38 tff(5389,plain,
% 2.23/2.38 (c1_1(a583)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[330, 5387])).
% 2.23/2.38 tff(5390,plain,
% 2.23/2.38 (c0_1(a583)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[338, 5387])).
% 2.23/2.38 tff(5391,plain,
% 2.23/2.38 (hskp4),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[4852, 5278, 2160, 2144, 2152, 5270, 1528, 1527, 66, 1526, 33, 5193, 5192, 5191, 5095])).
% 2.23/2.38 tff(5392,plain,
% 2.23/2.38 (hskp6),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[138, 5391, 44])).
% 2.23/2.38 tff(5393,plain,
% 2.23/2.38 (~c0_1(a590)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[606, 5392])).
% 2.23/2.38 tff(5394,plain,
% 2.23/2.38 (c3_1(a590)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[614, 5392])).
% 2.23/2.38 tff(5395,plain,
% 2.23/2.38 (c2_1(a590)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[622, 5392])).
% 2.23/2.38 tff(5396,plain,
% 2.23/2.38 (hskp28),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[3102, 101, 5193, 5192, 5270, 5278, 5191, 5095, 1625])).
% 2.23/2.38 tff(5397,plain,
% 2.23/2.38 (c3_1(a612)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1040, 5396])).
% 2.23/2.38 tff(5398,plain,
% 2.23/2.38 (c1_1(a612)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1321, 5396])).
% 2.23/2.38 tff(5399,plain,
% 2.23/2.38 (~c0_1(a612)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5305, 101, 5398, 5397, 5395, 5394, 66, 4509, 5393, 65, 1])).
% 2.23/2.38 tff(5400,plain,
% 2.23/2.38 (~c2_1(a588)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[115, 5391])).
% 2.23/2.38 tff(5401,plain,
% 2.23/2.38 (~c1_1(a588)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[121, 5391])).
% 2.23/2.38 tff(5402,plain,
% 2.23/2.38 (c2_1(a612)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[1048, 5396])).
% 2.23/2.38 tff(5403,plain,
% 2.23/2.38 (~c3_1(a588)),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[4761, 101, 2160, 2152, 2144, 5398, 5402, 5401, 5400, 11, 5399])).
% 2.23/2.38 tff(5404,plain,
% 2.23/2.38 (~hskp8),
% 2.23/2.38 inference(unit_resolution,[status(thm)],[5084, 5399, 1, 66, 5402, 5397])).
% 2.23/2.38 tff(5405,plain,
% 2.23/2.38 (^[U: $i] : refl((hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 2.23/2.38 inference(bind,[status(th)],[])).
% 2.23/2.38 tff(5406,plain,
% 2.23/2.38 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.23/2.38 inference(quant_intro,[status(thm)],[5405])).
% 2.23/2.38 tff(5407,plain,
% 2.23/2.38 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.23/2.38 inference(rewrite,[status(thm)],[])).
% 2.23/2.38 tff(5408,plain,
% 2.23/2.38 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) | hskp18) <=> ((hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp18))), rewrite(((hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp18) <=> (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) | hskp18) <=> (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 2.23/2.39 inference(bind,[status(th)],[])).
% 2.23/2.39 tff(5409,plain,
% 2.23/2.39 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) | hskp18) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.23/2.39 inference(quant_intro,[status(thm)],[5408])).
% 2.23/2.39 tff(5410,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 2.23/2.39 tff(5411,plain,
% 2.23/2.39 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5410, 5409])).
% 2.23/2.39 tff(5412,plain,
% 2.23/2.39 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5411, 5407])).
% 2.23/2.39 tff(5413,plain,(
% 2.23/2.39 ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.23/2.39 inference(skolemize,[status(sab)],[5412])).
% 2.23/2.39 tff(5414,plain,
% 2.23/2.39 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5413, 5406])).
% 2.23/2.39 tff(5415,plain,
% 2.23/2.39 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5416,plain,
% 2.23/2.39 ((hskp18 | hskp8 | (~ndr1_0) | c0_1(a607) | c3_1(a607) | (~c2_1(a607))) <=> (hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5417,plain,
% 2.23/2.39 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a607) | c3_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5416])).
% 2.23/2.39 tff(5418,plain,
% 2.23/2.39 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a607) | c3_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.23/2.39 inference(transitivity,[status(thm)],[5417, 5415])).
% 2.23/2.39 tff(5419,plain,
% 2.23/2.39 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a607) | c3_1(a607) | (~c2_1(a607)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(5420,plain,
% 2.23/2.39 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5419, 5418])).
% 2.23/2.39 tff(5421,plain,
% 2.23/2.39 (hskp18 | hskp8 | c3_1(a607) | c0_1(a607)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5420, 101, 4509, 5414])).
% 2.23/2.39 tff(5422,plain,
% 2.23/2.39 (hskp18),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5421, 5404, 33, 1])).
% 2.23/2.39 tff(5423,plain,
% 2.23/2.39 (~c2_1(a610)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1087, 5422])).
% 2.23/2.39 tff(5424,plain,
% 2.23/2.39 (~c0_1(a610)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1093, 5422])).
% 2.23/2.39 tff(5425,plain,
% 2.23/2.39 (c0_1(a588)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[129, 5391])).
% 2.23/2.39 tff(5426,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5427,plain,
% 2.23/2.39 (((~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)) | c3_1(a607) | c1_1(a607) | c0_1(a607)) <=> (c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5428,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610))))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5427])).
% 2.23/2.39 tff(5429,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610)))),
% 2.23/2.39 inference(transitivity,[status(thm)],[5428, 5426])).
% 2.23/2.39 tff(5430,plain,
% 2.23/2.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)) | c3_1(a607) | c1_1(a607) | c0_1(a607))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(5431,plain,
% 2.23/2.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5430, 5429])).
% 2.23/2.39 tff(5432,plain,
% 2.23/2.39 (~c1_1(a610)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5431, 101, 33, 5425, 5424, 5423, 66, 5400, 1349, 1, 5403])).
% 2.23/2.39 tff(5433,plain,
% 2.23/2.39 (hskp3),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[4818, 5270, 44, 66, 33, 5193, 5192, 1528, 5191, 5095, 1527])).
% 2.23/2.39 tff(5434,plain,
% 2.23/2.39 (~c1_1(a587)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[855, 5433])).
% 2.23/2.39 tff(5435,plain,
% 2.23/2.39 (hskp16),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[4870, 101, 5402, 5397, 5425, 5400, 2002, 5399, 5403])).
% 2.23/2.39 tff(5436,plain,
% 2.23/2.39 (~c2_1(a606)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1015, 5435])).
% 2.23/2.39 tff(5437,plain,
% 2.23/2.39 (c2_1(a587)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[863, 5433])).
% 2.23/2.39 tff(5438,plain,
% 2.23/2.39 (c0_1(a587)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[871, 5433])).
% 2.23/2.39 tff(5439,plain,
% 2.23/2.39 (c1_1(a606)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[992, 5435])).
% 2.23/2.39 tff(5440,plain,
% 2.23/2.39 (c0_1(a606)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[4884, 5439, 4510, 5438, 5437, 5436, 5434])).
% 2.23/2.39 tff(5441,plain,
% 2.23/2.39 (hskp10),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1418, 101, 5398, 5402, 5397, 1528, 1527, 1526, 21])).
% 2.23/2.39 tff(5442,plain,
% 2.23/2.39 (~c1_1(a598)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[827, 5441])).
% 2.23/2.39 tff(5443,plain,
% 2.23/2.39 (c3_1(a598)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[800, 5441])).
% 2.23/2.39 tff(5444,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5445,plain,
% 2.23/2.39 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5446,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598)))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5445])).
% 2.23/2.39 tff(5447,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598))),
% 2.23/2.39 inference(transitivity,[status(thm)],[5446, 5444])).
% 2.23/2.39 tff(5448,plain,
% 2.23/2.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(5449,plain,
% 2.23/2.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598)),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5448, 5447])).
% 2.23/2.39 tff(5450,plain,
% 2.23/2.39 (c2_1(a598)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5449, 101, 2160, 2152, 2144, 5398, 5402, 5443, 5442, 11, 5399])).
% 2.23/2.39 tff(5451,plain,
% 2.23/2.39 (c0_1(a598)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[808, 5441])).
% 2.23/2.39 tff(5452,plain,
% 2.23/2.39 (c3_1(a610)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1101, 5422])).
% 2.23/2.39 tff(5453,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5454,plain,
% 2.23/2.39 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5455,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610))))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5454])).
% 2.23/2.39 tff(5456,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 2.23/2.39 inference(transitivity,[status(thm)],[5455, 5453])).
% 2.23/2.39 tff(5457,plain,
% 2.23/2.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(5458,plain,
% 2.23/2.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5457, 5456])).
% 2.23/2.39 tff(5459,plain,
% 2.23/2.39 ($false),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5458, 101, 5452, 5439, 5451, 5443, 5423, 5436, 1010, 5450, 5440, 5432])).
% 2.23/2.39 tff(5460,plain,(c0_1(a607) | c3_1(a607) | c1_1(a607) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.23/2.39 tff(5461,plain,
% 2.23/2.39 (c0_1(a607)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5460, 5390, 66, 33, 5389, 5388, 5093])).
% 2.23/2.39 tff(5462,plain,
% 2.23/2.39 (hskp4 | c3_1(a583)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[3190, 101, 4510, 5390, 5389, 55])).
% 2.23/2.39 tff(5463,plain,
% 2.23/2.39 (c3_1(a583)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5462, 752])).
% 2.23/2.39 tff(5464,plain,
% 2.23/2.39 (hskp15),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[4485, 5463, 5390, 5389, 5388])).
% 2.23/2.39 tff(5465,plain,
% 2.23/2.39 (~c0_1(a604)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1474, 5464])).
% 2.23/2.39 tff(5466,plain,
% 2.23/2.39 (c1_1(a604)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1490, 5464])).
% 2.23/2.39 tff(5467,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5468,plain,
% 2.23/2.39 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5469,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607))))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5468])).
% 2.23/2.39 tff(5470,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.23/2.39 inference(transitivity,[status(thm)],[5469, 5467])).
% 2.23/2.39 tff(5471,plain,
% 2.23/2.39 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(5472,plain,
% 2.23/2.39 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5471, 5470])).
% 2.23/2.39 tff(5473,plain,
% 2.23/2.39 (c2_1(a604)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 5466, 66, 4509, 5465, 32, 5461])).
% 2.23/2.39 tff(5474,plain,
% 2.23/2.39 (c3_1(a604)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1482, 5464])).
% 2.23/2.39 tff(5475,assumption,(hskp16), introduced(assumption)).
% 2.23/2.39 tff(5476,plain,
% 2.23/2.39 (~c2_1(a606)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[1015, 5475])).
% 2.23/2.39 tff(5477,plain,
% 2.23/2.39 (c1_1(a606)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[992, 5475])).
% 2.23/2.39 tff(5478,plain,
% 2.23/2.39 (c0_1(a606)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[4884, 5477, 2849, 910, 909, 5476, 906])).
% 2.23/2.39 tff(5479,plain,
% 2.23/2.39 (~c3_1(a606)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[982, 5475])).
% 2.23/2.39 tff(5480,plain,
% 2.23/2.39 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5481,plain,
% 2.23/2.39 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606))) <=> (hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5482,plain,
% 2.23/2.39 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5481])).
% 2.23/2.39 tff(5483,plain,
% 2.23/2.39 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.23/2.39 inference(transitivity,[status(thm)],[5482, 5480])).
% 2.23/2.39 tff(5484,plain,
% 2.23/2.39 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(5485,plain,
% 2.23/2.39 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5484, 5483])).
% 2.23/2.39 tff(5486,plain,
% 2.23/2.39 ($false),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5485, 101, 2849, 752, 5477, 5479, 55, 5478])).
% 2.23/2.39 tff(5487,plain,((~hskp16) | hskp17 | hskp4 | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.39 tff(5488,plain,
% 2.23/2.39 (~hskp16),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5487, 752, 4510, 4669, 4668, 4663])).
% 2.23/2.39 tff(5489,assumption,(c0_1(a633)), introduced(assumption)).
% 2.23/2.39 tff(5490,assumption,(~hskp16), introduced(assumption)).
% 2.23/2.39 tff(5491,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5492,plain,
% 2.23/2.39 ((hskp16 | (~ndr1_0) | c2_1(a633) | c3_1(a633) | (~c0_1(a633)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604))) <=> (hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5493,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a633) | c3_1(a633) | (~c0_1(a633)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633)))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5492])).
% 2.23/2.39 tff(5494,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a633) | c3_1(a633) | (~c0_1(a633)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633))),
% 2.23/2.39 inference(transitivity,[status(thm)],[5493, 5491])).
% 2.23/2.39 tff(5495,plain,
% 2.23/2.39 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a633) | c3_1(a633) | (~c0_1(a633)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(5496,plain,
% 2.23/2.39 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633)),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5495, 5494])).
% 2.23/2.39 tff(5497,plain,
% 2.23/2.39 ($false),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5496, 101, 5490, 2410, 5489, 3839, 2340, 2002, 2403, 4338])).
% 2.23/2.39 tff(5498,plain,(c2_1(a633) | hskp16 | (~c3_1(a604)) | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~c2_1(a604))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.39 tff(5499,plain,
% 2.23/2.39 (c2_1(a633)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5498, 5488, 5474, 5092, 3839, 5465, 5473])).
% 2.23/2.39 tff(5500,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5501,plain,
% 2.23/2.39 ((hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604))) <=> (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5502,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623))))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5501])).
% 2.23/2.39 tff(5503,plain,
% 2.23/2.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623)))),
% 2.23/2.39 inference(transitivity,[status(thm)],[5502, 5500])).
% 2.23/2.39 tff(5504,plain,
% 2.23/2.39 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(5505,plain,
% 2.23/2.39 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[5504, 5503])).
% 2.23/2.39 tff(5506,plain,
% 2.23/2.39 (~c0_1(a623)),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[5505, 101, 5490, 2410, 650, 644, 2340, 2002, 2403])).
% 2.23/2.39 tff(5507,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5508,plain,
% 2.23/2.39 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(5509,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623)))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[5508])).
% 2.23/2.39 tff(5510,plain,
% 2.23/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5509, 5507])).
% 2.25/2.40 tff(5511,plain,
% 2.25/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5512,plain,
% 2.25/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623)),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5511, 5510])).
% 2.25/2.40 tff(5513,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5512, 101, 2410, 427, 426, 650, 644, 2340, 425, 1607, 2403, 5506])).
% 2.25/2.40 tff(5514,plain,((~hskp20) | (~c3_1(a604)) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | c1_1(a599) | (~c2_1(a604)) | hskp16), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5515,plain,
% 2.25/2.40 (~hskp20),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5514, 5474, 5201, 5200, 5465, 5172, 5473, 5488])).
% 2.25/2.40 tff(5516,plain,
% 2.25/2.40 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5517,plain,
% 2.25/2.40 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633))) <=> (hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5518,plain,
% 2.25/2.40 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5517])).
% 2.25/2.40 tff(5519,plain,
% 2.25/2.40 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5518, 5516])).
% 2.25/2.40 tff(5520,plain,
% 2.25/2.40 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5521,plain,
% 2.25/2.40 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5520, 5519])).
% 2.25/2.40 tff(5522,plain,
% 2.25/2.40 (hskp20 | hskp7 | (~c0_1(a633)) | (~c2_1(a633))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5521, 101, 3839, 1271])).
% 2.25/2.40 tff(5523,plain,
% 2.25/2.40 (hskp7),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5522, 5515, 5092, 5499])).
% 2.25/2.40 tff(5524,plain,
% 2.25/2.40 (hskp2),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5220, 5523, 5180, 3839, 5499, 33, 5201, 5200, 4509, 5172, 5461])).
% 2.25/2.40 tff(5525,plain,
% 2.25/2.40 (~c3_1(a586)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[206, 5524])).
% 2.25/2.40 tff(5526,plain,
% 2.25/2.40 (c1_1(a586)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[214, 5524])).
% 2.25/2.40 tff(5527,plain,
% 2.25/2.40 (c2_1(a586)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1357, 5524])).
% 2.25/2.40 tff(5528,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[4852, 5527, 5526, 5259, 5258, 5262, 752, 5390, 5389, 66, 5388, 33, 5201, 5200, 5172, 5525])).
% 2.25/2.40 tff(5529,plain,(hskp4 | c1_1(a607) | c3_1(a607) | c3_1(a633)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5530,plain,
% 2.25/2.40 (hskp4),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5529, 3839, 33, 66])).
% 2.25/2.40 tff(5531,plain,
% 2.25/2.40 (hskp6),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[138, 5530, 5093])).
% 2.25/2.40 tff(5532,plain,
% 2.25/2.40 (~c0_1(a590)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[606, 5531])).
% 2.25/2.40 tff(5533,plain,
% 2.25/2.40 (~c2_1(a588)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[115, 5530])).
% 2.25/2.40 tff(5534,plain,
% 2.25/2.40 (~c1_1(a588)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[121, 5530])).
% 2.25/2.40 tff(5535,plain,
% 2.25/2.40 (c0_1(a588)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[129, 5530])).
% 2.25/2.40 tff(5536,plain,
% 2.25/2.40 (hskp1),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5322, 101, 33, 5535, 4509, 5534, 5533, 1132, 5461])).
% 2.25/2.40 tff(5537,plain,
% 2.25/2.40 (~c0_1(a585)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1145, 5536])).
% 2.25/2.40 tff(5538,plain,
% 2.25/2.40 (c1_1(a585)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1161, 5536])).
% 2.25/2.40 tff(5539,plain,
% 2.25/2.40 (c3_1(a590)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[614, 5531])).
% 2.25/2.40 tff(5540,plain,
% 2.25/2.40 (c2_1(a590)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[622, 5531])).
% 2.25/2.40 tff(5541,plain,
% 2.25/2.40 (~c3_1(a583)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[4485, 3016, 1528, 1527, 1526])).
% 2.25/2.40 tff(5542,assumption,(~c0_1(a585)), introduced(assumption)).
% 2.25/2.40 tff(5543,assumption,(c1_1(a585)), introduced(assumption)).
% 2.25/2.40 tff(5544,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5545,plain,
% 2.25/2.40 ((hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c3_1(a585))) <=> (hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5546,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c3_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5545])).
% 2.25/2.40 tff(5547,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c3_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5546, 5544])).
% 2.25/2.40 tff(5548,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c3_1(a585)))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5549,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5548, 5547])).
% 2.25/2.40 tff(5550,plain,
% 2.25/2.40 (~c3_1(a585)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5549, 101, 3016, 1527, 1526, 5543, 5542, 2552, 5541])).
% 2.25/2.40 tff(5551,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5552,plain,
% 2.25/2.40 ((hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590))) <=> (hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5553,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5552])).
% 2.25/2.40 tff(5554,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5553, 5551])).
% 2.25/2.40 tff(5555,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5556,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5555, 5554])).
% 2.25/2.40 tff(5557,plain,
% 2.25/2.40 (~c1_1(a590)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5556, 101, 3016, 1527, 1526, 784, 45, 2552, 5541])).
% 2.25/2.40 tff(5558,plain,
% 2.25/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5559,plain,
% 2.25/2.40 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a585) | c0_1(a585) | (~c1_1(a585))) <=> (c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5560,plain,
% 2.25/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a585) | c0_1(a585) | (~c1_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5559])).
% 2.25/2.40 tff(5561,plain,
% 2.25/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a585) | c0_1(a585) | (~c1_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5560, 5558])).
% 2.25/2.40 tff(5562,plain,
% 2.25/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a585) | c0_1(a585) | (~c1_1(a585)))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5563,plain,
% 2.25/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5562, 5561])).
% 2.25/2.40 tff(5564,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5563, 101, 33, 785, 784, 5543, 5205, 5542, 240, 2351, 5557, 5550])).
% 2.25/2.40 tff(5565,plain,(hskp15 | c3_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a585)) | (~c2_1(a607)) | c0_1(a585) | (~c0_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | c0_1(a590) | (~c0_1(a583))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5566,plain,
% 2.25/2.40 (hskp15),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5565, 5540, 33, 5539, 5538, 4509, 5537, 5461, 5389, 5388, 5532, 5390])).
% 2.25/2.40 tff(5567,plain,
% 2.25/2.40 (~c0_1(a604)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1474, 5566])).
% 2.25/2.40 tff(5568,plain,
% 2.25/2.40 (c1_1(a604)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1490, 5566])).
% 2.25/2.40 tff(5569,plain,
% 2.25/2.40 (c2_1(a604)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 5568, 66, 4509, 5567, 32, 5461])).
% 2.25/2.40 tff(5570,plain,
% 2.25/2.40 (c3_1(a604)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1482, 5566])).
% 2.25/2.40 tff(5571,plain,
% 2.25/2.40 (c2_1(a585)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1153, 5536])).
% 2.25/2.40 tff(5572,plain,
% 2.25/2.40 (~c3_1(a588)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5294, 101, 5259, 5262, 5258, 5538, 5571, 5534, 5533, 5537, 11])).
% 2.25/2.40 tff(5573,plain,
% 2.25/2.40 (hskp16 | c3_1(a588)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[4556, 101, 5540, 5539, 5535, 5532, 5533, 2002])).
% 2.25/2.40 tff(5574,plain,
% 2.25/2.40 (hskp16),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5573, 5572])).
% 2.25/2.40 tff(5575,plain,
% 2.25/2.40 (~c2_1(a606)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1015, 5574])).
% 2.25/2.40 tff(5576,plain,
% 2.25/2.40 (c1_1(a606)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[992, 5574])).
% 2.25/2.40 tff(5577,plain,
% 2.25/2.40 (hskp12),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[4590, 101, 5390, 5389, 5388, 5538, 5571, 5537, 2589])).
% 2.25/2.40 tff(5578,plain,
% 2.25/2.40 (~c3_1(a600)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[675, 5577])).
% 2.25/2.40 tff(5579,plain,
% 2.25/2.40 (~c3_1(a606)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[982, 5574])).
% 2.25/2.40 tff(5580,plain,
% 2.25/2.40 (c2_1(a600)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[683, 5577])).
% 2.25/2.40 tff(5581,plain,
% 2.25/2.40 (c0_1(a600)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[691, 5577])).
% 2.25/2.40 tff(5582,plain,
% 2.25/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5583,plain,
% 2.25/2.40 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5584,plain,
% 2.25/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5583])).
% 2.25/2.40 tff(5585,plain,
% 2.25/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5584, 5582])).
% 2.25/2.40 tff(5586,plain,
% 2.25/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5587,plain,
% 2.25/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5586, 5585])).
% 2.25/2.40 tff(5588,plain,
% 2.25/2.40 (c0_1(a606)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5587, 101, 5576, 5581, 5580, 5201, 5200, 5579, 5578, 5172, 240])).
% 2.25/2.40 tff(5589,plain,
% 2.25/2.40 (~hskp13),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2418, 5569, 5201, 5200, 5588, 5172, 5567, 5259, 5262, 5258, 5576, 5575, 5570])).
% 2.25/2.40 tff(5590,plain,
% 2.25/2.40 (hskp19 | hskp13),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2446, 101, 5538, 5571, 5537, 2429])).
% 2.25/2.40 tff(5591,plain,
% 2.25/2.40 (hskp19),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5590, 5589])).
% 2.25/2.40 tff(5592,plain,
% 2.25/2.40 (~c1_1(a617)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2453, 5591])).
% 2.25/2.40 tff(5593,plain,
% 2.25/2.40 (~c0_1(a617)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2459, 5591])).
% 2.25/2.40 tff(5594,plain,
% 2.25/2.40 (c2_1(a617)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2467, 5591])).
% 2.25/2.40 tff(5595,plain,
% 2.25/2.40 (~c1_1(a678)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2474, 101, 5259, 5258, 5594, 5570, 5593, 5592, 5567, 65, 5569])).
% 2.25/2.40 tff(5596,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5597,plain,
% 2.25/2.40 ((hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5598,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5597])).
% 2.25/2.40 tff(5599,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5598, 5596])).
% 2.25/2.40 tff(5600,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5601,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5600, 5599])).
% 2.25/2.40 tff(5602,plain,
% 2.25/2.40 (hskp8),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5601, 101, 33, 5535, 4509, 5533, 4127, 5461, 5572])).
% 2.25/2.40 tff(5603,plain,
% 2.25/2.40 (c3_1(a593)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[469, 5602])).
% 2.25/2.40 tff(5604,plain,
% 2.25/2.40 (c1_1(a593)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[477, 5602])).
% 2.25/2.40 tff(5605,plain,
% 2.25/2.40 (~c0_1(a593)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2481, 101, 5594, 5570, 5604, 5603, 5593, 5592, 5567, 65, 5569])).
% 2.25/2.40 tff(5606,plain,
% 2.25/2.40 (~c2_1(a593)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[510, 5602])).
% 2.25/2.40 tff(5607,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2488, 101, 4510, 5259, 5262, 5604, 5606, 32, 5605, 5595])).
% 2.25/2.40 tff(5608,plain,(c3_1(a633) | c1_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5609,plain,
% 2.25/2.40 (c3_1(a633)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5608, 33, 66])).
% 2.25/2.40 tff(5610,plain,
% 2.25/2.40 (~hskp22),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[3833, 5609])).
% 2.25/2.40 tff(5611,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5460, 331, 339, 66, 33, 1, 365, 5610])).
% 2.25/2.40 tff(5612,plain,((~hskp26) | c1_1(a607) | c3_1(a607) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5613,plain,
% 2.25/2.40 (~hskp26),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5612, 1, 33, 66])).
% 2.25/2.40 tff(5614,plain,
% 2.25/2.40 (hskp4),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5197, 5613, 5610, 5094, 33, 66])).
% 2.25/2.40 tff(5615,plain,
% 2.25/2.40 (hskp6),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[138, 5614, 5610])).
% 2.25/2.40 tff(5616,plain,
% 2.25/2.40 (~c0_1(a590)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[606, 5615])).
% 2.25/2.40 tff(5617,plain,
% 2.25/2.40 (c3_1(a590)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[614, 5615])).
% 2.25/2.40 tff(5618,plain,
% 2.25/2.40 (c2_1(a590)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[622, 5615])).
% 2.25/2.40 tff(5619,plain,
% 2.25/2.40 (hskp29),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2135, 5610])).
% 2.25/2.40 tff(5620,plain,
% 2.25/2.40 (c3_1(a678)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2143, 5619])).
% 2.25/2.40 tff(5621,plain,
% 2.25/2.40 (c0_1(a678)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2159, 5619])).
% 2.25/2.40 tff(5622,plain,
% 2.25/2.40 (~c1_1(a678)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5152, 101, 5621, 5620, 5618, 5617, 66, 4509, 5616, 65, 1])).
% 2.25/2.40 tff(5623,plain,
% 2.25/2.40 (hskp11),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5170, 5610, 66, 33])).
% 2.25/2.40 tff(5624,plain,
% 2.25/2.40 (~c1_1(a599)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[395, 5623])).
% 2.25/2.40 tff(5625,plain,
% 2.25/2.40 (c3_1(a599)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[389, 5623])).
% 2.25/2.40 tff(5626,plain,
% 2.25/2.40 (c2_1(a599)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[403, 5623])).
% 2.25/2.40 tff(5627,plain,
% 2.25/2.40 (hskp28),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[3102, 101, 5626, 5625, 5270, 5278, 5624, 5095, 1625])).
% 2.25/2.40 tff(5628,plain,
% 2.25/2.40 (c3_1(a612)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1040, 5627])).
% 2.25/2.40 tff(5629,plain,
% 2.25/2.40 (c2_1(a612)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1048, 5627])).
% 2.25/2.40 tff(5630,plain,
% 2.25/2.40 (c1_1(a612)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1321, 5627])).
% 2.25/2.40 tff(5631,plain,
% 2.25/2.40 (~c0_1(a612)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5305, 101, 5630, 5628, 5618, 5617, 66, 4509, 5616, 65, 1])).
% 2.25/2.40 tff(5632,plain,
% 2.25/2.40 (~hskp8),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5084, 5631, 1, 66, 5629, 5628])).
% 2.25/2.40 tff(5633,plain,
% 2.25/2.40 (hskp18),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5421, 5632, 33, 1])).
% 2.25/2.40 tff(5634,plain,
% 2.25/2.40 (~c2_1(a610)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1087, 5633])).
% 2.25/2.40 tff(5635,plain,
% 2.25/2.40 (~c0_1(a610)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1093, 5633])).
% 2.25/2.40 tff(5636,plain,
% 2.25/2.40 (c2_1(a678)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[2151, 5619])).
% 2.25/2.40 tff(5637,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5638,plain,
% 2.25/2.40 ((hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610))) <=> (hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5639,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5638])).
% 2.25/2.40 tff(5640,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5639, 5637])).
% 2.25/2.40 tff(5641,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5642,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5641, 5640])).
% 2.25/2.40 tff(5643,plain,
% 2.25/2.40 (~c1_1(a610)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5642, 101, 4510, 5621, 5636, 5635, 5634, 32, 5622])).
% 2.25/2.40 tff(5644,plain,
% 2.25/2.40 (~hskp0),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[3666, 5622, 4510, 5636, 5621])).
% 2.25/2.40 tff(5645,plain,
% 2.25/2.40 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5646,plain,
% 2.25/2.40 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a610) | c1_1(a610) | c0_1(a610)) <=> (hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5647,plain,
% 2.25/2.40 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a610) | c1_1(a610) | c0_1(a610))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610)))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5646])).
% 2.25/2.40 tff(5648,plain,
% 2.25/2.40 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a610) | c1_1(a610) | c0_1(a610))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5647, 5645])).
% 2.25/2.40 tff(5649,plain,
% 2.25/2.40 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a610) | c1_1(a610) | c0_1(a610))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5650,plain,
% 2.25/2.40 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610)),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5649, 5648])).
% 2.25/2.40 tff(5651,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5650, 5613, 101, 5644, 5635, 5634, 942, 5643])).
% 2.25/2.40 tff(5652,plain,(c0_1(a607) | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5653,plain,
% 2.25/2.40 (c0_1(a607)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5652, 33, 66])).
% 2.25/2.40 tff(5654,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5655,plain,
% 2.25/2.40 ((hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c1_1(a623) | c2_1(a623)) <=> (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5656,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5655])).
% 2.25/2.40 tff(5657,plain,
% 2.25/2.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5656, 5654])).
% 2.25/2.40 tff(5658,plain,
% 2.25/2.40 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c1_1(a623) | c2_1(a623))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5659,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5658, 5657])).
% 2.25/2.41 tff(5660,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5659, 660, 101, 656, 650, 644, 66, 4509, 905, 2351])).
% 2.25/2.41 tff(5661,plain,((~hskp20) | hskp26 | c1_1(a607) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5662,plain,
% 2.25/2.41 (~hskp20),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5661, 660, 66, 5653])).
% 2.25/2.41 tff(5663,plain,
% 2.25/2.41 (hskp7),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5228, 5662, 33, 5653])).
% 2.25/2.41 tff(5664,plain,
% 2.25/2.41 (~c1_1(a592)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5211, 101, 33, 5626, 5625, 4509, 5624, 5204, 5203, 240, 5653])).
% 2.25/2.41 tff(5665,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5666,plain,
% 2.25/2.41 ((hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5667,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592)))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5666])).
% 2.25/2.41 tff(5668,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5667, 5665])).
% 2.25/2.41 tff(5669,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5670,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5669, 5668])).
% 2.25/2.41 tff(5671,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5670, 101, 1674, 33, 66, 4509, 5204, 5203, 188, 5664])).
% 2.25/2.41 tff(5672,plain,((~hskp7) | hskp2 | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5673,plain,
% 2.25/2.41 (hskp2),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5672, 5663, 33, 66])).
% 2.25/2.41 tff(5674,plain,
% 2.25/2.41 (hskp4),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5197, 5673, 5610, 660, 33, 66])).
% 2.25/2.41 tff(5675,plain,
% 2.25/2.41 (~c2_1(a588)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[115, 5674])).
% 2.25/2.41 tff(5676,plain,
% 2.25/2.41 (~c1_1(a588)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[121, 5674])).
% 2.25/2.41 tff(5677,plain,
% 2.25/2.41 (c0_1(a588)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[129, 5674])).
% 2.25/2.41 tff(5678,plain,
% 2.25/2.41 (hskp1),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5322, 101, 33, 5677, 4509, 5676, 5675, 1132, 5653])).
% 2.25/2.41 tff(5679,plain,
% 2.25/2.41 (~c0_1(a585)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1145, 5678])).
% 2.25/2.41 tff(5680,plain,
% 2.25/2.41 (c2_1(a585)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1153, 5678])).
% 2.25/2.41 tff(5681,plain,
% 2.25/2.41 (c1_1(a585)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1161, 5678])).
% 2.25/2.41 tff(5682,plain,
% 2.25/2.41 (~c3_1(a588)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5294, 101, 5621, 5636, 5620, 5681, 5680, 5676, 5675, 5679, 11])).
% 2.25/2.41 tff(5683,plain,
% 2.25/2.41 (~c3_1(a592)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[736, 5663])).
% 2.25/2.41 tff(5684,plain,
% 2.25/2.41 (~c0_1(a592)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[742, 5663])).
% 2.25/2.41 tff(5685,plain,
% 2.25/2.41 (~c1_1(a592)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5211, 101, 33, 5626, 5625, 4509, 5624, 5684, 5683, 240, 5653])).
% 2.25/2.41 tff(5686,plain,
% 2.25/2.41 (hskp6),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[138, 5674, 5610])).
% 2.25/2.41 tff(5687,plain,
% 2.25/2.41 (~c0_1(a590)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[606, 5686])).
% 2.25/2.41 tff(5688,plain,
% 2.25/2.41 (c3_1(a590)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[614, 5686])).
% 2.25/2.41 tff(5689,plain,
% 2.25/2.41 (c2_1(a590)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[622, 5686])).
% 2.25/2.41 tff(5690,plain,
% 2.25/2.41 (c2_1(a592)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[750, 5663])).
% 2.25/2.41 tff(5691,plain,
% 2.25/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5692,plain,
% 2.25/2.41 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5693,plain,
% 2.25/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592)))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5692])).
% 2.25/2.41 tff(5694,plain,
% 2.25/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5693, 5691])).
% 2.25/2.41 tff(5695,plain,
% 2.25/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5696,plain,
% 2.25/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5695, 5694])).
% 2.25/2.41 tff(5697,plain,
% 2.25/2.41 (~c1_1(a678)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5696, 101, 5621, 5620, 5690, 5689, 5688, 5684, 5687, 65, 5685])).
% 2.25/2.41 tff(5698,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5699,plain,
% 2.25/2.41 ((hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5700,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588)))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5699])).
% 2.25/2.41 tff(5701,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5700, 5698])).
% 2.25/2.41 tff(5702,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5703,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5702, 5701])).
% 2.25/2.41 tff(5704,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5703, 660, 101, 5621, 5636, 5676, 5675, 905, 5697, 5682])).
% 2.25/2.41 tff(5705,plain,(hskp26 | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5706,plain,
% 2.25/2.41 (hskp26),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5705, 33, 66])).
% 2.25/2.41 tff(5707,plain,
% 2.25/2.41 (c0_1(a583)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[338, 5706])).
% 2.25/2.41 tff(5708,plain,
% 2.25/2.41 (~hskp7),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5672, 1674, 33, 66])).
% 2.25/2.41 tff(5709,plain,
% 2.25/2.41 (hskp20),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5228, 5708, 33, 5653])).
% 2.25/2.41 tff(5710,plain,
% 2.25/2.41 (~c3_1(a623)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[643, 5709])).
% 2.25/2.41 tff(5711,plain,
% 2.25/2.41 (~c1_1(a623)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[655, 5709])).
% 2.25/2.41 tff(5712,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5713,plain,
% 2.25/2.41 ((hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a623) | c1_1(a623) | c0_1(a623)) <=> (hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5714,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a623) | c1_1(a623) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623)))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5713])).
% 2.25/2.41 tff(5715,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a623) | c1_1(a623) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5714, 5712])).
% 2.25/2.41 tff(5716,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a623) | c1_1(a623) | c0_1(a623))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5717,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5716, 5715])).
% 2.25/2.41 tff(5718,plain,
% 2.25/2.41 (c0_1(a623)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5717, 101, 1674, 33, 5711, 5710, 66, 4509, 188])).
% 2.25/2.41 tff(5719,plain,
% 2.25/2.41 (~c2_1(a623)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[649, 5709])).
% 2.25/2.41 tff(5720,plain,
% 2.25/2.41 (hskp6 | (~c0_1(a623))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3792, 101, 5610, 5711, 5719, 43])).
% 2.25/2.41 tff(5721,plain,
% 2.25/2.41 (hskp6),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5720, 5718])).
% 2.25/2.41 tff(5722,plain,
% 2.25/2.41 (c2_1(a590)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[622, 5721])).
% 2.25/2.41 tff(5723,plain,
% 2.25/2.41 (~c0_1(a590)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[606, 5721])).
% 2.25/2.41 tff(5724,plain,
% 2.25/2.41 (c3_1(a590)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[614, 5721])).
% 2.25/2.41 tff(5725,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5726,plain,
% 2.25/2.41 ((hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5727,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5726])).
% 2.25/2.41 tff(5728,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623)))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5727, 5725])).
% 2.25/2.41 tff(5729,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5730,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 2.25/2.41 tff(5731,plain,
% 2.25/2.41 (hskp16),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5730, 101, 5722, 5724, 5719, 5710, 5723, 2002, 5718])).
% 2.25/2.41 tff(5732,plain,
% 2.25/2.41 (~c2_1(a606)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1015, 5731])).
% 2.25/2.41 tff(5733,plain,
% 2.25/2.41 (c2_1(a583)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[364, 5706])).
% 2.25/2.41 tff(5734,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5735,plain,
% 2.25/2.41 ((hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a623) | c2_1(a623) | (~c0_1(a623))) <=> (hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5736,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5735])).
% 2.25/2.41 tff(5737,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5736, 5734])).
% 2.25/2.41 tff(5738,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a623) | c2_1(a623) | (~c0_1(a623)))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5739,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5738, 5737])).
% 2.25/2.41 tff(5740,plain,
% 2.25/2.41 (hskp1 | (~c0_1(a623))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5739, 101, 33, 5711, 5719, 4509, 1132, 5653])).
% 2.25/2.41 tff(5741,plain,
% 2.25/2.41 (hskp1),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5740, 5718])).
% 2.25/2.41 tff(5742,plain,
% 2.25/2.41 (~c0_1(a585)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1145, 5741])).
% 2.25/2.41 tff(5743,plain,
% 2.25/2.41 (c1_1(a585)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1161, 5741])).
% 2.25/2.41 tff(5744,plain,
% 2.25/2.41 (c1_1(a583)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[330, 5706])).
% 2.25/2.41 tff(5745,plain,
% 2.25/2.41 (hskp15),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5565, 5724, 33, 5744, 5722, 4509, 5743, 5653, 5742, 5733, 5723, 5707])).
% 2.25/2.41 tff(5746,plain,
% 2.25/2.41 (~c0_1(a604)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1474, 5745])).
% 2.25/2.41 tff(5747,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5748,plain,
% 2.25/2.41 ((hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623))) <=> (hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5749,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5748])).
% 2.25/2.41 tff(5750,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5749, 5747])).
% 2.25/2.41 tff(5751,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5752,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5751, 5750])).
% 2.25/2.41 tff(5753,plain,
% 2.25/2.41 (hskp8 | (~c0_1(a623))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5752, 101, 33, 5719, 5710, 4509, 4127, 5653])).
% 2.25/2.41 tff(5754,plain,
% 2.25/2.41 (hskp8),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5753, 5718])).
% 2.25/2.41 tff(5755,plain,
% 2.25/2.41 (~c2_1(a593)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[510, 5754])).
% 2.25/2.41 tff(5756,plain,
% 2.25/2.41 (c2_1(a585)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1153, 5741])).
% 2.25/2.41 tff(5757,plain,
% 2.25/2.41 (c3_1(a593)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[469, 5754])).
% 2.25/2.41 tff(5758,plain,
% 2.25/2.41 (c1_1(a593)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[477, 5754])).
% 2.25/2.41 tff(5759,plain,
% 2.25/2.41 (c1_1(a606)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[992, 5731])).
% 2.25/2.41 tff(5760,plain,
% 2.25/2.41 (hskp3),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5004, 101, 4510, 5758, 5757, 5755, 3282])).
% 2.25/2.41 tff(5761,plain,
% 2.25/2.41 (~c1_1(a587)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[855, 5760])).
% 2.25/2.41 tff(5762,plain,
% 2.25/2.41 (c2_1(a587)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[863, 5760])).
% 2.25/2.41 tff(5763,plain,
% 2.25/2.41 (c0_1(a587)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[871, 5760])).
% 2.25/2.41 tff(5764,plain,
% 2.25/2.41 (c0_1(a606)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[4884, 5759, 4510, 5763, 5762, 5732, 5761])).
% 2.25/2.41 tff(5765,plain,
% 2.25/2.41 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5766,plain,
% 2.25/2.41 ((hskp25 | hskp15 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606))) <=> (hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5767,plain,
% 2.25/2.41 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5766])).
% 2.25/2.41 tff(5768,plain,
% 2.25/2.41 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5767, 5765])).
% 2.25/2.41 tff(5769,plain,
% 2.25/2.41 ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5770,plain,
% 2.25/2.41 ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5769, 5768])).
% 2.25/2.41 tff(5771,plain,
% 2.25/2.41 (hskp25 | hskp15),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5770, 101, 1753, 1750, 2866, 2380])).
% 2.25/2.41 tff(5772,plain,
% 2.25/2.41 (hskp25),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5771, 2355])).
% 2.25/2.41 tff(5773,plain,
% 2.25/2.41 (~c3_1(a651)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[2329, 5772])).
% 2.25/2.41 tff(5774,plain,
% 2.25/2.41 (~c1_1(a651)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[2335, 5772])).
% 2.25/2.41 tff(5775,plain,
% 2.25/2.41 (c2_1(a651)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[2323, 5772])).
% 2.25/2.41 tff(5776,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5777,plain,
% 2.25/2.41 ((hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a604) | c1_1(a604) | c0_1(a604)) <=> (hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5778,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5777])).
% 2.25/2.41 tff(5779,plain,
% 2.25/2.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651)))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5778, 5776])).
% 2.25/2.41 tff(5780,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a604) | c1_1(a604) | c0_1(a604))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5781,plain,
% 2.25/2.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5780, 5779])).
% 2.25/2.41 tff(5782,plain,
% 2.25/2.41 (c1_1(a604)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5781, 101, 1674, 5775, 2354, 5774, 5773, 2340, 188])).
% 2.25/2.41 tff(5783,plain,
% 2.25/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5784,plain,
% 2.25/2.41 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5785,plain,
% 2.25/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5784])).
% 2.25/2.41 tff(5786,plain,
% 2.25/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5785, 5783])).
% 2.25/2.41 tff(5787,plain,
% 2.25/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5788,plain,
% 2.25/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5787, 5786])).
% 2.25/2.41 tff(5789,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5788, 101, 33, 5782, 2354, 427, 426, 5205, 2340, 425, 240, 2351])).
% 2.25/2.41 tff(5790,plain,(c3_1(a604) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~c0_1(a607)) | hskp2 | (~c1_1(a606)) | c2_1(a606) | (~c0_1(a606))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5791,plain,
% 2.25/2.41 (c3_1(a604)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5790, 2340, 427, 426, 4509, 33, 425, 2351, 1674, 1753, 1750, 2380])).
% 2.25/2.42 tff(5792,plain,
% 2.25/2.42 (~c2_1(a604)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2902, 2886, 2186, 2185, 2184, 1771, 1770, 784, 1780, 2340, 45, 785, 2849])).
% 2.25/2.42 tff(5793,plain,
% 2.25/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(5794,plain,
% 2.25/2.42 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(5795,plain,
% 2.25/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606))))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[5794])).
% 2.25/2.42 tff(5796,plain,
% 2.25/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.25/2.42 inference(transitivity,[status(thm)],[5795, 5793])).
% 2.25/2.42 tff(5797,plain,
% 2.25/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 2.25/2.42 inference(quant_inst,[status(thm)],[])).
% 2.25/2.42 tff(5798,plain,
% 2.25/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[5797, 5796])).
% 2.25/2.42 tff(5799,plain,
% 2.25/2.42 ($false),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5798, 101, 2186, 2185, 2184, 1753, 2886, 2410, 1750, 1010, 2380, 5792])).
% 2.25/2.42 tff(5800,plain,(c1_1(a604) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a606)) | (~c3_1(a604)) | c2_1(a606) | (~c0_1(a606)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a590)) | (~c3_1(a593)) | c0_1(a604) | c0_1(a590) | (~c2_1(a590)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.25/2.42 tff(5801,plain,
% 2.25/2.42 (c1_1(a604)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5800, 5791, 2185, 2184, 1753, 2186, 1750, 2380, 1771, 1770, 784, 1780, 2340, 45, 785, 4510])).
% 2.25/2.42 tff(5802,plain,
% 2.25/2.42 (c2_1(a604) | (~c1_1(a604))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 66, 4509, 2340, 32, 2351])).
% 2.25/2.42 tff(5803,plain,
% 2.25/2.42 (c2_1(a604)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5802, 5801])).
% 2.25/2.42 tff(5804,plain,
% 2.25/2.42 (~hskp13),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2418, 5803, 427, 426, 2380, 425, 2340, 2186, 2185, 2184, 1753, 1750, 5791])).
% 2.25/2.42 tff(5805,assumption,(c2_1(a585)), introduced(assumption)).
% 2.25/2.42 tff(5806,plain,
% 2.25/2.42 (hskp19 | hskp13),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2446, 101, 5543, 5805, 5542, 2429])).
% 2.25/2.42 tff(5807,plain,
% 2.25/2.42 (hskp19),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5806, 5804])).
% 2.25/2.42 tff(5808,plain,
% 2.25/2.42 (~c1_1(a617)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2453, 5807])).
% 2.25/2.42 tff(5809,plain,
% 2.25/2.42 (~c0_1(a617)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2459, 5807])).
% 2.25/2.42 tff(5810,plain,
% 2.25/2.42 (c2_1(a617)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2467, 5807])).
% 2.25/2.42 tff(5811,plain,
% 2.25/2.42 (~c1_1(a678)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2474, 101, 2186, 2184, 5810, 5791, 5809, 5808, 2340, 65, 5803])).
% 2.25/2.42 tff(5812,plain,
% 2.25/2.42 (~c0_1(a593)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2481, 101, 5810, 5791, 1771, 1780, 5809, 5808, 2340, 65, 5803])).
% 2.25/2.42 tff(5813,plain,
% 2.25/2.42 ($false),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2488, 101, 4510, 2186, 2185, 1771, 1770, 32, 5812, 5811])).
% 2.25/2.42 tff(5814,plain,(c0_1(a604) | (~c0_1(a678)) | (~c2_1(a678)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a593)) | (~c3_1(a678)) | (~c1_1(a585)) | (~c2_1(a585)) | c0_1(a585) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a606)) | c1_1(a599) | (~c1_1(a606)) | c2_1(a606) | c1_1(a607) | (~c0_1(a607)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a590)) | c3_1(a607) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.25/2.42 tff(5815,plain,
% 2.25/2.42 ($false),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5814, 5764, 5759, 5636, 1674, 5758, 5757, 5620, 5743, 5756, 5742, 5626, 5625, 5755, 5624, 5746, 5732, 66, 5653, 5724, 5723, 5722, 33, 5621])).
% 2.25/2.42 tff(5816,plain,(hskp2 | c1_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.42 tff(5817,plain,
% 2.25/2.42 (hskp2),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5816, 33, 66])).
% 2.25/2.42 tff(5818,plain,
% 2.25/2.42 (~c3_1(a586)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[206, 5817])).
% 2.25/2.42 tff(5819,plain,
% 2.25/2.42 (c1_1(a586)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[214, 5817])).
% 2.25/2.42 tff(5820,plain,
% 2.25/2.42 (c2_1(a586)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1357, 5817])).
% 2.25/2.42 tff(5821,plain,
% 2.25/2.42 (hskp4),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4852, 5820, 5621, 5620, 5636, 5707, 5744, 5819, 66, 5733, 33, 5626, 5625, 5624, 5818])).
% 2.25/2.42 tff(5822,plain,
% 2.25/2.42 (hskp6),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[138, 5821, 5610])).
% 2.25/2.42 tff(5823,plain,
% 2.25/2.42 (~c0_1(a590)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[606, 5822])).
% 2.25/2.42 tff(5824,plain,
% 2.25/2.42 (~c2_1(a588)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[115, 5821])).
% 2.25/2.42 tff(5825,plain,
% 2.25/2.42 (~c1_1(a588)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[121, 5821])).
% 2.25/2.42 tff(5826,plain,
% 2.25/2.42 (c0_1(a588)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[129, 5821])).
% 2.25/2.42 tff(5827,plain,
% 2.25/2.42 (hskp1),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5322, 101, 33, 5826, 4509, 5825, 5824, 1132, 5653])).
% 2.25/2.42 tff(5828,plain,
% 2.25/2.42 (~c0_1(a585)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1145, 5827])).
% 2.25/2.42 tff(5829,plain,
% 2.25/2.42 (c3_1(a590)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[614, 5822])).
% 2.25/2.42 tff(5830,plain,
% 2.25/2.42 (c2_1(a590)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[622, 5822])).
% 2.25/2.42 tff(5831,plain,
% 2.25/2.42 (c1_1(a585)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1161, 5827])).
% 2.25/2.42 tff(5832,plain,
% 2.25/2.42 (hskp15),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5565, 5831, 33, 5744, 5830, 4509, 5829, 5653, 5828, 5733, 5823, 5707])).
% 2.25/2.42 tff(5833,plain,
% 2.25/2.42 (~c0_1(a604)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1474, 5832])).
% 2.25/2.42 tff(5834,plain,
% 2.25/2.42 (c1_1(a604)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1490, 5832])).
% 2.25/2.42 tff(5835,plain,
% 2.25/2.42 (c2_1(a604)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 5834, 66, 4509, 5833, 32, 5653])).
% 2.25/2.42 tff(5836,plain,
% 2.25/2.42 (c3_1(a604)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1482, 5832])).
% 2.25/2.42 tff(5837,plain,
% 2.25/2.42 (c0_1(a586)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4803, 101, 33, 5626, 5625, 5819, 4509, 5624, 5818, 240, 5653])).
% 2.28/2.42 tff(5838,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5839,plain,
% 2.28/2.42 ((hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604))) <=> (hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5840,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604))))),
% 2.28/2.42 inference(monotonicity,[status(thm)],[5839])).
% 2.28/2.42 tff(5841,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.28/2.42 inference(transitivity,[status(thm)],[5840, 5838])).
% 2.28/2.42 tff(5842,plain,
% 2.28/2.42 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))),
% 2.28/2.42 inference(quant_inst,[status(thm)],[])).
% 2.28/2.42 tff(5843,plain,
% 2.28/2.42 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604))),
% 2.28/2.42 inference(modus_ponens,[status(thm)],[5842, 5841])).
% 2.28/2.42 tff(5844,plain,
% 2.28/2.42 (hskp16),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5843, 101, 5834, 5836, 5819, 5833, 5818, 1314, 5837])).
% 2.28/2.42 tff(5845,plain,
% 2.28/2.42 (~c2_1(a606)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[1015, 5844])).
% 2.28/2.42 tff(5846,plain,
% 2.28/2.42 (c1_1(a606)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[992, 5844])).
% 2.28/2.42 tff(5847,plain,
% 2.28/2.42 (hskp3),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[4818, 5819, 5610, 66, 33, 5626, 5625, 5707, 5624, 5818, 5744])).
% 2.28/2.42 tff(5848,plain,
% 2.28/2.42 (~c1_1(a587)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[855, 5847])).
% 2.28/2.42 tff(5849,plain,
% 2.28/2.42 (c2_1(a587)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[863, 5847])).
% 2.28/2.42 tff(5850,plain,
% 2.28/2.42 (c0_1(a587)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[871, 5847])).
% 2.28/2.42 tff(5851,plain,
% 2.28/2.42 (c0_1(a606)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[4884, 5846, 4510, 5850, 5849, 5845, 5848])).
% 2.28/2.42 tff(5852,plain,
% 2.28/2.42 (~hskp13),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[2418, 5851, 5626, 5625, 5835, 5624, 5833, 5621, 5636, 5620, 5846, 5845, 5836])).
% 2.28/2.42 tff(5853,plain,
% 2.28/2.42 (c2_1(a585)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[1153, 5827])).
% 2.28/2.42 tff(5854,plain,
% 2.28/2.42 (hskp19 | hskp13),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[2446, 101, 5831, 5853, 5828, 2429])).
% 2.28/2.42 tff(5855,plain,
% 2.28/2.42 (hskp19),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5854, 5852])).
% 2.28/2.42 tff(5856,plain,
% 2.28/2.42 (~c1_1(a617)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[2453, 5855])).
% 2.28/2.42 tff(5857,plain,
% 2.28/2.42 (~c0_1(a617)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[2459, 5855])).
% 2.28/2.42 tff(5858,plain,
% 2.28/2.42 (c2_1(a617)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[2467, 5855])).
% 2.28/2.42 tff(5859,plain,
% 2.28/2.42 (hskp28),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[3102, 101, 5626, 5625, 5819, 5820, 5624, 5818, 1625])).
% 2.28/2.42 tff(5860,plain,
% 2.28/2.42 (c3_1(a612)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[1040, 5859])).
% 2.28/2.42 tff(5861,plain,
% 2.28/2.42 (c1_1(a612)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[1321, 5859])).
% 2.28/2.42 tff(5862,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5863,plain,
% 2.28/2.42 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5864,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 2.28/2.42 inference(monotonicity,[status(thm)],[5863])).
% 2.28/2.42 tff(5865,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 2.28/2.42 inference(transitivity,[status(thm)],[5864, 5862])).
% 2.28/2.42 tff(5866,plain,
% 2.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 2.28/2.42 inference(quant_inst,[status(thm)],[])).
% 2.28/2.42 tff(5867,plain,
% 2.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 2.28/2.42 inference(modus_ponens,[status(thm)],[5866, 5865])).
% 2.28/2.42 tff(5868,plain,
% 2.28/2.42 (~c0_1(a612)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5867, 101, 5861, 5860, 5858, 5836, 5857, 5856, 5833, 65, 5835])).
% 2.28/2.42 tff(5869,plain,
% 2.28/2.42 (~c3_1(a588)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5294, 101, 5621, 5636, 5620, 5831, 5853, 5825, 5824, 5828, 11])).
% 2.28/2.42 tff(5870,plain,
% 2.28/2.42 (hskp8),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5601, 101, 33, 5826, 4509, 5824, 4127, 5653, 5869])).
% 2.28/2.42 tff(5871,plain,
% 2.28/2.42 (c3_1(a593)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[469, 5870])).
% 2.28/2.42 tff(5872,plain,
% 2.28/2.42 (c1_1(a593)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[477, 5870])).
% 2.28/2.42 tff(5873,plain,
% 2.28/2.42 (c2_1(a612)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[1048, 5859])).
% 2.28/2.42 tff(5874,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5875,plain,
% 2.28/2.42 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5876,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617))))),
% 2.28/2.42 inference(monotonicity,[status(thm)],[5875])).
% 2.28/2.42 tff(5877,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617)))),
% 2.28/2.42 inference(transitivity,[status(thm)],[5876, 5874])).
% 2.28/2.42 tff(5878,plain,
% 2.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 2.28/2.42 inference(quant_inst,[status(thm)],[])).
% 2.28/2.42 tff(5879,plain,
% 2.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617))),
% 2.28/2.42 inference(modus_ponens,[status(thm)],[5878, 5877])).
% 2.28/2.42 tff(5880,plain,
% 2.28/2.42 (~c0_1(a593)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5879, 101, 5873, 5860, 5858, 5872, 5871, 5857, 5856, 65, 5868])).
% 2.28/2.42 tff(5881,plain,
% 2.28/2.42 (~c2_1(a593)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[510, 5870])).
% 2.28/2.42 tff(5882,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5883,plain,
% 2.28/2.42 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5884,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))))),
% 2.28/2.42 inference(monotonicity,[status(thm)],[5883])).
% 2.28/2.42 tff(5885,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 2.28/2.42 inference(transitivity,[status(thm)],[5884, 5882])).
% 2.28/2.42 tff(5886,plain,
% 2.28/2.42 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 2.28/2.42 inference(quant_inst,[status(thm)],[])).
% 2.28/2.42 tff(5887,plain,
% 2.28/2.42 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))),
% 2.28/2.42 inference(modus_ponens,[status(thm)],[5886, 5885])).
% 2.28/2.42 tff(5888,plain,
% 2.28/2.42 ($false),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5887, 101, 4510, 5872, 66, 4509, 5881, 32, 5880, 5653])).
% 2.28/2.42 tff(5889,plain,(c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.42 tff(5890,plain,
% 2.28/2.42 (c3_1(a607)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5889, 66])).
% 2.28/2.42 tff(5891,assumption,(hskp28), introduced(assumption)).
% 2.28/2.42 tff(5892,plain,
% 2.28/2.42 (c3_1(a612)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[1040, 5891])).
% 2.28/2.42 tff(5893,plain,
% 2.28/2.42 (c1_1(a612)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[1321, 5891])).
% 2.28/2.42 tff(5894,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5895,plain,
% 2.28/2.42 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5896,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607))))),
% 2.28/2.42 inference(monotonicity,[status(thm)],[5895])).
% 2.28/2.42 tff(5897,plain,
% 2.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 2.28/2.42 inference(transitivity,[status(thm)],[5896, 5894])).
% 2.28/2.42 tff(5898,plain,
% 2.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 2.28/2.42 inference(quant_inst,[status(thm)],[])).
% 2.28/2.42 tff(5899,plain,
% 2.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607))),
% 2.28/2.42 inference(modus_ponens,[status(thm)],[5898, 5897])).
% 2.28/2.42 tff(5900,plain,
% 2.28/2.42 (~c0_1(a612)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5899, 101, 5893, 5892, 5890, 66, 4509, 65, 1])).
% 2.28/2.42 tff(5901,plain,
% 2.28/2.42 (c2_1(a612)),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[1048, 5891])).
% 2.28/2.42 tff(5902,plain,
% 2.28/2.42 (~hskp8),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5084, 5900, 1, 66, 5901, 5892])).
% 2.28/2.42 tff(5903,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5904,plain,
% 2.28/2.42 ((hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607))) <=> (hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 2.28/2.42 inference(rewrite,[status(thm)],[])).
% 2.28/2.42 tff(5905,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607))))),
% 2.28/2.42 inference(monotonicity,[status(thm)],[5904])).
% 2.28/2.42 tff(5906,plain,
% 2.28/2.42 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 2.28/2.42 inference(transitivity,[status(thm)],[5905, 5903])).
% 2.28/2.42 tff(5907,plain,
% 2.28/2.42 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))),
% 2.28/2.42 inference(quant_inst,[status(thm)],[])).
% 2.28/2.42 tff(5908,plain,
% 2.28/2.42 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607))),
% 2.28/2.42 inference(modus_ponens,[status(thm)],[5907, 5906])).
% 2.28/2.42 tff(5909,plain,
% 2.28/2.42 ($false),
% 2.28/2.42 inference(unit_resolution,[status(thm)],[5908, 101, 5902, 5893, 5901, 5890, 66, 1206, 1, 5900])).
% 2.28/2.42 tff(5910,plain,((~hskp28) | c1_1(a607) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.43 tff(5911,plain,
% 2.28/2.43 (~hskp28),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5910, 1, 66])).
% 2.28/2.43 tff(5912,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5913,plain,
% 2.28/2.43 ((hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607))) <=> (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5914,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607))))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[5913])).
% 2.28/2.43 tff(5915,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607)))),
% 2.28/2.43 inference(transitivity,[status(thm)],[5914, 5912])).
% 2.28/2.43 tff(5916,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(5917,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5916, 5915])).
% 2.28/2.43 tff(5918,plain,
% 2.28/2.43 ($false),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5917, 101, 1850, 5890, 5194, 5195, 66, 4509, 5189, 1625])).
% 2.28/2.43 tff(5919,plain,((~hskp2) | hskp28 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.43 tff(5920,plain,
% 2.28/2.43 (~hskp2),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5919, 5911, 66])).
% 2.28/2.43 tff(5921,plain,
% 2.28/2.43 (^[U: $i] : refl((hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 2.28/2.43 inference(bind,[status(th)],[])).
% 2.28/2.43 tff(5922,plain,
% 2.28/2.43 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.28/2.43 inference(quant_intro,[status(thm)],[5921])).
% 2.28/2.43 tff(5923,plain,
% 2.28/2.43 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5924,plain,
% 2.28/2.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp7) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 2.28/2.43 inference(bind,[status(th)],[])).
% 2.28/2.43 tff(5925,plain,
% 2.28/2.43 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp7) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.28/2.43 inference(quant_intro,[status(thm)],[5924])).
% 2.28/2.43 tff(5926,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 2.28/2.43 tff(5927,plain,
% 2.28/2.43 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5926, 5925])).
% 2.28/2.43 tff(5928,plain,
% 2.28/2.43 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5927, 5923])).
% 2.28/2.43 tff(5929,plain,(
% 2.28/2.43 ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.28/2.43 inference(skolemize,[status(sab)],[5928])).
% 2.28/2.43 tff(5930,plain,
% 2.28/2.43 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5929, 5922])).
% 2.28/2.43 tff(5931,plain,
% 2.28/2.43 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5932,plain,
% 2.28/2.43 ((hskp7 | hskp2 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5933,plain,
% 2.28/2.43 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[5932])).
% 2.28/2.43 tff(5934,plain,
% 2.28/2.43 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.28/2.43 inference(transitivity,[status(thm)],[5933, 5931])).
% 2.28/2.43 tff(5935,plain,
% 2.28/2.43 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(5936,plain,
% 2.28/2.43 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5935, 5934])).
% 2.28/2.43 tff(5937,plain,
% 2.28/2.43 (hskp7 | hskp2 | (~c2_1(a607)) | c0_1(a607)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5936, 101, 66, 5930])).
% 2.28/2.43 tff(5938,plain,
% 2.28/2.43 (hskp7),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5937, 5920, 4509, 1])).
% 2.28/2.43 tff(5939,plain,
% 2.28/2.43 (~c3_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[736, 5938])).
% 2.28/2.43 tff(5940,plain,
% 2.28/2.43 (c2_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[750, 5938])).
% 2.28/2.43 tff(5941,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5942,plain,
% 2.28/2.43 ((hskp28 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607))) <=> (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5943,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607))))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[5942])).
% 2.28/2.43 tff(5944,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607)))),
% 2.28/2.43 inference(transitivity,[status(thm)],[5943, 5941])).
% 2.28/2.43 tff(5945,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(5946,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5945, 5944])).
% 2.28/2.43 tff(5947,plain,
% 2.28/2.43 (~c1_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5946, 101, 5911, 5890, 5940, 66, 4509, 5939, 1625])).
% 2.28/2.43 tff(5948,plain,
% 2.28/2.43 (~c0_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[742, 5938])).
% 2.28/2.43 tff(5949,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5950,plain,
% 2.28/2.43 ((hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5951,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[5950])).
% 2.28/2.43 tff(5952,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.43 inference(transitivity,[status(thm)],[5951, 5949])).
% 2.28/2.43 tff(5953,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(5954,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5953, 5952])).
% 2.28/2.43 tff(5955,plain,
% 2.28/2.43 ($false),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5954, 101, 5920, 5940, 5948, 5939, 188, 5947])).
% 2.28/2.43 tff(5956,plain,(c0_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.43 tff(5957,plain,
% 2.28/2.43 (c0_1(a607)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5956, 66])).
% 2.28/2.43 tff(5958,assumption,(~hskp7), introduced(assumption)).
% 2.28/2.43 tff(5959,assumption,(~hskp20), introduced(assumption)).
% 2.28/2.43 tff(5960,plain,
% 2.28/2.43 (^[U: $i] : refl((hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 2.28/2.43 inference(bind,[status(th)],[])).
% 2.28/2.43 tff(5961,plain,
% 2.28/2.43 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.28/2.43 inference(quant_intro,[status(thm)],[5960])).
% 2.28/2.43 tff(5962,plain,
% 2.28/2.43 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5963,plain,
% 2.28/2.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp6) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp6))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp6) <=> (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp6) <=> (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 2.28/2.43 inference(bind,[status(th)],[])).
% 2.28/2.43 tff(5964,plain,
% 2.28/2.43 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp6) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.28/2.43 inference(quant_intro,[status(thm)],[5963])).
% 2.28/2.43 tff(5965,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 2.28/2.43 tff(5966,plain,
% 2.28/2.43 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5965, 5964])).
% 2.28/2.43 tff(5967,plain,
% 2.28/2.43 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5966, 5962])).
% 2.28/2.43 tff(5968,plain,(
% 2.28/2.43 ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.28/2.43 inference(skolemize,[status(sab)],[5967])).
% 2.28/2.43 tff(5969,plain,
% 2.28/2.43 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5968, 5961])).
% 2.28/2.43 tff(5970,plain,
% 2.28/2.43 (~hskp20),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5661, 660, 66, 5957])).
% 2.28/2.43 tff(5971,assumption,(hskp18), introduced(assumption)).
% 2.28/2.43 tff(5972,plain,
% 2.28/2.43 (~c2_1(a610)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[1087, 5971])).
% 2.28/2.43 tff(5973,plain,
% 2.28/2.43 (~c0_1(a610)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[1093, 5971])).
% 2.28/2.43 tff(5974,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5975,plain,
% 2.28/2.43 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5976,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607))))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[5975])).
% 2.28/2.43 tff(5977,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607)))),
% 2.28/2.43 inference(transitivity,[status(thm)],[5976, 5974])).
% 2.28/2.43 tff(5978,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(5979,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 2.28/2.43 tff(5980,plain,
% 2.28/2.43 ($false),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5979, 101, 4510, 3658, 66, 4509, 3657, 3656, 32, 2351])).
% 2.28/2.43 tff(5981,plain,((~hskp0) | c1_1(a607) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 2.28/2.43 tff(5982,plain,
% 2.28/2.43 (~hskp0),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5981, 5957, 66])).
% 2.28/2.43 tff(5983,plain,
% 2.28/2.43 (c1_1(a610)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5650, 660, 101, 5982, 5973, 5972, 942])).
% 2.28/2.43 tff(5984,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5985,plain,
% 2.28/2.43 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610))) <=> (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5986,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610))))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[5985])).
% 2.28/2.43 tff(5987,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610)))),
% 2.28/2.43 inference(transitivity,[status(thm)],[5986, 5984])).
% 2.28/2.43 tff(5988,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(5989,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[5988, 5987])).
% 2.28/2.43 tff(5990,plain,
% 2.28/2.43 ($false),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5989, 101, 4510, 5973, 5972, 66, 4509, 32, 5957, 5983])).
% 2.28/2.43 tff(5991,plain,((~hskp18) | c1_1(a607) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.28/2.43 tff(5992,plain,
% 2.28/2.43 (~hskp18),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5991, 660, 66])).
% 2.28/2.43 tff(5993,plain,
% 2.28/2.43 (hskp12),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[712, 1586, 660])).
% 2.28/2.43 tff(5994,plain,
% 2.28/2.43 (~c3_1(a600)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[675, 5993])).
% 2.28/2.43 tff(5995,plain,
% 2.28/2.43 (c2_1(a600)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[683, 5993])).
% 2.28/2.43 tff(5996,plain,
% 2.28/2.43 (c0_1(a600)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[691, 5993])).
% 2.28/2.43 tff(5997,plain,
% 2.28/2.43 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5998,plain,
% 2.28/2.43 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600))) <=> (hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(5999,plain,
% 2.28/2.43 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[5998])).
% 2.28/2.43 tff(6000,plain,
% 2.28/2.43 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.28/2.43 inference(transitivity,[status(thm)],[5999, 5997])).
% 2.28/2.43 tff(6001,plain,
% 2.28/2.43 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(6002,plain,
% 2.28/2.43 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[6001, 6000])).
% 2.28/2.43 tff(6003,plain,
% 2.28/2.43 (hskp7),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[6002, 101, 5959, 5996, 5995, 5994, 1271])).
% 2.28/2.43 tff(6004,plain,
% 2.28/2.43 (~c3_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[736, 6003])).
% 2.28/2.43 tff(6005,plain,
% 2.28/2.43 (~c0_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[742, 6003])).
% 2.28/2.43 tff(6006,plain,
% 2.28/2.43 (c2_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[750, 6003])).
% 2.28/2.43 tff(6007,assumption,(~hskp18), introduced(assumption)).
% 2.28/2.43 tff(6008,plain,
% 2.28/2.43 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(6009,plain,
% 2.28/2.43 ((hskp18 | hskp8 | (~ndr1_0) | c0_1(a592) | c3_1(a592) | (~c2_1(a592))) <=> (hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(6010,plain,
% 2.28/2.43 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a592) | c3_1(a592) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592))))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[6009])).
% 2.28/2.43 tff(6011,plain,
% 2.28/2.43 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a592) | c3_1(a592) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)))),
% 2.28/2.43 inference(transitivity,[status(thm)],[6010, 6008])).
% 2.28/2.43 tff(6012,plain,
% 2.28/2.43 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a592) | c3_1(a592) | (~c2_1(a592)))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(6013,plain,
% 2.28/2.43 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[6012, 6011])).
% 2.28/2.43 tff(6014,plain,
% 2.28/2.43 ($false),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[6013, 101, 6007, 1586, 6006, 6005, 6004, 5414])).
% 2.28/2.43 tff(6015,plain,(hskp8 | hskp18 | hskp20 | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.28/2.43 tff(6016,plain,
% 2.28/2.43 (hskp8),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[6015, 5992, 5970, 660])).
% 2.28/2.43 tff(6017,plain,
% 2.28/2.43 (~c2_1(a593)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[510, 6016])).
% 2.28/2.43 tff(6018,plain,
% 2.28/2.43 (c3_1(a593)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[469, 6016])).
% 2.28/2.43 tff(6019,plain,
% 2.28/2.43 (c1_1(a593)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[477, 6016])).
% 2.28/2.43 tff(6020,plain,
% 2.28/2.43 (hskp3),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[5004, 101, 4510, 6019, 6018, 6017, 3282])).
% 2.28/2.43 tff(6021,plain,
% 2.28/2.43 (~c1_1(a587)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[855, 6020])).
% 2.28/2.43 tff(6022,plain,
% 2.28/2.43 (hskp22),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[99, 251, 4510])).
% 2.28/2.43 tff(6023,plain,
% 2.28/2.43 (~c3_1(a633)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[3833, 6022])).
% 2.28/2.43 tff(6024,plain,
% 2.28/2.43 (c1_1(a633)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[3821, 6022])).
% 2.28/2.43 tff(6025,plain,
% 2.28/2.43 (~c2_1(a633)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[4420, 251, 101, 6007, 6024, 6023, 1673])).
% 2.28/2.43 tff(6026,plain,
% 2.28/2.43 (~c0_1(a633)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[3827, 6022])).
% 2.28/2.43 tff(6027,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(6028,plain,
% 2.28/2.43 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633))) <=> (hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 2.28/2.43 inference(rewrite,[status(thm)],[])).
% 2.28/2.43 tff(6029,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633))))),
% 2.28/2.43 inference(monotonicity,[status(thm)],[6028])).
% 2.28/2.43 tff(6030,plain,
% 2.28/2.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 2.28/2.43 inference(transitivity,[status(thm)],[6029, 6027])).
% 2.28/2.43 tff(6031,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))),
% 2.28/2.43 inference(quant_inst,[status(thm)],[])).
% 2.28/2.43 tff(6032,plain,
% 2.28/2.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633))),
% 2.28/2.43 inference(modus_ponens,[status(thm)],[6031, 6030])).
% 2.28/2.43 tff(6033,plain,
% 2.28/2.43 ($false),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[6032, 101, 4510, 6024, 6026, 66, 4509, 32, 5957, 6025])).
% 2.28/2.43 tff(6034,plain,(hskp29 | c1_1(a607) | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.28/2.43 tff(6035,plain,
% 2.28/2.43 (hskp29),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[6034, 5992, 66])).
% 2.28/2.43 tff(6036,plain,
% 2.28/2.43 (c3_1(a678)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[2143, 6035])).
% 2.28/2.43 tff(6037,plain,
% 2.28/2.43 (c2_1(a678)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[2151, 6035])).
% 2.28/2.43 tff(6038,plain,
% 2.28/2.43 (c0_1(a678)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[2159, 6035])).
% 2.28/2.43 tff(6039,plain,
% 2.28/2.43 (hskp14),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[3256, 101, 6038, 6037, 6036, 6019, 6018, 6017, 505])).
% 2.28/2.43 tff(6040,plain,
% 2.28/2.43 (~c3_1(a603)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[193, 6039])).
% 2.28/2.43 tff(6041,plain,
% 2.28/2.43 (~c1_1(a603)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[162, 6039])).
% 2.28/2.43 tff(6042,plain,
% 2.28/2.43 (c2_1(a587)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[863, 6020])).
% 2.28/2.43 tff(6043,plain,
% 2.28/2.43 (c0_1(a587)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[871, 6020])).
% 2.28/2.43 tff(6044,plain,
% 2.28/2.43 (c2_1(a603)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[916, 660, 101, 6043, 6042, 6041, 6040, 6021, 905])).
% 2.28/2.43 tff(6045,plain,
% 2.28/2.43 (c0_1(a603)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[170, 6039])).
% 2.28/2.43 tff(6046,plain,
% 2.28/2.43 (hskp7 | (~c2_1(a603))),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[1277, 101, 5970, 6045, 6040, 1271])).
% 2.28/2.43 tff(6047,plain,
% 2.28/2.43 (hskp7),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[6046, 6044])).
% 2.28/2.43 tff(6048,plain,
% 2.28/2.43 (~c3_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[736, 6047])).
% 2.28/2.43 tff(6049,plain,
% 2.28/2.43 (~c0_1(a592)),
% 2.28/2.43 inference(unit_resolution,[status(thm)],[742, 6047])).
% 2.28/2.43 tff(6050,plain,
% 2.28/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6051,plain,
% 2.28/2.44 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6052,plain,
% 2.28/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607))))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6051])).
% 2.28/2.44 tff(6053,plain,
% 2.28/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6052, 6050])).
% 2.28/2.44 tff(6054,plain,
% 2.28/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6055,plain,
% 2.28/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607))),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6054, 6053])).
% 2.28/2.44 tff(6056,plain,
% 2.28/2.44 (~c1_1(a592)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6055, 101, 5890, 6045, 66, 4509, 6040, 6049, 6048, 240, 6044])).
% 2.28/2.44 tff(6057,plain,
% 2.28/2.44 ($false),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1294, 101, 1674, 6041, 6040, 6049, 6048, 188, 6056, 6044])).
% 2.28/2.44 tff(6058,plain,(hskp26 | hskp2 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.44 tff(6059,plain,
% 2.28/2.44 (hskp26),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6058, 1674, 66])).
% 2.28/2.44 tff(6060,plain,
% 2.28/2.44 (c2_1(a583)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[364, 6059])).
% 2.28/2.44 tff(6061,plain,
% 2.28/2.44 (c1_1(a583)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[330, 6059])).
% 2.28/2.44 tff(6062,plain,
% 2.28/2.44 (c0_1(a583)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[338, 6059])).
% 2.28/2.44 tff(6063,plain,
% 2.28/2.44 (hskp11 | hskp23 | (~c0_1(a607)) | (~c3_1(a607))),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1543, 101, 66, 1525])).
% 2.28/2.44 tff(6064,plain,
% 2.28/2.44 (hskp23),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6063, 1515, 5890, 5957])).
% 2.28/2.44 tff(6065,plain,
% 2.28/2.44 (~c1_1(a636)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[439, 6064])).
% 2.28/2.44 tff(6066,plain,
% 2.28/2.44 (~c0_1(a636)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[445, 6064])).
% 2.28/2.44 tff(6067,plain,
% 2.28/2.44 (c3_1(a636)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[453, 6064])).
% 2.28/2.44 tff(6068,plain,
% 2.28/2.44 (hskp9),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1577, 101, 3183, 3184, 3192, 6067, 6066, 6065, 276])).
% 2.28/2.44 tff(6069,plain,
% 2.28/2.44 (~c3_1(a595)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1370, 6068])).
% 2.28/2.44 tff(6070,plain,
% 2.28/2.44 (~c1_1(a595)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1376, 6068])).
% 2.28/2.44 tff(6071,plain,
% 2.28/2.44 (~c0_1(a595)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1382, 6068])).
% 2.28/2.44 tff(6072,plain,
% 2.28/2.44 (~c2_1(a595)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1631, 101, 1674, 6071, 6070, 6069, 188])).
% 2.28/2.44 tff(6073,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6074,plain,
% 2.28/2.44 ((hskp11 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6075,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6074])).
% 2.28/2.44 tff(6076,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6075, 6073])).
% 2.28/2.44 tff(6077,plain,
% 2.28/2.44 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6078,plain,
% 2.28/2.44 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6077, 6076])).
% 2.28/2.44 tff(6079,plain,
% 2.28/2.44 ($false),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6078, 1515, 101, 5890, 4509, 6071, 6069, 250, 5957, 6072])).
% 2.28/2.44 tff(6080,plain,(hskp11 | hskp2 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.44 tff(6081,plain,
% 2.28/2.44 (hskp11),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6080, 1674, 66])).
% 2.28/2.44 tff(6082,plain,
% 2.28/2.44 (~c1_1(a599)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[395, 6081])).
% 2.28/2.44 tff(6083,plain,
% 2.28/2.44 (c2_1(a599)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[403, 6081])).
% 2.28/2.44 tff(6084,plain,
% 2.28/2.44 (c3_1(a599)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[389, 6081])).
% 2.28/2.44 tff(6085,assumption,(hskp22), introduced(assumption)).
% 2.28/2.44 tff(6086,plain,
% 2.28/2.44 (~c0_1(a633)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[3827, 6085])).
% 2.28/2.44 tff(6087,plain,
% 2.28/2.44 (c1_1(a633)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[3821, 6085])).
% 2.28/2.44 tff(6088,plain,
% 2.28/2.44 (~c3_1(a633)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[3833, 6085])).
% 2.28/2.44 tff(6089,plain,
% 2.28/2.44 (~hskp12),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[4198, 6086, 426, 427, 6087, 6088, 425])).
% 2.28/2.44 tff(6090,plain,
% 2.28/2.44 (~c2_1(a633)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[3857, 101, 6089, 1528, 1527, 1526, 6087, 6086, 2589])).
% 2.28/2.44 tff(6091,plain,
% 2.28/2.44 ($false),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6032, 101, 4510, 6087, 6086, 66, 4509, 32, 5957, 6090])).
% 2.28/2.44 tff(6092,plain,((~hskp22) | c1_1(a607) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.44 tff(6093,plain,
% 2.28/2.44 (~hskp22),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6092, 6062, 66, 6061, 6060, 6084, 6083, 6082])).
% 2.28/2.44 tff(6094,plain,
% 2.28/2.44 (hskp29),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[2135, 6093])).
% 2.28/2.44 tff(6095,plain,
% 2.28/2.44 (c3_1(a678)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[2143, 6094])).
% 2.28/2.44 tff(6096,plain,
% 2.28/2.44 (c2_1(a678)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[2151, 6094])).
% 2.28/2.44 tff(6097,plain,
% 2.28/2.44 (c0_1(a678)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[2159, 6094])).
% 2.28/2.44 tff(6098,plain,
% 2.28/2.44 (c2_1(a592)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[750, 5202])).
% 2.28/2.44 tff(6099,plain,
% 2.28/2.44 ($false),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6013, 101, 6007, 1586, 6098, 5204, 5203, 5414])).
% 2.28/2.44 tff(6100,plain,((~hskp7) | hskp18 | hskp8), inference(lemma,lemma(discharge,[]))).
% 2.28/2.44 tff(6101,plain,
% 2.28/2.44 (hskp18),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6100, 5202, 1586])).
% 2.28/2.44 tff(6102,plain,
% 2.28/2.44 (~c2_1(a610)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1087, 6101])).
% 2.28/2.44 tff(6103,plain,
% 2.28/2.44 (~c0_1(a610)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1093, 6101])).
% 2.28/2.44 tff(6104,plain,
% 2.28/2.44 (~c1_1(a610)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[5989, 101, 4510, 6103, 6102, 66, 4509, 32, 5957])).
% 2.28/2.44 tff(6105,plain,
% 2.28/2.44 (c3_1(a610)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1101, 6101])).
% 2.28/2.44 tff(6106,plain,
% 2.28/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6107,plain,
% 2.28/2.44 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592))) <=> (c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6108,plain,
% 2.28/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610))))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6107])).
% 2.28/2.44 tff(6109,plain,
% 2.28/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6108, 6106])).
% 2.28/2.44 tff(6110,plain,
% 2.28/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6111,plain,
% 2.28/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610))),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6110, 6109])).
% 2.28/2.44 tff(6112,plain,
% 2.28/2.44 (~c1_1(a592)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6111, 101, 6097, 6096, 6095, 6105, 6098, 6102, 5204, 11, 6104])).
% 2.28/2.44 tff(6113,plain,
% 2.28/2.44 (hskp9),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[3969, 101, 6062, 6061, 6060, 6105, 6103, 276, 6104])).
% 2.28/2.44 tff(6114,plain,
% 2.28/2.44 (~c3_1(a595)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1370, 6113])).
% 2.28/2.44 tff(6115,plain,
% 2.28/2.44 (~c1_1(a595)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1376, 6113])).
% 2.28/2.44 tff(6116,plain,
% 2.28/2.44 (~c0_1(a595)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1382, 6113])).
% 2.28/2.44 tff(6117,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6118,plain,
% 2.28/2.44 ((hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6119,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6118])).
% 2.28/2.44 tff(6120,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6119, 6117])).
% 2.28/2.44 tff(6121,plain,
% 2.28/2.44 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6122,plain,
% 2.28/2.44 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6121, 6120])).
% 2.28/2.44 tff(6123,plain,
% 2.28/2.44 ($false),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6122, 101, 1674, 6098, 6116, 6115, 6114, 5203, 188, 6112])).
% 2.28/2.44 tff(6124,plain,((~hskp7) | hskp2 | c1_1(a607) | hskp8), inference(lemma,lemma(discharge,[]))).
% 2.28/2.44 tff(6125,plain,
% 2.28/2.44 (~hskp7),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6124, 1586, 66, 1674])).
% 2.28/2.44 tff(6126,plain,
% 2.28/2.44 (c3_1(a583)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[4822, 3433])).
% 2.28/2.44 tff(6127,plain,
% 2.28/2.44 (hskp15),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[4485, 6126, 1528, 1527, 1526])).
% 2.28/2.44 tff(6128,plain,
% 2.28/2.44 (~c0_1(a604)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1474, 6127])).
% 2.28/2.44 tff(6129,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6130,plain,
% 2.28/2.44 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590))) <=> (hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6131,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607))))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6130])).
% 2.28/2.44 tff(6132,plain,
% 2.28/2.44 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607)))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6131, 6129])).
% 2.28/2.44 tff(6133,plain,
% 2.28/2.44 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6134,plain,
% 2.28/2.44 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607))),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6133, 6132])).
% 2.28/2.44 tff(6135,plain,
% 2.28/2.44 (c2_1(a590) | (~c1_1(a590))),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6134, 101, 4510, 66, 4509, 45, 32, 5957])).
% 2.28/2.44 tff(6136,plain,
% 2.28/2.44 (~c1_1(a590)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6135, 3046])).
% 2.28/2.44 tff(6137,plain,
% 2.28/2.44 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6138,plain,
% 2.28/2.44 ((hskp8 | hskp6 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c3_1(a590))) <=> (hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6139,plain,
% 2.28/2.44 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590)))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6138])).
% 2.28/2.44 tff(6140,plain,
% 2.28/2.44 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6139, 6137])).
% 2.28/2.44 tff(6141,plain,
% 2.28/2.44 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6142,plain,
% 2.28/2.44 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590)),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6141, 6140])).
% 2.28/2.44 tff(6143,plain,
% 2.28/2.44 (hskp6 | (~c3_1(a590)) | c1_1(a590)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6142, 101, 1586, 45, 414])).
% 2.28/2.44 tff(6144,plain,
% 2.28/2.44 (~c3_1(a590)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6143, 3245, 6136])).
% 2.28/2.44 tff(6145,plain,
% 2.28/2.44 (c3_1(a604)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1482, 6127])).
% 2.28/2.44 tff(6146,plain,
% 2.28/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6147,plain,
% 2.28/2.44 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a590) | c0_1(a590) | c2_1(a590)) <=> (c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6148,plain,
% 2.28/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a590) | c0_1(a590) | c2_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607))))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6147])).
% 2.28/2.44 tff(6149,plain,
% 2.28/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a590) | c0_1(a590) | c2_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6148, 6146])).
% 2.28/2.44 tff(6150,plain,
% 2.28/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a590) | c0_1(a590) | c2_1(a590))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6151,plain,
% 2.28/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607))),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6150, 6149])).
% 2.28/2.44 tff(6152,plain,
% 2.28/2.44 (~c2_1(a604)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6151, 101, 5890, 6145, 3046, 6144, 66, 4509, 6128, 45, 1607])).
% 2.28/2.44 tff(6153,plain,
% 2.28/2.44 (c1_1(a604)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1490, 6127])).
% 2.28/2.44 tff(6154,plain,
% 2.28/2.44 ($false),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 6153, 66, 4509, 6128, 32, 5957, 6152])).
% 2.28/2.44 tff(6155,plain,(c2_1(a590) | c1_1(a607) | c0_1(a590) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | hskp8 | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.28/2.44 tff(6156,plain,
% 2.28/2.44 (c2_1(a590)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6155, 45, 66, 6062, 6061, 6060, 1586, 6093])).
% 2.28/2.44 tff(6157,plain,
% 2.28/2.44 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6158,plain,
% 2.28/2.44 ((hskp18 | hskp8 | (~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590))) <=> (hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6159,plain,
% 2.28/2.44 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590))))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6158])).
% 2.28/2.44 tff(6160,plain,
% 2.28/2.44 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6159, 6157])).
% 2.28/2.44 tff(6161,plain,
% 2.28/2.44 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6162,plain,
% 2.28/2.44 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590))),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6161, 6160])).
% 2.28/2.44 tff(6163,plain,
% 2.28/2.44 (hskp18 | c3_1(a590) | (~c2_1(a590))),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6162, 101, 1586, 45, 5414])).
% 2.28/2.44 tff(6164,plain,
% 2.28/2.44 (hskp18),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6163, 3043, 785])).
% 2.28/2.44 tff(6165,plain,
% 2.28/2.44 (~c2_1(a610)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1087, 6164])).
% 2.28/2.44 tff(6166,plain,
% 2.28/2.44 (~c0_1(a610)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1093, 6164])).
% 2.28/2.44 tff(6167,plain,
% 2.28/2.44 (~c1_1(a610)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[5989, 101, 4510, 6166, 6165, 66, 4509, 32, 5957])).
% 2.28/2.44 tff(6168,plain,
% 2.28/2.44 (c3_1(a610)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[1101, 6164])).
% 2.28/2.44 tff(6169,plain,
% 2.28/2.44 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6170,plain,
% 2.28/2.44 ((hskp8 | hskp6 | (~ndr1_0) | c1_1(a610) | c0_1(a610) | (~c3_1(a610))) <=> (hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.44 inference(rewrite,[status(thm)],[])).
% 2.28/2.44 tff(6171,plain,
% 2.28/2.44 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610))))),
% 2.28/2.44 inference(monotonicity,[status(thm)],[6170])).
% 2.28/2.44 tff(6172,plain,
% 2.28/2.44 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.44 inference(transitivity,[status(thm)],[6171, 6169])).
% 2.28/2.44 tff(6173,plain,
% 2.28/2.44 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))),
% 2.28/2.44 inference(quant_inst,[status(thm)],[])).
% 2.28/2.44 tff(6174,plain,
% 2.28/2.44 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610))),
% 2.28/2.44 inference(modus_ponens,[status(thm)],[6173, 6172])).
% 2.28/2.44 tff(6175,plain,
% 2.28/2.44 ($false),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6174, 101, 1586, 3044, 6168, 6166, 414, 6167])).
% 2.28/2.44 tff(6176,plain,(c3_1(a590) | hskp8 | c1_1(a607) | (~c2_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.44 tff(6177,plain,
% 2.28/2.44 (c3_1(a590)),
% 2.28/2.44 inference(unit_resolution,[status(thm)],[6176, 6156, 66, 1586, 45])).
% 2.28/2.44 tff(6178,plain,
% 2.28/2.44 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6179,plain,
% 2.28/2.45 ((hskp7 | hskp2 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6180,plain,
% 2.28/2.45 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590)))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6179])).
% 2.28/2.45 tff(6181,plain,
% 2.28/2.45 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6180, 6178])).
% 2.28/2.45 tff(6182,plain,
% 2.28/2.45 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6183,plain,
% 2.28/2.45 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590)),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6182, 6181])).
% 2.28/2.45 tff(6184,plain,
% 2.28/2.45 (hskp7 | (~c2_1(a590)) | c1_1(a590)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6183, 101, 1674, 45, 5930])).
% 2.28/2.45 tff(6185,plain,
% 2.28/2.45 (c1_1(a590)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6184, 5958, 785])).
% 2.28/2.45 tff(6186,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6187,plain,
% 2.28/2.45 ((hskp10 | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a590)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6188,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a590)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590))))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6187])).
% 2.28/2.45 tff(6189,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a590)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6188, 6186])).
% 2.28/2.45 tff(6190,plain,
% 2.28/2.45 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a590)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6191,plain,
% 2.28/2.45 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590))),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6190, 6189])).
% 2.28/2.45 tff(6192,plain,
% 2.28/2.45 (hskp10 | (~c3_1(a590)) | (~c1_1(a590))),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6191, 101, 1528, 1527, 1526, 785, 21])).
% 2.28/2.45 tff(6193,plain,
% 2.28/2.45 (hskp10),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6192, 6185, 784])).
% 2.28/2.45 tff(6194,plain,
% 2.28/2.45 (~c1_1(a598)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[827, 6193])).
% 2.28/2.45 tff(6195,plain,
% 2.28/2.45 (c3_1(a598)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[800, 6193])).
% 2.28/2.45 tff(6196,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6197,plain,
% 2.28/2.45 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6198,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598)))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6197])).
% 2.28/2.45 tff(6199,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6198, 6196])).
% 2.28/2.45 tff(6200,plain,
% 2.28/2.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6201,plain,
% 2.28/2.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598)),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6200, 6199])).
% 2.28/2.45 tff(6202,plain,
% 2.28/2.45 (c2_1(a598)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6201, 101, 2186, 2185, 2184, 6195, 785, 6194, 45, 11, 6185])).
% 2.28/2.45 tff(6203,plain,
% 2.28/2.45 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6204,plain,
% 2.28/2.45 ((hskp20 | hskp7 | (~ndr1_0) | c0_1(a590) | (~c3_1(a590)) | (~c1_1(a590))) <=> (hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6205,plain,
% 2.28/2.45 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a590) | (~c3_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590))))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6204])).
% 2.28/2.45 tff(6206,plain,
% 2.28/2.45 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a590) | (~c3_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6205, 6203])).
% 2.28/2.45 tff(6207,plain,
% 2.28/2.45 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a590) | (~c3_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6208,plain,
% 2.28/2.45 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590))),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6207, 6206])).
% 2.28/2.45 tff(6209,plain,
% 2.28/2.45 (hskp20 | hskp7 | (~c3_1(a590)) | (~c1_1(a590))),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6208, 101, 45, 726])).
% 2.28/2.45 tff(6210,plain,
% 2.28/2.45 (hskp20),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6209, 6185, 784, 5958])).
% 2.28/2.45 tff(6211,plain,
% 2.28/2.45 (~c3_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[643, 6210])).
% 2.28/2.45 tff(6212,plain,
% 2.28/2.45 (~c2_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[649, 6210])).
% 2.28/2.45 tff(6213,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6214,plain,
% 2.28/2.45 (((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6215,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623)))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6214])).
% 2.28/2.45 tff(6216,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6215, 6213])).
% 2.28/2.45 tff(6217,plain,
% 2.28/2.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6218,plain,
% 2.28/2.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623)),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6217, 6216])).
% 2.28/2.45 tff(6219,plain,
% 2.28/2.45 (c0_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6218, 101, 6195, 785, 784, 6212, 6211, 6194, 45, 1607, 6202])).
% 2.28/2.45 tff(6220,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6221,plain,
% 2.28/2.45 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6222,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590))))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6221])).
% 2.28/2.45 tff(6223,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6222, 6220])).
% 2.28/2.45 tff(6224,plain,
% 2.28/2.45 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6225,plain,
% 2.28/2.45 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590))),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6224, 6223])).
% 2.28/2.45 tff(6226,plain,
% 2.28/2.45 (hskp12 | (~c2_1(a590)) | (~c1_1(a590))),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6225, 101, 1528, 1527, 1526, 45, 2589])).
% 2.28/2.45 tff(6227,plain,
% 2.28/2.45 (hskp12),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6226, 6185, 785])).
% 2.28/2.45 tff(6228,plain,
% 2.28/2.45 (~c3_1(a600)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[675, 6227])).
% 2.28/2.45 tff(6229,plain,
% 2.28/2.45 (c2_1(a600)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[683, 6227])).
% 2.28/2.45 tff(6230,plain,
% 2.28/2.45 (c0_1(a600)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[691, 6227])).
% 2.28/2.45 tff(6231,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6232,plain,
% 2.28/2.45 ((hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623))) <=> (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6233,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623))))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6232])).
% 2.28/2.45 tff(6234,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623)))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6233, 6231])).
% 2.28/2.45 tff(6235,plain,
% 2.28/2.45 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6236,plain,
% 2.28/2.45 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623))),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6235, 6234])).
% 2.28/2.45 tff(6237,plain,
% 2.28/2.45 ($false),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6236, 101, 1586, 6230, 6229, 6212, 6211, 6228, 4127, 6219])).
% 2.28/2.45 tff(6238,plain,(hskp7 | hskp8 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.28/2.45 tff(6239,plain,
% 2.28/2.45 ($false),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6238, 6177, 6156, 1586, 6125, 45, 6097, 6096, 6095, 6062, 6061, 6060, 1674])).
% 2.28/2.45 tff(6240,plain,(c0_1(a590) | hskp8 | hskp2 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.45 tff(6241,plain,
% 2.28/2.45 (c0_1(a590)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6240, 1586, 1674, 66])).
% 2.28/2.45 tff(6242,plain,
% 2.28/2.45 (~hskp6),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[606, 6241])).
% 2.28/2.45 tff(6243,plain,
% 2.28/2.45 (~hskp4),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[138, 6242, 6093])).
% 2.28/2.45 tff(6244,plain,
% 2.28/2.45 (hskp4 | c3_1(a583)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[3190, 101, 4510, 6062, 6061, 55])).
% 2.28/2.45 tff(6245,plain,
% 2.28/2.45 (c3_1(a583)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6244, 6243])).
% 2.28/2.45 tff(6246,plain,
% 2.28/2.45 (hskp15),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[4485, 6245, 6062, 6061, 6060])).
% 2.28/2.45 tff(6247,plain,
% 2.28/2.45 (c3_1(a604)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[1482, 6246])).
% 2.28/2.45 tff(6248,plain,
% 2.28/2.45 (~c0_1(a604)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[1474, 6246])).
% 2.28/2.45 tff(6249,plain,
% 2.28/2.45 (c1_1(a604)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[1490, 6246])).
% 2.28/2.45 tff(6250,plain,
% 2.28/2.45 (c2_1(a604)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 6249, 66, 4509, 6248, 32, 5957])).
% 2.28/2.45 tff(6251,plain,
% 2.28/2.45 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6252,plain,
% 2.28/2.45 ((hskp20 | hskp7 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604))) <=> (hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6253,plain,
% 2.28/2.45 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6252])).
% 2.28/2.45 tff(6254,plain,
% 2.28/2.45 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6253, 6251])).
% 2.28/2.45 tff(6255,plain,
% 2.28/2.45 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6256,plain,
% 2.28/2.45 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6255, 6254])).
% 2.28/2.45 tff(6257,plain,
% 2.28/2.45 (hskp20),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6256, 101, 6125, 6249, 6247, 6248, 726])).
% 2.28/2.45 tff(6258,plain,
% 2.28/2.45 (hskp16),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[5514, 6257, 6083, 6084, 6248, 6082, 6250, 6247])).
% 2.28/2.45 tff(6259,plain,
% 2.28/2.45 (~c3_1(a606)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[982, 6258])).
% 2.28/2.45 tff(6260,plain,
% 2.28/2.45 (~c2_1(a606)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[1015, 6258])).
% 2.28/2.45 tff(6261,plain,
% 2.28/2.45 (c1_1(a606)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[992, 6258])).
% 2.28/2.45 tff(6262,plain,
% 2.28/2.45 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6263,plain,
% 2.28/2.45 ((hskp8 | hskp6 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606))) <=> (hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6264,plain,
% 2.28/2.45 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606))))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6263])).
% 2.28/2.45 tff(6265,plain,
% 2.28/2.45 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6264, 6262])).
% 2.28/2.45 tff(6266,plain,
% 2.28/2.45 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6267,plain,
% 2.28/2.45 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606))),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6266, 6265])).
% 2.28/2.45 tff(6268,plain,
% 2.28/2.45 ($false),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6267, 101, 1586, 6242, 6261, 6260, 6259, 5969])).
% 2.28/2.45 tff(6269,plain,(hskp8 | c1_1(a607) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.28/2.45 tff(6270,plain,
% 2.28/2.45 (hskp8),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6269, 1674, 66])).
% 2.28/2.45 tff(6271,plain,
% 2.28/2.45 (~c2_1(a593)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[510, 6270])).
% 2.28/2.45 tff(6272,plain,
% 2.28/2.45 (c3_1(a593)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[469, 6270])).
% 2.28/2.45 tff(6273,plain,
% 2.28/2.45 (c1_1(a593)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[477, 6270])).
% 2.28/2.45 tff(6274,plain,
% 2.28/2.45 (hskp14),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[3256, 101, 6097, 6096, 6095, 6273, 6272, 6271, 505])).
% 2.28/2.45 tff(6275,plain,
% 2.28/2.45 (c0_1(a603)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[170, 6274])).
% 2.28/2.45 tff(6276,plain,
% 2.28/2.45 (~c3_1(a603)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[193, 6274])).
% 2.28/2.45 tff(6277,plain,
% 2.28/2.45 (~c1_1(a603)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[162, 6274])).
% 2.28/2.45 tff(6278,plain,
% 2.28/2.45 (c2_1(a603)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[1906, 67])).
% 2.28/2.45 tff(6279,plain,
% 2.28/2.45 (hskp20),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[1278, 6278, 5958])).
% 2.28/2.45 tff(6280,plain,
% 2.28/2.45 (~c2_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[649, 6279])).
% 2.28/2.45 tff(6281,plain,
% 2.28/2.45 (~c1_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[655, 6279])).
% 2.28/2.45 tff(6282,plain,
% 2.28/2.45 (~c0_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[3792, 101, 44, 67, 6281, 6280, 43])).
% 2.28/2.45 tff(6283,plain,
% 2.28/2.45 (~c3_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[643, 6279])).
% 2.28/2.45 tff(6284,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6285,plain,
% 2.28/2.45 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a623) | c1_1(a623) | c0_1(a623)) <=> (hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6286,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a623) | c1_1(a623) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623)))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6285])).
% 2.28/2.45 tff(6287,plain,
% 2.28/2.45 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a623) | c1_1(a623) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623))),
% 2.28/2.45 inference(transitivity,[status(thm)],[6286, 6284])).
% 2.28/2.45 tff(6288,plain,
% 2.28/2.45 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a623) | c1_1(a623) | c0_1(a623))),
% 2.28/2.45 inference(quant_inst,[status(thm)],[])).
% 2.28/2.45 tff(6289,plain,
% 2.28/2.45 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623)),
% 2.28/2.45 inference(modus_ponens,[status(thm)],[6288, 6287])).
% 2.28/2.45 tff(6290,plain,
% 2.28/2.45 ($false),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6289, 101, 1674, 6281, 6283, 908, 907, 188, 6278, 6282])).
% 2.28/2.45 tff(6291,plain,(hskp6 | hskp2 | c1_1(a603) | c3_1(a603) | hskp22 | hskp7 | (~c0_1(a603))), inference(lemma,lemma(discharge,[]))).
% 2.28/2.45 tff(6292,plain,
% 2.28/2.45 (hskp6),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6291, 5958, 6277, 6276, 6093, 1674, 6275])).
% 2.28/2.45 tff(6293,plain,
% 2.28/2.45 (hskp3),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[5004, 101, 4510, 6273, 6272, 6271, 3282])).
% 2.28/2.45 tff(6294,plain,
% 2.28/2.45 (~c1_1(a587)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[855, 6293])).
% 2.28/2.45 tff(6295,plain,
% 2.28/2.45 (c2_1(a590)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[622, 6292])).
% 2.28/2.45 tff(6296,plain,
% 2.28/2.45 (c1_1(a590)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6184, 6295, 5958])).
% 2.28/2.45 tff(6297,plain,
% 2.28/2.45 (c3_1(a590)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[614, 6292])).
% 2.28/2.45 tff(6298,plain,
% 2.28/2.45 (hskp20),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[6209, 6297, 5958, 6296])).
% 2.28/2.45 tff(6299,plain,
% 2.28/2.45 (~c3_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[643, 6298])).
% 2.28/2.45 tff(6300,plain,
% 2.28/2.45 (~c2_1(a623)),
% 2.28/2.45 inference(unit_resolution,[status(thm)],[649, 6298])).
% 2.28/2.45 tff(6301,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6302,plain,
% 2.28/2.45 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623))),
% 2.28/2.45 inference(rewrite,[status(thm)],[])).
% 2.28/2.45 tff(6303,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623)))),
% 2.28/2.45 inference(monotonicity,[status(thm)],[6302])).
% 2.28/2.45 tff(6304,plain,
% 2.28/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6303, 6301])).
% 2.28/2.46 tff(6305,plain,
% 2.28/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6306,plain,
% 2.28/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623)),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6305, 6304])).
% 2.28/2.46 tff(6307,plain,
% 2.28/2.46 (c0_1(a623)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6306, 101, 5890, 6295, 6297, 6300, 6299, 66, 4509, 45, 1607])).
% 2.28/2.46 tff(6308,plain,
% 2.28/2.46 (hskp16 | (~c0_1(a623))),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[5730, 101, 6295, 6297, 6300, 6299, 45, 2002])).
% 2.28/2.46 tff(6309,plain,
% 2.28/2.46 (hskp16),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6308, 6307])).
% 2.28/2.46 tff(6310,plain,
% 2.28/2.46 (~c2_1(a606)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1015, 6309])).
% 2.28/2.46 tff(6311,plain,
% 2.28/2.46 (c2_1(a587)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[863, 6293])).
% 2.28/2.46 tff(6312,plain,
% 2.28/2.46 (c0_1(a587)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[871, 6293])).
% 2.28/2.46 tff(6313,plain,
% 2.28/2.46 (c1_1(a606)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[992, 6309])).
% 2.28/2.46 tff(6314,plain,
% 2.28/2.46 (c0_1(a606)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[4884, 6313, 4510, 6312, 6311, 6310, 6294])).
% 2.28/2.46 tff(6315,plain,
% 2.28/2.46 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6316,plain,
% 2.28/2.46 ((hskp7 | hskp2 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6317,plain,
% 2.28/2.46 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617))))),
% 2.28/2.46 inference(monotonicity,[status(thm)],[6316])).
% 2.28/2.46 tff(6318,plain,
% 2.28/2.46 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6317, 6315])).
% 2.28/2.46 tff(6319,plain,
% 2.28/2.46 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6320,plain,
% 2.28/2.46 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617))),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6319, 6318])).
% 2.28/2.46 tff(6321,plain,
% 2.28/2.46 ($false),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6320, 101, 5958, 1674, 3611, 3610, 3609, 5930])).
% 2.28/2.46 tff(6322,plain,((~hskp19) | hskp7 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.28/2.46 tff(6323,plain,
% 2.28/2.46 (~hskp19),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6322, 5958, 1674])).
% 2.28/2.46 tff(6324,plain,
% 2.28/2.46 (hskp13),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[3729, 6323, 6295, 6296])).
% 2.28/2.46 tff(6325,plain,
% 2.28/2.46 (~c2_1(a601)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2388, 6324])).
% 2.28/2.46 tff(6326,plain,
% 2.28/2.46 (~c1_1(a601)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2394, 6324])).
% 2.28/2.46 tff(6327,plain,
% 2.28/2.46 (~c3_1(a601)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2401, 101, 6097, 6096, 6095, 6313, 6310, 6326, 6325, 1010, 6314])).
% 2.28/2.46 tff(6328,plain,
% 2.28/2.46 (~c0_1(a601)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2408, 6324])).
% 2.28/2.46 tff(6329,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6330,plain,
% 2.28/2.46 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | c0_1(a601) | c2_1(a601)) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6331,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | c0_1(a601) | c2_1(a601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607))))),
% 2.28/2.46 inference(monotonicity,[status(thm)],[6330])).
% 2.28/2.46 tff(6332,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | c0_1(a601) | c2_1(a601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607)))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6331, 6329])).
% 2.28/2.46 tff(6333,plain,
% 2.28/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | c0_1(a601) | c2_1(a601))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6334,plain,
% 2.28/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607))),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6333, 6332])).
% 2.28/2.46 tff(6335,plain,
% 2.28/2.46 ($false),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6334, 101, 5890, 6295, 6297, 66, 4509, 6328, 6325, 45, 1607, 6327])).
% 2.28/2.46 tff(6336,plain,(hskp7 | c1_1(a607) | c0_1(a590) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.28/2.46 tff(6337,plain,
% 2.28/2.46 (c0_1(a590)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6336, 5958, 66, 1674])).
% 2.28/2.46 tff(6338,plain,
% 2.28/2.46 ($false),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[606, 6337, 6292])).
% 2.28/2.46 tff(6339,plain,(hskp7 | c1_1(a607) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.28/2.46 tff(6340,plain,
% 2.28/2.46 (hskp7),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6339, 1674, 66])).
% 2.28/2.46 tff(6341,plain,
% 2.28/2.46 (~c3_1(a592)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[736, 6340])).
% 2.28/2.46 tff(6342,plain,
% 2.28/2.46 (~c0_1(a592)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[742, 6340])).
% 2.28/2.46 tff(6343,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6344,plain,
% 2.28/2.46 ((hskp15 | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6345,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.28/2.46 inference(monotonicity,[status(thm)],[6344])).
% 2.28/2.46 tff(6346,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6345, 6343])).
% 2.28/2.46 tff(6347,plain,
% 2.28/2.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6348,plain,
% 2.28/2.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6347, 6346])).
% 2.28/2.46 tff(6349,plain,
% 2.28/2.46 (hskp15 | (~c1_1(a678))),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6348, 101, 2186, 2184, 5890, 66, 1870, 5957])).
% 2.28/2.46 tff(6350,plain,
% 2.28/2.46 (~c1_1(a678)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6349, 3016])).
% 2.28/2.46 tff(6351,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6352,plain,
% 2.28/2.46 ((hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6353,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.28/2.46 inference(monotonicity,[status(thm)],[6352])).
% 2.28/2.46 tff(6354,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6353, 6351])).
% 2.28/2.46 tff(6355,plain,
% 2.28/2.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6356,plain,
% 2.28/2.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6355, 6354])).
% 2.28/2.46 tff(6357,plain,
% 2.28/2.46 (hskp15 | (~c0_1(a593))),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6356, 101, 5890, 1771, 1780, 66, 1870, 5957])).
% 2.28/2.46 tff(6358,plain,
% 2.28/2.46 (~c0_1(a593)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6357, 3016])).
% 2.28/2.46 tff(6359,plain,
% 2.28/2.46 ($false),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2488, 101, 4510, 2186, 2185, 1771, 1770, 32, 6358, 6350])).
% 2.28/2.46 tff(6360,plain,(hskp15 | (~c0_1(a678)) | (~c2_1(a678)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a593)) | c1_1(a607) | (~c3_1(a678))), inference(lemma,lemma(discharge,[]))).
% 2.28/2.46 tff(6361,plain,
% 2.28/2.46 (hskp15),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6360, 6097, 6096, 6273, 6271, 6272, 66, 6095])).
% 2.28/2.46 tff(6362,plain,
% 2.28/2.46 (~c0_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1474, 6361])).
% 2.28/2.46 tff(6363,plain,
% 2.28/2.46 (c1_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1490, 6361])).
% 2.28/2.46 tff(6364,plain,
% 2.28/2.46 (c2_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 6363, 66, 4509, 6362, 32, 5957])).
% 2.28/2.46 tff(6365,plain,
% 2.28/2.46 (hskp12 | (~c2_1(a604))),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2917, 101, 6062, 6061, 6060, 6363, 6362, 2589])).
% 2.28/2.46 tff(6366,plain,
% 2.28/2.46 (hskp12),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6365, 6364])).
% 2.28/2.46 tff(6367,plain,
% 2.28/2.46 (~c3_1(a600)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[675, 6366])).
% 2.28/2.46 tff(6368,plain,
% 2.28/2.46 (c2_1(a600)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[683, 6366])).
% 2.28/2.46 tff(6369,plain,
% 2.28/2.46 (c0_1(a600)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[691, 6366])).
% 2.28/2.46 tff(6370,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6371,plain,
% 2.28/2.46 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6372,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607))))),
% 2.28/2.46 inference(monotonicity,[status(thm)],[6371])).
% 2.28/2.46 tff(6373,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607)))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6372, 6370])).
% 2.28/2.46 tff(6374,plain,
% 2.28/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6375,plain,
% 2.28/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607))),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6374, 6373])).
% 2.28/2.46 tff(6376,plain,
% 2.28/2.46 (~c1_1(a592)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6375, 101, 5890, 6369, 6368, 66, 4509, 6367, 6342, 6341, 240])).
% 2.28/2.46 tff(6377,plain,
% 2.28/2.46 (c2_1(a592)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[750, 6340])).
% 2.28/2.46 tff(6378,plain,
% 2.28/2.46 ($false),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[5954, 101, 1674, 6377, 6342, 6341, 188, 6376])).
% 2.28/2.46 tff(6379,plain,(hskp2 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.46 tff(6380,plain,
% 2.28/2.46 (hskp2),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6379, 66])).
% 2.28/2.46 tff(6381,plain,
% 2.28/2.46 (hskp28),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[5919, 6380, 66])).
% 2.28/2.46 tff(6382,plain,
% 2.28/2.46 (c3_1(a612)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1040, 6381])).
% 2.28/2.46 tff(6383,plain,
% 2.28/2.46 (c1_1(a612)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1321, 6381])).
% 2.28/2.46 tff(6384,plain,
% 2.28/2.46 (hskp20 | hskp7 | c0_1(a612)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[4376, 101, 6383, 6382, 726])).
% 2.28/2.46 tff(6385,plain,
% 2.28/2.46 (c0_1(a612)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6384, 5959, 5958])).
% 2.28/2.46 tff(6386,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6387,plain,
% 2.28/2.46 ((hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6388,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.28/2.46 inference(monotonicity,[status(thm)],[6387])).
% 2.28/2.46 tff(6389,plain,
% 2.28/2.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6388, 6386])).
% 2.28/2.46 tff(6390,plain,
% 2.28/2.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6391,plain,
% 2.28/2.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6390, 6389])).
% 2.28/2.46 tff(6392,plain,
% 2.28/2.46 (hskp15 | (~c0_1(a612))),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6391, 101, 6383, 6382, 5890, 66, 1870, 5957])).
% 2.28/2.46 tff(6393,plain,
% 2.28/2.46 (hskp15),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6392, 6385])).
% 2.28/2.46 tff(6394,plain,
% 2.28/2.46 (~c0_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1474, 6393])).
% 2.28/2.46 tff(6395,plain,
% 2.28/2.46 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6396,plain,
% 2.28/2.46 ((hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612))) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6397,plain,
% 2.28/2.46 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612))))),
% 2.28/2.46 inference(monotonicity,[status(thm)],[6396])).
% 2.28/2.46 tff(6398,plain,
% 2.28/2.46 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6397, 6395])).
% 2.28/2.46 tff(6399,plain,
% 2.28/2.46 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6400,plain,
% 2.28/2.46 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612))),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6399, 6398])).
% 2.28/2.46 tff(6401,plain,
% 2.28/2.46 (hskp20 | hskp19 | (~c0_1(a612))),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6400, 101, 6383, 6382, 3630])).
% 2.28/2.46 tff(6402,plain,
% 2.28/2.46 (hskp19),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6401, 6385, 5959])).
% 2.28/2.46 tff(6403,plain,
% 2.28/2.46 (~c1_1(a617)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2453, 6402])).
% 2.28/2.46 tff(6404,plain,
% 2.28/2.46 (~c0_1(a617)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2459, 6402])).
% 2.28/2.46 tff(6405,plain,
% 2.28/2.46 (c3_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1482, 6393])).
% 2.28/2.46 tff(6406,plain,
% 2.28/2.46 (c2_1(a617)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2467, 6402])).
% 2.28/2.46 tff(6407,plain,
% 2.28/2.46 (~c2_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[5867, 101, 6383, 6382, 6406, 6405, 6404, 6403, 6394, 65, 6385])).
% 2.28/2.46 tff(6408,plain,
% 2.28/2.46 (c1_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1490, 6393])).
% 2.28/2.46 tff(6409,plain,
% 2.28/2.46 ($false),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 6408, 66, 4509, 6394, 32, 5957, 6407])).
% 2.28/2.46 tff(6410,plain,(hskp20 | c1_1(a607) | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.28/2.46 tff(6411,plain,
% 2.28/2.46 (hskp20),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6410, 5958, 66])).
% 2.28/2.46 tff(6412,plain,
% 2.28/2.46 (~c1_1(a623)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[655, 6411])).
% 2.28/2.46 tff(6413,plain,
% 2.28/2.46 (~c3_1(a623)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[643, 6411])).
% 2.28/2.46 tff(6414,plain,
% 2.28/2.46 (~c2_1(a623)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[649, 6411])).
% 2.28/2.46 tff(6415,plain,
% 2.28/2.46 (hskp29),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[4003, 5958, 4510])).
% 2.28/2.46 tff(6416,plain,
% 2.28/2.46 (c3_1(a678)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2143, 6415])).
% 2.28/2.46 tff(6417,plain,
% 2.28/2.46 (c0_1(a678)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2159, 6415])).
% 2.28/2.46 tff(6418,plain,
% 2.28/2.46 (c2_1(a678)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2151, 6415])).
% 2.28/2.46 tff(6419,plain,
% 2.28/2.46 (hskp15),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6360, 5064, 6418, 6417, 5072, 5063, 66, 6416])).
% 2.28/2.46 tff(6420,plain,
% 2.28/2.46 (~c0_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1474, 6419])).
% 2.28/2.46 tff(6421,plain,
% 2.28/2.46 (c1_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1490, 6419])).
% 2.28/2.46 tff(6422,plain,
% 2.28/2.46 (c2_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 6421, 66, 4509, 6420, 32, 5957])).
% 2.28/2.46 tff(6423,plain,
% 2.28/2.46 (c3_1(a604)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1482, 6419])).
% 2.28/2.46 tff(6424,plain,
% 2.28/2.46 (hskp20),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6256, 101, 5958, 6421, 6423, 6420, 726])).
% 2.28/2.46 tff(6425,plain,
% 2.28/2.46 (~c3_1(a623)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[643, 6424])).
% 2.28/2.46 tff(6426,plain,
% 2.28/2.46 (~c2_1(a623)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[649, 6424])).
% 2.28/2.46 tff(6427,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6428,plain,
% 2.28/2.46 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623))),
% 2.28/2.46 inference(rewrite,[status(thm)],[])).
% 2.28/2.46 tff(6429,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623)))),
% 2.28/2.46 inference(monotonicity,[status(thm)],[6428])).
% 2.28/2.46 tff(6430,plain,
% 2.28/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623))),
% 2.28/2.46 inference(transitivity,[status(thm)],[6429, 6427])).
% 2.28/2.46 tff(6431,plain,
% 2.28/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 2.28/2.46 inference(quant_inst,[status(thm)],[])).
% 2.28/2.46 tff(6432,plain,
% 2.28/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623)),
% 2.28/2.46 inference(modus_ponens,[status(thm)],[6431, 6430])).
% 2.28/2.46 tff(6433,plain,
% 2.28/2.46 (c0_1(a623)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6432, 101, 5890, 6423, 6426, 6425, 66, 4509, 6420, 1607, 6422])).
% 2.28/2.46 tff(6434,plain,
% 2.28/2.46 (hskp16 | (~c0_1(a623))),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[5505, 101, 6423, 6426, 6425, 6420, 2002, 6422])).
% 2.28/2.46 tff(6435,plain,
% 2.28/2.46 (hskp16),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6434, 6433])).
% 2.28/2.46 tff(6436,plain,
% 2.28/2.46 (~c2_1(a606)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[1015, 6435])).
% 2.28/2.46 tff(6437,plain,
% 2.28/2.46 (c1_1(a606)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[992, 6435])).
% 2.28/2.46 tff(6438,plain,
% 2.28/2.46 (c0_1(a606)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[4884, 6437, 4510, 5076, 5075, 6436, 5074])).
% 2.28/2.46 tff(6439,plain,
% 2.28/2.46 (hskp11),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2222, 101, 5982, 6437, 6436, 2215, 6438])).
% 2.28/2.46 tff(6440,plain,
% 2.28/2.46 (~c1_1(a599)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[395, 6439])).
% 2.28/2.46 tff(6441,plain,
% 2.28/2.46 (c2_1(a599)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[403, 6439])).
% 2.28/2.46 tff(6442,plain,
% 2.28/2.46 (c3_1(a599)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[389, 6439])).
% 2.28/2.46 tff(6443,plain,
% 2.28/2.46 (~hskp13),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2418, 6442, 6422, 6438, 6441, 6440, 6420, 6417, 6418, 6416, 6437, 6436, 6423])).
% 2.28/2.46 tff(6444,plain,
% 2.28/2.46 (hskp19 | hskp13 | (~c2_1(a604))),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2518, 101, 6421, 6420, 2429])).
% 2.28/2.46 tff(6445,plain,
% 2.28/2.46 (hskp19),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6444, 6443, 6422])).
% 2.28/2.46 tff(6446,plain,
% 2.28/2.46 (~c1_1(a617)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2453, 6445])).
% 2.28/2.46 tff(6447,plain,
% 2.28/2.46 (~c0_1(a617)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2459, 6445])).
% 2.28/2.46 tff(6448,plain,
% 2.28/2.46 (c2_1(a617)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2467, 6445])).
% 2.28/2.46 tff(6449,plain,
% 2.28/2.46 (~c1_1(a678)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2474, 101, 6417, 6416, 6448, 6423, 6447, 6446, 6420, 65, 6422])).
% 2.28/2.46 tff(6450,plain,
% 2.28/2.46 (~c0_1(a593)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2481, 101, 6448, 6423, 5064, 5063, 6447, 6446, 6420, 65, 6422])).
% 2.28/2.46 tff(6451,plain,
% 2.28/2.46 ($false),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[2488, 101, 4510, 6417, 6418, 5064, 5072, 32, 6450, 6449])).
% 2.28/2.46 tff(6452,plain,((~hskp8) | c1_1(a607) | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.28/2.46 tff(6453,plain,
% 2.28/2.46 (~hskp8),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6452, 5958, 66])).
% 2.28/2.46 tff(6454,plain,
% 2.28/2.46 ($false),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6015, 5970, 660, 1586, 5992])).
% 2.28/2.46 tff(6455,plain,(hskp26 | hskp8 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.46 tff(6456,plain,
% 2.28/2.46 (hskp26),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[6455, 1586, 66])).
% 2.28/2.46 tff(6457,plain,
% 2.28/2.46 (c0_1(a583)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[338, 6456])).
% 2.28/2.46 tff(6458,plain,
% 2.28/2.46 (c2_1(a583)),
% 2.28/2.46 inference(unit_resolution,[status(thm)],[364, 6456])).
% 2.28/2.47 tff(6459,plain,
% 2.28/2.47 (c1_1(a583)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[330, 6456])).
% 2.28/2.47 tff(6460,plain,
% 2.28/2.47 (~c3_1(a586)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[206, 6380])).
% 2.28/2.47 tff(6461,plain,
% 2.28/2.47 (c2_1(a586)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1357, 6380])).
% 2.28/2.47 tff(6462,plain,
% 2.28/2.47 (c1_1(a586)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[214, 6380])).
% 2.28/2.47 tff(6463,plain,
% 2.28/2.47 (c3_1(a590)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6176, 785, 66, 1586, 45])).
% 2.28/2.47 tff(6464,plain,
% 2.28/2.47 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6465,plain,
% 2.28/2.47 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586))) <=> (hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6466,plain,
% 2.28/2.47 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586))))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6465])).
% 2.28/2.47 tff(6467,plain,
% 2.28/2.47 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6466, 6464])).
% 2.28/2.47 tff(6468,plain,
% 2.28/2.47 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6469,plain,
% 2.28/2.47 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586))),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6468, 6467])).
% 2.28/2.47 tff(6470,plain,
% 2.28/2.47 (hskp20 | hskp7 | (~c0_1(a586))),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6469, 101, 4676, 4664, 1271])).
% 2.28/2.47 tff(6471,plain,
% 2.28/2.47 (~c0_1(a586)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6470, 5959, 5958])).
% 2.28/2.47 tff(6472,plain,
% 2.28/2.47 (hskp20 | (~c3_1(a590)) | (~c1_1(a590))),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6208, 101, 5958, 45, 726])).
% 2.28/2.47 tff(6473,plain,
% 2.28/2.47 (~c1_1(a590)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6472, 5959, 784])).
% 2.28/2.47 tff(6474,plain,
% 2.28/2.47 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6475,plain,
% 2.28/2.47 ((hskp8 | (~ndr1_0) | c0_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590))) <=> (hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6476,plain,
% 2.28/2.47 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590)))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6475])).
% 2.28/2.47 tff(6477,plain,
% 2.28/2.47 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6476, 6474])).
% 2.28/2.47 tff(6478,plain,
% 2.28/2.47 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6479,plain,
% 2.28/2.47 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590)),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6478, 6477])).
% 2.28/2.47 tff(6480,plain,
% 2.28/2.47 ($false),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6479, 101, 1586, 784, 4665, 4676, 45, 1206, 6473, 6471])).
% 2.28/2.47 tff(6481,plain,(hskp20 | hskp8 | (~c3_1(a590)) | (~c1_1(a586)) | (~c2_1(a586)) | c0_1(a590) | hskp7 | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.47 tff(6482,plain,
% 2.28/2.47 (hskp20),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6481, 6463, 1586, 6462, 6461, 45, 5958, 6460])).
% 2.28/2.47 tff(6483,plain,
% 2.28/2.47 (~c3_1(a623)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[643, 6482])).
% 2.28/2.47 tff(6484,plain,
% 2.28/2.47 (~c2_1(a623)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[649, 6482])).
% 2.28/2.47 tff(6485,plain,
% 2.28/2.47 (c0_1(a623)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6306, 101, 5890, 785, 6463, 6484, 6483, 66, 4509, 45, 1607])).
% 2.28/2.47 tff(6486,plain,
% 2.28/2.47 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6487,plain,
% 2.28/2.47 ((hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623))) <=> (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6488,plain,
% 2.28/2.47 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623))))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6487])).
% 2.28/2.47 tff(6489,plain,
% 2.28/2.47 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623)))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6488, 6486])).
% 2.28/2.47 tff(6490,plain,
% 2.28/2.47 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6491,plain,
% 2.28/2.47 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623))),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6490, 6489])).
% 2.28/2.47 tff(6492,plain,
% 2.28/2.47 (~c0_1(a586)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6491, 101, 1586, 6461, 6484, 6483, 6460, 4127, 6485])).
% 2.28/2.47 tff(6493,plain,
% 2.28/2.47 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6494,plain,
% 2.28/2.47 ((hskp18 | hskp8 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586))) <=> (hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6495,plain,
% 2.28/2.47 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586)))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6494])).
% 2.28/2.47 tff(6496,plain,
% 2.28/2.47 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6495, 6493])).
% 2.28/2.47 tff(6497,plain,
% 2.28/2.47 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6498,plain,
% 2.28/2.47 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586)),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6497, 6496])).
% 2.28/2.47 tff(6499,plain,
% 2.28/2.47 (hskp18 | hskp8 | c0_1(a586)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6498, 101, 6461, 6460, 5414])).
% 2.28/2.47 tff(6500,plain,
% 2.28/2.47 (hskp18),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6499, 6492, 1586])).
% 2.28/2.47 tff(6501,plain,
% 2.28/2.47 (~c2_1(a610)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1087, 6500])).
% 2.28/2.47 tff(6502,plain,
% 2.28/2.47 (~c0_1(a610)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1093, 6500])).
% 2.28/2.47 tff(6503,plain,
% 2.28/2.47 (~c1_1(a610)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[5989, 101, 4510, 6502, 6501, 66, 4509, 32, 5957])).
% 2.28/2.47 tff(6504,plain,
% 2.28/2.47 (hskp16 | (~c0_1(a623))),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[5730, 101, 785, 6463, 6484, 6483, 45, 2002])).
% 2.28/2.47 tff(6505,plain,
% 2.28/2.47 (hskp16),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6504, 6485])).
% 2.28/2.47 tff(6506,plain,
% 2.28/2.47 (~c3_1(a606)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[982, 6505])).
% 2.28/2.47 tff(6507,plain,
% 2.28/2.47 (~c2_1(a606)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1015, 6505])).
% 2.28/2.47 tff(6508,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6509,plain,
% 2.28/2.47 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6510,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607))))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6509])).
% 2.28/2.47 tff(6511,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607)))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6510, 6508])).
% 2.28/2.47 tff(6512,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6513,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607))),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6512, 6511])).
% 2.28/2.47 tff(6514,plain,
% 2.28/2.47 (c0_1(a606)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6513, 101, 5890, 785, 6463, 66, 4509, 6507, 6506, 45, 1607])).
% 2.28/2.47 tff(6515,plain,
% 2.28/2.47 (c2_1(a612)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1048, 6381])).
% 2.28/2.47 tff(6516,plain,
% 2.28/2.47 (hskp10),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1418, 101, 6383, 6515, 6382, 6457, 6459, 6458, 21])).
% 2.28/2.47 tff(6517,plain,
% 2.28/2.47 (~c1_1(a598)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[827, 6516])).
% 2.28/2.47 tff(6518,plain,
% 2.28/2.47 (c3_1(a598)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[800, 6516])).
% 2.28/2.47 tff(6519,plain,
% 2.28/2.47 (c2_1(a598)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[4847, 101, 6417, 6418, 6416, 6518, 6462, 6461, 6517, 11, 6492])).
% 2.28/2.47 tff(6520,plain,
% 2.28/2.47 (c0_1(a598)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[808, 6516])).
% 2.28/2.47 tff(6521,plain,
% 2.28/2.47 (c1_1(a606)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[992, 6505])).
% 2.28/2.47 tff(6522,plain,
% 2.28/2.47 (c3_1(a610)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1101, 6500])).
% 2.28/2.47 tff(6523,plain,
% 2.28/2.47 ($false),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[5458, 101, 6522, 6521, 6520, 6518, 6501, 6507, 1010, 6519, 6514, 6503])).
% 2.28/2.47 tff(6524,plain,((~c2_1(a590)) | c1_1(a607) | c0_1(a590) | hskp8 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.28/2.47 tff(6525,plain,
% 2.28/2.47 (~c2_1(a590)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6524, 1586, 45, 66, 5958])).
% 2.28/2.47 tff(6526,plain,
% 2.28/2.47 (hskp22),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6155, 6525, 66, 1586, 6459, 6458, 45, 6457])).
% 2.28/2.47 tff(6527,plain,
% 2.28/2.47 (c1_1(a633)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[3821, 6526])).
% 2.28/2.47 tff(6528,plain,
% 2.28/2.47 (~c0_1(a633)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[3827, 6526])).
% 2.28/2.47 tff(6529,plain,
% 2.28/2.47 (~c3_1(a633)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[3833, 6526])).
% 2.28/2.47 tff(6530,plain,
% 2.28/2.47 (hskp11),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[5013, 6529, 6528, 4510, 6527])).
% 2.28/2.47 tff(6531,plain,
% 2.28/2.47 (~c1_1(a599)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[395, 6530])).
% 2.28/2.47 tff(6532,plain,
% 2.28/2.47 (c2_1(a599)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[403, 6530])).
% 2.28/2.47 tff(6533,plain,
% 2.28/2.47 (c3_1(a599)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[389, 6530])).
% 2.28/2.47 tff(6534,plain,
% 2.28/2.47 ($false),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6092, 6533, 6532, 66, 6459, 6458, 6457, 6526, 6531])).
% 2.28/2.47 tff(6535,plain,(hskp8 | c1_1(a607) | c0_1(a590) | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.28/2.47 tff(6536,plain,
% 2.28/2.47 (c0_1(a590)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6535, 6453, 66, 5958])).
% 2.28/2.47 tff(6537,plain,
% 2.28/2.47 (~hskp6),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[606, 6536])).
% 2.28/2.47 tff(6538,plain,
% 2.28/2.47 (~hskp4),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[138, 44, 67])).
% 2.28/2.47 tff(6539,plain,
% 2.28/2.47 (hskp4 | (~c0_1(a586))),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[229, 101, 4510, 6462, 6460, 55])).
% 2.28/2.47 tff(6540,plain,
% 2.28/2.47 (~c0_1(a586)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6539, 6538])).
% 2.28/2.47 tff(6541,assumption,(~c2_1(a623)), introduced(assumption)).
% 2.28/2.47 tff(6542,assumption,(~c1_1(a623)), introduced(assumption)).
% 2.28/2.47 tff(6543,plain,
% 2.28/2.47 (hskp22 | (~c0_1(a623))),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[3792, 101, 67, 6542, 6541, 43])).
% 2.28/2.47 tff(6544,plain,
% 2.28/2.47 (~c0_1(a623)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6543, 44])).
% 2.28/2.47 tff(6545,assumption,(~c3_1(a623)), introduced(assumption)).
% 2.28/2.47 tff(6546,plain,
% 2.28/2.47 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6547,plain,
% 2.28/2.47 ((hskp14 | hskp4 | (~ndr1_0) | c2_1(a623) | c0_1(a623) | c3_1(a623)) <=> (hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6548,plain,
% 2.28/2.47 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a623) | c0_1(a623) | c3_1(a623))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623)))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6547])).
% 2.28/2.47 tff(6549,plain,
% 2.28/2.47 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a623) | c0_1(a623) | c3_1(a623))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6548, 6546])).
% 2.28/2.47 tff(6550,plain,
% 2.28/2.47 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a623) | c0_1(a623) | c3_1(a623))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6551,plain,
% 2.28/2.47 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623)),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6550, 6549])).
% 2.28/2.47 tff(6552,plain,
% 2.28/2.47 (hskp14 | hskp4 | c0_1(a623)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6551, 101, 6541, 6545, 149])).
% 2.28/2.47 tff(6553,plain,
% 2.28/2.47 (hskp14),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6552, 6538, 6544])).
% 2.28/2.47 tff(6554,plain,
% 2.28/2.47 (~c3_1(a603)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[193, 6553])).
% 2.28/2.47 tff(6555,plain,
% 2.28/2.47 (c0_1(a603)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[170, 6553])).
% 2.28/2.47 tff(6556,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6557,plain,
% 2.28/2.47 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6558,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607))))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6557])).
% 2.28/2.47 tff(6559,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6558, 6556])).
% 2.28/2.47 tff(6560,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6561,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607))),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6560, 6559])).
% 2.28/2.47 tff(6562,plain,
% 2.28/2.47 (~c2_1(a603)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6561, 101, 5890, 6555, 6462, 66, 4509, 6554, 6460, 240, 6540])).
% 2.28/2.47 tff(6563,plain,
% 2.28/2.47 (~c1_1(a603)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[162, 6553])).
% 2.28/2.47 tff(6564,plain,
% 2.28/2.47 ($false),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[177, 101, 44, 67, 6555, 6563, 43, 6562])).
% 2.28/2.47 tff(6565,plain,(hskp22 | hskp6 | c1_1(a607) | c2_1(a623) | c3_1(a623) | c1_1(a623)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.47 tff(6566,plain,
% 2.28/2.47 (hskp22),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6565, 6537, 66, 6414, 6413, 6412])).
% 2.28/2.47 tff(6567,plain,
% 2.28/2.47 (c1_1(a633)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[3821, 6566])).
% 2.28/2.47 tff(6568,plain,
% 2.28/2.47 (~c0_1(a633)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[3827, 6566])).
% 2.28/2.47 tff(6569,plain,
% 2.28/2.47 (~c3_1(a633)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[3833, 6566])).
% 2.28/2.47 tff(6570,plain,
% 2.28/2.47 (hskp11),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[5013, 6569, 6568, 4510, 6567])).
% 2.28/2.47 tff(6571,plain,
% 2.28/2.47 (~c1_1(a599)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[395, 6570])).
% 2.28/2.47 tff(6572,plain,
% 2.28/2.47 (hskp26),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6455, 6453, 66])).
% 2.28/2.47 tff(6573,plain,
% 2.28/2.47 (c0_1(a583)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[338, 6572])).
% 2.28/2.47 tff(6574,plain,
% 2.28/2.47 (c2_1(a583)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[364, 6572])).
% 2.28/2.47 tff(6575,plain,
% 2.28/2.47 (c1_1(a583)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[330, 6572])).
% 2.28/2.47 tff(6576,plain,
% 2.28/2.47 (c2_1(a599)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[403, 6570])).
% 2.28/2.47 tff(6577,plain,
% 2.28/2.47 (c3_1(a599)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[389, 6570])).
% 2.28/2.47 tff(6578,plain,
% 2.28/2.47 ($false),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6092, 6577, 6576, 66, 6575, 6574, 6573, 6566, 6571])).
% 2.28/2.47 tff(6579,plain,(hskp7 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.47 tff(6580,plain,
% 2.28/2.47 (hskp7),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6579, 66])).
% 2.28/2.47 tff(6581,plain,
% 2.28/2.47 (hskp18),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6100, 1586, 6580])).
% 2.28/2.47 tff(6582,plain,
% 2.28/2.47 (~c2_1(a610)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1087, 6581])).
% 2.28/2.47 tff(6583,plain,
% 2.28/2.47 (~c0_1(a610)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1093, 6581])).
% 2.28/2.47 tff(6584,plain,
% 2.28/2.47 (~c1_1(a610)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[5989, 101, 4510, 6583, 6582, 66, 4509, 32, 5957])).
% 2.28/2.47 tff(6585,plain,
% 2.28/2.47 (~c0_1(a592)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[742, 6580])).
% 2.28/2.47 tff(6586,plain,
% 2.28/2.47 (c2_1(a592)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[750, 6580])).
% 2.28/2.47 tff(6587,plain,
% 2.28/2.47 (c3_1(a610)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1101, 6581])).
% 2.28/2.47 tff(6588,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6589,plain,
% 2.28/2.47 (((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592))) <=> (c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6590,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610))))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6589])).
% 2.28/2.47 tff(6591,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6590, 6588])).
% 2.28/2.47 tff(6592,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6593,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610))),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6592, 6591])).
% 2.28/2.47 tff(6594,plain,
% 2.28/2.47 (~c1_1(a592)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6593, 101, 6587, 5890, 6586, 6582, 4509, 6585, 11, 5957, 6584])).
% 2.28/2.47 tff(6595,plain,
% 2.28/2.47 (hskp6),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6174, 101, 1586, 6587, 6583, 414, 6584])).
% 2.28/2.47 tff(6596,plain,
% 2.28/2.47 (~c0_1(a590)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[606, 6595])).
% 2.28/2.47 tff(6597,plain,
% 2.28/2.47 (c3_1(a590)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[614, 6595])).
% 2.28/2.47 tff(6598,plain,
% 2.28/2.47 (c2_1(a590)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[622, 6595])).
% 2.28/2.47 tff(6599,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6600,plain,
% 2.28/2.47 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6601,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592)))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6600])).
% 2.28/2.47 tff(6602,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6601, 6599])).
% 2.28/2.47 tff(6603,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6604,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592)),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6603, 6602])).
% 2.28/2.47 tff(6605,plain,
% 2.28/2.47 (~c0_1(a612)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6604, 101, 6383, 6382, 6586, 6598, 6597, 6585, 6596, 65, 6594])).
% 2.28/2.47 tff(6606,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6607,plain,
% 2.28/2.47 (((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.47 inference(rewrite,[status(thm)],[])).
% 2.28/2.47 tff(6608,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610))))),
% 2.28/2.47 inference(monotonicity,[status(thm)],[6607])).
% 2.28/2.47 tff(6609,plain,
% 2.28/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.47 inference(transitivity,[status(thm)],[6608, 6606])).
% 2.28/2.47 tff(6610,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 2.28/2.47 inference(quant_inst,[status(thm)],[])).
% 2.28/2.47 tff(6611,plain,
% 2.28/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610))),
% 2.28/2.47 inference(modus_ponens,[status(thm)],[6610, 6609])).
% 2.28/2.47 tff(6612,plain,
% 2.28/2.47 ($false),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6611, 101, 6383, 6515, 6587, 5890, 6582, 4509, 11, 5957, 6605, 6584])).
% 2.28/2.47 tff(6613,plain,(hskp8 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.47 tff(6614,plain,
% 2.28/2.47 (hskp8),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6613, 66])).
% 2.28/2.47 tff(6615,plain,
% 2.28/2.47 (c3_1(a593)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[469, 6614])).
% 2.28/2.47 tff(6616,plain,
% 2.28/2.47 (~c2_1(a593)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[510, 6614])).
% 2.28/2.47 tff(6617,plain,
% 2.28/2.47 (c1_1(a593)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[477, 6614])).
% 2.28/2.47 tff(6618,plain,
% 2.28/2.47 (hskp15),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[6360, 4228, 6617, 4229, 6616, 6615, 66, 4227])).
% 2.28/2.47 tff(6619,plain,
% 2.28/2.47 (~c0_1(a604)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1474, 6618])).
% 2.28/2.47 tff(6620,plain,
% 2.28/2.47 (c1_1(a604)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1490, 6618])).
% 2.28/2.47 tff(6621,plain,
% 2.28/2.47 (c2_1(a604)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 6620, 66, 4509, 6619, 32, 5957])).
% 2.28/2.47 tff(6622,plain,
% 2.28/2.47 (hskp3),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[5004, 101, 4510, 6617, 6615, 6616, 3282])).
% 2.28/2.47 tff(6623,plain,
% 2.28/2.47 (~c1_1(a587)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[855, 6622])).
% 2.28/2.47 tff(6624,plain,
% 2.28/2.47 (c3_1(a604)),
% 2.28/2.47 inference(unit_resolution,[status(thm)],[1482, 6618])).
% 2.28/2.47 tff(6625,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6626,plain,
% 2.28/2.48 ((hskp14 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6627,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.28/2.48 inference(monotonicity,[status(thm)],[6626])).
% 2.28/2.48 tff(6628,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.28/2.48 inference(transitivity,[status(thm)],[6627, 6625])).
% 2.28/2.48 tff(6629,plain,
% 2.28/2.48 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(6630,plain,
% 2.28/2.48 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[6629, 6628])).
% 2.28/2.48 tff(6631,plain,
% 2.28/2.48 (hskp14),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6630, 101, 5890, 6617, 6615, 4509, 6616, 505, 5957])).
% 2.28/2.48 tff(6632,plain,
% 2.28/2.48 (~c3_1(a603)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[193, 6631])).
% 2.28/2.48 tff(6633,plain,
% 2.28/2.48 (c0_1(a603)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[170, 6631])).
% 2.28/2.48 tff(6634,plain,
% 2.28/2.48 (c0_1(a586) | (~c2_1(a603))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6561, 101, 5890, 6633, 6462, 66, 4509, 6632, 6460, 240])).
% 2.28/2.48 tff(6635,plain,
% 2.28/2.48 (c0_1(a586)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6634, 920])).
% 2.28/2.48 tff(6636,plain,
% 2.28/2.48 (hskp16 | (~c0_1(a586))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[5843, 101, 4058, 2410, 6462, 2340, 6460, 1314])).
% 2.28/2.48 tff(6637,plain,
% 2.28/2.48 (hskp16),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6636, 6635])).
% 2.28/2.48 tff(6638,plain,
% 2.28/2.48 (~c2_1(a606)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[1015, 6637])).
% 2.28/2.48 tff(6639,plain,
% 2.28/2.48 (c2_1(a587)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[863, 6622])).
% 2.28/2.48 tff(6640,plain,
% 2.28/2.48 (c0_1(a587)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[871, 6622])).
% 2.28/2.48 tff(6641,plain,
% 2.28/2.48 (c1_1(a606)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[992, 6637])).
% 2.28/2.48 tff(6642,plain,
% 2.28/2.48 (c0_1(a606)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[4884, 6641, 4510, 6640, 6639, 6638, 6623])).
% 2.28/2.48 tff(6643,plain,
% 2.28/2.48 (~c3_1(a592)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[736, 6580])).
% 2.28/2.48 tff(6644,plain,
% 2.28/2.48 ((~c1_1(a592)) | (~c2_1(a603))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6055, 101, 5890, 6633, 66, 4509, 6632, 6585, 6643, 240])).
% 2.28/2.48 tff(6645,plain,
% 2.28/2.48 (~c1_1(a592)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6644, 920])).
% 2.28/2.48 tff(6646,plain,
% 2.28/2.48 (c2_1(a604)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[5472, 101, 4510, 4058, 66, 4509, 2340, 32, 5957])).
% 2.28/2.48 tff(6647,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6648,plain,
% 2.28/2.48 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6649,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604))))),
% 2.28/2.48 inference(monotonicity,[status(thm)],[6648])).
% 2.28/2.48 tff(6650,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(transitivity,[status(thm)],[6649, 6647])).
% 2.28/2.48 tff(6651,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(6652,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[6651, 6650])).
% 2.28/2.48 tff(6653,plain,
% 2.28/2.48 (~c0_1(a593)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6652, 101, 2410, 6617, 6615, 6586, 2340, 6585, 65, 6645, 6646])).
% 2.28/2.48 tff(6654,plain,
% 2.28/2.48 (~c3_1(a606)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[982, 6637])).
% 2.28/2.48 tff(6655,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6656,plain,
% 2.28/2.48 (((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6657,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))))),
% 2.28/2.48 inference(monotonicity,[status(thm)],[6656])).
% 2.28/2.48 tff(6658,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 2.28/2.48 inference(transitivity,[status(thm)],[6657, 6655])).
% 2.28/2.48 tff(6659,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(6660,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[6659, 6658])).
% 2.28/2.48 tff(6661,plain,
% 2.28/2.48 ($false),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6660, 101, 6617, 6638, 6654, 6616, 6585, 6643, 1349, 6653, 6645, 6642])).
% 2.28/2.48 tff(6662,plain,((~c2_1(a603)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.48 tff(6663,plain,
% 2.28/2.48 (~c2_1(a603)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6662, 6624, 6619, 6620, 66])).
% 2.28/2.48 tff(6664,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6665,plain,
% 2.28/2.48 ((hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604))) <=> (hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6666,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604))))),
% 2.28/2.48 inference(monotonicity,[status(thm)],[6665])).
% 2.28/2.48 tff(6667,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(transitivity,[status(thm)],[6666, 6664])).
% 2.28/2.48 tff(6668,plain,
% 2.28/2.48 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(6669,plain,
% 2.28/2.48 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[6668, 6667])).
% 2.28/2.48 tff(6670,plain,
% 2.28/2.48 (hskp16),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6669, 101, 6624, 6633, 6619, 6632, 2002, 6663, 6621])).
% 2.28/2.48 tff(6671,plain,
% 2.28/2.48 (~c2_1(a606)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[1015, 6670])).
% 2.28/2.48 tff(6672,plain,
% 2.28/2.48 (c1_1(a606)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[992, 6670])).
% 2.28/2.48 tff(6673,plain,
% 2.28/2.48 (c0_1(a606)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[4884, 6672, 4510, 6640, 6639, 6671, 6623])).
% 2.28/2.48 tff(6674,plain,
% 2.28/2.48 (~c1_1(a603)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[162, 6631])).
% 2.28/2.48 tff(6675,plain,
% 2.28/2.48 (hskp26 | c2_1(a603)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[916, 101, 6640, 6639, 6674, 6632, 6623, 905])).
% 2.28/2.48 tff(6676,plain,
% 2.28/2.48 (hskp26),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6675, 6663])).
% 2.28/2.48 tff(6677,plain,
% 2.28/2.48 (c2_1(a583)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[364, 6676])).
% 2.28/2.48 tff(6678,plain,
% 2.28/2.48 (c1_1(a583)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[330, 6676])).
% 2.28/2.48 tff(6679,plain,
% 2.28/2.48 (c0_1(a583)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[338, 6676])).
% 2.28/2.48 tff(6680,plain,
% 2.28/2.48 (hskp10),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[1418, 101, 6383, 6515, 6382, 6679, 6678, 6677, 21])).
% 2.28/2.48 tff(6681,plain,
% 2.28/2.48 (~c1_1(a598)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[827, 6680])).
% 2.28/2.48 tff(6682,plain,
% 2.28/2.48 (c3_1(a598)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[800, 6680])).
% 2.28/2.48 tff(6683,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6684,plain,
% 2.28/2.48 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598))) <=> (c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6685,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606))))),
% 2.28/2.48 inference(monotonicity,[status(thm)],[6684])).
% 2.28/2.48 tff(6686,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606)))),
% 2.28/2.48 inference(transitivity,[status(thm)],[6685, 6683])).
% 2.28/2.48 tff(6687,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(6688,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[6687, 6686])).
% 2.28/2.48 tff(6689,plain,
% 2.28/2.48 (c2_1(a598)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6688, 101, 4229, 4228, 4227, 6672, 6682, 6671, 6681, 1010, 6673])).
% 2.28/2.48 tff(6690,plain,
% 2.28/2.48 (hskp12),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[2917, 101, 6679, 6678, 6677, 6620, 6619, 2589, 6621])).
% 2.28/2.48 tff(6691,plain,
% 2.28/2.48 (~c3_1(a600)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[675, 6690])).
% 2.28/2.48 tff(6692,plain,
% 2.28/2.48 (c2_1(a600)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[683, 6690])).
% 2.28/2.48 tff(6693,plain,
% 2.28/2.48 (c0_1(a600)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[691, 6690])).
% 2.28/2.48 tff(6694,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6695,plain,
% 2.28/2.48 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6696,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600))))),
% 2.28/2.48 inference(monotonicity,[status(thm)],[6695])).
% 2.28/2.48 tff(6697,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)))),
% 2.28/2.48 inference(transitivity,[status(thm)],[6696, 6694])).
% 2.28/2.48 tff(6698,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(6699,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[6698, 6697])).
% 2.28/2.48 tff(6700,plain,
% 2.28/2.48 (~c1_1(a592)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6699, 101, 6693, 6692, 6682, 6691, 6681, 6585, 6643, 240, 6689])).
% 2.28/2.48 tff(6701,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6702,plain,
% 2.28/2.48 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6703,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604))))),
% 2.28/2.48 inference(monotonicity,[status(thm)],[6702])).
% 2.28/2.48 tff(6704,plain,
% 2.28/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.28/2.48 inference(transitivity,[status(thm)],[6703, 6701])).
% 2.28/2.48 tff(6705,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(6706,plain,
% 2.28/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[6705, 6704])).
% 2.28/2.48 tff(6707,plain,
% 2.28/2.48 (~c1_1(a678)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6706, 101, 4229, 4227, 6624, 6586, 6619, 6585, 65, 6700, 6621])).
% 2.28/2.48 tff(6708,plain,
% 2.28/2.48 (~c0_1(a593)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6652, 101, 6624, 6617, 6615, 6586, 6619, 6585, 65, 6700, 6621])).
% 2.28/2.48 tff(6709,plain,
% 2.28/2.48 ($false),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[2488, 101, 4510, 4229, 4228, 6617, 6616, 32, 6708, 6707])).
% 2.28/2.48 tff(6710,plain,((~hskp29) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.48 tff(6711,plain,
% 2.28/2.48 (~hskp29),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6710, 66])).
% 2.28/2.48 tff(6712,plain,
% 2.28/2.48 (hskp22),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[99, 6711, 4510])).
% 2.28/2.48 tff(6713,plain,
% 2.28/2.48 (c1_1(a633)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[3821, 6712])).
% 2.28/2.48 tff(6714,plain,
% 2.28/2.48 (~c0_1(a633)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[3827, 6712])).
% 2.28/2.48 tff(6715,plain,
% 2.28/2.48 (~c3_1(a633)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[3833, 6712])).
% 2.28/2.48 tff(6716,plain,
% 2.28/2.48 (hskp11),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[5013, 6715, 6714, 4510, 6713])).
% 2.28/2.48 tff(6717,plain,
% 2.28/2.48 (~c1_1(a599)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[395, 6716])).
% 2.28/2.48 tff(6718,plain,
% 2.28/2.48 (c2_1(a599)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[403, 6716])).
% 2.28/2.48 tff(6719,plain,
% 2.28/2.48 (hskp18),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6034, 6711, 66])).
% 2.28/2.48 tff(6720,plain,
% 2.28/2.48 (hskp26),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[5991, 6719, 66])).
% 2.28/2.48 tff(6721,plain,
% 2.28/2.48 (c0_1(a583)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[338, 6720])).
% 2.28/2.48 tff(6722,plain,
% 2.28/2.48 (c2_1(a583)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[364, 6720])).
% 2.28/2.48 tff(6723,plain,
% 2.28/2.48 (c1_1(a583)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[330, 6720])).
% 2.28/2.48 tff(6724,plain,
% 2.28/2.48 (c3_1(a599)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[389, 6716])).
% 2.28/2.48 tff(6725,plain,
% 2.28/2.48 ($false),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6092, 6724, 6723, 66, 6712, 6722, 6721, 6718, 6717])).
% 2.28/2.48 tff(6726,plain,(c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.48 tff(6727,plain,
% 2.28/2.48 (~hskp17),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[263, 6726])).
% 2.28/2.48 tff(6728,plain,
% 2.28/2.48 (hskp11 | c3_1(a633) | (~c1_1(a633)) | c0_1(a633)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[5013, 6727])).
% 2.28/2.48 tff(6729,plain,
% 2.28/2.48 (hskp11),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6728, 3834, 3828, 3822])).
% 2.28/2.48 tff(6730,plain,
% 2.28/2.48 (~c1_1(a599)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[395, 6729])).
% 2.28/2.48 tff(6731,plain,
% 2.28/2.48 (c2_1(a599)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[403, 6729])).
% 2.28/2.48 tff(6732,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6733,plain,
% 2.28/2.48 ((hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607))) <=> (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(6734,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607)))),
% 2.28/2.48 inference(monotonicity,[status(thm)],[6733])).
% 2.28/2.48 tff(6735,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607))),
% 2.28/2.48 inference(transitivity,[status(thm)],[6734, 6732])).
% 2.28/2.48 tff(6736,plain,
% 2.28/2.48 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(6737,plain,
% 2.28/2.48 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607)),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[6736, 6735])).
% 2.28/2.48 tff(6738,plain,
% 2.28/2.48 (~c0_1(a599)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6737, 101, 6727, 6731, 6726, 22, 6730, 32, 1])).
% 2.28/2.48 tff(6739,plain,
% 2.28/2.48 (c3_1(a599)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[389, 6729])).
% 2.28/2.48 tff(6740,plain,
% 2.28/2.48 ($false),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[4039, 101, 33, 6731, 6739, 22, 6730, 1607, 1, 6738])).
% 2.28/2.48 tff(6741,plain,(c0_1(a607) | c3_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.48 tff(6742,plain,
% 2.28/2.48 (c0_1(a607)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6741, 33, 22])).
% 2.28/2.48 tff(6743,plain,
% 2.28/2.48 (hskp3 | c3_1(a607) | (~c0_1(a607))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[2827, 101, 6727, 6726, 2236])).
% 2.28/2.48 tff(6744,plain,
% 2.28/2.48 (hskp3),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6743, 6742, 33])).
% 2.28/2.48 tff(6745,plain,
% 2.28/2.48 (~c1_1(a587)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[855, 6744])).
% 2.28/2.48 tff(6746,plain,
% 2.28/2.48 (c2_1(a587)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[863, 6744])).
% 2.28/2.48 tff(6747,plain,
% 2.28/2.48 (c0_1(a587)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[871, 6744])).
% 2.28/2.48 tff(6748,plain,
% 2.28/2.48 (c2_1(a633)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[4985, 101, 6727, 3822, 6747, 6746, 3828, 6745, 32])).
% 2.28/2.48 tff(6749,plain,
% 2.28/2.48 (hskp28 | (~c2_1(a633))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[4353, 101, 3822, 6731, 6739, 3834, 6730, 1625])).
% 2.28/2.48 tff(6750,plain,
% 2.28/2.48 (hskp28),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[6749, 6748])).
% 2.28/2.48 tff(6751,plain,
% 2.28/2.48 (c2_1(a612)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[1048, 6750])).
% 2.28/2.48 tff(6752,plain,
% 2.28/2.48 (c1_1(a612)),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[1321, 6750])).
% 2.28/2.48 tff(6753,plain,
% 2.28/2.48 (~hskp12),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[4198, 6739, 3822, 3828, 6731, 3834, 6730])).
% 2.28/2.48 tff(6754,plain,
% 2.28/2.48 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6755,plain,
% 2.28/2.49 ((hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6756,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6755])).
% 2.28/2.49 tff(6757,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6756, 6754])).
% 2.28/2.49 tff(6758,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6759,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[6758, 6757])).
% 2.28/2.49 tff(6760,plain,
% 2.28/2.49 (~c0_1(a612)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6759, 101, 6753, 6752, 6751, 3822, 3828, 2589, 6748])).
% 2.28/2.49 tff(6761,plain,
% 2.28/2.49 (hskp4 | c3_1(a607) | (~c0_1(a607))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[2780, 101, 6727, 6726, 55])).
% 2.28/2.49 tff(6762,plain,
% 2.28/2.49 (hskp4),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6761, 6742, 33])).
% 2.28/2.49 tff(6763,plain,
% 2.28/2.49 (hskp14),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[4404, 6748, 3828, 3834, 6762])).
% 2.28/2.49 tff(6764,plain,
% 2.28/2.49 (~c3_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[193, 6763])).
% 2.28/2.49 tff(6765,plain,
% 2.28/2.49 (c0_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[170, 6763])).
% 2.28/2.49 tff(6766,plain,
% 2.28/2.49 (~c2_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[4069, 101, 3822, 6765, 6731, 6739, 3828, 3834, 6764, 6730, 240])).
% 2.28/2.49 tff(6767,plain,
% 2.28/2.49 (~c1_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[162, 6763])).
% 2.28/2.49 tff(6768,plain,
% 2.28/2.49 (hskp26),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[916, 101, 6747, 6746, 6767, 6764, 6745, 905, 6766])).
% 2.28/2.49 tff(6769,plain,
% 2.28/2.49 (c2_1(a583)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[364, 6768])).
% 2.28/2.49 tff(6770,plain,
% 2.28/2.49 (c1_1(a583)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[330, 6768])).
% 2.28/2.49 tff(6771,plain,
% 2.28/2.49 (c0_1(a583)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[338, 6768])).
% 2.28/2.49 tff(6772,plain,
% 2.28/2.49 ($false),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[2596, 101, 6753, 6752, 6751, 6771, 6770, 6769, 2589, 6760])).
% 2.28/2.49 tff(6773,plain,(c3_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.49 tff(6774,plain,
% 2.28/2.49 (c3_1(a607)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6773, 22])).
% 2.28/2.49 tff(6775,plain,
% 2.28/2.49 (hskp3 | c2_1(a607) | (~c3_1(a607))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[3288, 101, 6727, 6726, 3282])).
% 2.28/2.49 tff(6776,plain,
% 2.28/2.49 (hskp3),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6775, 6774, 22])).
% 2.28/2.49 tff(6777,plain,
% 2.28/2.49 (c0_1(a587)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[871, 6776])).
% 2.28/2.49 tff(6778,plain,
% 2.28/2.49 (c2_1(a587)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[863, 6776])).
% 2.28/2.49 tff(6779,plain,
% 2.28/2.49 (~c1_1(a587)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[855, 6776])).
% 2.28/2.49 tff(6780,plain,
% 2.28/2.49 (c0_1(a607) | (~c0_1(a587)) | (~c2_1(a587)) | c2_1(a607) | c1_1(a587)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[3573, 6726])).
% 2.28/2.49 tff(6781,plain,
% 2.28/2.49 (c0_1(a607)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6780, 6779, 6778, 22, 6777])).
% 2.28/2.49 tff(6782,plain,
% 2.28/2.49 (c0_1(a599) | (~c3_1(a607)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c0_1(a607))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[3770, 6726])).
% 2.28/2.49 tff(6783,plain,
% 2.28/2.49 (c0_1(a599)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6782, 6781, 6739, 6731, 6730, 6774])).
% 2.28/2.49 tff(6784,plain,
% 2.28/2.49 ((~c0_1(a599)) | c2_1(a633)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[4015, 101, 6727, 3822, 6731, 3828, 6730, 32])).
% 2.28/2.49 tff(6785,plain,
% 2.28/2.49 (c2_1(a633)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6784, 6783])).
% 2.28/2.49 tff(6786,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6787,plain,
% 2.28/2.49 ((hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6788,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6787])).
% 2.28/2.49 tff(6789,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6788, 6786])).
% 2.28/2.49 tff(6790,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6791,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[6790, 6789])).
% 2.28/2.49 tff(6792,plain,
% 2.28/2.49 (hskp14 | (~c0_1(a599)) | (~c3_1(a607))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6791, 101, 6731, 6739, 6726, 22, 505])).
% 2.28/2.49 tff(6793,plain,
% 2.28/2.49 (hskp14),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6792, 6783, 6774])).
% 2.28/2.49 tff(6794,plain,
% 2.28/2.49 (~c3_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[193, 6793])).
% 2.28/2.49 tff(6795,plain,
% 2.28/2.49 (c0_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[170, 6793])).
% 2.28/2.49 tff(6796,plain,
% 2.28/2.49 (~c2_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[4069, 101, 3822, 6795, 6731, 6739, 3828, 3834, 6794, 6730, 240])).
% 2.28/2.49 tff(6797,plain,
% 2.28/2.49 (~c1_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[162, 6793])).
% 2.28/2.49 tff(6798,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6799,plain,
% 2.28/2.49 ((hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6800,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603)))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6799])).
% 2.28/2.49 tff(6801,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6800, 6798])).
% 2.28/2.49 tff(6802,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6803,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603)),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[6802, 6801])).
% 2.28/2.49 tff(6804,plain,
% 2.28/2.49 (hskp26),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6803, 101, 6731, 6797, 6794, 6730, 905, 6796, 6783])).
% 2.28/2.49 tff(6805,plain,
% 2.28/2.49 (c2_1(a583)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[364, 6804])).
% 2.28/2.49 tff(6806,plain,
% 2.28/2.49 (c1_1(a583)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[330, 6804])).
% 2.28/2.49 tff(6807,plain,
% 2.28/2.49 (c0_1(a583)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[338, 6804])).
% 2.28/2.49 tff(6808,plain,
% 2.28/2.49 ($false),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[3857, 101, 6753, 6807, 6806, 6805, 3822, 3828, 2589, 6785])).
% 2.28/2.49 tff(6809,plain,(c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.49 tff(6810,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6811,plain,
% 2.28/2.49 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6812,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607)))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6811])).
% 2.28/2.49 tff(6813,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6812, 6810])).
% 2.28/2.49 tff(6814,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6815,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607)),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[6814, 6813])).
% 2.28/2.49 tff(6816,plain,
% 2.28/2.49 (hskp12),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6815, 101, 3183, 3184, 3192, 6726, 6809, 2589, 1])).
% 2.28/2.49 tff(6817,plain,
% 2.28/2.49 (~c3_1(a600)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[675, 6816])).
% 2.28/2.49 tff(6818,plain,
% 2.28/2.49 (hskp14),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[700, 6816, 44])).
% 2.28/2.49 tff(6819,plain,
% 2.28/2.49 (~c3_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[193, 6818])).
% 2.28/2.49 tff(6820,plain,
% 2.28/2.49 (c2_1(a600)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[683, 6816])).
% 2.28/2.49 tff(6821,plain,
% 2.28/2.49 (c0_1(a600)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[691, 6816])).
% 2.28/2.49 tff(6822,plain,
% 2.28/2.49 (~c1_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[162, 6818])).
% 2.28/2.49 tff(6823,plain,
% 2.28/2.49 (c0_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[170, 6818])).
% 2.28/2.49 tff(6824,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6825,plain,
% 2.28/2.49 ((hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c2_1(a603) | (~c0_1(a603))) <=> (hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6826,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603))))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6825])).
% 2.28/2.49 tff(6827,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603)))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6826, 6824])).
% 2.28/2.49 tff(6828,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6829,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[6828, 6827])).
% 2.28/2.49 tff(6830,plain,
% 2.28/2.49 (hskp8 | c2_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6829, 101, 919, 4609, 4608, 907, 4601, 4127])).
% 2.28/2.49 tff(6831,plain,
% 2.28/2.49 (c2_1(a603)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6830, 1586])).
% 2.28/2.49 tff(6832,plain,
% 2.28/2.49 (hskp18 | hskp8 | c3_1(a607) | c0_1(a607)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[5420, 101, 6809, 5414])).
% 2.28/2.49 tff(6833,plain,
% 2.28/2.49 (hskp18),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6832, 1586, 33, 1])).
% 2.28/2.49 tff(6834,plain,
% 2.28/2.49 (~c2_1(a610)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[1087, 6833])).
% 2.28/2.49 tff(6835,plain,
% 2.28/2.49 (~c0_1(a610)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[1093, 6833])).
% 2.28/2.49 tff(6836,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6837,plain,
% 2.28/2.49 ((hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610))) <=> (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6838,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610))))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6837])).
% 2.28/2.49 tff(6839,plain,
% 2.28/2.49 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610)))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6838, 6836])).
% 2.28/2.49 tff(6840,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6841,plain,
% 2.28/2.49 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[6840, 6839])).
% 2.28/2.49 tff(6842,plain,
% 2.28/2.49 (~c1_1(a610)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6841, 101, 6727, 919, 6835, 6834, 908, 32, 6831])).
% 2.28/2.49 tff(6843,plain,
% 2.28/2.49 (c3_1(a610)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[1101, 6833])).
% 2.28/2.49 tff(6844,plain,
% 2.28/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6845,plain,
% 2.28/2.49 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> (c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6846,plain,
% 2.28/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610))))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6845])).
% 2.28/2.49 tff(6847,plain,
% 2.28/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610)))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6846, 6844])).
% 2.28/2.49 tff(6848,plain,
% 2.28/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6849,plain,
% 2.28/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[6848, 6847])).
% 2.28/2.49 tff(6850,plain,
% 2.28/2.49 ($false),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6849, 101, 2186, 2185, 2184, 6843, 6834, 6726, 6809, 11, 1, 6842])).
% 2.28/2.49 tff(6851,plain,(hskp8 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a607) | (~c0_1(a603)) | c1_1(a603) | (~c0_1(a600)) | (~c2_1(a600)) | c3_1(a603) | c3_1(a600) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.49 tff(6852,plain,
% 2.28/2.49 (hskp8),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6851, 6823, 2152, 2144, 1, 2160, 6822, 6821, 6820, 6819, 6817, 33])).
% 2.28/2.49 tff(6853,plain,
% 2.28/2.49 (~c2_1(a593)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[510, 6852])).
% 2.28/2.49 tff(6854,plain,
% 2.28/2.49 (c1_1(a593)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[477, 6852])).
% 2.28/2.49 tff(6855,plain,
% 2.28/2.49 (c3_1(a593)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[469, 6852])).
% 2.28/2.49 tff(6856,plain,
% 2.28/2.49 ($false),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[5011, 3656, 3658, 2849, 1771, 1780, 3657, 1770])).
% 2.28/2.49 tff(6857,plain,((~hskp0) | hskp17 | (~c1_1(a593)) | (~c3_1(a593)) | c2_1(a593)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.49 tff(6858,plain,
% 2.28/2.49 ((~hskp0) | (~c1_1(a593)) | (~c3_1(a593)) | c2_1(a593)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6857, 6727])).
% 2.28/2.49 tff(6859,plain,
% 2.28/2.49 (~hskp0),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6858, 6855, 6854, 6853])).
% 2.28/2.49 tff(6860,plain,
% 2.28/2.49 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6861,plain,
% 2.28/2.49 ((hskp11 | hskp0 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593))) <=> (hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6862,plain,
% 2.28/2.49 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593))))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6861])).
% 2.28/2.49 tff(6863,plain,
% 2.28/2.49 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6862, 6860])).
% 2.28/2.49 tff(6864,plain,
% 2.28/2.49 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6865,plain,
% 2.28/2.49 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[6864, 6863])).
% 2.28/2.49 tff(6866,plain,
% 2.28/2.49 (~c0_1(a593)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6865, 1515, 101, 6859, 6854, 6853, 2215])).
% 2.28/2.49 tff(6867,plain,
% 2.28/2.49 (hskp3),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[5004, 101, 6727, 6854, 6855, 6853, 3282])).
% 2.28/2.49 tff(6868,plain,
% 2.28/2.49 (~c1_1(a587)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[855, 6867])).
% 2.28/2.49 tff(6869,plain,
% 2.28/2.49 (c2_1(a587)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[863, 6867])).
% 2.28/2.49 tff(6870,plain,
% 2.28/2.49 (c0_1(a587)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[871, 6867])).
% 2.28/2.49 tff(6871,plain,
% 2.28/2.49 ($false),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[5082, 101, 6727, 6854, 6870, 6869, 6853, 6868, 32, 6866])).
% 2.28/2.49 tff(6872,plain,(hskp11 | c0_1(a607) | c3_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.28/2.49 tff(6873,plain,
% 2.28/2.49 (hskp11),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[6872, 44, 33, 1])).
% 2.28/2.49 tff(6874,plain,
% 2.28/2.49 (~c1_1(a599)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[395, 6873])).
% 2.28/2.49 tff(6875,plain,
% 2.28/2.49 (c2_1(a599)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[403, 6873])).
% 2.28/2.49 tff(6876,plain,
% 2.28/2.49 (c3_1(a599)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[389, 6873])).
% 2.28/2.49 tff(6877,plain,
% 2.28/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6878,plain,
% 2.28/2.49 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607))) <=> (c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(6879,plain,
% 2.28/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607)))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[6878])).
% 2.28/2.49 tff(6880,plain,
% 2.28/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607))),
% 2.28/2.49 inference(transitivity,[status(thm)],[6879, 6877])).
% 2.28/2.49 tff(6881,plain,
% 2.28/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(6882,plain,
% 2.28/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607)),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[6881, 6880])).
% 2.28/2.50 tff(6883,plain,
% 2.28/2.50 ($false),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[6882, 101, 33, 692, 684, 427, 426, 6726, 676, 425, 240, 1])).
% 2.28/2.50 tff(6884,plain,((~hskp12) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.50 tff(6885,plain,
% 2.28/2.50 (~hskp12),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[6884, 6876, 33, 6875, 6874, 1])).
% 2.28/2.50 tff(6886,plain,
% 2.28/2.50 (^[U: $i] : refl((hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 2.28/2.50 inference(bind,[status(th)],[])).
% 2.28/2.50 tff(6887,plain,
% 2.28/2.50 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.28/2.50 inference(quant_intro,[status(thm)],[6886])).
% 2.28/2.50 tff(6888,plain,
% 2.28/2.50 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(6889,plain,
% 2.28/2.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp10) <=> ((hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp10) <=> (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.28/2.50 inference(bind,[status(th)],[])).
% 2.28/2.50 tff(6890,plain,
% 2.28/2.50 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp10) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.28/2.50 inference(quant_intro,[status(thm)],[6889])).
% 2.28/2.50 tff(6891,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 2.35/2.50 tff(6892,plain,
% 2.35/2.50 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6891, 6890])).
% 2.35/2.50 tff(6893,plain,
% 2.35/2.50 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6892, 6888])).
% 2.35/2.50 tff(6894,plain,(
% 2.35/2.50 ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.35/2.50 inference(skolemize,[status(sab)],[6893])).
% 2.35/2.50 tff(6895,plain,
% 2.35/2.50 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6894, 6887])).
% 2.35/2.50 tff(6896,plain,
% 2.35/2.50 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp12 | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6897,plain,
% 2.35/2.50 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6898,plain,
% 2.35/2.50 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp12 | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6897, 6896])).
% 2.35/2.50 tff(6899,plain,
% 2.35/2.50 (hskp12 | hskp10),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6898, 101, 2160, 2152, 2144, 6895])).
% 2.35/2.50 tff(6900,plain,
% 2.35/2.50 (hskp10),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6899, 6885])).
% 2.35/2.50 tff(6901,plain,
% 2.35/2.50 (~c1_1(a598)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[827, 6900])).
% 2.35/2.50 tff(6902,plain,
% 2.35/2.50 (c3_1(a598)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[800, 6900])).
% 2.35/2.50 tff(6903,plain,
% 2.35/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6904,plain,
% 2.35/2.50 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> ((~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6905,plain,
% 2.35/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607)))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6904])).
% 2.35/2.50 tff(6906,plain,
% 2.35/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6905, 6903])).
% 2.35/2.50 tff(6907,plain,
% 2.35/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6908,plain,
% 2.35/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607)),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6907, 6906])).
% 2.35/2.50 tff(6909,plain,
% 2.35/2.50 (c2_1(a598)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6908, 101, 2160, 2152, 2144, 6902, 6726, 6809, 6901, 11, 1])).
% 2.35/2.50 tff(6910,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6911,plain,
% 2.35/2.50 ((hskp28 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599))) <=> (hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6912,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6911])).
% 2.35/2.50 tff(6913,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6912, 6910])).
% 2.35/2.50 tff(6914,plain,
% 2.35/2.50 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6915,plain,
% 2.35/2.50 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6914, 6913])).
% 2.35/2.50 tff(6916,plain,
% 2.35/2.50 (hskp28),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6915, 101, 33, 6875, 6876, 6726, 6809, 6874, 1625])).
% 2.35/2.50 tff(6917,plain,
% 2.35/2.50 (c2_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1048, 6916])).
% 2.35/2.50 tff(6918,plain,
% 2.35/2.50 (c1_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1321, 6916])).
% 2.35/2.50 tff(6919,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6920,plain,
% 2.35/2.50 ((hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6921,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607)))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6920])).
% 2.35/2.50 tff(6922,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6921, 6919])).
% 2.35/2.50 tff(6923,plain,
% 2.35/2.50 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6924,plain,
% 2.35/2.50 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607)),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6923, 6922])).
% 2.35/2.50 tff(6925,plain,
% 2.35/2.50 (~c0_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6924, 101, 6885, 6918, 6917, 6726, 6809, 2589, 1])).
% 2.35/2.50 tff(6926,plain,
% 2.35/2.50 (c3_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1040, 6916])).
% 2.35/2.50 tff(6927,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6928,plain,
% 2.35/2.50 ((hskp15 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))) <=> (hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6929,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6928])).
% 2.35/2.50 tff(6930,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6929, 6927])).
% 2.35/2.50 tff(6931,plain,
% 2.35/2.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6932,plain,
% 2.35/2.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6931, 6930])).
% 2.35/2.50 tff(6933,plain,
% 2.35/2.50 (hskp15),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6932, 101, 6918, 6926, 33, 6726, 6809, 2552, 6925])).
% 2.35/2.50 tff(6934,plain,
% 2.35/2.50 (~c0_1(a604)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1474, 6933])).
% 2.35/2.50 tff(6935,plain,
% 2.35/2.50 (c0_1(a598)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[808, 6900])).
% 2.35/2.50 tff(6936,plain,
% 2.35/2.50 (c1_1(a604)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1490, 6933])).
% 2.35/2.50 tff(6937,plain,
% 2.35/2.50 (c2_1(a604)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[4646, 101, 6727, 6936, 6935, 6934, 6901, 32, 6909])).
% 2.35/2.50 tff(6938,plain,
% 2.35/2.50 (~hskp12),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6884, 426, 33, 427, 425, 1])).
% 2.35/2.50 tff(6939,plain,
% 2.35/2.50 (hskp8),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[712, 660, 6938])).
% 2.35/2.50 tff(6940,plain,
% 2.35/2.50 (~c2_1(a593)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[510, 6939])).
% 2.35/2.50 tff(6941,plain,
% 2.35/2.50 (c3_1(a593)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[469, 6939])).
% 2.35/2.50 tff(6942,plain,
% 2.35/2.50 (c1_1(a593)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[477, 6939])).
% 2.35/2.50 tff(6943,plain,
% 2.35/2.50 (hskp3),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[5004, 101, 6727, 6942, 6941, 6940, 3282])).
% 2.35/2.50 tff(6944,plain,
% 2.35/2.50 (~c1_1(a587)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[855, 6943])).
% 2.35/2.50 tff(6945,plain,
% 2.35/2.50 (hskp14),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3256, 101, 2186, 2185, 2184, 6942, 6941, 6940, 505])).
% 2.35/2.50 tff(6946,plain,
% 2.35/2.50 (~c3_1(a603)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[193, 6945])).
% 2.35/2.50 tff(6947,plain,
% 2.35/2.50 (~c1_1(a603)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[162, 6945])).
% 2.35/2.50 tff(6948,plain,
% 2.35/2.50 (c2_1(a587)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[863, 6943])).
% 2.35/2.50 tff(6949,plain,
% 2.35/2.50 (c0_1(a587)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[871, 6943])).
% 2.35/2.50 tff(6950,plain,
% 2.35/2.50 (c2_1(a603)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[916, 660, 101, 6949, 6948, 6947, 6946, 6944, 905])).
% 2.35/2.50 tff(6951,plain,
% 2.35/2.50 (c0_1(a603)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[170, 6945])).
% 2.35/2.50 tff(6952,plain,
% 2.35/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6953,plain,
% 2.35/2.50 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607))) <=> (c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6954,plain,
% 2.35/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607)))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6953])).
% 2.35/2.50 tff(6955,plain,
% 2.35/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6954, 6952])).
% 2.35/2.50 tff(6956,plain,
% 2.35/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6957,plain,
% 2.35/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607)),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6956, 6955])).
% 2.35/2.50 tff(6958,plain,
% 2.35/2.50 ($false),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6957, 101, 33, 6951, 427, 426, 6726, 6946, 425, 240, 1, 6950])).
% 2.35/2.50 tff(6959,plain,(hskp26 | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a607) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.50 tff(6960,plain,
% 2.35/2.50 (hskp26),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6959, 6875, 33, 6876, 6874, 1, 2160, 2152, 2144])).
% 2.35/2.50 tff(6961,plain,
% 2.35/2.50 (c2_1(a583)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[364, 6960])).
% 2.35/2.50 tff(6962,plain,
% 2.35/2.50 (c1_1(a583)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[330, 6960])).
% 2.35/2.50 tff(6963,plain,
% 2.35/2.50 (c0_1(a583)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[338, 6960])).
% 2.35/2.50 tff(6964,plain,
% 2.35/2.50 ($false),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2917, 101, 6885, 6963, 6962, 6961, 6936, 6934, 2589, 6937])).
% 2.35/2.50 tff(6965,plain,(hskp22 | c3_1(a607) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.50 tff(6966,plain,
% 2.35/2.50 (hskp22),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6965, 1, 33])).
% 2.35/2.50 tff(6967,plain,
% 2.35/2.50 (c1_1(a633)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3821, 6966])).
% 2.35/2.50 tff(6968,plain,
% 2.35/2.50 (~c0_1(a633)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3827, 6966])).
% 2.35/2.50 tff(6969,plain,
% 2.35/2.50 (~c3_1(a633)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3833, 6966])).
% 2.35/2.50 tff(6970,plain,
% 2.35/2.50 (hskp11),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6728, 6969, 6968, 6967])).
% 2.35/2.50 tff(6971,plain,
% 2.35/2.50 (~c1_1(a599)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[395, 6970])).
% 2.35/2.50 tff(6972,plain,
% 2.35/2.50 (c3_1(a599)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[389, 6970])).
% 2.35/2.50 tff(6973,plain,
% 2.35/2.50 (c2_1(a599)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[403, 6970])).
% 2.35/2.50 tff(6974,plain,
% 2.35/2.50 (hskp28),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6915, 101, 33, 6973, 6972, 6726, 6809, 6971, 1625])).
% 2.35/2.50 tff(6975,plain,
% 2.35/2.50 (c2_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1048, 6974])).
% 2.35/2.50 tff(6976,plain,
% 2.35/2.50 (c1_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1321, 6974])).
% 2.35/2.50 tff(6977,plain,
% 2.35/2.50 (~hskp12),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6884, 6972, 33, 6973, 6971, 1])).
% 2.35/2.50 tff(6978,plain,
% 2.35/2.50 (~c0_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6924, 101, 6977, 6976, 6975, 6726, 6809, 2589, 1])).
% 2.35/2.50 tff(6979,plain,
% 2.35/2.50 (c3_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1040, 6974])).
% 2.35/2.50 tff(6980,plain,
% 2.35/2.50 (c2_1(a633)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[5060, 101, 6975, 6979, 6973, 6972, 6968, 6969, 6971, 1607, 6978])).
% 2.35/2.50 tff(6981,plain,
% 2.35/2.50 (hskp8),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[712, 660, 6977])).
% 2.35/2.50 tff(6982,plain,
% 2.35/2.50 (~c2_1(a593)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[510, 6981])).
% 2.35/2.50 tff(6983,plain,
% 2.35/2.50 (c3_1(a593)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[469, 6981])).
% 2.35/2.50 tff(6984,plain,
% 2.35/2.50 (c1_1(a593)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[477, 6981])).
% 2.35/2.50 tff(6985,plain,
% 2.35/2.50 (hskp3),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[5004, 101, 6727, 6984, 6983, 6982, 3282])).
% 2.35/2.50 tff(6986,plain,
% 2.35/2.50 (~c1_1(a587)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[855, 6985])).
% 2.35/2.50 tff(6987,plain,
% 2.35/2.50 (c2_1(a587)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[863, 6985])).
% 2.35/2.50 tff(6988,plain,
% 2.35/2.50 (c0_1(a587)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[871, 6985])).
% 2.35/2.50 tff(6989,plain,
% 2.35/2.50 (~hskp0),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6858, 6983, 6984, 6982])).
% 2.35/2.50 tff(6990,plain,
% 2.35/2.50 (~c1_1(a610)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3906, 101, 6727, 910, 909, 5973, 5972, 906, 32])).
% 2.35/2.50 tff(6991,plain,
% 2.35/2.50 ($false),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[5650, 660, 101, 3466, 5973, 5972, 942, 6990])).
% 2.35/2.50 tff(6992,plain,((~hskp18) | hskp26 | hskp0 | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.50 tff(6993,plain,
% 2.35/2.50 (~hskp18),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6992, 660, 6989, 6988, 6987, 6986])).
% 2.35/2.50 tff(6994,plain,
% 2.35/2.50 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6995,plain,
% 2.35/2.50 ((hskp29 | hskp18 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607))) <=> (hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6996,plain,
% 2.35/2.50 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0)))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6995])).
% 2.35/2.50 tff(6997,plain,
% 2.35/2.50 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6996, 6994])).
% 2.35/2.50 tff(6998,plain,
% 2.35/2.50 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6999,plain,
% 2.35/2.50 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0)),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6998, 6997])).
% 2.35/2.50 tff(7000,plain,
% 2.35/2.50 (hskp29 | hskp18 | c3_1(a607) | (~c2_1(a607))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6999, 101, 6726, 1673])).
% 2.35/2.50 tff(7001,plain,
% 2.35/2.50 (hskp29),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[7000, 6993, 33, 6809])).
% 2.35/2.50 tff(7002,plain,
% 2.35/2.50 (c3_1(a678)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2143, 7001])).
% 2.35/2.50 tff(7003,plain,
% 2.35/2.50 (c0_1(a678)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2159, 7001])).
% 2.35/2.50 tff(7004,plain,
% 2.35/2.50 (c2_1(a678)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2151, 7001])).
% 2.35/2.50 tff(7005,plain,
% 2.35/2.50 ($false),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6959, 7004, 7003, 33, 6972, 6971, 1, 6973, 660, 7002])).
% 2.35/2.50 tff(7006,plain,(hskp26 | c3_1(a607) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.50 tff(7007,plain,
% 2.35/2.50 (hskp26),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[7006, 1, 33])).
% 2.35/2.50 tff(7008,plain,
% 2.35/2.50 (c2_1(a583)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[364, 7007])).
% 2.35/2.50 tff(7009,plain,
% 2.35/2.50 (c1_1(a583)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[330, 7007])).
% 2.35/2.50 tff(7010,plain,
% 2.35/2.50 (c0_1(a583)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[338, 7007])).
% 2.35/2.50 tff(7011,plain,
% 2.35/2.50 ($false),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3857, 101, 6977, 7010, 7009, 7008, 6967, 6968, 2589, 6980])).
% 2.35/2.50 tff(7012,plain,(c0_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.50 tff(7013,plain,
% 2.35/2.50 (c0_1(a607)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[7012, 33])).
% 2.35/2.50 tff(7014,plain,
% 2.35/2.50 (hskp3),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6743, 7013, 33])).
% 2.35/2.50 tff(7015,plain,
% 2.35/2.50 (~c1_1(a587)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[855, 7014])).
% 2.35/2.50 tff(7016,plain,
% 2.35/2.50 (hskp4),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6761, 7013, 33])).
% 2.35/2.50 tff(7017,plain,
% 2.35/2.50 (~c2_1(a588)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[115, 7016])).
% 2.35/2.50 tff(7018,plain,
% 2.35/2.50 (~c1_1(a588)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[121, 7016])).
% 2.35/2.50 tff(7019,plain,
% 2.35/2.50 (c0_1(a588)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[129, 7016])).
% 2.35/2.50 tff(7020,plain,
% 2.35/2.50 (hskp1),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[5322, 101, 33, 7019, 6809, 7018, 7017, 1132, 7013])).
% 2.35/2.50 tff(7021,plain,
% 2.35/2.50 (~c0_1(a585)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1145, 7020])).
% 2.35/2.50 tff(7022,plain,
% 2.35/2.50 (c2_1(a585)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1153, 7020])).
% 2.35/2.50 tff(7023,plain,
% 2.35/2.50 (c1_1(a585)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1161, 7020])).
% 2.35/2.50 tff(7024,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(7025,plain,
% 2.35/2.50 ((hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(7026,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[7025])).
% 2.35/2.50 tff(7027,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607)))),
% 2.35/2.50 inference(transitivity,[status(thm)],[7026, 7024])).
% 2.35/2.50 tff(7028,plain,
% 2.35/2.50 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(7029,plain,
% 2.35/2.50 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[7028, 7027])).
% 2.35/2.50 tff(7030,plain,
% 2.35/2.50 (hskp12),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[7029, 101, 7023, 7022, 6726, 6809, 7021, 2589, 7013])).
% 2.35/2.50 tff(7031,plain,
% 2.35/2.50 ($false),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[4198, 6086, 6087, 670, 426, 427, 6088, 425])).
% 2.35/2.50 tff(7032,plain,((~hskp22) | (~hskp12) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.50 tff(7033,plain,
% 2.35/2.50 (~hskp22),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[7032, 984, 7030, 985, 922])).
% 2.35/2.50 tff(7034,plain,
% 2.35/2.50 (hskp29),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2135, 7033])).
% 2.35/2.50 tff(7035,plain,
% 2.35/2.50 (c3_1(a678)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2143, 7034])).
% 2.35/2.50 tff(7036,plain,
% 2.35/2.50 (c2_1(a678)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2151, 7034])).
% 2.35/2.50 tff(7037,plain,
% 2.35/2.50 (c0_1(a678)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2159, 7034])).
% 2.35/2.50 tff(7038,plain,
% 2.35/2.50 (~c3_1(a588)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[5294, 101, 7037, 7036, 7035, 7023, 7022, 7018, 7017, 7021, 11])).
% 2.35/2.50 tff(7039,plain,
% 2.35/2.50 (hskp28),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6915, 101, 33, 985, 984, 6726, 6809, 922, 1625])).
% 2.35/2.50 tff(7040,plain,
% 2.35/2.50 (c3_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1040, 7039])).
% 2.35/2.50 tff(7041,plain,
% 2.35/2.50 (c2_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1048, 7039])).
% 2.35/2.50 tff(7042,plain,
% 2.35/2.50 (c1_1(a612)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1321, 7039])).
% 2.35/2.50 tff(7043,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(7044,plain,
% 2.35/2.50 ((hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607))) <=> (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(7045,plain,
% 2.35/2.50 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7044])).
% 2.35/2.51 tff(7046,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7045, 7043])).
% 2.35/2.51 tff(7047,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7048,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7047, 7046])).
% 2.35/2.51 tff(7049,plain,
% 2.35/2.51 (hskp10),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7048, 101, 7042, 7041, 7040, 6726, 6809, 21, 7013])).
% 2.35/2.51 tff(7050,plain,
% 2.35/2.51 (~c1_1(a598)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[827, 7049])).
% 2.35/2.51 tff(7051,plain,
% 2.35/2.51 (c3_1(a598)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[800, 7049])).
% 2.35/2.51 tff(7052,plain,
% 2.35/2.51 (c2_1(a598)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4638, 101, 7037, 7036, 7035, 7051, 7023, 7022, 7050, 7021, 11])).
% 2.35/2.51 tff(7053,plain,
% 2.35/2.51 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7054,plain,
% 2.35/2.51 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607))) <=> (hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7055,plain,
% 2.35/2.51 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7054])).
% 2.35/2.51 tff(7056,plain,
% 2.35/2.51 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7055, 7053])).
% 2.35/2.51 tff(7057,plain,
% 2.35/2.51 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7058,plain,
% 2.35/2.51 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7057, 7056])).
% 2.35/2.51 tff(7059,plain,
% 2.35/2.51 (hskp22 | hskp14 | c3_1(a607) | (~c0_1(a607))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7058, 101, 6809, 357])).
% 2.35/2.51 tff(7060,plain,
% 2.35/2.51 (hskp14),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7059, 7033, 33, 7013])).
% 2.35/2.51 tff(7061,plain,
% 2.35/2.51 (~c3_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[193, 7060])).
% 2.35/2.51 tff(7062,plain,
% 2.35/2.51 (~c1_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[162, 7060])).
% 2.35/2.51 tff(7063,plain,
% 2.35/2.51 (c0_1(a598)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[808, 7049])).
% 2.35/2.51 tff(7064,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7065,plain,
% 2.35/2.51 ((hskp26 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7066,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603)))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7065])).
% 2.35/2.51 tff(7067,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7066, 7064])).
% 2.35/2.51 tff(7068,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7069,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603)),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7068, 7067])).
% 2.35/2.51 tff(7070,plain,
% 2.35/2.51 (c2_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7069, 660, 101, 7063, 7062, 7061, 7050, 905, 7052])).
% 2.35/2.51 tff(7071,plain,
% 2.35/2.51 (c0_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[170, 7060])).
% 2.35/2.51 tff(7072,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4782, 660, 101, 7071, 7062, 7018, 7017, 905, 7070, 7038])).
% 2.35/2.51 tff(7073,plain,(hskp26 | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(7074,plain,
% 2.35/2.51 (hskp26),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7073, 33])).
% 2.35/2.51 tff(7075,plain,
% 2.35/2.51 (c0_1(a583)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[338, 7074])).
% 2.35/2.51 tff(7076,plain,
% 2.35/2.51 (hskp11 | hskp21),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4964, 101, 7019, 7018, 7017, 4954])).
% 2.35/2.51 tff(7077,plain,
% 2.35/2.51 (hskp21),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7076, 1515])).
% 2.35/2.51 tff(7078,plain,
% 2.35/2.51 (~c3_1(a629)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4699, 7077])).
% 2.35/2.51 tff(7079,plain,
% 2.35/2.51 (~c2_1(a629)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4705, 7077])).
% 2.35/2.51 tff(7080,plain,
% 2.35/2.51 (c0_1(a629)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4720, 7077])).
% 2.35/2.51 tff(7081,plain,
% 2.35/2.51 (hskp8),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5160, 101, 7080, 33, 7079, 7078, 6809, 4127, 7013])).
% 2.35/2.51 tff(7082,plain,
% 2.35/2.51 (~c2_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[510, 7081])).
% 2.35/2.51 tff(7083,plain,
% 2.35/2.51 (c1_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[477, 7081])).
% 2.35/2.51 tff(7084,plain,
% 2.35/2.51 (c3_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[469, 7081])).
% 2.35/2.51 tff(7085,plain,
% 2.35/2.51 (~hskp0),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6858, 7084, 7083, 7082])).
% 2.35/2.51 tff(7086,plain,
% 2.35/2.51 (~c0_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6865, 1515, 101, 7085, 7083, 7082, 2215])).
% 2.35/2.51 tff(7087,plain,
% 2.35/2.51 (c2_1(a587)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[863, 7014])).
% 2.35/2.51 tff(7088,plain,
% 2.35/2.51 (c0_1(a587)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[871, 7014])).
% 2.35/2.51 tff(7089,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5082, 101, 6727, 7083, 7088, 7087, 7082, 7015, 32, 7086])).
% 2.35/2.51 tff(7090,plain,(hskp11 | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(7091,plain,
% 2.35/2.51 (hskp11),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7090, 33])).
% 2.35/2.51 tff(7092,plain,
% 2.35/2.51 (~c1_1(a599)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[395, 7091])).
% 2.35/2.51 tff(7093,plain,
% 2.35/2.51 (c2_1(a599)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[403, 7091])).
% 2.35/2.51 tff(7094,plain,
% 2.35/2.51 (c3_1(a599)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[389, 7091])).
% 2.35/2.51 tff(7095,plain,
% 2.35/2.51 (~hskp22),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7032, 7094, 7030, 7093, 7092])).
% 2.35/2.51 tff(7096,plain,
% 2.35/2.51 (hskp6),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[138, 7095, 7016])).
% 2.35/2.51 tff(7097,plain,
% 2.35/2.51 (~c0_1(a590)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[606, 7096])).
% 2.35/2.51 tff(7098,plain,
% 2.35/2.51 (c2_1(a583)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[364, 7074])).
% 2.35/2.51 tff(7099,plain,
% 2.35/2.51 (c3_1(a590)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[614, 7096])).
% 2.35/2.51 tff(7100,plain,
% 2.35/2.51 (c1_1(a583)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[330, 7074])).
% 2.35/2.51 tff(7101,plain,
% 2.35/2.51 (c2_1(a590)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[622, 7096])).
% 2.35/2.51 tff(7102,plain,
% 2.35/2.51 (hskp15),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5565, 7101, 33, 7013, 7100, 6809, 7099, 7023, 7021, 7098, 7097, 7075])).
% 2.35/2.51 tff(7103,plain,
% 2.35/2.51 (~c0_1(a604)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1474, 7102])).
% 2.35/2.51 tff(7104,plain,
% 2.35/2.51 (c1_1(a604)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1490, 7102])).
% 2.35/2.51 tff(7105,plain,
% 2.35/2.51 (c2_1(a604)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2982, 101, 6727, 7104, 7088, 7087, 7103, 7015, 32])).
% 2.35/2.51 tff(7106,plain,
% 2.35/2.51 (c3_1(a604)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1482, 7102])).
% 2.35/2.51 tff(7107,plain,
% 2.35/2.51 (hskp29),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2135, 7095])).
% 2.35/2.51 tff(7108,plain,
% 2.35/2.51 (c3_1(a678)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2143, 7107])).
% 2.35/2.51 tff(7109,plain,
% 2.35/2.51 (c2_1(a678)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2151, 7107])).
% 2.35/2.51 tff(7110,plain,
% 2.35/2.51 (c0_1(a678)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2159, 7107])).
% 2.35/2.51 tff(7111,plain,
% 2.35/2.51 (~c3_1(a588)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5294, 101, 7110, 7109, 7108, 7023, 7022, 7018, 7017, 7021, 11])).
% 2.35/2.51 tff(7112,plain,
% 2.35/2.51 (hskp16),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4556, 101, 7101, 7099, 7019, 7097, 7017, 2002, 7111])).
% 2.35/2.51 tff(7113,plain,
% 2.35/2.51 (~c2_1(a606)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1015, 7112])).
% 2.35/2.51 tff(7114,plain,
% 2.35/2.51 (c1_1(a606)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[992, 7112])).
% 2.35/2.51 tff(7115,plain,
% 2.35/2.51 (c0_1(a606) | (~c1_1(a606)) | (~c0_1(a587)) | (~c2_1(a587)) | c2_1(a606) | c1_1(a587)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4884, 6727])).
% 2.35/2.51 tff(7116,plain,
% 2.35/2.51 (c0_1(a606)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7115, 7114, 7088, 7087, 7113, 7015])).
% 2.35/2.51 tff(7117,plain,
% 2.35/2.51 (~hskp13),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2418, 7116, 7094, 7105, 7093, 7092, 7103, 7110, 7109, 7108, 7114, 7113, 7106])).
% 2.35/2.51 tff(7118,plain,
% 2.35/2.51 (hskp19 | hskp13),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2446, 101, 7023, 7022, 7021, 2429])).
% 2.35/2.51 tff(7119,plain,
% 2.35/2.51 (hskp19),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7118, 7117])).
% 2.35/2.51 tff(7120,plain,
% 2.35/2.51 (~c1_1(a617)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2453, 7119])).
% 2.35/2.51 tff(7121,plain,
% 2.35/2.51 (~c0_1(a617)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2459, 7119])).
% 2.35/2.51 tff(7122,plain,
% 2.35/2.51 (c2_1(a617)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2467, 7119])).
% 2.35/2.51 tff(7123,plain,
% 2.35/2.51 (hskp28),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6915, 101, 33, 7093, 7094, 6726, 6809, 7092, 1625])).
% 2.35/2.51 tff(7124,plain,
% 2.35/2.51 (c3_1(a612)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1040, 7123])).
% 2.35/2.51 tff(7125,plain,
% 2.35/2.51 (c1_1(a612)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1321, 7123])).
% 2.35/2.51 tff(7126,plain,
% 2.35/2.51 (~c0_1(a612)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5867, 101, 7125, 7124, 7122, 7106, 7121, 7120, 7103, 65, 7105])).
% 2.35/2.51 tff(7127,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7128,plain,
% 2.35/2.51 ((hskp10 | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7129,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7128])).
% 2.35/2.51 tff(7130,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7129, 7127])).
% 2.35/2.51 tff(7131,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7132,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7131, 7130])).
% 2.35/2.51 tff(7133,plain,
% 2.35/2.51 (hskp10),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7132, 101, 7075, 7100, 7098, 7104, 7106, 21, 7105])).
% 2.35/2.51 tff(7134,plain,
% 2.35/2.51 (~c1_1(a598)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[827, 7133])).
% 2.35/2.51 tff(7135,plain,
% 2.35/2.51 (c3_1(a598)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[800, 7133])).
% 2.35/2.51 tff(7136,plain,
% 2.35/2.51 (c2_1(a612)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1048, 7123])).
% 2.35/2.51 tff(7137,plain,
% 2.35/2.51 (c2_1(a598)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5449, 101, 7110, 7109, 7108, 7125, 7136, 7135, 7134, 11, 7126])).
% 2.35/2.51 tff(7138,plain,
% 2.35/2.51 (hskp8),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5601, 101, 33, 7019, 6809, 7017, 4127, 7013, 7111])).
% 2.35/2.51 tff(7139,plain,
% 2.35/2.51 (c3_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[469, 7138])).
% 2.35/2.51 tff(7140,plain,
% 2.35/2.51 (c1_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[477, 7138])).
% 2.35/2.51 tff(7141,plain,
% 2.35/2.51 (~c0_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5879, 101, 7136, 7124, 7122, 7140, 7139, 7121, 7120, 65, 7126])).
% 2.35/2.51 tff(7142,plain,
% 2.35/2.51 (~c2_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[510, 7138])).
% 2.35/2.51 tff(7143,plain,
% 2.35/2.51 (c0_1(a598)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[808, 7133])).
% 2.35/2.51 tff(7144,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7145,plain,
% 2.35/2.51 ((hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7146,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7145])).
% 2.35/2.51 tff(7147,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7146, 7144])).
% 2.35/2.51 tff(7148,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7149,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7148, 7147])).
% 2.35/2.51 tff(7150,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7149, 101, 6727, 7143, 7140, 7134, 7142, 32, 7141, 7137])).
% 2.35/2.51 tff(7151,plain,(c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(7152,assumption,(~hskp12), introduced(assumption)).
% 2.35/2.51 tff(7153,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7154,plain,
% 2.35/2.51 ((hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7155,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607)))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7154])).
% 2.35/2.51 tff(7156,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7155, 7153])).
% 2.35/2.51 tff(7157,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7158,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607)),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7157, 7156])).
% 2.35/2.51 tff(7159,plain,
% 2.35/2.51 (~c1_1(a678)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7158, 101, 7152, 4229, 4228, 6726, 6809, 2589, 1])).
% 2.35/2.51 tff(7160,plain,
% 2.35/2.51 (hskp8),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[712, 7152, 660])).
% 2.35/2.51 tff(7161,plain,
% 2.35/2.51 (~c2_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[510, 7160])).
% 2.35/2.51 tff(7162,plain,
% 2.35/2.51 (c3_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[469, 7160])).
% 2.35/2.51 tff(7163,plain,
% 2.35/2.51 (c1_1(a593)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[477, 7160])).
% 2.35/2.51 tff(7164,plain,
% 2.35/2.51 (hskp14),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[3256, 101, 4229, 4228, 4227, 7163, 7162, 7161, 505])).
% 2.35/2.51 tff(7165,plain,
% 2.35/2.51 (~c3_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[193, 7164])).
% 2.35/2.51 tff(7166,plain,
% 2.35/2.51 (~c1_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[162, 7164])).
% 2.35/2.51 tff(7167,plain,
% 2.35/2.51 (c2_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4774, 660, 101, 4229, 4228, 7166, 7165, 905, 7159])).
% 2.35/2.51 tff(7168,plain,
% 2.35/2.51 (c0_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[170, 7164])).
% 2.35/2.51 tff(7169,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[3647, 660, 101, 919, 656, 650, 644, 908, 905, 920])).
% 2.35/2.51 tff(7170,plain,((~hskp20) | hskp26 | (~c0_1(a603)) | c1_1(a603) | (~c2_1(a603))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(7171,plain,
% 2.35/2.51 (~hskp20),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7170, 7168, 660, 7166, 7167])).
% 2.35/2.51 tff(7172,plain,
% 2.35/2.51 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7173,plain,
% 2.35/2.51 ((hskp20 | hskp7 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607))) <=> (hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7174,plain,
% 2.35/2.51 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7173])).
% 2.35/2.51 tff(7175,plain,
% 2.35/2.51 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7174, 7172])).
% 2.35/2.51 tff(7176,plain,
% 2.35/2.51 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7177,plain,
% 2.35/2.51 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7176, 7175])).
% 2.35/2.51 tff(7178,plain,
% 2.35/2.51 (hskp20 | hskp7 | c0_1(a607) | (~c3_1(a607))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7177, 101, 6726, 726])).
% 2.35/2.51 tff(7179,plain,
% 2.35/2.51 (hskp7),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7178, 7171, 7151, 1])).
% 2.35/2.51 tff(7180,plain,
% 2.35/2.51 (~c3_1(a592)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[736, 7179])).
% 2.35/2.51 tff(7181,plain,
% 2.35/2.51 (~c0_1(a592)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[742, 7179])).
% 2.35/2.51 tff(7182,plain,
% 2.35/2.51 (~c1_1(a592)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1287, 101, 7168, 985, 984, 7165, 922, 7181, 7180, 240, 7167])).
% 2.35/2.51 tff(7183,plain,
% 2.35/2.51 (hskp2),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1294, 101, 7166, 7165, 7181, 7180, 188, 7182, 7167])).
% 2.35/2.51 tff(7184,plain,
% 2.35/2.51 (~c3_1(a586)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[206, 7183])).
% 2.35/2.51 tff(7185,plain,
% 2.35/2.51 (hskp3),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5004, 101, 6727, 7163, 7162, 7161, 3282])).
% 2.35/2.51 tff(7186,plain,
% 2.35/2.51 (~c1_1(a587)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[855, 7185])).
% 2.35/2.51 tff(7187,plain,
% 2.35/2.51 (c2_1(a587)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[863, 7185])).
% 2.35/2.51 tff(7188,plain,
% 2.35/2.51 (c0_1(a587)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[871, 7185])).
% 2.35/2.51 tff(7189,plain,
% 2.35/2.51 (c1_1(a586)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[214, 7183])).
% 2.35/2.51 tff(7190,plain,
% 2.35/2.51 (c0_1(a586)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4673, 7189, 7188, 7187, 7186, 985, 984, 7164, 922, 7184, 660])).
% 2.35/2.51 tff(7191,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7192,plain,
% 2.35/2.51 ((hskp1 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7193,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7192])).
% 2.35/2.51 tff(7194,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7193, 7191])).
% 2.35/2.51 tff(7195,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7196,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7195, 7194])).
% 2.35/2.51 tff(7197,plain,
% 2.35/2.51 (hskp1),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7196, 101, 7151, 6726, 7181, 7180, 1438, 7182, 1])).
% 2.35/2.51 tff(7198,plain,
% 2.35/2.51 (~c0_1(a585)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1145, 7197])).
% 2.35/2.51 tff(7199,plain,
% 2.35/2.51 (c2_1(a585)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1153, 7197])).
% 2.35/2.51 tff(7200,plain,
% 2.35/2.51 (c1_1(a585)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1161, 7197])).
% 2.35/2.51 tff(7201,plain,
% 2.35/2.51 (c2_1(a586)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1357, 7183])).
% 2.35/2.51 tff(7202,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7203,plain,
% 2.35/2.51 ((hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(7204,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[7203])).
% 2.35/2.51 tff(7205,plain,
% 2.35/2.51 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[7204, 7202])).
% 2.35/2.51 tff(7206,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(7207,plain,
% 2.35/2.51 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[7206, 7205])).
% 2.35/2.51 tff(7208,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7207, 101, 7152, 7189, 7201, 7200, 7199, 7198, 2589, 7190])).
% 2.35/2.51 tff(7209,plain,((~hskp29) | hskp12 | hskp26 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(7210,plain,
% 2.35/2.51 (~hskp29),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7209, 7152, 660, 1])).
% 2.35/2.51 tff(7211,plain,
% 2.35/2.51 (hskp29 | hskp22),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[99, 6727])).
% 2.35/2.51 tff(7212,plain,
% 2.35/2.51 (hskp22),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7211, 7210])).
% 2.35/2.51 tff(7213,plain,
% 2.35/2.51 (~c3_1(a633)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[3833, 7212])).
% 2.35/2.51 tff(7214,plain,
% 2.35/2.51 (c1_1(a633)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[3821, 7212])).
% 2.35/2.51 tff(7215,plain,
% 2.35/2.51 (~hskp0),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6858, 7162, 7163, 7161])).
% 2.35/2.51 tff(7216,plain,
% 2.35/2.51 (~hskp18),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6992, 7188, 660, 7215, 7187, 7186])).
% 2.35/2.51 tff(7217,plain,
% 2.35/2.51 (~c2_1(a633)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4420, 7210, 101, 7216, 7214, 7213, 1673])).
% 2.35/2.51 tff(7218,plain,
% 2.35/2.51 (~c0_1(a633)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[3827, 7212])).
% 2.35/2.51 tff(7219,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4985, 101, 6727, 7214, 7188, 7187, 7218, 7186, 32, 7217])).
% 2.35/2.51 tff(7220,plain,(hskp12 | hskp26 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(7221,plain,
% 2.35/2.51 (hskp12),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7220, 660, 1])).
% 2.35/2.51 tff(7222,plain,
% 2.35/2.51 (~c3_1(a600)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[675, 7221])).
% 2.35/2.51 tff(7223,plain,
% 2.35/2.51 (~hskp22),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[7032, 7221, 984, 985, 922])).
% 2.35/2.51 tff(7224,plain,
% 2.35/2.51 (hskp14),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[700, 7221, 7223])).
% 2.35/2.51 tff(7225,plain,
% 2.35/2.51 (~c3_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[193, 7224])).
% 2.35/2.51 tff(7226,plain,
% 2.35/2.51 (c2_1(a600)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[683, 7221])).
% 2.35/2.51 tff(7227,plain,
% 2.35/2.51 (c0_1(a600)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[691, 7221])).
% 2.35/2.51 tff(7228,plain,
% 2.35/2.51 (~c1_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[162, 7224])).
% 2.35/2.51 tff(7229,plain,
% 2.35/2.51 (c0_1(a603)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[170, 7224])).
% 2.35/2.52 tff(7230,plain,
% 2.35/2.52 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7231,plain,
% 2.35/2.52 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a600) | (~c1_1(a600)) | (~c0_1(a600))) <=> (hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7232,plain,
% 2.35/2.52 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a600) | (~c1_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7231])).
% 2.35/2.52 tff(7233,plain,
% 2.35/2.52 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a600) | (~c1_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600)))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7232, 7230])).
% 2.35/2.52 tff(7234,plain,
% 2.35/2.52 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a600) | (~c1_1(a600)) | (~c0_1(a600)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7235,plain,
% 2.35/2.52 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7234, 7233])).
% 2.35/2.52 tff(7236,plain,
% 2.35/2.52 (hskp3 | (~c1_1(a600))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7235, 101, 6727, 4609, 4601, 2236])).
% 2.35/2.52 tff(7237,plain,
% 2.35/2.52 (~c1_1(a600)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7236, 288])).
% 2.35/2.52 tff(7238,plain,
% 2.35/2.52 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7239,plain,
% 2.35/2.52 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c2_1(a600))) <=> (hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7240,plain,
% 2.35/2.52 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c2_1(a600)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600)))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7239])).
% 2.35/2.52 tff(7241,plain,
% 2.35/2.52 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c2_1(a600)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7240, 7238])).
% 2.35/2.52 tff(7242,plain,
% 2.35/2.52 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c2_1(a600)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7243,plain,
% 2.35/2.52 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600)),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7242, 7241])).
% 2.35/2.52 tff(7244,plain,
% 2.35/2.52 (hskp4 | hskp3 | c1_1(a600)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7243, 101, 4608, 4601, 762])).
% 2.35/2.52 tff(7245,plain,
% 2.35/2.52 (hskp4),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7244, 288, 7237])).
% 2.35/2.52 tff(7246,plain,
% 2.35/2.52 (~c2_1(a588)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[115, 7245])).
% 2.35/2.52 tff(7247,plain,
% 2.35/2.52 (~c1_1(a588)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[121, 7245])).
% 2.35/2.52 tff(7248,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7249,plain,
% 2.35/2.52 ((hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c0_1(a600)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588))) <=> (hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7250,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c0_1(a600)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600)))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7249])).
% 2.35/2.52 tff(7251,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c0_1(a600)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7250, 7248])).
% 2.35/2.52 tff(7252,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c0_1(a600)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7253,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600)),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7252, 7251])).
% 2.35/2.52 tff(7254,plain,
% 2.35/2.52 (~c3_1(a588)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7253, 101, 288, 4609, 4601, 7247, 7246, 298, 7237])).
% 2.35/2.52 tff(7255,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7256,plain,
% 2.35/2.52 ((hskp26 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7257,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603)))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7256])).
% 2.35/2.52 tff(7258,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7257, 7255])).
% 2.35/2.52 tff(7259,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7260,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603)),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7259, 7258])).
% 2.35/2.52 tff(7261,plain,
% 2.35/2.52 (c2_1(a603)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7260, 660, 101, 4609, 4608, 908, 907, 905, 7237])).
% 2.35/2.52 tff(7262,plain,
% 2.35/2.52 ($false),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[4782, 660, 101, 919, 908, 7247, 7246, 905, 7261, 7254])).
% 2.35/2.52 tff(7263,plain,(hskp3 | hskp26 | (~c0_1(a603)) | c1_1(a603) | (~c0_1(a600)) | (~c2_1(a600)) | c3_1(a603) | c3_1(a600)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.52 tff(7264,plain,
% 2.35/2.52 (hskp3),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7263, 660, 7229, 7228, 7227, 7226, 7225, 7222])).
% 2.35/2.52 tff(7265,plain,
% 2.35/2.52 (~c1_1(a587)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[855, 7264])).
% 2.35/2.52 tff(7266,plain,
% 2.35/2.52 (c2_1(a587)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[863, 7264])).
% 2.35/2.52 tff(7267,plain,
% 2.35/2.52 (c0_1(a587)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[871, 7264])).
% 2.35/2.52 tff(7268,plain,
% 2.35/2.52 (c2_1(a603)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[916, 660, 101, 7267, 7266, 7228, 7225, 7265, 905])).
% 2.35/2.52 tff(7269,plain,
% 2.35/2.52 (~hskp20),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7170, 7268, 660, 7228, 7229])).
% 2.35/2.52 tff(7270,plain,
% 2.35/2.52 (hskp7),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7178, 7269, 7151, 1])).
% 2.35/2.52 tff(7271,plain,
% 2.35/2.52 (~c3_1(a592)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[736, 7270])).
% 2.35/2.52 tff(7272,plain,
% 2.35/2.52 (~c0_1(a592)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[742, 7270])).
% 2.35/2.52 tff(7273,plain,
% 2.35/2.52 (~c1_1(a592)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1287, 101, 7229, 985, 984, 7225, 922, 7272, 7271, 240, 7268])).
% 2.35/2.52 tff(7274,plain,
% 2.35/2.52 (hskp2),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1294, 101, 7228, 7225, 7272, 7271, 188, 7273, 7268])).
% 2.35/2.52 tff(7275,plain,
% 2.35/2.52 (~c3_1(a586)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[206, 7274])).
% 2.35/2.52 tff(7276,plain,
% 2.35/2.52 (c1_1(a586)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[214, 7274])).
% 2.35/2.52 tff(7277,plain,
% 2.35/2.52 (c0_1(a586)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[4673, 7276, 7267, 7266, 7265, 985, 984, 7224, 922, 7275, 660])).
% 2.35/2.52 tff(7278,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7279,plain,
% 2.35/2.52 ((hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7280,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7279])).
% 2.35/2.52 tff(7281,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7280, 7278])).
% 2.35/2.52 tff(7282,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7283,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7282, 7281])).
% 2.35/2.52 tff(7284,plain,
% 2.35/2.52 (hskp16),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7283, 101, 7151, 7276, 6726, 7275, 1314, 1, 7277])).
% 2.35/2.52 tff(7285,plain,
% 2.35/2.52 (~c2_1(a606)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1015, 7284])).
% 2.35/2.52 tff(7286,plain,
% 2.35/2.52 (c1_1(a606)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[992, 7284])).
% 2.35/2.52 tff(7287,plain,
% 2.35/2.52 (c0_1(a606)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7115, 7286, 7267, 7266, 7285, 7265])).
% 2.35/2.52 tff(7288,plain,
% 2.35/2.52 (c2_1(a592)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[750, 7270])).
% 2.35/2.52 tff(7289,plain,
% 2.35/2.52 (hskp29),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2135, 7223])).
% 2.35/2.52 tff(7290,plain,
% 2.35/2.52 (c3_1(a678)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2143, 7289])).
% 2.35/2.52 tff(7291,plain,
% 2.35/2.52 (c0_1(a678)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2159, 7289])).
% 2.35/2.52 tff(7292,plain,
% 2.35/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7293,plain,
% 2.35/2.52 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> ((~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7294,plain,
% 2.35/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7293])).
% 2.35/2.52 tff(7295,plain,
% 2.35/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7294, 7292])).
% 2.35/2.52 tff(7296,plain,
% 2.35/2.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7297,plain,
% 2.35/2.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7296, 7295])).
% 2.35/2.52 tff(7298,plain,
% 2.35/2.52 (~c1_1(a678)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7297, 101, 7291, 7290, 7151, 7288, 6809, 7272, 65, 7273, 1])).
% 2.35/2.52 tff(7299,plain,
% 2.35/2.52 (c2_1(a586)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1357, 7274])).
% 2.35/2.52 tff(7300,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7301,plain,
% 2.35/2.52 ((hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7302,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7301])).
% 2.35/2.52 tff(7303,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7302, 7300])).
% 2.35/2.52 tff(7304,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7305,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7304, 7303])).
% 2.35/2.52 tff(7306,plain,
% 2.35/2.52 (hskp15),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7305, 101, 7151, 7276, 7299, 6726, 7275, 2552, 1])).
% 2.35/2.52 tff(7307,plain,
% 2.35/2.52 (~c0_1(a604)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1474, 7306])).
% 2.35/2.52 tff(7308,plain,
% 2.35/2.52 (c1_1(a604)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1490, 7306])).
% 2.35/2.52 tff(7309,plain,
% 2.35/2.52 (c2_1(a678)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2151, 7289])).
% 2.35/2.52 tff(7310,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7311,plain,
% 2.35/2.52 ((hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7312,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7311])).
% 2.35/2.52 tff(7313,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604)))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7312, 7310])).
% 2.35/2.52 tff(7314,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7315,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7314, 7313])).
% 2.35/2.52 tff(7316,plain,
% 2.35/2.52 (c2_1(a604)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7315, 101, 6727, 7291, 7309, 7308, 7307, 32, 7298])).
% 2.35/2.52 tff(7317,plain,
% 2.35/2.52 ((~hskp0) | (~c0_1(a678)) | (~c2_1(a678)) | c1_1(a678)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[3666, 6727])).
% 2.35/2.52 tff(7318,plain,
% 2.35/2.52 (~hskp0),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7317, 7298, 7309, 7291])).
% 2.35/2.52 tff(7319,plain,
% 2.35/2.52 (~hskp18),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6992, 7318, 660, 7267, 7266, 7265])).
% 2.35/2.52 tff(7320,plain,
% 2.35/2.52 (hskp8),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6100, 7319, 7270])).
% 2.35/2.52 tff(7321,plain,
% 2.35/2.52 (c3_1(a593)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[469, 7320])).
% 2.35/2.52 tff(7322,plain,
% 2.35/2.52 (c1_1(a593)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[477, 7320])).
% 2.35/2.52 tff(7323,plain,
% 2.35/2.52 (c3_1(a604)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1482, 7306])).
% 2.35/2.52 tff(7324,plain,
% 2.35/2.52 (~c0_1(a593)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6652, 101, 7323, 7322, 7321, 7288, 7307, 7272, 65, 7273, 7316])).
% 2.35/2.52 tff(7325,plain,
% 2.35/2.52 (~c2_1(a593)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[510, 7320])).
% 2.35/2.52 tff(7326,plain,
% 2.35/2.52 (~c3_1(a606)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[982, 7284])).
% 2.35/2.52 tff(7327,plain,
% 2.35/2.52 ($false),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6660, 101, 7322, 7285, 7326, 7325, 7272, 7271, 1349, 7324, 7273, 7287])).
% 2.35/2.52 tff(7328,plain,(hskp26 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.52 tff(7329,plain,
% 2.35/2.52 (hskp26),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7328, 1])).
% 2.35/2.52 tff(7330,plain,
% 2.35/2.52 (c2_1(a583)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[364, 7329])).
% 2.35/2.52 tff(7331,plain,
% 2.35/2.52 (c1_1(a583)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[330, 7329])).
% 2.35/2.52 tff(7332,plain,
% 2.35/2.52 (c0_1(a583)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[338, 7329])).
% 2.35/2.52 tff(7333,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7334,plain,
% 2.35/2.52 ((hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7335,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7334])).
% 2.35/2.52 tff(7336,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607)))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7335, 7333])).
% 2.35/2.52 tff(7337,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7338,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7337, 7336])).
% 2.35/2.52 tff(7339,plain,
% 2.35/2.52 (hskp10),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7338, 101, 7332, 7331, 7330, 7151, 6726, 6809, 21])).
% 2.35/2.52 tff(7340,plain,
% 2.35/2.52 (~c1_1(a598)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[827, 7339])).
% 2.35/2.52 tff(7341,plain,
% 2.35/2.52 (c3_1(a598)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[800, 7339])).
% 2.35/2.52 tff(7342,plain,
% 2.35/2.52 (c0_1(a598)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[808, 7339])).
% 2.35/2.52 tff(7343,plain,
% 2.35/2.52 (hskp11 | hskp23),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1565, 101, 7342, 7341, 7340, 1525])).
% 2.35/2.52 tff(7344,plain,
% 2.35/2.52 (hskp23),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7343, 1515])).
% 2.35/2.52 tff(7345,plain,
% 2.35/2.52 (~c1_1(a636)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[439, 7344])).
% 2.35/2.52 tff(7346,plain,
% 2.35/2.52 (~c0_1(a636)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[445, 7344])).
% 2.35/2.52 tff(7347,plain,
% 2.35/2.52 (c3_1(a636)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[453, 7344])).
% 2.35/2.52 tff(7348,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7349,plain,
% 2.35/2.52 ((hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636)))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7350,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7349])).
% 2.35/2.52 tff(7351,plain,
% 2.35/2.52 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636)))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7350, 7348])).
% 2.35/2.52 tff(7352,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7353,plain,
% 2.35/2.52 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7352, 7351])).
% 2.35/2.52 tff(7354,plain,
% 2.35/2.52 (hskp8),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7353, 101, 7347, 7346, 7345, 6726, 6809, 1206, 1])).
% 2.35/2.52 tff(7355,plain,
% 2.35/2.52 (~c2_1(a593)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[510, 7354])).
% 2.35/2.52 tff(7356,plain,
% 2.35/2.52 (c1_1(a593)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[477, 7354])).
% 2.35/2.52 tff(7357,plain,
% 2.35/2.52 (c3_1(a593)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[469, 7354])).
% 2.35/2.52 tff(7358,plain,
% 2.35/2.52 (~hskp0),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6858, 7357, 7356, 7355])).
% 2.35/2.52 tff(7359,plain,
% 2.35/2.52 (~c0_1(a593)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6865, 1515, 101, 7358, 7356, 7355, 2215])).
% 2.35/2.52 tff(7360,plain,
% 2.35/2.52 (hskp3),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[5004, 101, 6727, 7356, 7357, 7355, 3282])).
% 2.35/2.52 tff(7361,plain,
% 2.35/2.52 (~c1_1(a587)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[855, 7360])).
% 2.35/2.52 tff(7362,plain,
% 2.35/2.52 (c2_1(a587)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[863, 7360])).
% 2.35/2.52 tff(7363,plain,
% 2.35/2.52 (c0_1(a587)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[871, 7360])).
% 2.35/2.52 tff(7364,plain,
% 2.35/2.52 ($false),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[5082, 101, 6727, 7356, 7363, 7362, 7355, 7361, 32, 7359])).
% 2.35/2.52 tff(7365,plain,(hskp11 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.52 tff(7366,plain,
% 2.35/2.52 (hskp11),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7365, 1])).
% 2.35/2.52 tff(7367,plain,
% 2.35/2.52 (~c1_1(a599)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[395, 7366])).
% 2.35/2.52 tff(7368,plain,
% 2.35/2.52 (c2_1(a599)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[403, 7366])).
% 2.35/2.52 tff(7369,plain,
% 2.35/2.52 (hskp12),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6815, 101, 7332, 7331, 7330, 6726, 6809, 2589, 1])).
% 2.35/2.52 tff(7370,plain,
% 2.35/2.52 (c3_1(a599)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[389, 7366])).
% 2.35/2.52 tff(7371,plain,
% 2.35/2.52 (~hskp22),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7032, 7370, 7369, 7368, 7367])).
% 2.35/2.52 tff(7372,plain,
% 2.35/2.52 (hskp29),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2135, 7371])).
% 2.35/2.53 tff(7373,plain,
% 2.35/2.53 (c3_1(a678)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2143, 7372])).
% 2.35/2.53 tff(7374,plain,
% 2.35/2.53 (c2_1(a678)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2151, 7372])).
% 2.35/2.53 tff(7375,plain,
% 2.35/2.53 (c0_1(a678)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2159, 7372])).
% 2.35/2.53 tff(7376,plain,
% 2.35/2.53 (c2_1(a598)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[6908, 101, 7375, 7374, 7373, 7341, 6726, 6809, 7340, 11, 1])).
% 2.35/2.53 tff(7377,plain,
% 2.35/2.53 (~c3_1(a600)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[675, 7369])).
% 2.35/2.53 tff(7378,plain,
% 2.35/2.53 (c2_1(a600)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[683, 7369])).
% 2.35/2.53 tff(7379,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7380,plain,
% 2.35/2.53 ((hskp15 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7381,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7380])).
% 2.35/2.53 tff(7382,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607)))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7381, 7379])).
% 2.35/2.53 tff(7383,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7384,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7383, 7382])).
% 2.35/2.53 tff(7385,plain,
% 2.35/2.53 (hskp15 | (~c1_1(a600))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7384, 101, 7151, 7378, 6726, 7377, 2552, 1])).
% 2.35/2.53 tff(7386,plain,
% 2.35/2.53 (~c1_1(a600)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7385, 3016])).
% 2.35/2.53 tff(7387,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7388,plain,
% 2.35/2.53 ((hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599))) <=> (hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7389,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607)))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7388])).
% 2.35/2.53 tff(7390,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7389, 7387])).
% 2.35/2.53 tff(7391,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7392,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607)),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7391, 7390])).
% 2.35/2.53 tff(7393,plain,
% 2.35/2.53 (hskp8 | c0_1(a599)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7392, 101, 7370, 6726, 6809, 7367, 1206, 1])).
% 2.35/2.53 tff(7394,plain,
% 2.35/2.53 (c0_1(a599)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7393, 1586])).
% 2.35/2.53 tff(7395,plain,
% 2.35/2.53 (c0_1(a600)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[691, 7369])).
% 2.35/2.53 tff(7396,plain,
% 2.35/2.53 (hskp27 | hskp8),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2606, 101, 7395, 7378, 7377, 1957])).
% 2.35/2.53 tff(7397,plain,
% 2.35/2.53 (hskp27),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7396, 1586])).
% 2.35/2.53 tff(7398,plain,
% 2.35/2.53 (c3_1(a611)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[566, 7397])).
% 2.35/2.53 tff(7399,plain,
% 2.35/2.53 (c1_1(a611)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[574, 7397])).
% 2.35/2.53 tff(7400,plain,
% 2.35/2.53 (c0_1(a611)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[582, 7397])).
% 2.35/2.53 tff(7401,plain,
% 2.35/2.53 (hskp15),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2741, 101, 7400, 7399, 7398, 7370, 7367, 1870, 7394])).
% 2.35/2.53 tff(7402,plain,
% 2.35/2.53 (c3_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1482, 7401])).
% 2.35/2.53 tff(7403,plain,
% 2.35/2.53 (~c0_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1474, 7401])).
% 2.35/2.53 tff(7404,plain,
% 2.35/2.53 (hskp14),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[700, 7371, 7369])).
% 2.35/2.53 tff(7405,plain,
% 2.35/2.53 (~c3_1(a603)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[193, 7404])).
% 2.35/2.53 tff(7406,plain,
% 2.35/2.53 (c0_1(a603)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[170, 7404])).
% 2.35/2.53 tff(7407,plain,
% 2.35/2.53 (hskp8 | c2_1(a603)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[6829, 101, 7406, 7395, 7378, 7405, 7377, 4127])).
% 2.35/2.53 tff(7408,plain,
% 2.35/2.53 (c2_1(a603)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7407, 1586])).
% 2.35/2.53 tff(7409,plain,
% 2.35/2.53 (~c1_1(a603)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[162, 7404])).
% 2.35/2.53 tff(7410,plain,
% 2.35/2.53 (c1_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1490, 7401])).
% 2.35/2.53 tff(7411,plain,
% 2.35/2.53 (c2_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3389, 101, 6727, 7410, 7406, 7403, 7409, 32, 7408])).
% 2.35/2.53 tff(7412,assumption,(c3_1(a611)), introduced(assumption)).
% 2.35/2.53 tff(7413,assumption,(c1_1(a611)), introduced(assumption)).
% 2.35/2.53 tff(7414,assumption,(c0_1(a611)), introduced(assumption)).
% 2.35/2.53 tff(7415,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2771, 101, 7414, 7413, 7412, 3611, 2410, 3610, 3609, 2340, 65, 2403])).
% 2.35/2.53 tff(7416,plain,((~hskp19) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a611)) | (~c3_1(a604)) | c0_1(a604) | (~c2_1(a604))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7417,plain,
% 2.35/2.53 (~hskp19),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7416, 7400, 7399, 7398, 7402, 7403, 7411])).
% 2.35/2.53 tff(7418,plain,
% 2.35/2.53 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7419,plain,
% 2.35/2.53 ((hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611))) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7420,plain,
% 2.35/2.53 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7419])).
% 2.35/2.53 tff(7421,plain,
% 2.35/2.53 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7420, 7418])).
% 2.35/2.53 tff(7422,plain,
% 2.35/2.53 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7423,plain,
% 2.35/2.53 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7422, 7421])).
% 2.35/2.53 tff(7424,plain,
% 2.35/2.53 (hskp20 | hskp19),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7423, 101, 7400, 7399, 7398, 3630])).
% 2.35/2.53 tff(7425,plain,
% 2.35/2.53 (hskp20),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7424, 7417])).
% 2.35/2.53 tff(7426,plain,
% 2.35/2.53 (hskp16),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[5514, 7425, 7411, 7370, 7403, 7367, 7368, 7402])).
% 2.35/2.53 tff(7427,plain,
% 2.35/2.53 (~c2_1(a606)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1015, 7426])).
% 2.35/2.53 tff(7428,plain,
% 2.35/2.53 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7429,plain,
% 2.35/2.53 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607))) <=> (hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7430,plain,
% 2.35/2.53 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7429])).
% 2.35/2.53 tff(7431,plain,
% 2.35/2.53 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7430, 7428])).
% 2.35/2.53 tff(7432,plain,
% 2.35/2.53 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7433,plain,
% 2.35/2.53 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7432, 7431])).
% 2.35/2.53 tff(7434,plain,
% 2.35/2.53 (hskp19 | hskp13 | (~c2_1(a607)) | c0_1(a607)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7433, 101, 6726, 2429])).
% 2.35/2.53 tff(7435,plain,
% 2.35/2.53 (hskp13),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7434, 7417, 6809, 1])).
% 2.35/2.53 tff(7436,plain,
% 2.35/2.53 (c1_1(a606)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[992, 7426])).
% 2.35/2.53 tff(7437,plain,
% 2.35/2.53 (hskp3 | c3_1(a583)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3885, 101, 6727, 1528, 1527, 2236])).
% 2.35/2.53 tff(7438,plain,
% 2.35/2.53 (c3_1(a583)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7437, 288])).
% 2.35/2.53 tff(7439,plain,
% 2.35/2.53 (hskp15),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[4485, 7438, 1528, 1527, 1526])).
% 2.35/2.53 tff(7440,plain,
% 2.35/2.53 (c3_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1482, 7439])).
% 2.35/2.53 tff(7441,plain,
% 2.35/2.53 (c1_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1490, 7439])).
% 2.35/2.53 tff(7442,plain,
% 2.35/2.53 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7443,plain,
% 2.35/2.53 ((hskp17 | hskp3 | (~ndr1_0) | c2_1(a604) | (~c3_1(a604)) | (~c1_1(a604))) <=> (hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7444,plain,
% 2.35/2.53 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7443])).
% 2.35/2.53 tff(7445,plain,
% 2.35/2.53 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604)))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7444, 7442])).
% 2.35/2.53 tff(7446,plain,
% 2.35/2.53 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7447,plain,
% 2.35/2.53 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7446, 7445])).
% 2.35/2.53 tff(7448,plain,
% 2.35/2.53 (c2_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7447, 101, 6727, 288, 7441, 7440, 3282])).
% 2.35/2.53 tff(7449,plain,
% 2.35/2.53 (~c0_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1474, 7439])).
% 2.35/2.53 tff(7450,plain,
% 2.35/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7451,plain,
% 2.35/2.53 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7452,plain,
% 2.35/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7451])).
% 2.35/2.53 tff(7453,plain,
% 2.35/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7452, 7450])).
% 2.35/2.53 tff(7454,plain,
% 2.35/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7455,plain,
% 2.35/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7454, 7453])).
% 2.35/2.53 tff(7456,plain,
% 2.35/2.53 (~c3_1(a588)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7455, 101, 2186, 2185, 2184, 7441, 7449, 7247, 7246, 11, 7448])).
% 2.35/2.53 tff(7457,plain,
% 2.35/2.53 (c0_1(a588)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[129, 7245])).
% 2.35/2.53 tff(7458,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7459,plain,
% 2.35/2.53 ((hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604))) <=> (hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7460,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7459])).
% 2.35/2.53 tff(7461,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7460, 7458])).
% 2.35/2.53 tff(7462,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7463,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7462, 7461])).
% 2.35/2.53 tff(7464,plain,
% 2.35/2.53 (hskp16),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7463, 101, 7440, 7457, 7449, 7246, 2002, 7448, 7456])).
% 2.35/2.53 tff(7465,plain,
% 2.35/2.53 (~c3_1(a606)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[982, 7464])).
% 2.35/2.53 tff(7466,plain,
% 2.35/2.53 (c1_1(a606)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[992, 7464])).
% 2.35/2.53 tff(7467,plain,
% 2.35/2.53 (c0_1(a606)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[5587, 101, 7466, 4609, 4608, 427, 426, 7465, 4601, 425, 240])).
% 2.35/2.53 tff(7468,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2242, 101, 6727, 288, 7466, 7465, 2236, 7467])).
% 2.35/2.53 tff(7469,plain,(hskp3 | (~c0_1(a600)) | (~c2_1(a600)) | (~c2_1(a599)) | (~c3_1(a599)) | c3_1(a600) | c1_1(a599) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7470,plain,
% 2.35/2.53 (hskp3),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7469, 7395, 7378, 7368, 7370, 7377, 7367, 7375, 7374, 7373, 7332, 7331, 7330])).
% 2.35/2.53 tff(7471,plain,
% 2.35/2.53 (~c1_1(a587)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[855, 7470])).
% 2.35/2.53 tff(7472,plain,
% 2.35/2.53 (c2_1(a587)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[863, 7470])).
% 2.35/2.53 tff(7473,plain,
% 2.35/2.53 (c0_1(a587)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[871, 7470])).
% 2.35/2.53 tff(7474,plain,
% 2.35/2.53 (c0_1(a606)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7115, 7436, 7473, 7472, 7427, 7471])).
% 2.35/2.53 tff(7475,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2418, 7474, 7436, 7370, 7411, 7368, 7367, 7403, 7375, 7374, 7373, 7435, 7427, 7402])).
% 2.35/2.53 tff(7476,plain,(hskp8 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7477,plain,
% 2.35/2.53 (hskp8),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7476, 1])).
% 2.35/2.53 tff(7478,plain,
% 2.35/2.53 (c3_1(a593)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[469, 7477])).
% 2.35/2.53 tff(7479,plain,
% 2.35/2.53 (c1_1(a593)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[477, 7477])).
% 2.35/2.53 tff(7480,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7481,plain,
% 2.35/2.53 ((hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7482,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7481])).
% 2.35/2.53 tff(7483,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7482, 7480])).
% 2.35/2.53 tff(7484,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7485,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7484, 7483])).
% 2.35/2.53 tff(7486,plain,
% 2.35/2.53 (hskp15 | (~c0_1(a593))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7485, 101, 7342, 7341, 7479, 7478, 7340, 1870])).
% 2.35/2.53 tff(7487,plain,
% 2.35/2.53 (~c0_1(a593)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7486, 3016])).
% 2.35/2.53 tff(7488,plain,
% 2.35/2.53 (~c2_1(a593)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[510, 7477])).
% 2.35/2.53 tff(7489,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7490,plain,
% 2.35/2.53 ((hskp17 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7491,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600)))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7490])).
% 2.35/2.53 tff(7492,plain,
% 2.35/2.53 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7491, 7489])).
% 2.35/2.53 tff(7493,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7494,plain,
% 2.35/2.53 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600)),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7493, 7492])).
% 2.35/2.53 tff(7495,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7494, 101, 6727, 7395, 7378, 7479, 7488, 32, 7487, 7386])).
% 2.35/2.53 tff(7496,plain,(hskp15 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7497,plain,
% 2.35/2.53 (hskp15),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7496, 1])).
% 2.35/2.53 tff(7498,plain,
% 2.35/2.53 (~c0_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1474, 7497])).
% 2.35/2.53 tff(7499,plain,
% 2.35/2.53 (c1_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1490, 7497])).
% 2.35/2.53 tff(7500,plain,
% 2.35/2.53 (c2_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[4646, 101, 6727, 7499, 7342, 7498, 7340, 32, 7376])).
% 2.35/2.53 tff(7501,plain,
% 2.35/2.53 (c3_1(a604)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[1482, 7497])).
% 2.35/2.53 tff(7502,plain,
% 2.35/2.53 (~c1_1(a678)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2474, 101, 2186, 2184, 3611, 2410, 3610, 3609, 2340, 65, 2403])).
% 2.35/2.53 tff(7503,plain,
% 2.35/2.53 (~c0_1(a593)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2481, 101, 3611, 2410, 1771, 1780, 3610, 3609, 2340, 65, 2403])).
% 2.35/2.53 tff(7504,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2488, 101, 6727, 2186, 2185, 1771, 1770, 32, 7503, 7502])).
% 2.35/2.53 tff(7505,plain,((~hskp19) | (~c0_1(a678)) | (~c2_1(a678)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a604)) | (~c3_1(a593)) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a678))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7506,plain,
% 2.35/2.53 (~hskp19),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7505, 7375, 7374, 7479, 7488, 7501, 7478, 7498, 7500, 7373])).
% 2.35/2.53 tff(7507,plain,
% 2.35/2.53 (hskp13),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7434, 7506, 6809, 1])).
% 2.35/2.53 tff(7508,plain,
% 2.35/2.53 (~c2_1(a601)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2388, 7507])).
% 2.35/2.53 tff(7509,plain,
% 2.35/2.53 (~c1_1(a601)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2394, 7507])).
% 2.35/2.53 tff(7510,plain,
% 2.35/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7511,plain,
% 2.35/2.53 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7512,plain,
% 2.35/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7511])).
% 2.35/2.53 tff(7513,plain,
% 2.35/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7512, 7510])).
% 2.35/2.53 tff(7514,plain,
% 2.35/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7515,plain,
% 2.35/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7514, 7513])).
% 2.35/2.54 tff(7516,plain,
% 2.35/2.54 (~c3_1(a601)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7515, 101, 7375, 7374, 7373, 7499, 7498, 7509, 7508, 11, 7500])).
% 2.35/2.54 tff(7517,plain,
% 2.35/2.54 (~c0_1(a601)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2408, 7507])).
% 2.35/2.54 tff(7518,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2416, 101, 7501, 7368, 7370, 7498, 7517, 7508, 7367, 1607, 7500, 7516])).
% 2.35/2.54 tff(7519,plain,(c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7520,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7521,plain,
% 2.35/2.54 ((hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607))) <=> (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7522,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7521])).
% 2.35/2.54 tff(7523,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7522, 7520])).
% 2.35/2.54 tff(7524,plain,
% 2.35/2.54 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7525,plain,
% 2.35/2.54 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7524, 7523])).
% 2.35/2.54 tff(7526,plain,
% 2.35/2.54 (hskp10 | (~c0_1(a607)) | (~c3_1(a607))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7525, 101, 6726, 6809, 21])).
% 2.35/2.54 tff(7527,plain,
% 2.35/2.54 (hskp10),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7526, 7519, 7151])).
% 2.35/2.54 tff(7528,plain,
% 2.35/2.54 (~c1_1(a598)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[827, 7527])).
% 2.35/2.54 tff(7529,plain,
% 2.35/2.54 (c3_1(a598)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[800, 7527])).
% 2.35/2.54 tff(7530,plain,
% 2.35/2.54 (c0_1(a598)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[808, 7527])).
% 2.35/2.54 tff(7531,plain,
% 2.35/2.54 (hskp11 | hskp23),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[1565, 101, 7530, 7529, 7528, 1525])).
% 2.35/2.54 tff(7532,plain,
% 2.35/2.54 (hskp23),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7531, 1515])).
% 2.35/2.54 tff(7533,plain,
% 2.35/2.54 (~c1_1(a636)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[439, 7532])).
% 2.35/2.54 tff(7534,plain,
% 2.35/2.54 (~c0_1(a636)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[445, 7532])).
% 2.35/2.54 tff(7535,plain,
% 2.35/2.54 (c3_1(a636)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[453, 7532])).
% 2.35/2.54 tff(7536,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7537,plain,
% 2.35/2.54 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636))) <=> (c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7538,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7537])).
% 2.35/2.54 tff(7539,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7538, 7536])).
% 2.35/2.54 tff(7540,plain,
% 2.35/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7541,plain,
% 2.35/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7540, 7539])).
% 2.35/2.54 tff(7542,plain,
% 2.35/2.54 (~c2_1(a636)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7541, 101, 7535, 7151, 7534, 7533, 6726, 65, 7519])).
% 2.35/2.54 tff(7543,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7544,plain,
% 2.35/2.54 ((hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7545,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7544])).
% 2.35/2.54 tff(7546,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7545, 7543])).
% 2.35/2.54 tff(7547,plain,
% 2.35/2.54 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7548,plain,
% 2.35/2.54 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7547, 7546])).
% 2.35/2.54 tff(7549,plain,
% 2.35/2.54 (hskp15),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7548, 101, 7151, 7530, 7529, 6726, 7528, 1870, 7519])).
% 2.35/2.54 tff(7550,plain,
% 2.35/2.54 (~c0_1(a604)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[1474, 7549])).
% 2.35/2.54 tff(7551,plain,
% 2.35/2.54 (c1_1(a604)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[1490, 7549])).
% 2.35/2.54 tff(7552,plain,
% 2.35/2.54 (hskp11),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[6728, 6088, 6086, 6087])).
% 2.35/2.54 tff(7553,plain,
% 2.35/2.54 (~c1_1(a599)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[395, 7552])).
% 2.35/2.54 tff(7554,plain,
% 2.35/2.54 (c2_1(a599)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[403, 7552])).
% 2.35/2.54 tff(7555,plain,
% 2.35/2.54 (c3_1(a599)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[389, 7552])).
% 2.35/2.54 tff(7556,plain,
% 2.35/2.54 (~hskp12),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7032, 7555, 6085, 7554, 7553])).
% 2.35/2.54 tff(7557,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7558,plain,
% 2.35/2.54 ((hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7559,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7558])).
% 2.35/2.54 tff(7560,plain,
% 2.35/2.54 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7559, 7557])).
% 2.35/2.54 tff(7561,plain,
% 2.35/2.54 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7562,plain,
% 2.35/2.54 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7561, 7560])).
% 2.35/2.54 tff(7563,plain,
% 2.35/2.54 (hskp12 | (~c2_1(a604))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7562, 101, 7551, 6726, 6809, 7550, 2589, 7519])).
% 2.35/2.54 tff(7564,plain,
% 2.35/2.54 (~c2_1(a604)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7563, 7556])).
% 2.35/2.54 tff(7565,plain,
% 2.35/2.54 (c0_1(a599)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[6782, 7554, 7151, 7519, 7553, 7555])).
% 2.35/2.54 tff(7566,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2750, 101, 6727, 7551, 7554, 7550, 7553, 32, 7565, 7564])).
% 2.35/2.54 tff(7567,plain,(~hskp22), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7568,plain,
% 2.35/2.54 (hskp29),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2135, 7567])).
% 2.35/2.54 tff(7569,plain,
% 2.35/2.54 (c3_1(a678)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2143, 7568])).
% 2.35/2.54 tff(7570,plain,
% 2.35/2.54 (c2_1(a678)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2151, 7568])).
% 2.35/2.54 tff(7571,plain,
% 2.35/2.54 (c0_1(a678)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2159, 7568])).
% 2.35/2.54 tff(7572,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7573,plain,
% 2.35/2.54 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7574,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636)))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7573])).
% 2.35/2.54 tff(7575,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7574, 7572])).
% 2.35/2.54 tff(7576,plain,
% 2.35/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7577,plain,
% 2.35/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636)),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7576, 7575])).
% 2.35/2.54 tff(7578,plain,
% 2.35/2.54 (~c2_1(a604)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7577, 101, 7571, 7570, 7569, 7535, 7551, 7533, 7550, 11, 7542])).
% 2.35/2.54 tff(7579,plain,
% 2.35/2.54 (hskp9),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[1577, 101, 3183, 3184, 3192, 7535, 7534, 7533, 276])).
% 2.35/2.54 tff(7580,plain,
% 2.35/2.54 (~c3_1(a595)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[1370, 7579])).
% 2.35/2.54 tff(7581,plain,
% 2.35/2.54 (~c1_1(a595)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[1376, 7579])).
% 2.35/2.54 tff(7582,plain,
% 2.35/2.54 (~c0_1(a595)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[1382, 7579])).
% 2.35/2.54 tff(7583,plain,
% 2.35/2.54 ((~c2_1(a598)) | c2_1(a604)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[4646, 101, 6727, 7551, 7530, 7550, 7528, 32])).
% 2.35/2.54 tff(7584,plain,
% 2.35/2.54 (~c2_1(a598)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7583, 7578])).
% 2.35/2.54 tff(7585,plain,
% 2.35/2.54 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7586,plain,
% 2.35/2.54 ((hskp11 | hskp21 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598))) <=> (hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7587,plain,
% 2.35/2.54 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7586])).
% 2.35/2.54 tff(7588,plain,
% 2.35/2.54 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7587, 7585])).
% 2.35/2.54 tff(7589,plain,
% 2.35/2.54 ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7590,plain,
% 2.35/2.54 ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7589, 7588])).
% 2.35/2.54 tff(7591,plain,
% 2.35/2.54 (hskp11 | hskp21 | c2_1(a598)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7590, 101, 7530, 7528, 4954])).
% 2.35/2.54 tff(7592,plain,
% 2.35/2.54 (hskp21),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7591, 7584, 1515])).
% 2.35/2.54 tff(7593,plain,
% 2.35/2.54 (~c3_1(a629)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[4699, 7592])).
% 2.35/2.54 tff(7594,plain,
% 2.35/2.54 (~c2_1(a629)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[4705, 7592])).
% 2.35/2.54 tff(7595,plain,
% 2.35/2.54 (c0_1(a629)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[4720, 7592])).
% 2.35/2.54 tff(7596,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7597,plain,
% 2.35/2.54 (((~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7598,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7597])).
% 2.35/2.54 tff(7599,plain,
% 2.35/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7598, 7596])).
% 2.35/2.54 tff(7600,plain,
% 2.35/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7601,plain,
% 2.35/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7600, 7599])).
% 2.35/2.54 tff(7602,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7601, 101, 7595, 7551, 7594, 7593, 7550, 7582, 7581, 7580, 1349, 7578])).
% 2.35/2.54 tff(7603,plain,(hskp11), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7604,plain,
% 2.35/2.54 (c3_1(a599)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[389, 7603])).
% 2.35/2.54 tff(7605,plain,
% 2.35/2.54 (~c1_1(a599)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[395, 7603])).
% 2.35/2.54 tff(7606,plain,
% 2.35/2.54 (c2_1(a599)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[403, 7603])).
% 2.35/2.54 tff(7607,plain,
% 2.35/2.54 (c0_1(a599)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[6782, 7606, 7151, 7519, 7605, 7604])).
% 2.35/2.54 tff(7608,plain,
% 2.35/2.54 (c2_1(a604)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2750, 101, 6727, 7551, 7606, 7550, 7605, 32, 7607])).
% 2.35/2.54 tff(7609,plain,
% 2.35/2.54 (c3_1(a604)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[1482, 7549])).
% 2.35/2.54 tff(7610,plain,
% 2.35/2.54 ((~hskp19) | (~c3_1(a607)) | (~c3_1(a604)) | c0_1(a604) | (~c0_1(a607)) | (~c2_1(a604))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[3619, 6726])).
% 2.35/2.54 tff(7611,plain,
% 2.35/2.54 (~hskp19),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7610, 7608, 7151, 7519, 7609, 7550])).
% 2.35/2.55 tff(7612,plain,
% 2.35/2.55 (hskp20 | hskp19 | (~c0_1(a607)) | (~c3_1(a607))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[3636, 101, 6726, 3630])).
% 2.35/2.55 tff(7613,plain,
% 2.35/2.55 (hskp20),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7612, 7611, 7151, 7519])).
% 2.35/2.55 tff(7614,plain,
% 2.35/2.55 (hskp16),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[5514, 7613, 7608, 7604, 7550, 7605, 7606, 7609])).
% 2.35/2.55 tff(7615,plain,
% 2.35/2.55 (~c2_1(a606)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[1015, 7614])).
% 2.35/2.55 tff(7616,plain,
% 2.35/2.55 (hskp19 | hskp13 | (~c2_1(a604))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[2518, 101, 7551, 7550, 2429])).
% 2.35/2.55 tff(7617,plain,
% 2.35/2.55 (hskp13),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7616, 7611, 7608])).
% 2.35/2.55 tff(7618,plain,
% 2.35/2.55 (c1_1(a606)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[992, 7614])).
% 2.35/2.55 tff(7619,plain,
% 2.35/2.55 (~c0_1(a606)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[2418, 7618, 7604, 7609, 7606, 7605, 7617, 7571, 7570, 7569, 7550, 7615, 7608])).
% 2.35/2.55 tff(7620,plain,
% 2.35/2.55 (hskp12),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7563, 7608])).
% 2.35/2.55 tff(7621,plain,
% 2.35/2.55 (~c3_1(a600)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[675, 7620])).
% 2.35/2.55 tff(7622,plain,
% 2.35/2.55 (~c3_1(a606)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[982, 7614])).
% 2.35/2.55 tff(7623,plain,
% 2.35/2.55 (c2_1(a600)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[683, 7620])).
% 2.35/2.55 tff(7624,plain,
% 2.35/2.55 (c0_1(a600)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[691, 7620])).
% 2.35/2.55 tff(7625,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[5587, 101, 7618, 7624, 7623, 7606, 7604, 7622, 7621, 7605, 240, 7619])).
% 2.35/2.55 % SZS output end Proof
% 2.35/2.55 % E exiting
%------------------------------------------------------------------------------