%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN469-1 : 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 05:39:14 AM UTC 2025
% Result : Unsatisfiable 0.91s 1.11s
% Output : Proof 1.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN469-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % 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 12:36:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.91/1.11 % SZS status Unsatisfiable
% 0.91/1.11 % SZS output start Proof
% 0.91/1.11 tff(c3_1_type, type, (
% 0.91/1.11 c3_1: $i > $o)).
% 0.91/1.11 tff(a451_type, type, (
% 0.91/1.11 a451: $i)).
% 0.91/1.11 tff(c1_1_type, type, (
% 0.91/1.11 c1_1: $i > $o)).
% 0.91/1.11 tff(a477_type, type, (
% 0.91/1.11 a477: $i)).
% 0.91/1.11 tff(c2_1_type, type, (
% 0.91/1.11 c2_1: $i > $o)).
% 0.91/1.11 tff(c0_1_type, type, (
% 0.91/1.11 c0_1: $i > $o)).
% 0.91/1.11 tff(ndr1_0_type, type, (
% 0.91/1.11 ndr1_0: $o)).
% 0.91/1.11 tff(a401_type, type, (
% 0.91/1.11 a401: $i)).
% 0.91/1.11 tff(hskp1_type, type, (
% 0.91/1.11 hskp1: $o)).
% 0.91/1.11 tff(a402_type, type, (
% 0.91/1.11 a402: $i)).
% 0.91/1.11 tff(hskp2_type, type, (
% 0.91/1.11 hskp2: $o)).
% 0.91/1.11 tff(a410_type, type, (
% 0.91/1.11 a410: $i)).
% 0.91/1.11 tff(hskp7_type, type, (
% 0.91/1.11 hskp7: $o)).
% 0.91/1.11 tff(a403_type, type, (
% 0.91/1.11 a403: $i)).
% 0.91/1.11 tff(hskp3_type, type, (
% 0.91/1.11 hskp3: $o)).
% 0.91/1.11 tff(a420_type, type, (
% 0.91/1.11 a420: $i)).
% 0.91/1.11 tff(a408_type, type, (
% 0.91/1.11 a408: $i)).
% 0.91/1.11 tff(hskp5_type, type, (
% 0.91/1.11 hskp5: $o)).
% 0.91/1.11 tff(hskp24_type, type, (
% 0.91/1.11 hskp24: $o)).
% 0.91/1.11 tff(a428_type, type, (
% 0.91/1.11 a428: $i)).
% 0.91/1.11 tff(a445_type, type, (
% 0.91/1.11 a445: $i)).
% 0.91/1.11 tff(hskp19_type, type, (
% 0.91/1.11 hskp19: $o)).
% 0.91/1.11 tff(a450_type, type, (
% 0.91/1.11 a450: $i)).
% 0.91/1.11 tff(hskp0_type, type, (
% 0.91/1.11 hskp0: $o)).
% 0.91/1.11 tff(hskp21_type, type, (
% 0.91/1.11 hskp21: $o)).
% 0.91/1.11 tff(a405_type, type, (
% 0.91/1.11 a405: $i)).
% 0.91/1.11 tff(hskp25_type, type, (
% 0.91/1.11 hskp25: $o)).
% 0.91/1.11 tff(a434_type, type, (
% 0.91/1.11 a434: $i)).
% 0.91/1.11 tff(a460_type, type, (
% 0.91/1.11 a460: $i)).
% 0.91/1.11 tff(hskp23_type, type, (
% 0.91/1.11 hskp23: $o)).
% 0.91/1.11 tff(hskp27_type, type, (
% 0.91/1.11 hskp27: $o)).
% 0.91/1.11 tff(a412_type, type, (
% 0.91/1.11 a412: $i)).
% 0.91/1.11 tff(a427_type, type, (
% 0.91/1.11 a427: $i)).
% 0.91/1.11 tff(hskp13_type, type, (
% 0.91/1.11 hskp13: $o)).
% 0.91/1.11 tff(hskp14_type, type, (
% 0.91/1.11 hskp14: $o)).
% 0.91/1.11 tff(a400_type, type, (
% 0.91/1.11 a400: $i)).
% 0.91/1.11 tff(hskp11_type, type, (
% 0.91/1.11 hskp11: $o)).
% 0.91/1.11 tff(a449_type, type, (
% 0.91/1.11 a449: $i)).
% 0.91/1.11 tff(hskp20_type, type, (
% 0.91/1.11 hskp20: $o)).
% 0.91/1.11 tff(a416_type, type, (
% 0.91/1.11 a416: $i)).
% 0.91/1.11 tff(a426_type, type, (
% 0.91/1.11 a426: $i)).
% 0.91/1.11 tff(hskp12_type, type, (
% 0.91/1.11 hskp12: $o)).
% 0.91/1.11 tff(hskp9_type, type, (
% 0.91/1.11 hskp9: $o)).
% 0.91/1.11 tff(hskp22_type, type, (
% 0.91/1.11 hskp22: $o)).
% 0.91/1.11 tff(hskp16_type, type, (
% 0.91/1.11 hskp16: $o)).
% 0.91/1.11 tff(a440_type, type, (
% 0.91/1.11 a440: $i)).
% 0.91/1.11 tff(hskp18_type, type, (
% 0.91/1.11 hskp18: $o)).
% 0.91/1.11 tff(a430_type, type, (
% 0.91/1.11 a430: $i)).
% 0.91/1.11 tff(hskp15_type, type, (
% 0.91/1.11 hskp15: $o)).
% 0.91/1.11 tff(a418_type, type, (
% 0.91/1.11 a418: $i)).
% 0.91/1.11 tff(hskp10_type, type, (
% 0.91/1.11 hskp10: $o)).
% 0.91/1.11 tff(hskp28_type, type, (
% 0.91/1.11 hskp28: $o)).
% 0.91/1.11 tff(a414_type, type, (
% 0.91/1.11 a414: $i)).
% 0.91/1.11 tff(a404_type, type, (
% 0.91/1.11 a404: $i)).
% 0.91/1.11 tff(hskp4_type, type, (
% 0.91/1.11 hskp4: $o)).
% 0.91/1.11 tff(a415_type, type, (
% 0.91/1.11 a415: $i)).
% 0.91/1.11 tff(hskp8_type, type, (
% 0.91/1.11 hskp8: $o)).
% 0.91/1.11 tff(1,assumption,(~c1_1(a477)), introduced(assumption)).
% 0.91/1.11 tff(2,plain,
% 0.91/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(3,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[2])).
% 0.91/1.11 tff(4,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(5,plain,
% 0.91/1.11 (^[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(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~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(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~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(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_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)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_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)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(6,plain,
% 0.91/1.11 (![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(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)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[5])).
% 0.91/1.11 tff(7,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(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.91/1.11 tff(8,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.91/1.11 tff(9,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.91/1.11 tff(10,plain,(
% 0.91/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.91/1.11 inference(skolemize,[status(sab)],[9])).
% 0.91/1.11 tff(11,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.91/1.11 tff(12,assumption,(~hskp1), introduced(assumption)).
% 0.91/1.11 tff(13,plain,
% 0.91/1.11 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(14,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[13])).
% 0.91/1.11 tff(15,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(16,plain,
% 0.91/1.11 (^[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)) | (~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(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_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(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_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(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_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(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(17,plain,
% 0.91/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[16])).
% 0.91/1.11 tff(18,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.91/1.11 tff(19,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.91/1.11 tff(20,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.91/1.11 tff(21,plain,(
% 0.91/1.11 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.91/1.11 inference(skolemize,[status(sab)],[20])).
% 0.91/1.11 tff(22,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.91/1.11 tff(23,assumption,(~hskp2), introduced(assumption)).
% 0.91/1.11 tff(24,plain,
% 0.91/1.11 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(25,plain,
% 0.91/1.11 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[24])).
% 0.91/1.11 tff(26,plain,
% 0.91/1.11 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(27,plain,
% 0.91/1.11 (^[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)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(28,plain,
% 0.91/1.11 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[27])).
% 0.91/1.11 tff(29,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.91/1.11 tff(30,plain,
% 0.91/1.11 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.91/1.11 tff(31,plain,
% 0.91/1.11 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.91/1.11 tff(32,plain,(
% 0.91/1.11 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.91/1.11 inference(skolemize,[status(sab)],[31])).
% 0.91/1.11 tff(33,plain,
% 0.91/1.11 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.91/1.11 tff(34,plain,
% 0.91/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(35,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[34])).
% 0.91/1.11 tff(36,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(37,plain,
% 0.91/1.11 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(38,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[37])).
% 0.91/1.11 tff(39,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.91/1.11 tff(40,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.91/1.11 tff(41,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.91/1.11 tff(42,plain,(
% 0.91/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.91/1.11 inference(skolemize,[status(sab)],[41])).
% 0.91/1.11 tff(43,plain,
% 0.91/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.91/1.11 tff(44,assumption,(~hskp3), introduced(assumption)).
% 0.91/1.11 tff(45,plain,
% 0.91/1.11 (^[U: $i] : refl((hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(46,plain,
% 0.91/1.11 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[45])).
% 0.91/1.11 tff(47,plain,
% 0.91/1.11 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(48,plain,
% 0.91/1.11 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp3) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp3) <=> (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(49,plain,
% 0.91/1.11 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp3) <=> ![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[48])).
% 0.91/1.11 tff(50,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.91/1.11 tff(51,plain,
% 0.91/1.11 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.91/1.11 tff(52,plain,
% 0.91/1.11 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.91/1.11 tff(53,plain,(
% 0.91/1.11 ![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.91/1.11 inference(skolemize,[status(sab)],[52])).
% 0.91/1.11 tff(54,plain,
% 0.91/1.11 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.91/1.11 tff(55,assumption,(~hskp24), introduced(assumption)).
% 0.91/1.11 tff(56,assumption,(~hskp21), introduced(assumption)).
% 0.91/1.11 tff(57,plain,
% 0.91/1.11 ((hskp25 | hskp24 | hskp21) <=> (hskp25 | hskp24 | hskp21)),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(58,plain,
% 0.91/1.11 (((hskp25 | hskp24) | hskp21) <=> (hskp25 | hskp24 | hskp21)),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(59,plain,
% 0.91/1.11 ((hskp25 | hskp24) <=> (hskp25 | hskp24)),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(60,plain,
% 0.91/1.11 (((hskp25 | hskp24) | hskp21) <=> ((hskp25 | hskp24) | hskp21)),
% 0.91/1.11 inference(monotonicity,[status(thm)],[59])).
% 0.91/1.11 tff(61,plain,
% 0.91/1.11 (((hskp25 | hskp24) | hskp21) <=> (hskp25 | hskp24 | hskp21)),
% 0.91/1.11 inference(transitivity,[status(thm)],[60, 58])).
% 0.91/1.11 tff(62,axiom,((hskp25 | hskp24) | hskp21), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 0.91/1.11 tff(63,plain,
% 0.91/1.11 (hskp25 | hskp24 | hskp21),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.91/1.11 tff(64,plain,
% 0.91/1.11 (hskp25 | hskp24 | hskp21),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[63, 57])).
% 0.91/1.11 tff(65,plain,
% 0.91/1.11 (hskp25 | hskp24 | hskp21),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.91/1.11 tff(66,plain,
% 0.91/1.11 (hskp25 | hskp24 | hskp21),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[65, 57])).
% 0.91/1.11 tff(67,plain,
% 0.91/1.11 (hskp25 | hskp24 | hskp21),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[66, 57])).
% 0.91/1.11 tff(68,plain,
% 0.91/1.11 (hskp25),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[67, 56, 55])).
% 0.91/1.11 tff(69,plain,
% 0.91/1.11 (((~hskp25) | c3_1(a405)) <=> ((~hskp25) | c3_1(a405))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(70,axiom,((~hskp25) | c3_1(a405)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.91/1.11 tff(71,plain,
% 0.91/1.11 ((~hskp25) | c3_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.91/1.11 tff(72,plain,
% 0.91/1.11 ((~hskp25) | c3_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[71, 69])).
% 0.91/1.11 tff(73,plain,
% 0.91/1.11 ((~hskp25) | c3_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.91/1.11 tff(74,plain,
% 0.91/1.11 ((~hskp25) | c3_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.91/1.11 tff(75,plain,
% 0.91/1.11 ((~hskp25) | c3_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[74, 69])).
% 0.91/1.11 tff(76,plain,
% 0.91/1.11 (c3_1(a405)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[75, 68])).
% 0.91/1.11 tff(77,plain,
% 0.91/1.11 (((~hskp25) | c1_1(a405)) <=> ((~hskp25) | c1_1(a405))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(78,axiom,((~hskp25) | c1_1(a405)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.91/1.11 tff(79,plain,
% 0.91/1.11 ((~hskp25) | c1_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.91/1.11 tff(80,plain,
% 0.91/1.11 ((~hskp25) | c1_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.91/1.11 tff(81,plain,
% 0.91/1.11 ((~hskp25) | c1_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.91/1.11 tff(82,plain,
% 0.91/1.11 ((~hskp25) | c1_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.91/1.11 tff(83,plain,
% 0.91/1.11 ((~hskp25) | c1_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[82, 77])).
% 0.91/1.11 tff(84,plain,
% 0.91/1.11 (c1_1(a405)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[83, 68])).
% 0.91/1.11 tff(85,plain,
% 0.91/1.11 (((~hskp25) | c0_1(a405)) <=> ((~hskp25) | c0_1(a405))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(86,axiom,((~hskp25) | c0_1(a405)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.91/1.11 tff(87,plain,
% 0.91/1.11 ((~hskp25) | c0_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.91/1.11 tff(88,plain,
% 0.91/1.11 ((~hskp25) | c0_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[87, 85])).
% 0.91/1.11 tff(89,plain,
% 0.91/1.11 ((~hskp25) | c0_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.91/1.11 tff(90,plain,
% 0.91/1.11 ((~hskp25) | c0_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.91/1.11 tff(91,plain,
% 0.91/1.11 ((~hskp25) | c0_1(a405)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.91/1.11 tff(92,plain,
% 0.91/1.11 (c0_1(a405)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[91, 68])).
% 0.91/1.11 tff(93,assumption,(~c1_1(a402)), introduced(assumption)).
% 0.91/1.11 tff(94,assumption,(c3_1(a405)), introduced(assumption)).
% 0.91/1.11 tff(95,assumption,(c1_1(a405)), introduced(assumption)).
% 0.91/1.11 tff(96,assumption,(c0_1(a405)), introduced(assumption)).
% 0.91/1.11 tff(97,plain,
% 0.91/1.11 (^[U: $i] : refl((hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(98,plain,
% 0.91/1.11 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[97])).
% 0.91/1.11 tff(99,plain,
% 0.91/1.11 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(100,plain,
% 0.91/1.11 (^[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)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.95/1.11 inference(bind,[status(th)],[])).
% 0.95/1.11 tff(101,plain,
% 0.95/1.11 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.95/1.11 inference(quant_intro,[status(thm)],[100])).
% 0.95/1.11 tff(102,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.95/1.11 tff(103,plain,
% 0.95/1.11 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.95/1.11 tff(104,plain,
% 0.95/1.11 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.95/1.11 tff(105,plain,(
% 0.95/1.11 ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.95/1.11 inference(skolemize,[status(sab)],[104])).
% 0.95/1.11 tff(106,plain,
% 0.95/1.11 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.95/1.11 tff(107,assumption,(~hskp19), introduced(assumption)).
% 0.95/1.11 tff(108,plain,
% 0.95/1.11 (^[U: $i] : refl((hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.95/1.11 inference(bind,[status(th)],[])).
% 0.95/1.11 tff(109,plain,
% 0.95/1.11 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.11 inference(quant_intro,[status(thm)],[108])).
% 0.95/1.11 tff(110,plain,
% 0.95/1.11 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(111,plain,
% 0.95/1.11 (^[U: $i] : 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)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp24) <=> ((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp24) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.95/1.11 inference(bind,[status(th)],[])).
% 0.95/1.11 tff(112,plain,
% 0.95/1.11 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp24) <=> ![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(quant_intro,[status(thm)],[111])).
% 0.95/1.12 tff(113,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.95/1.12 tff(114,plain,
% 0.95/1.12 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.95/1.12 tff(115,plain,
% 0.95/1.12 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.95/1.12 tff(116,plain,(
% 0.95/1.12 ![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(skolemize,[status(sab)],[115])).
% 0.95/1.12 tff(117,plain,
% 0.95/1.12 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.95/1.12 tff(118,assumption,(~ndr1_0), introduced(assumption)).
% 0.95/1.12 tff(119,plain,
% 0.95/1.12 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(120,plain,
% 0.95/1.12 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(121,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.95/1.12 tff(122,plain,
% 0.95/1.12 (ndr1_0 | (~hskp21)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.95/1.12 tff(123,plain,
% 0.95/1.12 (ndr1_0 | (~hskp21)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[122, 119])).
% 0.95/1.12 tff(124,plain,
% 0.95/1.12 (~hskp21),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[123, 118])).
% 0.95/1.12 tff(125,plain,
% 0.95/1.12 ((ndr1_0 | (~hskp25)) <=> (ndr1_0 | (~hskp25))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(126,plain,
% 0.95/1.12 (((~hskp25) | ndr1_0) <=> (ndr1_0 | (~hskp25))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(127,axiom,((~hskp25) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.95/1.12 tff(128,plain,
% 0.95/1.12 (ndr1_0 | (~hskp25)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.95/1.12 tff(129,plain,
% 0.95/1.12 (ndr1_0 | (~hskp25)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[128, 125])).
% 0.95/1.12 tff(130,plain,
% 0.95/1.12 (~hskp25),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[129, 118])).
% 0.95/1.12 tff(131,plain,
% 0.95/1.12 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(132,plain,
% 0.95/1.12 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(133,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.95/1.12 tff(134,plain,
% 0.95/1.12 (ndr1_0 | (~hskp24)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.95/1.12 tff(135,plain,
% 0.95/1.12 (ndr1_0 | (~hskp24)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[134, 131])).
% 0.95/1.12 tff(136,plain,
% 0.95/1.12 (~hskp24),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[135, 118])).
% 0.95/1.12 tff(137,plain,
% 0.95/1.12 ($false),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[67, 136, 130, 124])).
% 0.95/1.12 tff(138,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.95/1.12 tff(139,plain,
% 0.95/1.12 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(140,plain,
% 0.95/1.12 ((hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a405)) | (~c1_1(a405)) | (~c0_1(a405))) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(141,plain,
% 0.95/1.12 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a405)) | (~c1_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[140])).
% 0.95/1.12 tff(142,plain,
% 0.95/1.12 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a405)) | (~c1_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405)))),
% 0.95/1.12 inference(transitivity,[status(thm)],[141, 139])).
% 0.95/1.12 tff(143,plain,
% 0.95/1.12 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a405)) | (~c1_1(a405)) | (~c0_1(a405)))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(144,plain,
% 0.95/1.12 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.95/1.12 tff(145,plain,
% 0.95/1.12 (hskp19 | (~c2_1(a405))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[144, 138, 55, 96, 95, 117])).
% 0.95/1.12 tff(146,plain,
% 0.95/1.12 (~c2_1(a405)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[145, 107])).
% 0.95/1.12 tff(147,assumption,(hskp27), introduced(assumption)).
% 0.95/1.12 tff(148,plain,
% 0.95/1.12 (((~hskp27) | c2_1(a412)) <=> ((~hskp27) | c2_1(a412))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(149,axiom,((~hskp27) | c2_1(a412)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.95/1.12 tff(150,plain,
% 0.95/1.12 ((~hskp27) | c2_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.95/1.12 tff(151,plain,
% 0.95/1.12 ((~hskp27) | c2_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[150, 148])).
% 0.95/1.12 tff(152,plain,
% 0.95/1.12 ((~hskp27) | c2_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[151, 148])).
% 0.95/1.12 tff(153,plain,
% 0.95/1.12 ((~hskp27) | c2_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.95/1.12 tff(154,plain,
% 0.95/1.12 ((~hskp27) | c2_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[153, 148])).
% 0.95/1.12 tff(155,plain,
% 0.95/1.12 (c2_1(a412)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[154, 147])).
% 0.95/1.12 tff(156,plain,
% 0.95/1.12 (((~hskp27) | c1_1(a412)) <=> ((~hskp27) | c1_1(a412))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(157,axiom,((~hskp27) | c1_1(a412)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.95/1.12 tff(158,plain,
% 0.95/1.12 ((~hskp27) | c1_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.95/1.12 tff(159,plain,
% 0.95/1.12 ((~hskp27) | c1_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[158, 156])).
% 0.95/1.12 tff(160,plain,
% 0.95/1.12 ((~hskp27) | c1_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[159, 156])).
% 0.95/1.12 tff(161,plain,
% 0.95/1.12 ((~hskp27) | c1_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.95/1.12 tff(162,plain,
% 0.95/1.12 ((~hskp27) | c1_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[161, 156])).
% 0.95/1.12 tff(163,plain,
% 0.95/1.12 (c1_1(a412)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[162, 147])).
% 0.95/1.12 tff(164,plain,
% 0.95/1.12 (((~hskp27) | c0_1(a412)) <=> ((~hskp27) | c0_1(a412))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(165,axiom,((~hskp27) | c0_1(a412)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.95/1.12 tff(166,plain,
% 0.95/1.12 ((~hskp27) | c0_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.95/1.12 tff(167,plain,
% 0.95/1.12 ((~hskp27) | c0_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[166, 164])).
% 0.95/1.12 tff(168,plain,
% 0.95/1.12 ((~hskp27) | c0_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[167, 164])).
% 0.95/1.12 tff(169,plain,
% 0.95/1.12 ((~hskp27) | c0_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.95/1.12 tff(170,plain,
% 0.95/1.12 ((~hskp27) | c0_1(a412)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[169, 164])).
% 0.95/1.12 tff(171,plain,
% 0.95/1.12 (c0_1(a412)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[170, 147])).
% 0.95/1.12 tff(172,plain,
% 0.95/1.12 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(173,plain,
% 0.95/1.12 ((hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412))) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(174,plain,
% 0.95/1.12 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[173])).
% 0.95/1.12 tff(175,plain,
% 0.95/1.12 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 0.95/1.12 inference(transitivity,[status(thm)],[174, 172])).
% 0.95/1.12 tff(176,plain,
% 0.95/1.12 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(177,plain,
% 0.95/1.12 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.95/1.12 tff(178,plain,
% 0.95/1.12 ($false),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[177, 138, 55, 107, 171, 163, 155, 117])).
% 0.95/1.12 tff(179,plain,((~hskp27) | hskp24 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.95/1.12 tff(180,plain,
% 0.95/1.12 (~hskp27),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[179, 107, 55])).
% 0.95/1.12 tff(181,plain,
% 0.95/1.12 (^[U: $i] : refl((hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.95/1.12 inference(bind,[status(th)],[])).
% 0.95/1.12 tff(182,plain,
% 0.95/1.12 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(quant_intro,[status(thm)],[181])).
% 0.95/1.12 tff(183,plain,
% 0.95/1.12 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(184,plain,
% 0.95/1.12 (^[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)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp23) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp23) <=> (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.95/1.12 inference(bind,[status(th)],[])).
% 0.95/1.12 tff(185,plain,
% 0.95/1.12 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp23) <=> ![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(quant_intro,[status(thm)],[184])).
% 0.95/1.12 tff(186,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.95/1.12 tff(187,plain,
% 0.95/1.12 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.95/1.12 tff(188,plain,
% 0.95/1.12 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.95/1.12 tff(189,plain,(
% 0.95/1.12 ![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(skolemize,[status(sab)],[188])).
% 0.95/1.12 tff(190,plain,
% 0.95/1.12 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.95/1.12 tff(191,plain,
% 0.95/1.12 (((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405)))) <=> ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(192,plain,
% 0.95/1.12 ((hskp27 | hskp23 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c0_1(a405))) <=> (hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(193,plain,
% 0.95/1.12 (((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[192])).
% 0.95/1.12 tff(194,plain,
% 0.95/1.12 (((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405)))),
% 0.95/1.12 inference(transitivity,[status(thm)],[193, 191])).
% 0.95/1.12 tff(195,plain,
% 0.95/1.12 ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c0_1(a405)))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(196,plain,
% 0.95/1.12 ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.95/1.12 tff(197,plain,
% 0.95/1.12 (hskp27 | hskp23 | c2_1(a405)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[196, 138, 96, 95, 190])).
% 0.95/1.12 tff(198,plain,
% 0.95/1.12 (hskp23),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[197, 180, 146])).
% 0.95/1.12 tff(199,plain,
% 0.95/1.12 (((~hskp23) | (~c3_1(a460))) <=> ((~hskp23) | (~c3_1(a460)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(200,plain,
% 0.95/1.12 (((~c3_1(a460)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a460)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(201,axiom,((~c3_1(a460)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.95/1.12 tff(202,plain,
% 0.95/1.12 ((~hskp23) | (~c3_1(a460))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.95/1.12 tff(203,plain,
% 0.95/1.12 ((~hskp23) | (~c3_1(a460))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[202, 199])).
% 0.95/1.12 tff(204,plain,
% 0.95/1.12 (~c3_1(a460)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[203, 198])).
% 0.95/1.12 tff(205,plain,
% 0.95/1.12 (((~hskp23) | (~c2_1(a460))) <=> ((~hskp23) | (~c2_1(a460)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(206,plain,
% 0.95/1.12 (((~c2_1(a460)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a460)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(207,axiom,((~c2_1(a460)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.95/1.12 tff(208,plain,
% 0.95/1.12 ((~hskp23) | (~c2_1(a460))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.95/1.12 tff(209,plain,
% 0.95/1.12 ((~hskp23) | (~c2_1(a460))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[208, 205])).
% 0.95/1.12 tff(210,plain,
% 0.95/1.12 (~c2_1(a460)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[209, 198])).
% 0.95/1.12 tff(211,plain,
% 0.95/1.12 (((~hskp23) | c1_1(a460)) <=> ((~hskp23) | c1_1(a460))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(212,axiom,((~hskp23) | c1_1(a460)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.95/1.12 tff(213,plain,
% 0.95/1.12 ((~hskp23) | c1_1(a460)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.95/1.12 tff(214,plain,
% 0.95/1.12 ((~hskp23) | c1_1(a460)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[213, 211])).
% 0.95/1.12 tff(215,plain,
% 0.95/1.12 ((~hskp23) | c1_1(a460)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[214, 211])).
% 0.95/1.12 tff(216,plain,
% 0.95/1.12 ((~hskp23) | c1_1(a460)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.95/1.12 tff(217,plain,
% 0.95/1.12 ((~hskp23) | c1_1(a460)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[216, 211])).
% 0.95/1.12 tff(218,plain,
% 0.95/1.12 (c1_1(a460)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[217, 198])).
% 0.95/1.12 tff(219,plain,
% 0.95/1.12 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(220,plain,
% 0.95/1.12 ((hskp7 | hskp2 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460))) <=> (hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(221,plain,
% 0.95/1.12 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[220])).
% 0.95/1.12 tff(222,plain,
% 0.95/1.12 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460)))),
% 0.95/1.12 inference(transitivity,[status(thm)],[221, 219])).
% 0.95/1.12 tff(223,plain,
% 0.95/1.12 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(224,plain,
% 0.95/1.12 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.95/1.12 tff(225,plain,
% 0.95/1.12 (hskp7),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[224, 138, 23, 218, 210, 204, 106])).
% 0.95/1.12 tff(226,plain,
% 0.95/1.12 (((~hskp7) | (~c3_1(a410))) <=> ((~hskp7) | (~c3_1(a410)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(227,plain,
% 0.95/1.12 (((~c3_1(a410)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a410)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(228,axiom,((~c3_1(a410)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.95/1.12 tff(229,plain,
% 0.95/1.12 ((~hskp7) | (~c3_1(a410))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.95/1.12 tff(230,plain,
% 0.95/1.12 ((~hskp7) | (~c3_1(a410))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[229, 226])).
% 0.95/1.12 tff(231,plain,
% 0.95/1.12 (~c3_1(a410)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[230, 225])).
% 0.95/1.12 tff(232,plain,
% 0.95/1.12 (((~hskp7) | (~c1_1(a410))) <=> ((~hskp7) | (~c1_1(a410)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(233,plain,
% 0.95/1.12 (((~c1_1(a410)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a410)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(234,axiom,((~c1_1(a410)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.95/1.12 tff(235,plain,
% 0.95/1.12 ((~hskp7) | (~c1_1(a410))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.95/1.12 tff(236,plain,
% 0.95/1.12 ((~hskp7) | (~c1_1(a410))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[235, 232])).
% 0.95/1.12 tff(237,plain,
% 0.95/1.12 (~c1_1(a410)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[236, 225])).
% 0.95/1.12 tff(238,plain,
% 0.95/1.12 (^[U: $i] : refl((hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.95/1.12 inference(bind,[status(th)],[])).
% 0.95/1.12 tff(239,plain,
% 0.95/1.12 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.95/1.12 inference(quant_intro,[status(thm)],[238])).
% 0.95/1.12 tff(240,plain,
% 0.95/1.12 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(241,plain,
% 0.95/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) | hskp13) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp13))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) | hskp13) <=> (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.95/1.12 inference(bind,[status(th)],[])).
% 0.95/1.12 tff(242,plain,
% 0.95/1.12 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) | hskp13) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.95/1.12 inference(quant_intro,[status(thm)],[241])).
% 0.95/1.12 tff(243,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.95/1.12 tff(244,plain,
% 0.95/1.12 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.95/1.12 tff(245,plain,
% 0.95/1.12 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.95/1.12 tff(246,plain,(
% 0.95/1.12 ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.95/1.12 inference(skolemize,[status(sab)],[245])).
% 0.95/1.12 tff(247,plain,
% 0.95/1.12 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[246, 239])).
% 0.95/1.12 tff(248,plain,
% 0.95/1.12 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(249,plain,
% 0.95/1.12 ((hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405))) <=> (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(250,plain,
% 0.95/1.12 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[249])).
% 0.95/1.12 tff(251,plain,
% 0.95/1.12 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.95/1.12 inference(transitivity,[status(thm)],[250, 248])).
% 0.95/1.12 tff(252,plain,
% 0.95/1.12 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(253,plain,
% 0.95/1.12 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.95/1.12 tff(254,plain,
% 0.95/1.12 (hskp13 | hskp2 | c2_1(a405)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[253, 138, 95, 94, 247])).
% 0.95/1.12 tff(255,plain,
% 0.95/1.12 (hskp13),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[254, 146, 23])).
% 0.95/1.12 tff(256,plain,
% 0.95/1.12 (((~hskp13) | (~c0_1(a427))) <=> ((~hskp13) | (~c0_1(a427)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(257,plain,
% 0.95/1.12 (((~c0_1(a427)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a427)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(258,axiom,((~c0_1(a427)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.95/1.12 tff(259,plain,
% 0.95/1.12 ((~hskp13) | (~c0_1(a427))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.95/1.12 tff(260,plain,
% 0.95/1.12 ((~hskp13) | (~c0_1(a427))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[259, 256])).
% 0.95/1.12 tff(261,plain,
% 0.95/1.12 (~c0_1(a427)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[260, 255])).
% 0.95/1.12 tff(262,plain,
% 0.95/1.12 (((~hskp7) | c0_1(a410)) <=> ((~hskp7) | c0_1(a410))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(263,axiom,((~hskp7) | c0_1(a410)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.95/1.12 tff(264,plain,
% 0.95/1.12 ((~hskp7) | c0_1(a410)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.95/1.12 tff(265,plain,
% 0.95/1.12 ((~hskp7) | c0_1(a410)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[264, 262])).
% 0.95/1.12 tff(266,plain,
% 0.95/1.12 ((~hskp7) | c0_1(a410)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[265, 262])).
% 0.95/1.12 tff(267,plain,
% 0.95/1.12 ((~hskp7) | c0_1(a410)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.95/1.12 tff(268,plain,
% 0.95/1.12 ((~hskp7) | c0_1(a410)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[267, 262])).
% 0.95/1.12 tff(269,plain,
% 0.95/1.12 (c0_1(a410)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[268, 225])).
% 0.95/1.12 tff(270,plain,
% 0.95/1.12 (((~hskp13) | c2_1(a427)) <=> ((~hskp13) | c2_1(a427))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(271,axiom,((~hskp13) | c2_1(a427)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.95/1.12 tff(272,plain,
% 0.95/1.12 ((~hskp13) | c2_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.95/1.12 tff(273,plain,
% 0.95/1.12 ((~hskp13) | c2_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[272, 270])).
% 0.95/1.12 tff(274,plain,
% 0.95/1.12 ((~hskp13) | c2_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[273, 270])).
% 0.95/1.12 tff(275,plain,
% 0.95/1.12 ((~hskp13) | c2_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.95/1.12 tff(276,plain,
% 0.95/1.12 ((~hskp13) | c2_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[275, 270])).
% 0.95/1.12 tff(277,plain,
% 0.95/1.12 (c2_1(a427)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[276, 255])).
% 0.95/1.12 tff(278,plain,
% 0.95/1.12 (((~hskp13) | c1_1(a427)) <=> ((~hskp13) | c1_1(a427))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(279,axiom,((~hskp13) | c1_1(a427)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.95/1.12 tff(280,plain,
% 0.95/1.12 ((~hskp13) | c1_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.95/1.12 tff(281,plain,
% 0.95/1.12 ((~hskp13) | c1_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[280, 278])).
% 0.95/1.12 tff(282,plain,
% 0.95/1.12 ((~hskp13) | c1_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[281, 278])).
% 0.95/1.12 tff(283,plain,
% 0.95/1.12 ((~hskp13) | c1_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.95/1.12 tff(284,plain,
% 0.95/1.12 ((~hskp13) | c1_1(a427)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[283, 278])).
% 0.95/1.12 tff(285,plain,
% 0.95/1.12 (c1_1(a427)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[284, 255])).
% 0.95/1.12 tff(286,plain,
% 0.95/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(287,plain,
% 0.95/1.12 ((hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(288,plain,
% 0.95/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[287])).
% 0.95/1.12 tff(289,plain,
% 0.95/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 0.95/1.12 inference(transitivity,[status(thm)],[288, 286])).
% 0.95/1.12 tff(290,plain,
% 0.95/1.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(291,plain,
% 0.95/1.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.95/1.12 tff(292,plain,
% 0.95/1.12 ($false),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[291, 138, 12, 285, 277, 269, 261, 237, 231, 22])).
% 0.95/1.12 tff(293,plain,(hskp19 | hskp1 | hskp2 | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.95/1.12 tff(294,plain,
% 0.95/1.12 (hskp19),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[293, 23, 12, 96, 95, 94, 55])).
% 0.95/1.12 tff(295,plain,
% 0.95/1.12 (((~hskp19) | (~c0_1(a445))) <=> ((~hskp19) | (~c0_1(a445)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(296,plain,
% 0.95/1.12 (((~c0_1(a445)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a445)))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(297,axiom,((~c0_1(a445)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.95/1.12 tff(298,plain,
% 0.95/1.12 ((~hskp19) | (~c0_1(a445))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.95/1.12 tff(299,plain,
% 0.95/1.12 ((~hskp19) | (~c0_1(a445))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[298, 295])).
% 0.95/1.12 tff(300,plain,
% 0.95/1.12 (~c0_1(a445)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[299, 294])).
% 0.95/1.12 tff(301,assumption,(~c3_1(a403)), introduced(assumption)).
% 0.95/1.12 tff(302,assumption,(~c2_1(a403)), introduced(assumption)).
% 0.95/1.12 tff(303,assumption,(~c0_1(a403)), introduced(assumption)).
% 0.95/1.12 tff(304,plain,
% 0.95/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 0.95/1.12 inference(bind,[status(th)],[])).
% 0.95/1.12 tff(305,plain,
% 0.95/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.95/1.12 inference(quant_intro,[status(thm)],[304])).
% 0.95/1.12 tff(306,plain,
% 0.95/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(307,plain,
% 0.95/1.13 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W) | c2_1(W))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W) | c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 0.95/1.13 inference(bind,[status(th)],[])).
% 0.95/1.13 tff(308,plain,
% 0.95/1.13 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.95/1.13 inference(quant_intro,[status(thm)],[307])).
% 0.95/1.13 tff(309,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.95/1.13 tff(310,plain,
% 0.95/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.95/1.13 tff(311,plain,
% 0.95/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.95/1.13 tff(312,plain,(
% 0.95/1.13 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.95/1.13 inference(skolemize,[status(sab)],[311])).
% 0.95/1.13 tff(313,plain,
% 0.95/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[312, 305])).
% 0.95/1.13 tff(314,plain,
% 0.95/1.13 (^[U: $i] : refl((hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.95/1.13 inference(bind,[status(th)],[])).
% 0.95/1.13 tff(315,plain,
% 0.95/1.13 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.95/1.13 inference(quant_intro,[status(thm)],[314])).
% 0.95/1.13 tff(316,plain,
% 0.95/1.13 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(317,plain,
% 0.95/1.13 (^[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)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp0))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp0) <=> (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.95/1.13 inference(bind,[status(th)],[])).
% 0.95/1.13 tff(318,plain,
% 0.95/1.13 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.95/1.13 inference(quant_intro,[status(thm)],[317])).
% 0.95/1.13 tff(319,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.95/1.13 tff(320,plain,
% 0.95/1.13 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.95/1.13 tff(321,plain,
% 0.95/1.13 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[320, 316])).
% 0.95/1.13 tff(322,plain,(
% 0.95/1.13 ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.95/1.13 inference(skolemize,[status(sab)],[321])).
% 0.95/1.13 tff(323,plain,
% 0.95/1.13 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[322, 315])).
% 0.95/1.13 tff(324,plain,
% 0.95/1.13 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(325,plain,
% 0.95/1.13 ((hskp27 | hskp0 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | c3_1(a403)) <=> (hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(326,plain,
% 0.95/1.13 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | c3_1(a403))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0)))),
% 0.95/1.13 inference(monotonicity,[status(thm)],[325])).
% 0.95/1.13 tff(327,plain,
% 0.95/1.13 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | c3_1(a403))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 0.95/1.13 inference(transitivity,[status(thm)],[326, 324])).
% 0.95/1.13 tff(328,plain,
% 0.95/1.13 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | c3_1(a403))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(329,plain,
% 0.95/1.13 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.95/1.13 tff(330,plain,
% 0.95/1.13 (hskp27 | hskp0 | c0_1(a403) | c2_1(a403)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[329, 138, 301, 323])).
% 0.95/1.13 tff(331,plain,
% 0.95/1.13 (hskp0),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[330, 180, 303, 302])).
% 0.95/1.13 tff(332,plain,
% 0.95/1.13 (((~hskp0) | c2_1(a400)) <=> ((~hskp0) | c2_1(a400))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(333,axiom,((~hskp0) | c2_1(a400)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.95/1.13 tff(334,plain,
% 0.95/1.13 ((~hskp0) | c2_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.95/1.13 tff(335,plain,
% 0.95/1.13 ((~hskp0) | c2_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[334, 332])).
% 0.95/1.13 tff(336,plain,
% 0.95/1.13 ((~hskp0) | c2_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[335, 332])).
% 0.95/1.13 tff(337,plain,
% 0.95/1.13 ((~hskp0) | c2_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[336, 332])).
% 0.95/1.13 tff(338,plain,
% 0.95/1.13 ((~hskp0) | c2_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[337, 332])).
% 0.95/1.13 tff(339,plain,
% 0.95/1.13 (c2_1(a400)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[338, 331])).
% 0.95/1.13 tff(340,plain,
% 0.95/1.13 (((~hskp0) | c1_1(a400)) <=> ((~hskp0) | c1_1(a400))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(341,axiom,((~hskp0) | c1_1(a400)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.95/1.13 tff(342,plain,
% 0.95/1.13 ((~hskp0) | c1_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.95/1.13 tff(343,plain,
% 0.95/1.13 ((~hskp0) | c1_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[342, 340])).
% 0.95/1.13 tff(344,plain,
% 0.95/1.13 ((~hskp0) | c1_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[343, 340])).
% 0.95/1.13 tff(345,plain,
% 0.95/1.13 ((~hskp0) | c1_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[344, 340])).
% 0.95/1.13 tff(346,plain,
% 0.95/1.13 ((~hskp0) | c1_1(a400)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[345, 340])).
% 0.95/1.13 tff(347,plain,
% 0.95/1.13 (c1_1(a400)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[346, 331])).
% 0.95/1.13 tff(348,plain,
% 0.95/1.13 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(349,plain,
% 0.95/1.13 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(350,plain,
% 0.95/1.13 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.95/1.13 tff(351,plain,
% 0.95/1.13 (~c0_1(a400)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[350, 138, 55, 107, 347, 339, 117])).
% 0.95/1.13 tff(352,plain,
% 0.95/1.13 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.95/1.13 inference(bind,[status(th)],[])).
% 0.95/1.13 tff(353,plain,
% 0.95/1.13 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.95/1.13 inference(quant_intro,[status(thm)],[352])).
% 0.95/1.13 tff(354,plain,
% 0.95/1.13 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(355,plain,
% 0.95/1.13 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.95/1.13 inference(bind,[status(th)],[])).
% 0.95/1.13 tff(356,plain,
% 0.95/1.13 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.95/1.13 inference(quant_intro,[status(thm)],[355])).
% 0.95/1.13 tff(357,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.95/1.13 tff(358,plain,
% 0.95/1.13 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.95/1.13 tff(359,plain,
% 0.95/1.13 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[358, 354])).
% 0.95/1.13 tff(360,plain,(
% 0.95/1.13 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.95/1.13 inference(skolemize,[status(sab)],[359])).
% 0.95/1.13 tff(361,plain,
% 0.95/1.13 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[360, 353])).
% 0.95/1.13 tff(362,plain,
% 0.95/1.13 (((~hskp0) | (~c3_1(a400))) <=> ((~hskp0) | (~c3_1(a400)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(363,plain,
% 0.95/1.13 (((~c3_1(a400)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a400)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(364,axiom,((~c3_1(a400)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.95/1.13 tff(365,plain,
% 0.95/1.13 ((~hskp0) | (~c3_1(a400))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.95/1.13 tff(366,plain,
% 0.95/1.13 ((~hskp0) | (~c3_1(a400))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[365, 362])).
% 0.95/1.13 tff(367,plain,
% 0.95/1.13 (~c3_1(a400)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[366, 331])).
% 0.95/1.13 tff(368,assumption,(~hskp14), introduced(assumption)).
% 0.95/1.13 tff(369,plain,
% 0.95/1.13 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(370,plain,
% 0.95/1.13 ((hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400))) <=> (hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(371,plain,
% 0.95/1.13 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405))))),
% 0.95/1.13 inference(monotonicity,[status(thm)],[370])).
% 0.95/1.13 tff(372,plain,
% 0.95/1.13 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405)))),
% 0.95/1.13 inference(transitivity,[status(thm)],[371, 369])).
% 0.95/1.13 tff(373,plain,
% 0.95/1.13 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(374,plain,
% 0.95/1.13 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.95/1.13 tff(375,plain,
% 0.95/1.13 ($false),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[374, 138, 368, 95, 94, 339, 367, 361, 146, 351])).
% 0.95/1.13 tff(376,plain,(hskp19 | hskp14 | (~c1_1(a405)) | (~c3_1(a405)) | hskp24 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.13 tff(377,plain,
% 0.95/1.13 (hskp14),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[376, 107, 95, 94, 55, 303, 302, 301, 96])).
% 0.95/1.13 tff(378,plain,
% 0.95/1.13 (((~hskp14) | (~c1_1(a428))) <=> ((~hskp14) | (~c1_1(a428)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(379,plain,
% 0.95/1.13 (((~c1_1(a428)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a428)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(380,axiom,((~c1_1(a428)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.95/1.13 tff(381,plain,
% 0.95/1.13 ((~hskp14) | (~c1_1(a428))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.95/1.13 tff(382,plain,
% 0.95/1.13 ((~hskp14) | (~c1_1(a428))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[381, 378])).
% 0.95/1.13 tff(383,plain,
% 0.95/1.13 (~c1_1(a428)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[382, 377])).
% 0.95/1.13 tff(384,plain,
% 0.95/1.13 (((~hskp14) | (~c0_1(a428))) <=> ((~hskp14) | (~c0_1(a428)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(385,plain,
% 0.95/1.13 (((~c0_1(a428)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a428)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(386,axiom,((~c0_1(a428)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.95/1.13 tff(387,plain,
% 0.95/1.13 ((~hskp14) | (~c0_1(a428))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.95/1.13 tff(388,plain,
% 0.95/1.13 ((~hskp14) | (~c0_1(a428))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[387, 384])).
% 0.95/1.13 tff(389,plain,
% 0.95/1.13 (~c0_1(a428)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[388, 377])).
% 0.95/1.13 tff(390,plain,
% 0.95/1.13 (((~hskp14) | c2_1(a428)) <=> ((~hskp14) | c2_1(a428))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(391,axiom,((~hskp14) | c2_1(a428)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.95/1.13 tff(392,plain,
% 0.95/1.13 ((~hskp14) | c2_1(a428)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.95/1.13 tff(393,plain,
% 0.95/1.13 ((~hskp14) | c2_1(a428)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[392, 390])).
% 0.95/1.13 tff(394,plain,
% 0.95/1.13 ((~hskp14) | c2_1(a428)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[393, 390])).
% 0.95/1.13 tff(395,plain,
% 0.95/1.13 ((~hskp14) | c2_1(a428)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[394, 390])).
% 0.95/1.13 tff(396,plain,
% 0.95/1.13 ((~hskp14) | c2_1(a428)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[395, 390])).
% 0.95/1.13 tff(397,plain,
% 0.95/1.13 (c2_1(a428)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[396, 377])).
% 0.95/1.13 tff(398,plain,
% 0.95/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(399,plain,
% 0.95/1.13 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a403) | c0_1(a403) | c2_1(a403)) <=> (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(400,plain,
% 0.95/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460))))),
% 0.95/1.13 inference(monotonicity,[status(thm)],[399])).
% 0.95/1.13 tff(401,plain,
% 0.95/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460)))),
% 0.95/1.13 inference(transitivity,[status(thm)],[400, 398])).
% 0.95/1.13 tff(402,plain,
% 0.95/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a403) | c0_1(a403) | c2_1(a403))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(403,plain,
% 0.95/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.95/1.13 tff(404,plain,
% 0.95/1.13 ($false),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[403, 138, 218, 397, 210, 204, 389, 383, 303, 302, 301, 313])).
% 0.95/1.13 tff(405,plain,(hskp19 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.95/1.13 tff(406,plain,
% 0.95/1.13 (hskp19),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[405, 303, 302, 301, 96, 95, 94, 55])).
% 0.95/1.13 tff(407,plain,
% 0.95/1.13 (((~hskp19) | c1_1(a445)) <=> ((~hskp19) | c1_1(a445))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(408,axiom,((~hskp19) | c1_1(a445)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.95/1.13 tff(409,plain,
% 0.95/1.13 ((~hskp19) | c1_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.95/1.13 tff(410,plain,
% 0.95/1.13 ((~hskp19) | c1_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[409, 407])).
% 0.95/1.13 tff(411,plain,
% 0.95/1.13 ((~hskp19) | c1_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[410, 407])).
% 0.95/1.13 tff(412,plain,
% 0.95/1.13 ((~hskp19) | c1_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[411, 407])).
% 0.95/1.13 tff(413,plain,
% 0.95/1.13 ((~hskp19) | c1_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[412, 407])).
% 0.95/1.13 tff(414,plain,
% 0.95/1.13 (c1_1(a445)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[413, 406])).
% 0.95/1.13 tff(415,plain,
% 0.95/1.13 (~c0_1(a445)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[299, 406])).
% 0.95/1.13 tff(416,plain,
% 0.95/1.13 (((~hskp19) | c3_1(a445)) <=> ((~hskp19) | c3_1(a445))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(417,axiom,((~hskp19) | c3_1(a445)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.95/1.13 tff(418,plain,
% 0.95/1.13 ((~hskp19) | c3_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.95/1.13 tff(419,plain,
% 0.95/1.13 ((~hskp19) | c3_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[418, 416])).
% 0.95/1.13 tff(420,plain,
% 0.95/1.13 ((~hskp19) | c3_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[419, 416])).
% 0.95/1.13 tff(421,plain,
% 0.95/1.13 ((~hskp19) | c3_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[420, 416])).
% 0.95/1.13 tff(422,plain,
% 0.95/1.13 ((~hskp19) | c3_1(a445)),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[421, 416])).
% 0.95/1.13 tff(423,plain,
% 0.95/1.13 (c3_1(a445)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[422, 406])).
% 0.95/1.13 tff(424,assumption,(~c0_1(a445)), introduced(assumption)).
% 0.95/1.13 tff(425,assumption,(c3_1(a445)), introduced(assumption)).
% 0.95/1.13 tff(426,plain,
% 0.95/1.13 (^[U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.95/1.13 inference(bind,[status(th)],[])).
% 0.95/1.13 tff(427,plain,
% 0.95/1.13 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.13 inference(quant_intro,[status(thm)],[426])).
% 0.95/1.13 tff(428,plain,
% 0.95/1.13 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(429,plain,
% 0.95/1.13 (^[U: $i] : 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)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.95/1.13 inference(bind,[status(th)],[])).
% 0.95/1.13 tff(430,plain,
% 0.95/1.13 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.13 inference(quant_intro,[status(thm)],[429])).
% 0.95/1.13 tff(431,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.95/1.13 tff(432,plain,
% 0.95/1.13 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.95/1.13 tff(433,plain,
% 0.95/1.13 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[432, 428])).
% 0.95/1.13 tff(434,plain,(
% 0.95/1.13 ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.13 inference(skolemize,[status(sab)],[433])).
% 0.95/1.13 tff(435,plain,
% 0.95/1.13 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[434, 427])).
% 0.95/1.13 tff(436,assumption,(c1_1(a445)), introduced(assumption)).
% 0.95/1.13 tff(437,assumption,(~hskp11), introduced(assumption)).
% 0.95/1.13 tff(438,plain,
% 0.95/1.13 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))))),
% 0.95/1.13 inference(bind,[status(th)],[])).
% 0.95/1.13 tff(439,plain,
% 0.95/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.95/1.13 inference(quant_intro,[status(thm)],[438])).
% 0.95/1.13 tff(440,plain,
% 0.95/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(441,plain,
% 0.95/1.13 (^[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))) | (~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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))))),
% 0.95/1.14 inference(bind,[status(th)],[])).
% 0.95/1.14 tff(442,plain,
% 0.95/1.14 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.95/1.14 inference(quant_intro,[status(thm)],[441])).
% 0.95/1.14 tff(443,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.95/1.14 tff(444,plain,
% 0.95/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.95/1.14 tff(445,plain,
% 0.95/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[444, 440])).
% 0.95/1.14 tff(446,plain,(
% 0.95/1.14 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.95/1.14 inference(skolemize,[status(sab)],[445])).
% 0.95/1.14 tff(447,plain,
% 0.95/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[446, 439])).
% 0.95/1.14 tff(448,assumption,(~c1_1(a403)), introduced(assumption)).
% 0.95/1.14 tff(449,plain,
% 0.95/1.14 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(450,plain,
% 0.95/1.14 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a403) | c1_1(a403) | c0_1(a403)) <=> (hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(451,plain,
% 0.95/1.14 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403)))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[450])).
% 0.95/1.14 tff(452,plain,
% 0.95/1.14 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403))),
% 0.95/1.14 inference(transitivity,[status(thm)],[451, 449])).
% 0.95/1.14 tff(453,plain,
% 0.95/1.14 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a403) | c1_1(a403) | c0_1(a403))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(454,plain,
% 0.95/1.14 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.95/1.14 tff(455,plain,
% 0.95/1.14 (hskp2 | hskp1 | c0_1(a403) | c1_1(a403)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[454, 138, 302, 33])).
% 0.95/1.14 tff(456,plain,
% 0.95/1.14 (hskp2),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[455, 12, 303, 448])).
% 0.95/1.14 tff(457,plain,
% 0.95/1.14 (((~hskp2) | (~c2_1(a402))) <=> ((~hskp2) | (~c2_1(a402)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(458,plain,
% 0.95/1.14 (((~c2_1(a402)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a402)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(459,axiom,((~c2_1(a402)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.95/1.14 tff(460,plain,
% 0.95/1.14 ((~hskp2) | (~c2_1(a402))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.95/1.14 tff(461,plain,
% 0.95/1.14 ((~hskp2) | (~c2_1(a402))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[460, 457])).
% 0.95/1.14 tff(462,plain,
% 0.95/1.14 (~c2_1(a402)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[461, 456])).
% 0.95/1.14 tff(463,plain,
% 0.95/1.14 (((~hskp2) | c0_1(a402)) <=> ((~hskp2) | c0_1(a402))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(464,axiom,((~hskp2) | c0_1(a402)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.95/1.14 tff(465,plain,
% 0.95/1.14 ((~hskp2) | c0_1(a402)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.95/1.14 tff(466,plain,
% 0.95/1.14 ((~hskp2) | c0_1(a402)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[465, 463])).
% 0.95/1.14 tff(467,plain,
% 0.95/1.14 ((~hskp2) | c0_1(a402)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[466, 463])).
% 0.95/1.14 tff(468,plain,
% 0.95/1.14 ((~hskp2) | c0_1(a402)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[467, 463])).
% 0.95/1.14 tff(469,plain,
% 0.95/1.14 ((~hskp2) | c0_1(a402)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[468, 463])).
% 0.95/1.14 tff(470,plain,
% 0.95/1.14 (c0_1(a402)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[469, 456])).
% 0.95/1.14 tff(471,plain,
% 0.95/1.14 (^[V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.95/1.14 inference(bind,[status(th)],[])).
% 0.95/1.14 tff(472,plain,
% 0.95/1.14 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.95/1.14 inference(quant_intro,[status(thm)],[471])).
% 0.95/1.14 tff(473,plain,
% 0.95/1.14 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(474,plain,
% 0.95/1.14 (^[V: $i, U: $i] : 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)) | (~c3_1(V)) | (~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)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.95/1.14 inference(bind,[status(th)],[])).
% 0.95/1.14 tff(475,plain,
% 0.95/1.14 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.95/1.14 inference(quant_intro,[status(thm)],[474])).
% 0.95/1.14 tff(476,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.95/1.14 tff(477,plain,
% 0.95/1.14 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.95/1.14 tff(478,plain,
% 0.95/1.14 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.95/1.14 tff(479,plain,(
% 0.95/1.14 ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.95/1.14 inference(skolemize,[status(sab)],[478])).
% 0.95/1.14 tff(480,plain,
% 0.95/1.14 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[479, 472])).
% 0.95/1.14 tff(481,plain,
% 0.95/1.14 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(482,plain,
% 0.95/1.14 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445))) <=> (c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(483,plain,
% 0.95/1.14 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[482])).
% 0.95/1.14 tff(484,plain,
% 0.95/1.14 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.95/1.14 inference(transitivity,[status(thm)],[483, 481])).
% 0.95/1.14 tff(485,plain,
% 0.95/1.14 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(486,plain,
% 0.95/1.14 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.95/1.14 tff(487,plain,
% 0.95/1.14 ((~c3_1(a402)) | (~c0_1(a402))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[486, 138, 436, 425, 424, 93, 480])).
% 0.95/1.14 tff(488,plain,
% 0.95/1.14 (~c3_1(a402)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[487, 470])).
% 0.95/1.14 tff(489,plain,
% 0.95/1.14 (^[U: $i] : refl((hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.95/1.14 inference(bind,[status(th)],[])).
% 0.95/1.14 tff(490,plain,
% 0.95/1.14 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/1.14 inference(quant_intro,[status(thm)],[489])).
% 0.95/1.14 tff(491,plain,
% 0.95/1.14 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(492,plain,
% 0.95/1.14 (^[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)) | 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) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp1) <=> ((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp1))), rewrite(((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp1) <=> (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp1) <=> (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.95/1.14 inference(bind,[status(th)],[])).
% 0.95/1.14 tff(493,plain,
% 0.95/1.14 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp1) <=> ![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/1.14 inference(quant_intro,[status(thm)],[492])).
% 0.95/1.14 tff(494,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.95/1.14 tff(495,plain,
% 0.95/1.14 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.95/1.14 tff(496,plain,
% 0.95/1.14 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[495, 491])).
% 0.95/1.14 tff(497,plain,(
% 0.95/1.14 ![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/1.14 inference(skolemize,[status(sab)],[496])).
% 0.95/1.14 tff(498,plain,
% 0.95/1.14 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[497, 490])).
% 0.95/1.14 tff(499,plain,
% 0.95/1.14 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(500,plain,
% 0.95/1.14 ((hskp12 | hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(501,plain,
% 0.95/1.14 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[500])).
% 0.95/1.14 tff(502,plain,
% 0.95/1.14 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)))),
% 0.95/1.14 inference(transitivity,[status(thm)],[501, 499])).
% 0.95/1.14 tff(503,plain,
% 0.95/1.14 ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(504,plain,
% 0.95/1.14 ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.95/1.14 tff(505,plain,
% 0.95/1.14 (hskp12 | hskp1 | c3_1(a402) | (~c0_1(a402))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[504, 138, 93, 498])).
% 0.95/1.14 tff(506,plain,
% 0.95/1.14 (hskp12),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[505, 488, 12, 470])).
% 0.95/1.14 tff(507,plain,
% 0.95/1.14 (((~hskp12) | (~c2_1(a426))) <=> ((~hskp12) | (~c2_1(a426)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(508,plain,
% 0.95/1.14 (((~c2_1(a426)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a426)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(509,axiom,((~c2_1(a426)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.95/1.14 tff(510,plain,
% 0.95/1.14 ((~hskp12) | (~c2_1(a426))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.95/1.14 tff(511,plain,
% 0.95/1.14 ((~hskp12) | (~c2_1(a426))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[510, 507])).
% 0.95/1.14 tff(512,plain,
% 0.95/1.14 (~c2_1(a426)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[511, 506])).
% 0.95/1.14 tff(513,plain,
% 0.95/1.14 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(514,plain,
% 0.95/1.14 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445))) <=> (hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(515,plain,
% 0.95/1.14 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[514])).
% 0.95/1.14 tff(516,plain,
% 0.95/1.14 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 0.95/1.14 inference(transitivity,[status(thm)],[515, 513])).
% 0.95/1.14 tff(517,plain,
% 0.95/1.14 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(518,plain,
% 0.95/1.14 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[517, 516])).
% 0.95/1.14 tff(519,plain,
% 0.95/1.14 (hskp1 | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[518, 138, 436, 424, 93, 22])).
% 0.95/1.14 tff(520,plain,
% 0.95/1.14 (~c2_1(a445)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[519, 488, 12, 470])).
% 0.95/1.14 tff(521,plain,
% 0.95/1.14 (^[U: $i] : refl((hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.95/1.14 inference(bind,[status(th)],[])).
% 0.95/1.14 tff(522,plain,
% 0.95/1.14 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.95/1.14 inference(quant_intro,[status(thm)],[521])).
% 0.95/1.14 tff(523,plain,
% 0.95/1.14 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(524,plain,
% 0.95/1.14 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp11) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.95/1.14 inference(bind,[status(th)],[])).
% 0.95/1.14 tff(525,plain,
% 0.95/1.14 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp11) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.95/1.14 inference(quant_intro,[status(thm)],[524])).
% 0.95/1.14 tff(526,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.95/1.14 tff(527,plain,
% 0.95/1.14 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.95/1.14 tff(528,plain,
% 0.95/1.14 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[527, 523])).
% 0.95/1.14 tff(529,plain,(
% 0.95/1.14 ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.95/1.14 inference(skolemize,[status(sab)],[528])).
% 0.95/1.14 tff(530,plain,
% 0.95/1.14 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[529, 522])).
% 0.95/1.14 tff(531,plain,
% 0.95/1.14 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(532,plain,
% 0.95/1.14 ((hskp11 | hskp0 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445))) <=> (hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(533,plain,
% 0.95/1.14 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[532])).
% 0.95/1.14 tff(534,plain,
% 0.95/1.14 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 0.95/1.14 inference(transitivity,[status(thm)],[533, 531])).
% 0.95/1.14 tff(535,plain,
% 0.95/1.14 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(536,plain,
% 0.95/1.14 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.95/1.14 tff(537,plain,
% 0.95/1.14 (hskp11 | hskp0 | c2_1(a445)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[536, 138, 425, 424, 530])).
% 0.95/1.14 tff(538,plain,
% 0.95/1.14 (hskp0),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[537, 520, 437])).
% 0.95/1.14 tff(539,plain,
% 0.95/1.14 (c2_1(a400)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[338, 538])).
% 0.95/1.14 tff(540,plain,
% 0.95/1.14 (c1_1(a400)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[346, 538])).
% 0.95/1.14 tff(541,plain,
% 0.95/1.14 (((~hskp12) | c1_1(a426)) <=> ((~hskp12) | c1_1(a426))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(542,axiom,((~hskp12) | c1_1(a426)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.95/1.14 tff(543,plain,
% 0.95/1.14 ((~hskp12) | c1_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.95/1.14 tff(544,plain,
% 0.95/1.14 ((~hskp12) | c1_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[543, 541])).
% 0.95/1.14 tff(545,plain,
% 0.95/1.14 ((~hskp12) | c1_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[544, 541])).
% 0.95/1.14 tff(546,plain,
% 0.95/1.14 ((~hskp12) | c1_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[545, 541])).
% 0.95/1.14 tff(547,plain,
% 0.95/1.14 ((~hskp12) | c1_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[546, 541])).
% 0.95/1.14 tff(548,plain,
% 0.95/1.14 (c1_1(a426)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[547, 506])).
% 0.95/1.14 tff(549,plain,
% 0.95/1.14 (((~hskp12) | c0_1(a426)) <=> ((~hskp12) | c0_1(a426))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(550,axiom,((~hskp12) | c0_1(a426)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.95/1.14 tff(551,plain,
% 0.95/1.14 ((~hskp12) | c0_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.95/1.14 tff(552,plain,
% 0.95/1.14 ((~hskp12) | c0_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[551, 549])).
% 0.95/1.14 tff(553,plain,
% 0.95/1.14 ((~hskp12) | c0_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[552, 549])).
% 0.95/1.14 tff(554,plain,
% 0.95/1.14 ((~hskp12) | c0_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[553, 549])).
% 0.95/1.14 tff(555,plain,
% 0.95/1.14 ((~hskp12) | c0_1(a426)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[554, 549])).
% 0.95/1.14 tff(556,plain,
% 0.95/1.14 (c0_1(a426)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[555, 506])).
% 0.95/1.14 tff(557,plain,
% 0.95/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(558,plain,
% 0.95/1.14 (((~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402))) <=> (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(559,plain,
% 0.95/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[558])).
% 0.95/1.15 tff(560,plain,
% 0.95/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)))),
% 0.95/1.15 inference(transitivity,[status(thm)],[559, 557])).
% 0.95/1.15 tff(561,plain,
% 0.95/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))),
% 0.95/1.15 inference(quant_inst,[status(thm)],[])).
% 0.95/1.15 tff(562,plain,
% 0.95/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426))),
% 0.95/1.15 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.95/1.15 tff(563,plain,
% 0.95/1.15 (~c0_1(a400)),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[562, 138, 556, 548, 470, 540, 539, 512, 93, 462, 447])).
% 0.95/1.15 tff(564,plain,
% 0.95/1.15 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402)))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(565,plain,
% 0.95/1.15 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400))) <=> (hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402)))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(566,plain,
% 0.95/1.15 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[565])).
% 0.95/1.15 tff(567,plain,
% 0.95/1.15 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402)))),
% 0.95/1.15 inference(transitivity,[status(thm)],[566, 564])).
% 0.95/1.15 tff(568,plain,
% 0.95/1.15 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))),
% 0.95/1.15 inference(quant_inst,[status(thm)],[])).
% 0.95/1.15 tff(569,plain,
% 0.95/1.15 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.98/1.15 tff(570,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[569, 138, 12, 470, 540, 539, 93, 22, 488, 563])).
% 0.98/1.15 tff(571,plain,(hskp1 | c1_1(a402) | hskp11 | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445)) | c0_1(a403) | c1_1(a403) | c2_1(a403)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(572,plain,
% 0.98/1.15 (c1_1(a403)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[571, 12, 93, 425, 424, 436, 303, 437, 302])).
% 0.98/1.15 tff(573,assumption,(c1_1(a403)), introduced(assumption)).
% 0.98/1.15 tff(574,plain,
% 0.98/1.15 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.98/1.15 inference(bind,[status(th)],[])).
% 0.98/1.15 tff(575,plain,
% 0.98/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.98/1.15 inference(quant_intro,[status(thm)],[574])).
% 0.98/1.15 tff(576,plain,
% 0.98/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(577,plain,
% 0.98/1.15 (^[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)) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_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) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.98/1.15 inference(bind,[status(th)],[])).
% 0.98/1.15 tff(578,plain,
% 0.98/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.98/1.15 inference(quant_intro,[status(thm)],[577])).
% 0.98/1.15 tff(579,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.98/1.15 tff(580,plain,
% 0.98/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.98/1.15 tff(581,plain,
% 0.98/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[580, 576])).
% 0.98/1.15 tff(582,plain,(
% 0.98/1.15 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.98/1.15 inference(skolemize,[status(sab)],[581])).
% 0.98/1.15 tff(583,plain,
% 0.98/1.15 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[582, 575])).
% 0.98/1.15 tff(584,plain,
% 0.98/1.15 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(585,plain,
% 0.98/1.15 ((hskp7 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403))) <=> (hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(586,plain,
% 0.98/1.15 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[585])).
% 0.98/1.15 tff(587,plain,
% 0.98/1.15 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 0.98/1.15 inference(transitivity,[status(thm)],[586, 584])).
% 0.98/1.15 tff(588,plain,
% 0.98/1.15 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(589,plain,
% 0.98/1.15 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.98/1.15 tff(590,plain,
% 0.98/1.15 (hskp7 | hskp2 | c2_1(a403) | (~c1_1(a403))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[589, 138, 301, 106])).
% 0.98/1.15 tff(591,plain,
% 0.98/1.15 (hskp7),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[590, 23, 302, 573])).
% 0.98/1.15 tff(592,plain,
% 0.98/1.15 (~c3_1(a410)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[230, 591])).
% 0.98/1.15 tff(593,plain,
% 0.98/1.15 (~c1_1(a410)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[236, 591])).
% 0.98/1.15 tff(594,plain,
% 0.98/1.15 (c0_1(a410)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[268, 591])).
% 0.98/1.15 tff(595,plain,
% 0.98/1.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(596,plain,
% 0.98/1.15 ((hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403))) <=> (hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(597,plain,
% 0.98/1.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[596])).
% 0.98/1.15 tff(598,plain,
% 0.98/1.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410)))),
% 0.98/1.15 inference(transitivity,[status(thm)],[597, 595])).
% 0.98/1.15 tff(599,plain,
% 0.98/1.15 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(600,plain,
% 0.98/1.15 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.98/1.15 tff(601,plain,
% 0.98/1.15 (hskp9),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[600, 138, 594, 593, 592, 303, 301, 583, 573])).
% 0.98/1.15 tff(602,plain,
% 0.98/1.15 (((~hskp9) | (~c1_1(a416))) <=> ((~hskp9) | (~c1_1(a416)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(603,plain,
% 0.98/1.15 (((~c1_1(a416)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a416)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(604,axiom,((~c1_1(a416)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.98/1.15 tff(605,plain,
% 0.98/1.15 ((~hskp9) | (~c1_1(a416))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[604, 603])).
% 0.98/1.15 tff(606,plain,
% 0.98/1.15 ((~hskp9) | (~c1_1(a416))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[605, 602])).
% 0.98/1.15 tff(607,plain,
% 0.98/1.15 (~c1_1(a416)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[606, 601])).
% 0.98/1.15 tff(608,plain,
% 0.98/1.15 (((~hskp9) | (~c0_1(a416))) <=> ((~hskp9) | (~c0_1(a416)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(609,plain,
% 0.98/1.15 (((~c0_1(a416)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a416)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(610,axiom,((~c0_1(a416)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.98/1.15 tff(611,plain,
% 0.98/1.15 ((~hskp9) | (~c0_1(a416))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.98/1.15 tff(612,plain,
% 0.98/1.15 ((~hskp9) | (~c0_1(a416))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[611, 608])).
% 0.98/1.15 tff(613,plain,
% 0.98/1.15 (~c0_1(a416)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[612, 601])).
% 0.98/1.15 tff(614,plain,
% 0.98/1.15 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(615,plain,
% 0.98/1.15 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | c0_1(a416)) <=> (hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(616,plain,
% 0.98/1.15 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | c0_1(a416))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416)))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[615])).
% 0.98/1.15 tff(617,plain,
% 0.98/1.15 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | c0_1(a416))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416))),
% 0.98/1.15 inference(transitivity,[status(thm)],[616, 614])).
% 0.98/1.15 tff(618,plain,
% 0.98/1.15 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | c0_1(a416))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(619,plain,
% 0.98/1.15 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416)),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.98/1.15 tff(620,plain,
% 0.98/1.15 (c2_1(a416)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[619, 138, 23, 12, 613, 607, 33])).
% 0.98/1.15 tff(621,plain,
% 0.98/1.15 (^[U: $i] : refl((hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.98/1.15 inference(bind,[status(th)],[])).
% 0.98/1.15 tff(622,plain,
% 0.98/1.15 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/1.15 inference(quant_intro,[status(thm)],[621])).
% 0.98/1.15 tff(623,plain,
% 0.98/1.15 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(624,plain,
% 0.98/1.15 (^[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)) | 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)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | 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) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp11) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp11))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp11) <=> (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.98/1.15 inference(bind,[status(th)],[])).
% 0.98/1.15 tff(625,plain,
% 0.98/1.15 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp11) <=> ![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/1.15 inference(quant_intro,[status(thm)],[624])).
% 0.98/1.15 tff(626,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.98/1.15 tff(627,plain,
% 0.98/1.15 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.98/1.15 tff(628,plain,
% 0.98/1.15 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[627, 623])).
% 0.98/1.15 tff(629,plain,(
% 0.98/1.15 ![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/1.15 inference(skolemize,[status(sab)],[628])).
% 0.98/1.15 tff(630,plain,
% 0.98/1.15 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[629, 622])).
% 0.98/1.15 tff(631,plain,
% 0.98/1.15 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(632,plain,
% 0.98/1.15 ((hskp11 | hskp2 | (~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410))) <=> (hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(633,plain,
% 0.98/1.15 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410)))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[632])).
% 0.98/1.15 tff(634,plain,
% 0.98/1.15 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410))),
% 0.98/1.15 inference(transitivity,[status(thm)],[633, 631])).
% 0.98/1.15 tff(635,plain,
% 0.98/1.15 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(636,plain,
% 0.98/1.15 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410)),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.98/1.15 tff(637,plain,
% 0.98/1.15 (c2_1(a410)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[636, 138, 437, 23, 594, 592, 630])).
% 0.98/1.15 tff(638,plain,
% 0.98/1.15 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.98/1.15 inference(bind,[status(th)],[])).
% 0.98/1.15 tff(639,plain,
% 0.98/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_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) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/1.15 inference(quant_intro,[status(thm)],[638])).
% 0.98/1.15 tff(640,plain,
% 0.98/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_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) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(641,plain,
% 0.98/1.15 (^[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)) | (~c2_1(V)) | (~c3_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))))), (((((((~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)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_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)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_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) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_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) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.98/1.15 inference(bind,[status(th)],[])).
% 0.98/1.15 tff(642,plain,
% 0.98/1.15 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/1.15 inference(quant_intro,[status(thm)],[641])).
% 0.98/1.15 tff(643,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.98/1.15 tff(644,plain,
% 0.98/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.98/1.16 tff(645,plain,
% 0.98/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[644, 640])).
% 0.98/1.16 tff(646,plain,(
% 0.98/1.16 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/1.16 inference(skolemize,[status(sab)],[645])).
% 0.98/1.16 tff(647,plain,
% 0.98/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[646, 639])).
% 0.98/1.16 tff(648,plain,
% 0.98/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(649,plain,
% 0.98/1.16 ((hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445))) <=> (hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(650,plain,
% 0.98/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[649])).
% 0.98/1.16 tff(651,plain,
% 0.98/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 0.98/1.16 inference(transitivity,[status(thm)],[650, 648])).
% 0.98/1.16 tff(652,plain,
% 0.98/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(653,plain,
% 0.98/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.98/1.16 tff(654,plain,
% 0.98/1.16 (~c2_1(a445)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[653, 138, 12, 436, 594, 424, 593, 592, 22])).
% 0.98/1.16 tff(655,plain,
% 0.98/1.16 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(656,plain,
% 0.98/1.16 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(657,plain,
% 0.98/1.16 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a445) | (~c1_1(a445)) | (~c3_1(a445))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.98/1.16 tff(658,plain,
% 0.98/1.16 (hskp13 | hskp2 | c2_1(a445)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[657, 138, 436, 425, 247])).
% 0.98/1.16 tff(659,plain,
% 0.98/1.16 (hskp13),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[658, 654, 23])).
% 0.98/1.16 tff(660,plain,
% 0.98/1.16 (~c0_1(a427)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[260, 659])).
% 0.98/1.16 tff(661,plain,
% 0.98/1.16 (((~hskp9) | c3_1(a416)) <=> ((~hskp9) | c3_1(a416))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(662,axiom,((~hskp9) | c3_1(a416)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.98/1.16 tff(663,plain,
% 0.98/1.16 ((~hskp9) | c3_1(a416)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.98/1.16 tff(664,plain,
% 0.98/1.16 ((~hskp9) | c3_1(a416)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[663, 661])).
% 0.98/1.16 tff(665,plain,
% 0.98/1.16 ((~hskp9) | c3_1(a416)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[664, 661])).
% 0.98/1.16 tff(666,plain,
% 0.98/1.16 ((~hskp9) | c3_1(a416)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[665, 661])).
% 0.98/1.16 tff(667,plain,
% 0.98/1.16 ((~hskp9) | c3_1(a416)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[666, 661])).
% 0.98/1.16 tff(668,plain,
% 0.98/1.16 (c3_1(a416)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[667, 601])).
% 0.98/1.16 tff(669,plain,
% 0.98/1.16 (c2_1(a427)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[276, 659])).
% 0.98/1.16 tff(670,plain,
% 0.98/1.16 (c1_1(a427)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[284, 659])).
% 0.98/1.16 tff(671,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(672,plain,
% 0.98/1.16 (((~ndr1_0) | c3_1(a410) | (~c2_1(a410)) | (~c0_1(a410)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(673,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a410) | (~c2_1(a410)) | (~c0_1(a410)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[672])).
% 0.98/1.16 tff(674,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a410) | (~c2_1(a410)) | (~c0_1(a410)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 0.98/1.16 inference(transitivity,[status(thm)],[673, 671])).
% 0.98/1.16 tff(675,plain,
% 0.98/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a410) | (~c2_1(a410)) | (~c0_1(a410)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(676,plain,
% 0.98/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.98/1.16 tff(677,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[676, 138, 670, 669, 668, 594, 660, 607, 592, 647, 637, 620])).
% 0.98/1.16 tff(678,plain,(hskp2 | hskp1 | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)) | c0_1(a445) | hskp11 | c2_1(a403)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(679,plain,
% 0.98/1.16 (hskp2),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[678, 12, 436, 425, 303, 301, 572, 424, 437, 302])).
% 0.98/1.16 tff(680,plain,
% 0.98/1.16 (c0_1(a402)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[469, 679])).
% 0.98/1.16 tff(681,plain,
% 0.98/1.16 (~c3_1(a402)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[487, 680])).
% 0.98/1.16 tff(682,plain,
% 0.98/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(683,plain,
% 0.98/1.16 ((hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403))) <=> (hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(684,plain,
% 0.98/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[683])).
% 0.98/1.16 tff(685,plain,
% 0.98/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 0.98/1.16 inference(transitivity,[status(thm)],[684, 682])).
% 0.98/1.16 tff(686,plain,
% 0.98/1.16 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(687,plain,
% 0.98/1.16 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.98/1.16 tff(688,plain,
% 0.98/1.16 (hskp9 | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[687, 138, 303, 301, 93, 583])).
% 0.98/1.16 tff(689,plain,
% 0.98/1.16 (hskp9),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[688, 681, 572, 680])).
% 0.98/1.16 tff(690,plain,
% 0.98/1.16 (~c1_1(a416)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[606, 689])).
% 0.98/1.16 tff(691,plain,
% 0.98/1.16 (~c0_1(a416)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[612, 689])).
% 0.98/1.16 tff(692,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(693,plain,
% 0.98/1.16 (((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a403) | c0_1(a403) | c2_1(a403)) <=> (c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(694,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[693])).
% 0.98/1.16 tff(695,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416)))),
% 0.98/1.16 inference(transitivity,[status(thm)],[694, 692])).
% 0.98/1.16 tff(696,plain,
% 0.98/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a403) | c0_1(a403) | c2_1(a403))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(697,plain,
% 0.98/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[696, 695])).
% 0.98/1.16 tff(698,plain,
% 0.98/1.16 (~c2_1(a416)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[697, 138, 691, 690, 303, 302, 301, 313, 572])).
% 0.98/1.16 tff(699,plain,
% 0.98/1.16 (~c2_1(a402)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[461, 679])).
% 0.98/1.16 tff(700,plain,
% 0.98/1.16 (hskp12),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[505, 681, 12, 680])).
% 0.98/1.16 tff(701,plain,
% 0.98/1.16 (~c2_1(a426)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[511, 700])).
% 0.98/1.16 tff(702,plain,
% 0.98/1.16 (~c2_1(a445)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[519, 681, 12, 680])).
% 0.98/1.16 tff(703,plain,
% 0.98/1.16 (hskp0),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[537, 702, 437])).
% 0.98/1.16 tff(704,plain,
% 0.98/1.16 (c2_1(a400)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[338, 703])).
% 0.98/1.16 tff(705,plain,
% 0.98/1.16 (c1_1(a400)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[346, 703])).
% 0.98/1.16 tff(706,plain,
% 0.98/1.16 (c1_1(a426)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[547, 700])).
% 0.98/1.16 tff(707,plain,
% 0.98/1.16 (c0_1(a426)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[555, 700])).
% 0.98/1.16 tff(708,plain,
% 0.98/1.16 (~c0_1(a400)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[562, 138, 707, 706, 680, 705, 704, 701, 93, 699, 447])).
% 0.98/1.16 tff(709,plain,
% 0.98/1.16 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.98/1.16 inference(bind,[status(th)],[])).
% 0.98/1.16 tff(710,plain,
% 0.98/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.98/1.16 inference(quant_intro,[status(thm)],[709])).
% 0.98/1.16 tff(711,plain,
% 0.98/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(712,plain,
% 0.98/1.16 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.98/1.16 inference(bind,[status(th)],[])).
% 0.98/1.16 tff(713,plain,
% 0.98/1.16 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.98/1.16 inference(quant_intro,[status(thm)],[712])).
% 0.98/1.16 tff(714,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.98/1.16 tff(715,plain,
% 0.98/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.98/1.16 tff(716,plain,
% 0.98/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[715, 711])).
% 0.98/1.16 tff(717,plain,(
% 0.98/1.16 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.98/1.16 inference(skolemize,[status(sab)],[716])).
% 0.98/1.16 tff(718,plain,
% 0.98/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[717, 710])).
% 0.98/1.16 tff(719,plain,
% 0.98/1.16 (~c3_1(a400)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[366, 703])).
% 0.98/1.16 tff(720,plain,
% 0.98/1.16 (c3_1(a416)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[667, 689])).
% 0.98/1.16 tff(721,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(722,plain,
% 0.98/1.16 (((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416))) <=> (c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(723,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[722])).
% 0.98/1.16 tff(724,plain,
% 0.98/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.16 inference(transitivity,[status(thm)],[723, 721])).
% 0.98/1.16 tff(725,plain,
% 0.98/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(726,plain,
% 0.98/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.98/1.16 tff(727,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[726, 138, 720, 704, 691, 690, 719, 718, 708, 698])).
% 0.98/1.16 tff(728,plain,(hskp1 | c1_1(a402) | c0_1(a403) | c2_1(a403) | c3_1(a403) | hskp11 | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(729,plain,
% 0.98/1.16 (hskp1),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[728, 437, 303, 302, 301, 93, 425, 424, 436])).
% 0.98/1.16 tff(730,plain,
% 0.98/1.16 (((~hskp1) | (~c3_1(a401))) <=> ((~hskp1) | (~c3_1(a401)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(731,plain,
% 0.98/1.16 (((~c3_1(a401)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a401)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(732,axiom,((~c3_1(a401)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.98/1.16 tff(733,plain,
% 0.98/1.16 ((~hskp1) | (~c3_1(a401))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.98/1.16 tff(734,plain,
% 0.98/1.16 ((~hskp1) | (~c3_1(a401))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[733, 730])).
% 0.98/1.16 tff(735,plain,
% 0.98/1.16 (~c3_1(a401)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[734, 729])).
% 0.98/1.16 tff(736,plain,
% 0.98/1.16 (((~hskp1) | c1_1(a401)) <=> ((~hskp1) | c1_1(a401))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(737,axiom,((~hskp1) | c1_1(a401)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.98/1.16 tff(738,plain,
% 0.98/1.16 ((~hskp1) | c1_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.98/1.16 tff(739,plain,
% 0.98/1.16 ((~hskp1) | c1_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[738, 736])).
% 0.98/1.16 tff(740,plain,
% 0.98/1.16 ((~hskp1) | c1_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[739, 736])).
% 0.98/1.16 tff(741,plain,
% 0.98/1.16 ((~hskp1) | c1_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[740, 736])).
% 0.98/1.16 tff(742,plain,
% 0.98/1.16 ((~hskp1) | c1_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[741, 736])).
% 0.98/1.16 tff(743,plain,
% 0.98/1.16 (c1_1(a401)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[742, 729])).
% 0.98/1.16 tff(744,plain,
% 0.98/1.16 (((~hskp1) | c0_1(a401)) <=> ((~hskp1) | c0_1(a401))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(745,axiom,((~hskp1) | c0_1(a401)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.98/1.16 tff(746,plain,
% 0.98/1.16 ((~hskp1) | c0_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[745, 744])).
% 0.98/1.16 tff(747,plain,
% 0.98/1.16 ((~hskp1) | c0_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[746, 744])).
% 0.98/1.16 tff(748,plain,
% 0.98/1.16 ((~hskp1) | c0_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[747, 744])).
% 0.98/1.16 tff(749,plain,
% 0.98/1.16 ((~hskp1) | c0_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[748, 744])).
% 0.98/1.16 tff(750,plain,
% 0.98/1.16 ((~hskp1) | c0_1(a401)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[749, 744])).
% 0.98/1.16 tff(751,plain,
% 0.98/1.16 (c0_1(a401)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[750, 729])).
% 0.98/1.16 tff(752,plain,
% 0.98/1.16 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(753,plain,
% 0.98/1.16 ((hskp20 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401))) <=> (hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(754,plain,
% 0.98/1.16 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[753])).
% 0.98/1.16 tff(755,plain,
% 0.98/1.16 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 0.98/1.16 inference(transitivity,[status(thm)],[754, 752])).
% 0.98/1.16 tff(756,plain,
% 0.98/1.16 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(757,plain,
% 0.98/1.16 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.98/1.16 tff(758,plain,
% 0.98/1.16 (hskp20),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[757, 138, 751, 743, 735, 435])).
% 0.98/1.16 tff(759,plain,
% 0.98/1.16 (((~hskp20) | c1_1(a449)) <=> ((~hskp20) | c1_1(a449))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(760,axiom,((~hskp20) | c1_1(a449)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.98/1.16 tff(761,plain,
% 0.98/1.16 ((~hskp20) | c1_1(a449)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.98/1.16 tff(762,plain,
% 0.98/1.16 ((~hskp20) | c1_1(a449)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[761, 759])).
% 0.98/1.16 tff(763,plain,
% 0.98/1.16 ((~hskp20) | c1_1(a449)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[762, 759])).
% 0.98/1.16 tff(764,plain,
% 0.98/1.16 ((~hskp20) | c1_1(a449)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[763, 759])).
% 0.98/1.16 tff(765,plain,
% 0.98/1.16 ((~hskp20) | c1_1(a449)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[764, 759])).
% 0.98/1.16 tff(766,plain,
% 0.98/1.16 (c1_1(a449)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[765, 758])).
% 0.98/1.16 tff(767,assumption,(c0_1(a401)), introduced(assumption)).
% 0.98/1.16 tff(768,assumption,(~c3_1(a401)), introduced(assumption)).
% 0.98/1.16 tff(769,assumption,(c1_1(a401)), introduced(assumption)).
% 0.98/1.16 tff(770,assumption,(hskp22), introduced(assumption)).
% 0.98/1.16 tff(771,plain,
% 0.98/1.16 (((~hskp22) | (~c1_1(a451))) <=> ((~hskp22) | (~c1_1(a451)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(772,plain,
% 0.98/1.16 (((~c1_1(a451)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a451)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(773,axiom,((~c1_1(a451)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.98/1.16 tff(774,plain,
% 0.98/1.16 ((~hskp22) | (~c1_1(a451))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.98/1.16 tff(775,plain,
% 0.98/1.16 ((~hskp22) | (~c1_1(a451))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[774, 771])).
% 0.98/1.16 tff(776,plain,
% 0.98/1.16 (~c1_1(a451)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[775, 770])).
% 0.98/1.16 tff(777,plain,
% 0.98/1.16 (((~hskp22) | c2_1(a451)) <=> ((~hskp22) | c2_1(a451))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(778,axiom,((~hskp22) | c2_1(a451)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.98/1.16 tff(779,plain,
% 0.98/1.16 ((~hskp22) | c2_1(a451)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.98/1.16 tff(780,plain,
% 0.98/1.16 ((~hskp22) | c2_1(a451)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[779, 777])).
% 0.98/1.16 tff(781,plain,
% 0.98/1.16 ((~hskp22) | c2_1(a451)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[780, 777])).
% 0.98/1.16 tff(782,plain,
% 0.98/1.16 ((~hskp22) | c2_1(a451)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[781, 777])).
% 0.98/1.16 tff(783,plain,
% 0.98/1.16 ((~hskp22) | c2_1(a451)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[782, 777])).
% 0.98/1.16 tff(784,plain,
% 0.98/1.16 (c2_1(a451)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[783, 770])).
% 0.98/1.16 tff(785,plain,
% 0.98/1.16 (((~hskp22) | c0_1(a451)) <=> ((~hskp22) | c0_1(a451))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(786,axiom,((~hskp22) | c0_1(a451)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.98/1.17 tff(787,plain,
% 0.98/1.17 ((~hskp22) | c0_1(a451)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.98/1.17 tff(788,plain,
% 0.98/1.17 ((~hskp22) | c0_1(a451)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[787, 785])).
% 0.98/1.17 tff(789,plain,
% 0.98/1.17 ((~hskp22) | c0_1(a451)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[788, 785])).
% 0.98/1.17 tff(790,plain,
% 0.98/1.17 ((~hskp22) | c0_1(a451)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[789, 785])).
% 0.98/1.17 tff(791,plain,
% 0.98/1.17 ((~hskp22) | c0_1(a451)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[790, 785])).
% 0.98/1.17 tff(792,plain,
% 0.98/1.17 (c0_1(a451)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[791, 770])).
% 0.98/1.17 tff(793,assumption,(~c1_1(a451)), introduced(assumption)).
% 0.98/1.17 tff(794,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(795,plain,
% 0.98/1.17 (((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445))) <=> (c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(796,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[795])).
% 0.98/1.17 tff(797,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 0.98/1.17 inference(transitivity,[status(thm)],[796, 794])).
% 0.98/1.17 tff(798,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(799,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[798, 797])).
% 0.98/1.17 tff(800,plain,
% 0.98/1.17 ((~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[799, 138, 793, 424, 480])).
% 0.98/1.17 tff(801,plain,
% 0.98/1.17 (~c3_1(a451)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[800, 792, 425, 436])).
% 0.98/1.17 tff(802,plain,
% 0.98/1.17 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.98/1.17 inference(bind,[status(th)],[])).
% 0.98/1.17 tff(803,plain,
% 0.98/1.17 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.17 inference(quant_intro,[status(thm)],[802])).
% 0.98/1.17 tff(804,plain,
% 0.98/1.17 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(805,plain,
% 0.98/1.17 (^[V: $i, U: $i] : 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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.98/1.17 inference(bind,[status(th)],[])).
% 0.98/1.17 tff(806,plain,
% 0.98/1.17 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.17 inference(quant_intro,[status(thm)],[805])).
% 0.98/1.17 tff(807,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.98/1.17 tff(808,plain,
% 0.98/1.17 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.98/1.17 tff(809,plain,
% 0.98/1.17 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[808, 804])).
% 0.98/1.17 tff(810,plain,(
% 0.98/1.17 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.17 inference(skolemize,[status(sab)],[809])).
% 0.98/1.17 tff(811,plain,
% 0.98/1.17 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[810, 803])).
% 0.98/1.17 tff(812,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(813,plain,
% 0.98/1.17 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451))) <=> (c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(814,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451)))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[813])).
% 0.98/1.17 tff(815,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451))),
% 0.98/1.17 inference(transitivity,[status(thm)],[814, 812])).
% 0.98/1.17 tff(816,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(817,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.98/1.17 tff(818,plain,
% 0.98/1.17 ((~c2_1(a451)) | c3_1(a451)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[817, 138, 767, 769, 793, 768, 811])).
% 0.98/1.17 tff(819,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[818, 801, 784])).
% 0.98/1.17 tff(820,plain,((~hskp22) | (~c0_1(a401)) | (~c1_1(a401)) | c1_1(a451) | c3_1(a401) | (~c3_1(a445)) | (~c1_1(a445)) | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(821,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[820, 776, 770, 425, 769, 768, 767, 436, 424])).
% 0.98/1.17 tff(822,plain,((~hskp22) | (~c3_1(a445)) | (~c1_1(a401)) | c3_1(a401) | (~c0_1(a401)) | (~c1_1(a445)) | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(823,plain,
% 0.98/1.17 (~hskp22),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[822, 735, 425, 743, 751, 436, 424])).
% 0.98/1.17 tff(824,plain,
% 0.98/1.17 (((~hskp20) | c3_1(a449)) <=> ((~hskp20) | c3_1(a449))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(825,axiom,((~hskp20) | c3_1(a449)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.98/1.17 tff(826,plain,
% 0.98/1.17 ((~hskp20) | c3_1(a449)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.98/1.17 tff(827,plain,
% 0.98/1.17 ((~hskp20) | c3_1(a449)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[826, 824])).
% 0.98/1.17 tff(828,plain,
% 0.98/1.17 ((~hskp20) | c3_1(a449)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[827, 824])).
% 0.98/1.17 tff(829,plain,
% 0.98/1.17 ((~hskp20) | c3_1(a449)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[828, 824])).
% 0.98/1.17 tff(830,plain,
% 0.98/1.17 ((~hskp20) | c3_1(a449)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[829, 824])).
% 0.98/1.17 tff(831,plain,
% 0.98/1.17 (c3_1(a449)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[830, 758])).
% 0.98/1.17 tff(832,plain,
% 0.98/1.17 (((~hskp20) | (~c2_1(a449))) <=> ((~hskp20) | (~c2_1(a449)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(833,plain,
% 0.98/1.17 (((~c2_1(a449)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a449)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(834,axiom,((~c2_1(a449)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.98/1.17 tff(835,plain,
% 0.98/1.17 ((~hskp20) | (~c2_1(a449))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.98/1.17 tff(836,plain,
% 0.98/1.17 ((~hskp20) | (~c2_1(a449))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[835, 832])).
% 0.98/1.17 tff(837,plain,
% 0.98/1.17 (~c2_1(a449)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[836, 758])).
% 0.98/1.17 tff(838,assumption,(hskp2), introduced(assumption)).
% 0.98/1.17 tff(839,plain,
% 0.98/1.17 (c0_1(a402)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[469, 838])).
% 0.98/1.17 tff(840,plain,
% 0.98/1.17 ((~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[486, 138, 424, 93, 480])).
% 0.98/1.17 tff(841,plain,
% 0.98/1.17 (~c3_1(a402)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[840, 839, 436, 425])).
% 0.98/1.17 tff(842,plain,
% 0.98/1.17 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.98/1.17 inference(bind,[status(th)],[])).
% 0.98/1.17 tff(843,plain,
% 0.98/1.17 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.98/1.17 inference(quant_intro,[status(thm)],[842])).
% 0.98/1.17 tff(844,plain,
% 0.98/1.17 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(845,plain,
% 0.98/1.17 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.98/1.17 inference(bind,[status(th)],[])).
% 0.98/1.17 tff(846,plain,
% 0.98/1.17 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.98/1.17 inference(quant_intro,[status(thm)],[845])).
% 0.98/1.17 tff(847,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.98/1.17 tff(848,plain,
% 0.98/1.17 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.98/1.17 tff(849,plain,
% 0.98/1.17 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[848, 844])).
% 0.98/1.17 tff(850,plain,(
% 0.98/1.17 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.98/1.17 inference(skolemize,[status(sab)],[849])).
% 0.98/1.17 tff(851,plain,
% 0.98/1.17 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[850, 843])).
% 0.98/1.17 tff(852,plain,
% 0.98/1.17 (~c2_1(a402)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[461, 838])).
% 0.98/1.17 tff(853,assumption,(~c2_1(a449)), introduced(assumption)).
% 0.98/1.17 tff(854,assumption,(c3_1(a449)), introduced(assumption)).
% 0.98/1.17 tff(855,assumption,(c1_1(a449)), introduced(assumption)).
% 0.98/1.17 tff(856,assumption,(~hskp22), introduced(assumption)).
% 0.98/1.17 tff(857,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(858,plain,
% 0.98/1.17 ((hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(859,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[858])).
% 0.98/1.17 tff(860,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.17 inference(transitivity,[status(thm)],[859, 857])).
% 0.98/1.17 tff(861,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(862,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.98/1.17 tff(863,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[862, 138, 856, 855, 854, 839, 853, 852, 851, 841])).
% 0.98/1.17 tff(864,plain,((~hskp2) | hskp22 | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a449) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(865,plain,
% 0.98/1.17 (~hskp2),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[864, 837, 436, 831, 823, 766, 425, 424, 93])).
% 0.98/1.17 tff(866,plain,
% 0.98/1.17 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(867,plain,
% 0.98/1.17 ((hskp11 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c0_1(a401))) <=> (hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(868,plain,
% 0.98/1.17 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[867])).
% 0.98/1.17 tff(869,plain,
% 0.98/1.17 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401)))),
% 0.98/1.17 inference(transitivity,[status(thm)],[868, 866])).
% 0.98/1.17 tff(870,plain,
% 0.98/1.17 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c0_1(a401)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(871,plain,
% 0.98/1.17 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.98/1.17 tff(872,plain,
% 0.98/1.17 (hskp2 | c2_1(a401)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[871, 138, 437, 751, 735, 630])).
% 0.98/1.17 tff(873,plain,
% 0.98/1.17 (c2_1(a401)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[872, 865])).
% 0.98/1.17 tff(874,plain,
% 0.98/1.17 (^[U: $i] : refl((hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.98/1.17 inference(bind,[status(th)],[])).
% 0.98/1.17 tff(875,plain,
% 0.98/1.17 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.17 inference(quant_intro,[status(thm)],[874])).
% 0.98/1.17 tff(876,plain,
% 0.98/1.17 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(877,plain,
% 0.98/1.17 (^[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)) | hskp22) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> ((hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.98/1.17 inference(bind,[status(th)],[])).
% 0.98/1.17 tff(878,plain,
% 0.98/1.17 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.17 inference(quant_intro,[status(thm)],[877])).
% 0.98/1.17 tff(879,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.98/1.17 tff(880,plain,
% 0.98/1.17 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[879, 878])).
% 0.98/1.17 tff(881,plain,
% 0.98/1.17 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[880, 876])).
% 0.98/1.17 tff(882,plain,(
% 0.98/1.17 ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.17 inference(skolemize,[status(sab)],[881])).
% 0.98/1.17 tff(883,plain,
% 0.98/1.17 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[882, 875])).
% 0.98/1.17 tff(884,plain,
% 0.98/1.17 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(885,plain,
% 0.98/1.17 ((hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(886,plain,
% 0.98/1.17 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[885])).
% 0.98/1.17 tff(887,plain,
% 0.98/1.17 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)))),
% 0.98/1.17 inference(transitivity,[status(thm)],[886, 884])).
% 0.98/1.17 tff(888,plain,
% 0.98/1.17 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(889,plain,
% 0.98/1.17 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.98/1.17 tff(890,plain,
% 0.98/1.17 (hskp22 | hskp11 | (~c2_1(a405))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[889, 138, 96, 94, 883])).
% 0.98/1.17 tff(891,plain,
% 0.98/1.17 (~c2_1(a405)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[890, 823, 437])).
% 0.98/1.17 tff(892,assumption,(hskp7), introduced(assumption)).
% 0.98/1.17 tff(893,plain,
% 0.98/1.17 (~c3_1(a410)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[230, 892])).
% 0.98/1.17 tff(894,plain,
% 0.98/1.17 (~c1_1(a410)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[236, 892])).
% 0.98/1.17 tff(895,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(896,plain,
% 0.98/1.17 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410))) <=> (c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(897,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[896])).
% 0.98/1.17 tff(898,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410)))),
% 0.98/1.17 inference(transitivity,[status(thm)],[897, 895])).
% 0.98/1.17 tff(899,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(900,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.98/1.17 tff(901,plain,
% 0.98/1.17 (~c2_1(a410)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[900, 138, 767, 769, 894, 893, 768, 811])).
% 0.98/1.17 tff(902,plain,
% 0.98/1.17 (hskp20),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[757, 138, 767, 769, 768, 435])).
% 0.98/1.17 tff(903,plain,
% 0.98/1.17 (~c2_1(a449)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[836, 902])).
% 0.98/1.17 tff(904,plain,
% 0.98/1.17 (c0_1(a410)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[268, 892])).
% 0.98/1.17 tff(905,plain,
% 0.98/1.17 (c3_1(a449)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[830, 902])).
% 0.98/1.17 tff(906,plain,
% 0.98/1.17 (c1_1(a449)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[765, 902])).
% 0.98/1.17 tff(907,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(908,plain,
% 0.98/1.17 ((hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a410) | c3_1(a410) | (~c0_1(a410))) <=> (hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(909,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[908])).
% 0.98/1.17 tff(910,plain,
% 0.98/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.17 inference(transitivity,[status(thm)],[909, 907])).
% 0.98/1.17 tff(911,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(912,plain,
% 0.98/1.17 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[911, 910])).
% 0.98/1.18 tff(913,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[912, 138, 856, 906, 905, 904, 903, 893, 851, 901])).
% 0.98/1.18 tff(914,plain,((~hskp7) | hskp22 | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(915,plain,
% 0.98/1.18 (~hskp7),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[914, 823, 751, 743, 735])).
% 0.98/1.18 tff(916,plain,
% 0.98/1.18 (^[U: $i] : refl((hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.98/1.18 inference(bind,[status(th)],[])).
% 0.98/1.18 tff(917,plain,
% 0.98/1.18 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.18 inference(quant_intro,[status(thm)],[916])).
% 0.98/1.18 tff(918,plain,
% 0.98/1.18 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(919,plain,
% 0.98/1.18 (^[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)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) | hskp16) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.98/1.18 inference(bind,[status(th)],[])).
% 0.98/1.18 tff(920,plain,
% 0.98/1.18 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) | hskp16) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.18 inference(quant_intro,[status(thm)],[919])).
% 0.98/1.18 tff(921,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.98/1.18 tff(922,plain,
% 0.98/1.18 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[921, 920])).
% 0.98/1.18 tff(923,plain,
% 0.98/1.18 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[922, 918])).
% 0.98/1.18 tff(924,plain,(
% 0.98/1.18 ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.18 inference(skolemize,[status(sab)],[923])).
% 0.98/1.18 tff(925,plain,
% 0.98/1.18 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[924, 917])).
% 0.98/1.18 tff(926,plain,
% 0.98/1.18 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(927,plain,
% 0.98/1.18 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c0_1(a405))) <=> (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(928,plain,
% 0.98/1.18 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[927])).
% 0.98/1.18 tff(929,plain,
% 0.98/1.18 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405)))),
% 0.98/1.18 inference(transitivity,[status(thm)],[928, 926])).
% 0.98/1.18 tff(930,plain,
% 0.98/1.18 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c0_1(a405)))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(931,plain,
% 0.98/1.18 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[930, 929])).
% 0.98/1.18 tff(932,plain,
% 0.98/1.18 (hskp16 | hskp7 | c2_1(a405)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[931, 138, 96, 94, 925])).
% 0.98/1.18 tff(933,plain,
% 0.98/1.18 (hskp16),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[932, 915, 891])).
% 0.98/1.18 tff(934,plain,
% 0.98/1.18 (((~hskp16) | (~c3_1(a434))) <=> ((~hskp16) | (~c3_1(a434)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(935,plain,
% 0.98/1.18 (((~c3_1(a434)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a434)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(936,axiom,((~c3_1(a434)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.98/1.18 tff(937,plain,
% 0.98/1.18 ((~hskp16) | (~c3_1(a434))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[936, 935])).
% 0.98/1.18 tff(938,plain,
% 0.98/1.18 ((~hskp16) | (~c3_1(a434))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[937, 934])).
% 0.98/1.18 tff(939,plain,
% 0.98/1.18 (~c3_1(a434)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[938, 933])).
% 0.98/1.18 tff(940,plain,
% 0.98/1.18 (((~hskp16) | (~c0_1(a434))) <=> ((~hskp16) | (~c0_1(a434)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(941,plain,
% 0.98/1.18 (((~c0_1(a434)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a434)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(942,axiom,((~c0_1(a434)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.98/1.18 tff(943,plain,
% 0.98/1.18 ((~hskp16) | (~c0_1(a434))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[942, 941])).
% 0.98/1.18 tff(944,plain,
% 0.98/1.18 ((~hskp16) | (~c0_1(a434))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[943, 940])).
% 0.98/1.18 tff(945,plain,
% 0.98/1.18 (~c0_1(a434)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[944, 933])).
% 0.98/1.18 tff(946,assumption,(~c2_1(a434)), introduced(assumption)).
% 0.98/1.18 tff(947,assumption,(~hskp7), introduced(assumption)).
% 0.98/1.18 tff(948,assumption,(~c3_1(a434)), introduced(assumption)).
% 0.98/1.18 tff(949,plain,
% 0.98/1.18 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(950,plain,
% 0.98/1.18 ((hskp7 | hskp2 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434))) <=> (hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(951,plain,
% 0.98/1.18 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[950])).
% 0.98/1.18 tff(952,plain,
% 0.98/1.18 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 0.98/1.18 inference(transitivity,[status(thm)],[951, 949])).
% 0.98/1.18 tff(953,plain,
% 0.98/1.18 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(954,plain,
% 0.98/1.18 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.98/1.18 tff(955,plain,
% 0.98/1.18 (hskp7 | hskp2 | c2_1(a434) | (~c1_1(a434))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[954, 138, 948, 106])).
% 0.98/1.18 tff(956,plain,
% 0.98/1.18 (~c1_1(a434)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[955, 946, 23, 947])).
% 0.98/1.18 tff(957,plain,
% 0.98/1.18 (((~hskp16) | c1_1(a434)) <=> ((~hskp16) | c1_1(a434))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(958,axiom,((~hskp16) | c1_1(a434)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.98/1.18 tff(959,plain,
% 0.98/1.18 ((~hskp16) | c1_1(a434)),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.98/1.18 tff(960,plain,
% 0.98/1.18 ((~hskp16) | c1_1(a434)),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[959, 957])).
% 0.98/1.18 tff(961,plain,
% 0.98/1.18 ((~hskp16) | c1_1(a434)),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[960, 957])).
% 0.98/1.18 tff(962,plain,
% 0.98/1.18 ((~hskp16) | c1_1(a434)),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[961, 957])).
% 0.98/1.18 tff(963,plain,
% 0.98/1.18 ((~hskp16) | c1_1(a434)),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[962, 957])).
% 0.98/1.18 tff(964,plain,
% 0.98/1.18 (~hskp16),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[963, 956])).
% 0.98/1.18 tff(965,plain,
% 0.98/1.18 (c2_1(a405)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[932, 964, 947])).
% 0.98/1.18 tff(966,assumption,(~c0_1(a434)), introduced(assumption)).
% 0.98/1.18 tff(967,plain,
% 0.98/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(968,plain,
% 0.98/1.18 (((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(969,plain,
% 0.98/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434)))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[968])).
% 0.98/1.18 tff(970,plain,
% 0.98/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434))),
% 0.98/1.18 inference(transitivity,[status(thm)],[969, 967])).
% 0.98/1.18 tff(971,plain,
% 0.98/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a434) | c0_1(a434) | c2_1(a434))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(972,plain,
% 0.98/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434)),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.98/1.18 tff(973,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[972, 138, 96, 94, 956, 767, 769, 966, 768, 11, 965, 946])).
% 0.98/1.18 tff(974,plain,(c2_1(a434) | (~c0_1(a405)) | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c0_1(a434) | c3_1(a401) | hskp7 | hskp2 | c3_1(a434)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(975,plain,
% 0.98/1.18 (c2_1(a434)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[974, 865, 94, 751, 743, 945, 735, 915, 939, 96])).
% 0.98/1.18 tff(976,assumption,(~c2_1(a405)), introduced(assumption)).
% 0.98/1.18 tff(977,assumption,(hskp16), introduced(assumption)).
% 0.98/1.18 tff(978,plain,
% 0.98/1.18 (~c0_1(a434)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[944, 977])).
% 0.98/1.18 tff(979,plain,
% 0.98/1.18 (~c3_1(a434)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[938, 977])).
% 0.98/1.18 tff(980,plain,
% 0.98/1.18 (c2_1(a434)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[974, 948, 94, 767, 769, 966, 768, 947, 23, 96])).
% 0.98/1.18 tff(981,plain,
% 0.98/1.18 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(982,plain,
% 0.98/1.18 ((hskp14 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(983,plain,
% 0.98/1.18 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[982])).
% 0.98/1.18 tff(984,plain,
% 0.98/1.18 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 0.98/1.18 inference(transitivity,[status(thm)],[983, 981])).
% 0.98/1.18 tff(985,plain,
% 0.98/1.18 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(986,plain,
% 0.98/1.18 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.98/1.18 tff(987,plain,
% 0.98/1.18 (c3_1(a434) | (~c2_1(a434))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[986, 138, 368, 906, 905, 903, 966, 361])).
% 0.98/1.18 tff(988,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[987, 980, 948])).
% 0.98/1.18 tff(989,plain,(c3_1(a434) | hskp14 | c0_1(a434) | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp7 | hskp2 | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(990,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[989, 979, 978, 368, 94, 767, 769, 768, 947, 23, 96])).
% 0.98/1.18 tff(991,plain,((~hskp16) | hskp14 | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp7 | hskp2 | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(992,plain,
% 0.98/1.18 (~hskp16),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[991, 947, 94, 767, 769, 768, 368, 23, 96])).
% 0.98/1.18 tff(993,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[932, 992, 947, 976])).
% 0.98/1.18 tff(994,plain,(hskp7 | c2_1(a405) | (~c0_1(a405)) | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(995,plain,
% 0.98/1.18 (hskp14),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[994, 865, 96, 94, 751, 743, 735, 891, 915])).
% 0.98/1.18 tff(996,plain,
% 0.98/1.18 (~c1_1(a428)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[382, 995])).
% 0.98/1.18 tff(997,plain,
% 0.98/1.18 (c2_1(a428)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[396, 995])).
% 0.98/1.18 tff(998,plain,
% 0.98/1.18 (c1_1(a434)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[963, 933])).
% 0.98/1.18 tff(999,plain,
% 0.98/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1000,plain,
% 0.98/1.18 (((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1001,plain,
% 0.98/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[1000])).
% 0.98/1.18 tff(1002,plain,
% 0.98/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.18 inference(transitivity,[status(thm)],[1001, 999])).
% 0.98/1.18 tff(1003,plain,
% 0.98/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(1004,plain,
% 0.98/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 0.98/1.18 tff(1005,plain,
% 0.98/1.18 (~c3_1(a428)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1004, 138, 998, 997, 751, 945, 996, 735, 647, 975, 873])).
% 0.98/1.18 tff(1006,plain,
% 0.98/1.18 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1007,plain,
% 0.98/1.18 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428))) <=> (c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1008,plain,
% 0.98/1.18 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428)))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[1007])).
% 0.98/1.18 tff(1009,plain,
% 0.98/1.18 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428))),
% 0.98/1.18 inference(transitivity,[status(thm)],[1008, 1006])).
% 0.98/1.18 tff(1010,plain,
% 0.98/1.18 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(1011,plain,
% 0.98/1.18 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428)),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.98/1.18 tff(1012,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1011, 138, 997, 751, 743, 996, 735, 811, 1005])).
% 0.98/1.18 tff(1013,plain,(hskp11 | (~c3_1(a405)) | (~c0_1(a405)) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c1_1(a402) | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(1014,plain,
% 0.98/1.18 (hskp11),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1013, 414, 96, 94, 423, 415, 93, 303, 302, 301])).
% 0.98/1.18 tff(1015,plain,
% 0.98/1.18 (((~hskp11) | (~c0_1(a420))) <=> ((~hskp11) | (~c0_1(a420)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1016,plain,
% 0.98/1.18 (((~c0_1(a420)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a420)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1017,axiom,((~c0_1(a420)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.98/1.18 tff(1018,plain,
% 0.98/1.18 ((~hskp11) | (~c0_1(a420))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 0.98/1.18 tff(1019,plain,
% 0.98/1.18 ((~hskp11) | (~c0_1(a420))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1018, 1015])).
% 0.98/1.18 tff(1020,plain,
% 0.98/1.18 (~c0_1(a420)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1019, 1014])).
% 0.98/1.18 tff(1021,plain,
% 0.98/1.18 (((~hskp11) | (~c1_1(a420))) <=> ((~hskp11) | (~c1_1(a420)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1022,plain,
% 0.98/1.18 (((~c1_1(a420)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a420)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1023,axiom,((~c1_1(a420)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.98/1.18 tff(1024,plain,
% 0.98/1.18 ((~hskp11) | (~c1_1(a420))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.98/1.18 tff(1025,plain,
% 0.98/1.18 ((~hskp11) | (~c1_1(a420))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1024, 1021])).
% 0.98/1.18 tff(1026,plain,
% 0.98/1.18 (~c1_1(a420)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1025, 1014])).
% 0.98/1.18 tff(1027,plain,
% 0.98/1.18 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.98/1.18 inference(bind,[status(th)],[])).
% 0.98/1.18 tff(1028,plain,
% 0.98/1.18 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.98/1.18 inference(quant_intro,[status(thm)],[1027])).
% 0.98/1.18 tff(1029,plain,
% 0.98/1.18 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(1030,plain,
% 0.98/1.18 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_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)) | (~c2_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) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_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)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.98/1.19 inference(bind,[status(th)],[])).
% 0.98/1.19 tff(1031,plain,
% 0.98/1.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.98/1.19 inference(quant_intro,[status(thm)],[1030])).
% 0.98/1.19 tff(1032,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.98/1.19 tff(1033,plain,
% 0.98/1.19 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 0.98/1.19 tff(1034,plain,
% 0.98/1.19 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1033, 1029])).
% 0.98/1.19 tff(1035,plain,(
% 0.98/1.19 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.98/1.19 inference(skolemize,[status(sab)],[1034])).
% 0.98/1.19 tff(1036,plain,
% 0.98/1.19 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1035, 1028])).
% 0.98/1.19 tff(1037,assumption,(~c0_1(a420)), introduced(assumption)).
% 0.98/1.19 tff(1038,assumption,(~c1_1(a420)), introduced(assumption)).
% 0.98/1.19 tff(1039,assumption,(~c2_1(a420)), introduced(assumption)).
% 0.98/1.19 tff(1040,plain,
% 0.98/1.19 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1041,plain,
% 0.98/1.19 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a420) | c1_1(a420) | c0_1(a420)) <=> (hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1042,plain,
% 0.98/1.19 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0)))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1041])).
% 0.98/1.19 tff(1043,plain,
% 0.98/1.19 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0))),
% 0.98/1.19 inference(transitivity,[status(thm)],[1042, 1040])).
% 0.98/1.19 tff(1044,plain,
% 0.98/1.19 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a420) | c1_1(a420) | c0_1(a420))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(1045,plain,
% 0.98/1.19 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0)),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.98/1.19 tff(1046,plain,
% 0.98/1.19 (hskp2 | hskp1 | c0_1(a420) | c1_1(a420)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1045, 138, 1039, 33])).
% 0.98/1.19 tff(1047,plain,
% 0.98/1.19 (hskp2),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1046, 12, 1037, 1038])).
% 0.98/1.19 tff(1048,plain,
% 0.98/1.19 (c0_1(a402)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[469, 1047])).
% 0.98/1.19 tff(1049,assumption,(~c2_1(a426)), introduced(assumption)).
% 0.98/1.19 tff(1050,plain,
% 0.98/1.19 (~c2_1(a402)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[461, 1047])).
% 0.98/1.19 tff(1051,plain,
% 0.98/1.19 (~c3_1(a402)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[840, 1048, 436, 425])).
% 0.98/1.19 tff(1052,plain,
% 0.98/1.19 (hskp12),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[505, 1048, 12, 1051])).
% 0.98/1.19 tff(1053,plain,
% 0.98/1.19 (c0_1(a426)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[555, 1052])).
% 0.98/1.19 tff(1054,plain,
% 0.98/1.19 (c1_1(a426)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[547, 1052])).
% 0.98/1.19 tff(1055,assumption,(c2_1(a412)), introduced(assumption)).
% 0.98/1.19 tff(1056,assumption,(c1_1(a412)), introduced(assumption)).
% 0.98/1.19 tff(1057,assumption,(c0_1(a412)), introduced(assumption)).
% 0.98/1.19 tff(1058,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1059,plain,
% 0.98/1.19 (((~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402))) <=> (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1060,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1059])).
% 0.98/1.19 tff(1061,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 0.98/1.19 inference(transitivity,[status(thm)],[1060, 1058])).
% 0.98/1.19 tff(1062,plain,
% 0.98/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(1063,plain,
% 0.98/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 0.98/1.19 tff(1064,plain,
% 0.98/1.19 (c2_1(a402) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1063, 138, 1057, 1056, 1055, 1049, 93, 447])).
% 0.98/1.19 tff(1065,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1064, 1054, 1053, 1048, 1050])).
% 0.98/1.19 tff(1066,plain,(hskp1 | (~c0_1(a412)) | (~c1_1(a412)) | (~c2_1(a412)) | c2_1(a426) | c1_1(a402) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1067,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1066, 155, 171, 436, 12, 1049, 93, 163, 425, 424, 1037, 1038, 1039])).
% 0.98/1.19 tff(1068,plain,((~hskp27) | (~c1_1(a445)) | hskp1 | c2_1(a426) | c1_1(a402) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1069,plain,
% 0.98/1.19 (~hskp27),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1068, 12, 436, 1049, 93, 425, 424, 1037, 1038, 1039])).
% 0.98/1.19 tff(1070,plain,
% 0.98/1.19 (hskp0),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[330, 1069, 303, 302])).
% 0.98/1.19 tff(1071,plain,
% 0.98/1.19 (c1_1(a400)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[346, 1070])).
% 0.98/1.19 tff(1072,plain,
% 0.98/1.19 (c2_1(a400)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[338, 1070])).
% 0.98/1.19 tff(1073,plain,
% 0.98/1.19 (hskp12),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[505, 1051, 12, 1048])).
% 0.98/1.19 tff(1074,plain,
% 0.98/1.19 (c0_1(a426)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[555, 1073])).
% 0.98/1.19 tff(1075,plain,
% 0.98/1.19 (c1_1(a426)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[547, 1073])).
% 0.98/1.19 tff(1076,assumption,(c2_1(a400)), introduced(assumption)).
% 0.98/1.19 tff(1077,assumption,(c1_1(a400)), introduced(assumption)).
% 0.98/1.19 tff(1078,plain,
% 0.98/1.19 (c2_1(a402) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[562, 138, 1077, 1076, 1049, 93, 447])).
% 0.98/1.19 tff(1079,plain,
% 0.98/1.19 (~c0_1(a400)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1078, 1075, 1048, 1050, 1074])).
% 0.98/1.19 tff(1080,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[569, 138, 12, 1048, 1077, 1076, 93, 22, 1051, 1079])).
% 0.98/1.19 tff(1081,plain,(hskp1 | (~c1_1(a400)) | (~c2_1(a400)) | c1_1(a402) | c2_1(a426) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1082,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1081, 1072, 1071, 12, 93, 1049, 436, 425, 424, 1037, 1038, 1039])).
% 0.98/1.19 tff(1083,plain,(hskp1 | c1_1(a402) | c2_1(a426) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1084,plain,
% 0.98/1.19 (c2_1(a426)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1083, 12, 436, 93, 425, 424, 1037, 1038, 1039, 303, 302, 301])).
% 0.98/1.19 tff(1085,plain,
% 0.98/1.19 (~hskp12),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[511, 1084])).
% 0.98/1.19 tff(1086,plain,
% 0.98/1.19 (~c3_1(a402)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[487, 1048])).
% 0.98/1.19 tff(1087,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[505, 1086, 1085, 12, 1048])).
% 0.98/1.19 tff(1088,plain,(hskp1 | c1_1(a402) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1089,plain,
% 0.98/1.19 (hskp1),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1088, 1039, 93, 425, 424, 436, 1037, 1038, 303, 302, 301])).
% 0.98/1.19 tff(1090,plain,
% 0.98/1.19 (~c3_1(a401)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[734, 1089])).
% 0.98/1.19 tff(1091,plain,
% 0.98/1.19 (c1_1(a401)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[742, 1089])).
% 0.98/1.19 tff(1092,plain,
% 0.98/1.19 (c0_1(a401)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[750, 1089])).
% 0.98/1.19 tff(1093,plain,
% 0.98/1.19 (hskp20),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[757, 138, 1092, 1091, 1090, 435])).
% 0.98/1.19 tff(1094,plain,
% 0.98/1.19 (c1_1(a449)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[765, 1093])).
% 0.98/1.19 tff(1095,plain,
% 0.98/1.19 (~hskp22),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[822, 1091, 425, 1090, 1092, 436, 424])).
% 0.98/1.19 tff(1096,plain,
% 0.98/1.19 (c3_1(a449)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[830, 1093])).
% 0.98/1.19 tff(1097,plain,
% 0.98/1.19 (~c2_1(a449)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[836, 1093])).
% 0.98/1.19 tff(1098,plain,
% 0.98/1.19 (~hskp2),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[864, 1097, 436, 1096, 1095, 1094, 425, 424, 93])).
% 0.98/1.19 tff(1099,plain,
% 0.98/1.19 (~hskp7),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[914, 1095, 1092, 1091, 1090])).
% 0.98/1.19 tff(1100,plain,
% 0.98/1.19 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1101,plain,
% 0.98/1.19 ((hskp7 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401))) <=> (hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1102,plain,
% 0.98/1.19 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1101])).
% 0.98/1.19 tff(1103,plain,
% 0.98/1.19 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401)))),
% 0.98/1.19 inference(transitivity,[status(thm)],[1102, 1100])).
% 0.98/1.19 tff(1104,plain,
% 0.98/1.19 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(1105,plain,
% 0.98/1.19 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 0.98/1.19 tff(1106,plain,
% 0.98/1.19 (hskp7 | hskp2 | c2_1(a401)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1105, 138, 1091, 1090, 106])).
% 0.98/1.19 tff(1107,plain,
% 0.98/1.19 (c2_1(a401)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1106, 1099, 1098])).
% 0.98/1.19 tff(1108,assumption,(c2_1(a405)), introduced(assumption)).
% 0.98/1.19 tff(1109,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1110,plain,
% 0.98/1.19 (((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420)) <=> (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1111,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1110])).
% 0.98/1.19 tff(1112,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 0.98/1.19 inference(transitivity,[status(thm)],[1111, 1109])).
% 0.98/1.19 tff(1113,plain,
% 0.98/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(1114,plain,
% 0.98/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 0.98/1.19 tff(1115,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1114, 138, 96, 94, 767, 769, 1037, 1038, 1039, 768, 11, 1108])).
% 0.98/1.19 tff(1116,plain,((~c2_1(a405)) | (~c0_1(a405)) | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1117,plain,
% 0.98/1.19 (~c2_1(a405)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1116, 1092, 94, 96, 1091, 1037, 1038, 1039, 1090])).
% 0.98/1.19 tff(1118,plain,
% 0.98/1.19 (hskp16),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[932, 1099, 1117])).
% 0.98/1.19 tff(1119,plain,
% 0.98/1.19 (~c0_1(a434)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[944, 1118])).
% 0.98/1.19 tff(1120,plain,
% 0.98/1.19 (~c3_1(a434)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[938, 1118])).
% 0.98/1.19 tff(1121,plain,
% 0.98/1.19 (c2_1(a434)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[974, 1120, 94, 1092, 1091, 1119, 1090, 1099, 1098, 96])).
% 0.98/1.19 tff(1122,plain,
% 0.98/1.19 (hskp14),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[994, 1099, 96, 94, 1092, 1091, 1090, 1117, 1098])).
% 0.98/1.19 tff(1123,plain,
% 0.98/1.19 (~c1_1(a428)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[382, 1122])).
% 0.98/1.19 tff(1124,plain,
% 0.98/1.19 (c2_1(a428)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[396, 1122])).
% 0.98/1.19 tff(1125,plain,
% 0.98/1.19 (c1_1(a434)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[963, 1118])).
% 0.98/1.19 tff(1126,plain,
% 0.98/1.19 (~c3_1(a428)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1004, 138, 1125, 1124, 1092, 1119, 1123, 1090, 647, 1121, 1107])).
% 0.98/1.19 tff(1127,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1011, 138, 1124, 1092, 1091, 1123, 1090, 811, 1126])).
% 0.98/1.19 tff(1128,plain,(c2_1(a420) | (~c3_1(a405)) | (~c0_1(a405)) | c0_1(a420) | c1_1(a420) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c1_1(a402) | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1129,plain,
% 0.98/1.19 (c2_1(a420)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1128, 1038, 96, 1037, 94, 436, 425, 424, 93, 303, 302, 301])).
% 0.98/1.19 tff(1130,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1131,plain,
% 0.98/1.19 (((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a420) | c0_1(a420) | (~c2_1(a420)) | c3_1(a403) | c0_1(a403) | c2_1(a403)) <=> (c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1132,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a420) | c0_1(a420) | (~c2_1(a420)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1131])).
% 0.98/1.19 tff(1133,plain,
% 0.98/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a420) | c0_1(a420) | (~c2_1(a420)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 0.98/1.19 inference(transitivity,[status(thm)],[1132, 1130])).
% 0.98/1.19 tff(1134,plain,
% 0.98/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a420) | c0_1(a420) | (~c2_1(a420)) | c3_1(a403) | c0_1(a403) | c2_1(a403))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(1135,plain,
% 0.98/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.98/1.19 tff(1136,plain,
% 0.98/1.19 ((~c2_1(a420)) | (~c1_1(a403))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1135, 138, 1037, 1038, 303, 302, 301, 313])).
% 0.98/1.19 tff(1137,plain,
% 0.98/1.19 (~c1_1(a403)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1136, 1129])).
% 0.98/1.19 tff(1138,plain,
% 0.98/1.19 (((~hskp11) | (~c2_1(a420))) <=> ((~hskp11) | (~c2_1(a420)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1139,plain,
% 0.98/1.19 (((~c2_1(a420)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a420)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1140,axiom,((~c2_1(a420)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.98/1.19 tff(1141,plain,
% 0.98/1.19 ((~hskp11) | (~c2_1(a420))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.98/1.19 tff(1142,plain,
% 0.98/1.19 ((~hskp11) | (~c2_1(a420))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1141, 1138])).
% 0.98/1.19 tff(1143,plain,
% 0.98/1.19 (~hskp11),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1142, 1129])).
% 0.98/1.19 tff(1144,plain,
% 0.98/1.19 (hskp1),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[571, 1143, 93, 425, 424, 436, 303, 1137, 302])).
% 0.98/1.19 tff(1145,plain,
% 0.98/1.19 (~c3_1(a401)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[734, 1144])).
% 0.98/1.19 tff(1146,plain,
% 0.98/1.19 (c1_1(a401)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[742, 1144])).
% 0.98/1.19 tff(1147,plain,
% 0.98/1.19 (c0_1(a401)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[750, 1144])).
% 0.98/1.19 tff(1148,plain,
% 0.98/1.19 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1149,plain,
% 0.98/1.19 ((hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a420) | (~c2_1(a420)) | (~c3_1(a420))) <=> (hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1150,plain,
% 0.98/1.19 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a420) | (~c2_1(a420)) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1149])).
% 0.98/1.19 tff(1151,plain,
% 0.98/1.19 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a420) | (~c2_1(a420)) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420)))),
% 0.98/1.19 inference(transitivity,[status(thm)],[1150, 1148])).
% 0.98/1.19 tff(1152,plain,
% 0.98/1.19 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a420) | (~c2_1(a420)) | (~c3_1(a420)))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(1153,plain,
% 0.98/1.19 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 0.98/1.19 tff(1154,plain,
% 0.98/1.19 (~c3_1(a420)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1153, 138, 1143, 1147, 1146, 1037, 1129, 1145, 1036])).
% 0.98/1.19 tff(1155,plain,
% 0.98/1.19 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1156,plain,
% 0.98/1.19 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c3_1(a420) | (~c2_1(a420))) <=> (c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1157,plain,
% 0.98/1.19 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420)))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1156])).
% 0.98/1.19 tff(1158,plain,
% 0.98/1.19 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420))),
% 0.98/1.19 inference(transitivity,[status(thm)],[1157, 1155])).
% 0.98/1.19 tff(1159,plain,
% 0.98/1.19 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(1160,plain,
% 0.98/1.19 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420)),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.98/1.19 tff(1161,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1160, 138, 1147, 1146, 1038, 1129, 1145, 811, 1154])).
% 0.98/1.19 tff(1162,plain,(c1_1(a420) | c0_1(a420) | c1_1(a402) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~c0_1(a405)) | (~c3_1(a405))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1163,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1162, 1026, 1020, 93, 423, 415, 414, 303, 302, 301, 96, 94])).
% 0.98/1.19 tff(1164,plain,(c0_1(a403) | c1_1(a402) | c2_1(a403) | c3_1(a403) | (~c0_1(a405)) | (~c3_1(a405)) | (~c1_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(1165,plain,
% 0.98/1.19 (c0_1(a403)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1164, 302, 93, 301, 96, 94, 95, 55])).
% 0.98/1.19 tff(1166,plain,
% 0.98/1.19 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.98/1.19 inference(bind,[status(th)],[])).
% 0.98/1.19 tff(1167,plain,
% 0.98/1.19 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.98/1.19 inference(quant_intro,[status(thm)],[1166])).
% 0.98/1.19 tff(1168,plain,
% 0.98/1.19 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(1169,plain,
% 0.98/1.19 (^[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)) | (~c2_1(V)) | (~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)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.98/1.19 inference(bind,[status(th)],[])).
% 0.98/1.19 tff(1170,plain,
% 0.98/1.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.98/1.19 inference(quant_intro,[status(thm)],[1169])).
% 0.98/1.19 tff(1171,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.98/1.20 tff(1172,plain,
% 0.98/1.20 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 0.98/1.20 tff(1173,plain,
% 0.98/1.20 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1172, 1168])).
% 0.98/1.20 tff(1174,plain,(
% 0.98/1.20 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.98/1.20 inference(skolemize,[status(sab)],[1173])).
% 0.98/1.20 tff(1175,plain,
% 0.98/1.20 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1174, 1167])).
% 0.98/1.20 tff(1176,assumption,(c0_1(a403)), introduced(assumption)).
% 0.98/1.20 tff(1177,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1178,plain,
% 0.98/1.20 ((hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c3_1(a403) | (~c0_1(a403))) <=> (hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1179,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))))),
% 0.98/1.20 inference(monotonicity,[status(thm)],[1178])).
% 0.98/1.20 tff(1180,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.98/1.20 inference(transitivity,[status(thm)],[1179, 1177])).
% 0.98/1.20 tff(1181,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))),
% 0.98/1.20 inference(quant_inst,[status(thm)],[])).
% 0.98/1.20 tff(1182,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.98/1.20 tff(1183,plain,
% 0.98/1.20 (hskp22),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1182, 138, 95, 94, 1176, 302, 301, 851, 146])).
% 0.98/1.20 tff(1184,plain,
% 0.98/1.20 (~c1_1(a451)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[775, 1183])).
% 0.98/1.20 tff(1185,plain,
% 0.98/1.20 (c2_1(a451)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[783, 1183])).
% 0.98/1.20 tff(1186,plain,
% 0.98/1.20 (c0_1(a451)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[791, 1183])).
% 0.98/1.20 tff(1187,plain,
% 0.98/1.20 (((~hskp3) | (~c0_1(a403))) <=> ((~hskp3) | (~c0_1(a403)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1188,plain,
% 0.98/1.20 (((~c0_1(a403)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a403)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1189,axiom,((~c0_1(a403)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.98/1.20 tff(1190,plain,
% 0.98/1.20 ((~hskp3) | (~c0_1(a403))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.98/1.20 tff(1191,plain,
% 0.98/1.20 ((~hskp3) | (~c0_1(a403))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1190, 1187])).
% 0.98/1.20 tff(1192,plain,
% 0.98/1.20 (~hskp3),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1191, 1176])).
% 0.98/1.20 tff(1193,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1194,plain,
% 0.98/1.20 ((hskp3 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451))) <=> (hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1195,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))))),
% 0.98/1.20 inference(monotonicity,[status(thm)],[1194])).
% 0.98/1.20 tff(1196,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 0.98/1.20 inference(transitivity,[status(thm)],[1195, 1193])).
% 0.98/1.20 tff(1197,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))),
% 0.98/1.20 inference(quant_inst,[status(thm)],[])).
% 0.98/1.20 tff(1198,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 0.98/1.20 tff(1199,plain,
% 0.98/1.20 (~c3_1(a451)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1198, 138, 1192, 1186, 1185, 1184, 1175])).
% 0.98/1.20 tff(1200,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1201,plain,
% 0.98/1.20 (((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451))) <=> (c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1202,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460))))),
% 0.98/1.20 inference(monotonicity,[status(thm)],[1201])).
% 0.98/1.20 tff(1203,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.98/1.20 inference(transitivity,[status(thm)],[1202, 1200])).
% 0.98/1.20 tff(1204,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))),
% 0.98/1.20 inference(quant_inst,[status(thm)],[])).
% 0.98/1.20 tff(1205,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.98/1.20 tff(1206,plain,
% 0.98/1.20 (~c0_1(a460)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1205, 138, 218, 1185, 204, 1184, 811, 1199])).
% 0.98/1.20 tff(1207,plain,
% 0.98/1.20 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1208,plain,
% 0.98/1.20 ((hskp27 | hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460)) <=> (hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1209,plain,
% 0.98/1.20 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460)))),
% 0.98/1.20 inference(monotonicity,[status(thm)],[1208])).
% 0.98/1.20 tff(1210,plain,
% 0.98/1.20 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460))),
% 0.98/1.20 inference(transitivity,[status(thm)],[1209, 1207])).
% 0.98/1.20 tff(1211,plain,
% 0.98/1.20 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460))),
% 0.98/1.20 inference(quant_inst,[status(thm)],[])).
% 0.98/1.20 tff(1212,plain,
% 0.98/1.20 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 0.98/1.20 tff(1213,plain,
% 0.98/1.20 (hskp0 | c0_1(a460)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1212, 138, 180, 210, 204, 323])).
% 0.98/1.20 tff(1214,plain,
% 0.98/1.20 (hskp0),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1213, 1206])).
% 0.98/1.20 tff(1215,plain,
% 0.98/1.20 (~c3_1(a400)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[366, 1214])).
% 0.98/1.20 tff(1216,plain,
% 0.98/1.20 (c1_1(a400)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[346, 1214])).
% 0.98/1.20 tff(1217,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1218,plain,
% 0.98/1.20 (((~ndr1_0) | c3_1(a400) | (~c1_1(a400)) | (~c0_1(a400)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451))) <=> (c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1219,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a400) | (~c1_1(a400)) | (~c0_1(a400)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451)))),
% 0.98/1.20 inference(monotonicity,[status(thm)],[1218])).
% 0.98/1.20 tff(1220,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a400) | (~c1_1(a400)) | (~c0_1(a400)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451))),
% 0.98/1.20 inference(transitivity,[status(thm)],[1219, 1217])).
% 0.98/1.20 tff(1221,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a400) | (~c1_1(a400)) | (~c0_1(a400)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))),
% 0.98/1.20 inference(quant_inst,[status(thm)],[])).
% 0.98/1.20 tff(1222,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 0.98/1.20 tff(1223,plain,
% 0.98/1.20 (~c0_1(a400)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1222, 138, 1185, 1216, 1184, 1215, 811, 1199])).
% 0.98/1.20 tff(1224,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1225,plain,
% 0.98/1.20 ((hskp9 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460))) <=> (hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1226,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460))))),
% 0.98/1.20 inference(monotonicity,[status(thm)],[1225])).
% 0.98/1.20 tff(1227,plain,
% 0.98/1.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.20 inference(transitivity,[status(thm)],[1226, 1224])).
% 0.98/1.20 tff(1228,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))),
% 0.98/1.20 inference(quant_inst,[status(thm)],[])).
% 0.98/1.20 tff(1229,plain,
% 0.98/1.20 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.98/1.20 tff(1230,plain,
% 0.98/1.20 (hskp9),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1229, 138, 218, 1186, 204, 1184, 583, 1206, 1199])).
% 0.98/1.20 tff(1231,plain,
% 0.98/1.20 (~c1_1(a416)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[606, 1230])).
% 0.98/1.20 tff(1232,plain,
% 0.98/1.20 (c2_1(a400)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[338, 1214])).
% 0.98/1.20 tff(1233,plain,
% 0.98/1.20 (c3_1(a416)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[667, 1230])).
% 0.98/1.20 tff(1234,plain,
% 0.98/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1235,plain,
% 0.98/1.20 (((~ndr1_0) | c3_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400))) <=> (c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1236,plain,
% 0.98/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451))))),
% 0.98/1.20 inference(monotonicity,[status(thm)],[1235])).
% 0.98/1.20 tff(1237,plain,
% 0.98/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451)))),
% 0.98/1.20 inference(transitivity,[status(thm)],[1236, 1234])).
% 0.98/1.20 tff(1238,plain,
% 0.98/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))),
% 0.98/1.20 inference(quant_inst,[status(thm)],[])).
% 0.98/1.20 tff(1239,plain,
% 0.98/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 0.98/1.20 tff(1240,plain,
% 0.98/1.20 (~c2_1(a416)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1239, 138, 1186, 1185, 1233, 1216, 1232, 1231, 647, 1223, 1199])).
% 0.98/1.20 tff(1241,plain,
% 0.98/1.20 (~c0_1(a416)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[612, 1230])).
% 0.98/1.20 tff(1242,plain,
% 0.98/1.20 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1243,plain,
% 0.98/1.20 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a416) | c0_1(a416) | (~c3_1(a416))) <=> (hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1244,plain,
% 0.98/1.20 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416))))),
% 0.98/1.20 inference(monotonicity,[status(thm)],[1243])).
% 0.98/1.20 tff(1245,plain,
% 0.98/1.20 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.20 inference(transitivity,[status(thm)],[1244, 1242])).
% 0.98/1.20 tff(1246,plain,
% 0.98/1.20 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a416) | c0_1(a416) | (~c3_1(a416)))),
% 0.98/1.20 inference(quant_inst,[status(thm)],[])).
% 0.98/1.20 tff(1247,plain,
% 0.98/1.20 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 0.98/1.20 tff(1248,plain,
% 0.98/1.20 (hskp5),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1247, 138, 1192, 1233, 1241, 54, 1240])).
% 0.98/1.20 tff(1249,plain,
% 0.98/1.20 (((~hskp5) | (~c0_1(a408))) <=> ((~hskp5) | (~c0_1(a408)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1250,plain,
% 0.98/1.20 (((~c0_1(a408)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a408)))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1251,axiom,((~c0_1(a408)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.98/1.20 tff(1252,plain,
% 0.98/1.20 ((~hskp5) | (~c0_1(a408))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 0.98/1.20 tff(1253,plain,
% 0.98/1.20 ((~hskp5) | (~c0_1(a408))),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1252, 1249])).
% 0.98/1.20 tff(1254,plain,
% 0.98/1.20 (~c0_1(a408)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1253, 1248])).
% 0.98/1.20 tff(1255,plain,
% 0.98/1.20 (((~hskp5) | c3_1(a408)) <=> ((~hskp5) | c3_1(a408))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1256,axiom,((~hskp5) | c3_1(a408)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.98/1.20 tff(1257,plain,
% 0.98/1.20 ((~hskp5) | c3_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 0.98/1.20 tff(1258,plain,
% 0.98/1.20 ((~hskp5) | c3_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1257, 1255])).
% 0.98/1.20 tff(1259,plain,
% 0.98/1.20 ((~hskp5) | c3_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1258, 1255])).
% 0.98/1.20 tff(1260,plain,
% 0.98/1.20 ((~hskp5) | c3_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1259, 1255])).
% 0.98/1.20 tff(1261,plain,
% 0.98/1.20 ((~hskp5) | c3_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1260, 1255])).
% 0.98/1.20 tff(1262,plain,
% 0.98/1.20 (c3_1(a408)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1261, 1248])).
% 0.98/1.20 tff(1263,plain,
% 0.98/1.20 (((~hskp5) | c2_1(a408)) <=> ((~hskp5) | c2_1(a408))),
% 0.98/1.20 inference(rewrite,[status(thm)],[])).
% 0.98/1.20 tff(1264,axiom,((~hskp5) | c2_1(a408)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.98/1.20 tff(1265,plain,
% 0.98/1.20 ((~hskp5) | c2_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 0.98/1.20 tff(1266,plain,
% 0.98/1.20 ((~hskp5) | c2_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1265, 1263])).
% 0.98/1.20 tff(1267,plain,
% 0.98/1.20 ((~hskp5) | c2_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1266, 1263])).
% 0.98/1.20 tff(1268,plain,
% 0.98/1.20 ((~hskp5) | c2_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1267, 1263])).
% 0.98/1.20 tff(1269,plain,
% 0.98/1.20 ((~hskp5) | c2_1(a408)),
% 0.98/1.20 inference(modus_ponens,[status(thm)],[1268, 1263])).
% 0.98/1.20 tff(1270,plain,
% 0.98/1.20 (c2_1(a408)),
% 0.98/1.20 inference(unit_resolution,[status(thm)],[1269, 1248])).
% 0.98/1.20 tff(1271,plain,
% 0.98/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1272,plain,
% 0.98/1.21 (((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460))) <=> (c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1273,plain,
% 0.98/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460))))),
% 0.98/1.21 inference(monotonicity,[status(thm)],[1272])).
% 0.98/1.21 tff(1274,plain,
% 0.98/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.21 inference(transitivity,[status(thm)],[1273, 1271])).
% 0.98/1.21 tff(1275,plain,
% 0.98/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))),
% 0.98/1.21 inference(quant_inst,[status(thm)],[])).
% 0.98/1.21 tff(1276,plain,
% 0.98/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 0.98/1.21 tff(1277,plain,
% 0.98/1.21 ($false),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1276, 138, 218, 1233, 1270, 1262, 210, 1231, 1254, 43, 1206, 1240])).
% 0.98/1.21 tff(1278,plain,(hskp19 | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.98/1.21 tff(1279,plain,
% 0.98/1.21 (hskp19),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1278, 1165, 94, 95, 302, 301, 96, 55])).
% 0.98/1.21 tff(1280,plain,
% 0.98/1.21 (~c0_1(a445)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[299, 1279])).
% 0.98/1.21 tff(1281,plain,
% 0.98/1.21 (c3_1(a445)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[422, 1279])).
% 0.98/1.21 tff(1282,plain,
% 0.98/1.21 (c1_1(a445)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[413, 1279])).
% 0.98/1.21 tff(1283,plain,
% 0.98/1.21 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1284,plain,
% 0.98/1.21 ((hskp11 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c0_1(a403))) <=> (hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1285,plain,
% 0.98/1.21 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0)))),
% 0.98/1.21 inference(monotonicity,[status(thm)],[1284])).
% 0.98/1.21 tff(1286,plain,
% 0.98/1.21 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 0.98/1.21 inference(transitivity,[status(thm)],[1285, 1283])).
% 0.98/1.21 tff(1287,plain,
% 0.98/1.21 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))),
% 0.98/1.21 inference(quant_inst,[status(thm)],[])).
% 0.98/1.21 tff(1288,plain,
% 0.98/1.21 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0)),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 0.98/1.21 tff(1289,plain,
% 0.98/1.21 (hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1288, 138, 301, 630])).
% 0.98/1.21 tff(1290,plain,
% 0.98/1.21 (hskp11),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1289, 23, 1176, 302])).
% 0.98/1.21 tff(1291,plain,
% 0.98/1.21 (~c2_1(a420)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1142, 1290])).
% 0.98/1.21 tff(1292,plain,
% 0.98/1.21 (~c1_1(a420)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1025, 1290])).
% 0.98/1.21 tff(1293,plain,
% 0.98/1.21 (~c0_1(a420)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1019, 1290])).
% 0.98/1.21 tff(1294,plain,
% 0.98/1.21 (hskp1),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1045, 138, 23, 1293, 1292, 1291, 33])).
% 0.98/1.21 tff(1295,plain,
% 0.98/1.21 (~c3_1(a401)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[734, 1294])).
% 0.98/1.21 tff(1296,plain,
% 0.98/1.21 (c1_1(a401)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[742, 1294])).
% 0.98/1.21 tff(1297,plain,
% 0.98/1.21 (c0_1(a401)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[750, 1294])).
% 0.98/1.21 tff(1298,plain,
% 0.98/1.21 (~hskp22),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[822, 1295, 425, 1296, 1297, 436, 424])).
% 0.98/1.21 tff(1299,plain,
% 0.98/1.21 (~hskp7),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[914, 1298, 1297, 1296, 1295])).
% 0.98/1.21 tff(1300,plain,
% 0.98/1.21 (^[U: $i] : refl((hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.98/1.21 inference(bind,[status(th)],[])).
% 0.98/1.21 tff(1301,plain,
% 0.98/1.21 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/1.21 inference(quant_intro,[status(thm)],[1300])).
% 0.98/1.21 tff(1302,plain,
% 0.98/1.21 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1303,plain,
% 0.98/1.21 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp3) <=> ((hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp3))), rewrite(((hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp3) <=> (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp3) <=> (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.98/1.21 inference(bind,[status(th)],[])).
% 0.98/1.21 tff(1304,plain,
% 0.98/1.21 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp3) <=> ![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/1.21 inference(quant_intro,[status(thm)],[1303])).
% 0.98/1.21 tff(1305,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.98/1.21 tff(1306,plain,
% 0.98/1.21 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 0.98/1.21 tff(1307,plain,
% 0.98/1.21 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1306, 1302])).
% 0.98/1.21 tff(1308,plain,(
% 0.98/1.21 ![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/1.21 inference(skolemize,[status(sab)],[1307])).
% 0.98/1.21 tff(1309,plain,
% 0.98/1.21 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1308, 1301])).
% 0.98/1.21 tff(1310,plain,
% 0.98/1.21 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1311,plain,
% 0.98/1.21 ((hskp16 | hskp3 | (~ndr1_0) | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445))) <=> (hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1312,plain,
% 0.98/1.21 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445))))),
% 0.98/1.21 inference(monotonicity,[status(thm)],[1311])).
% 0.98/1.21 tff(1313,plain,
% 0.98/1.21 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.98/1.21 inference(transitivity,[status(thm)],[1312, 1310])).
% 0.98/1.21 tff(1314,plain,
% 0.98/1.21 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))),
% 0.98/1.21 inference(quant_inst,[status(thm)],[])).
% 0.98/1.21 tff(1315,plain,
% 0.98/1.21 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.98/1.21 tff(1316,plain,
% 0.98/1.21 (hskp16),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1315, 138, 1192, 436, 425, 424, 1309])).
% 0.98/1.21 tff(1317,plain,
% 0.98/1.21 (~c3_1(a434)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[938, 1316])).
% 0.98/1.21 tff(1318,plain,
% 0.98/1.21 (c1_1(a434)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[963, 1316])).
% 0.98/1.21 tff(1319,plain,
% 0.98/1.21 (hskp7 | hskp2 | c2_1(a434)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[954, 138, 1318, 1317, 106])).
% 0.98/1.21 tff(1320,plain,
% 0.98/1.21 (c2_1(a434)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1319, 1299, 23])).
% 0.98/1.21 tff(1321,plain,
% 0.98/1.21 (~c0_1(a434)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[944, 1316])).
% 0.98/1.21 tff(1322,plain,
% 0.98/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1323,plain,
% 0.98/1.21 (((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a420) | c0_1(a420) | (~c3_1(a420))) <=> (c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1324,plain,
% 0.98/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434))))),
% 0.98/1.21 inference(monotonicity,[status(thm)],[1323])).
% 0.98/1.21 tff(1325,plain,
% 0.98/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434)))),
% 0.98/1.21 inference(transitivity,[status(thm)],[1324, 1322])).
% 0.98/1.21 tff(1326,plain,
% 0.98/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a420) | c0_1(a420) | (~c3_1(a420)))),
% 0.98/1.21 inference(quant_inst,[status(thm)],[])).
% 0.98/1.21 tff(1327,plain,
% 0.98/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 0.98/1.21 tff(1328,plain,
% 0.98/1.21 ((~c3_1(a420)) | (~c2_1(a434))),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1327, 138, 1321, 1317, 1293, 1292, 1291, 718])).
% 0.98/1.21 tff(1329,plain,
% 0.98/1.21 (~c3_1(a420)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1328, 1320])).
% 0.98/1.21 tff(1330,plain,
% 0.98/1.21 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.98/1.21 inference(bind,[status(th)],[])).
% 0.98/1.21 tff(1331,plain,
% 0.98/1.21 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.98/1.21 inference(quant_intro,[status(thm)],[1330])).
% 0.98/1.21 tff(1332,plain,
% 0.98/1.21 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1333,plain,
% 0.98/1.21 (^[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(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)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_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(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_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(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_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(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.98/1.21 inference(bind,[status(th)],[])).
% 0.98/1.21 tff(1334,plain,
% 0.98/1.21 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.98/1.21 inference(quant_intro,[status(thm)],[1333])).
% 0.98/1.21 tff(1335,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.98/1.21 tff(1336,plain,
% 0.98/1.21 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 0.98/1.21 tff(1337,plain,
% 0.98/1.21 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1336, 1332])).
% 0.98/1.21 tff(1338,plain,(
% 0.98/1.21 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.98/1.21 inference(skolemize,[status(sab)],[1337])).
% 0.98/1.21 tff(1339,plain,
% 0.98/1.21 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1338, 1331])).
% 0.98/1.21 tff(1340,plain,
% 0.98/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1341,plain,
% 0.98/1.21 ((hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a420) | c0_1(a420) | c3_1(a420)) <=> (hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1342,plain,
% 0.98/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a420) | c0_1(a420) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434))))),
% 0.98/1.21 inference(monotonicity,[status(thm)],[1341])).
% 0.98/1.21 tff(1343,plain,
% 0.98/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a420) | c0_1(a420) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.21 inference(transitivity,[status(thm)],[1342, 1340])).
% 0.98/1.21 tff(1344,plain,
% 0.98/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a420) | c0_1(a420) | c3_1(a420))),
% 0.98/1.21 inference(quant_inst,[status(thm)],[])).
% 0.98/1.21 tff(1345,plain,
% 0.98/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 0.98/1.21 tff(1346,plain,
% 0.98/1.21 (c3_1(a420) | (~c2_1(a434))),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1345, 138, 1192, 1318, 1317, 1293, 1292, 1339])).
% 0.98/1.21 tff(1347,plain,
% 0.98/1.21 ($false),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1346, 1329, 1320])).
% 0.98/1.21 tff(1348,plain,(hskp2 | (~c3_1(a445)) | (~c1_1(a445)) | c0_1(a445) | (~c0_1(a403)) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.21 tff(1349,plain,
% 0.98/1.21 (hskp2),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1348, 1281, 1282, 1280, 1165, 302, 301])).
% 0.98/1.21 tff(1350,plain,
% 0.98/1.21 (c0_1(a402)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[469, 1349])).
% 0.98/1.21 tff(1351,plain,
% 0.98/1.21 (~hskp3),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1191, 1165])).
% 0.98/1.21 tff(1352,assumption,(c0_1(a402)), introduced(assumption)).
% 0.98/1.21 tff(1353,plain,
% 0.98/1.21 (~c3_1(a402)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[487, 1352])).
% 0.98/1.21 tff(1354,plain,
% 0.98/1.21 (~c2_1(a445)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[519, 12, 1353, 1352])).
% 0.98/1.21 tff(1355,plain,
% 0.98/1.21 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1356,plain,
% 0.98/1.21 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445))) <=> (hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1357,plain,
% 0.98/1.21 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445))))),
% 0.98/1.21 inference(monotonicity,[status(thm)],[1356])).
% 0.98/1.21 tff(1358,plain,
% 0.98/1.21 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 0.98/1.21 inference(transitivity,[status(thm)],[1357, 1355])).
% 0.98/1.21 tff(1359,plain,
% 0.98/1.21 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))),
% 0.98/1.21 inference(quant_inst,[status(thm)],[])).
% 0.98/1.21 tff(1360,plain,
% 0.98/1.21 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 0.98/1.21 tff(1361,plain,
% 0.98/1.21 (hskp5 | c2_1(a445)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1360, 138, 44, 425, 424, 54])).
% 0.98/1.21 tff(1362,plain,
% 0.98/1.21 (hskp5),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1361, 1354])).
% 0.98/1.21 tff(1363,plain,
% 0.98/1.21 (~c0_1(a408)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1253, 1362])).
% 0.98/1.21 tff(1364,plain,
% 0.98/1.21 (c2_1(a408)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1269, 1362])).
% 0.98/1.21 tff(1365,plain,
% 0.98/1.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1366,plain,
% 0.98/1.21 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a408) | (~c2_1(a408)) | (~c1_1(a408))) <=> (hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1367,plain,
% 0.98/1.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a408) | (~c2_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408))))),
% 0.98/1.21 inference(monotonicity,[status(thm)],[1366])).
% 0.98/1.21 tff(1368,plain,
% 0.98/1.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a408) | (~c2_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408)))),
% 0.98/1.21 inference(transitivity,[status(thm)],[1367, 1365])).
% 0.98/1.21 tff(1369,plain,
% 0.98/1.21 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a408) | (~c2_1(a408)) | (~c1_1(a408)))),
% 0.98/1.21 inference(quant_inst,[status(thm)],[])).
% 0.98/1.21 tff(1370,plain,
% 0.98/1.21 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408))),
% 0.98/1.21 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 0.98/1.21 tff(1371,plain,
% 0.98/1.21 (~c1_1(a408)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1370, 138, 12, 1364, 1352, 1363, 93, 22, 1353])).
% 0.98/1.21 tff(1372,plain,
% 0.98/1.21 (hskp16),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[1315, 138, 44, 436, 425, 424, 1309])).
% 0.98/1.21 tff(1373,plain,
% 0.98/1.21 (~c0_1(a434)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[944, 1372])).
% 0.98/1.21 tff(1374,plain,
% 0.98/1.21 (c1_1(a434)),
% 0.98/1.21 inference(unit_resolution,[status(thm)],[963, 1372])).
% 0.98/1.21 tff(1375,plain,
% 0.98/1.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1376,plain,
% 0.98/1.21 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.21 inference(rewrite,[status(thm)],[])).
% 0.98/1.21 tff(1377,plain,
% 0.98/1.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434))))),
% 0.98/1.22 inference(monotonicity,[status(thm)],[1376])).
% 0.98/1.22 tff(1378,plain,
% 0.98/1.22 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.22 inference(transitivity,[status(thm)],[1377, 1375])).
% 0.98/1.22 tff(1379,plain,
% 0.98/1.22 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 0.98/1.22 inference(quant_inst,[status(thm)],[])).
% 0.98/1.22 tff(1380,plain,
% 0.98/1.22 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 0.98/1.22 tff(1381,plain,
% 0.98/1.22 (hskp1 | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434))),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1380, 138, 1374, 1373, 93, 22])).
% 0.98/1.22 tff(1382,plain,
% 0.98/1.22 (~c2_1(a434)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1381, 12, 1353, 1352])).
% 0.98/1.22 tff(1383,plain,
% 0.98/1.22 (~c3_1(a434)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[938, 1372])).
% 0.98/1.22 tff(1384,plain,
% 0.98/1.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1385,plain,
% 0.98/1.22 ((hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434))) <=> (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1386,plain,
% 0.98/1.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434))))),
% 0.98/1.22 inference(monotonicity,[status(thm)],[1385])).
% 0.98/1.22 tff(1387,plain,
% 0.98/1.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434)))),
% 0.98/1.22 inference(transitivity,[status(thm)],[1386, 1384])).
% 0.98/1.22 tff(1388,plain,
% 0.98/1.22 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))),
% 0.98/1.22 inference(quant_inst,[status(thm)],[])).
% 0.98/1.22 tff(1389,plain,
% 0.98/1.22 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 0.98/1.22 tff(1390,plain,
% 0.98/1.22 (hskp9 | c3_1(a402) | (~c0_1(a402))),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1389, 138, 1374, 1373, 1383, 93, 583])).
% 0.98/1.22 tff(1391,plain,
% 0.98/1.22 (hskp9),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1390, 1352, 1353])).
% 0.98/1.22 tff(1392,plain,
% 0.98/1.22 (~c1_1(a416)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[606, 1391])).
% 0.98/1.22 tff(1393,plain,
% 0.98/1.22 (~c0_1(a416)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[612, 1391])).
% 0.98/1.22 tff(1394,plain,
% 0.98/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1395,plain,
% 0.98/1.22 (((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1396,plain,
% 0.98/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434))))),
% 0.98/1.22 inference(monotonicity,[status(thm)],[1395])).
% 0.98/1.22 tff(1397,plain,
% 0.98/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434)))),
% 0.98/1.22 inference(transitivity,[status(thm)],[1396, 1394])).
% 0.98/1.22 tff(1398,plain,
% 0.98/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))),
% 0.98/1.22 inference(quant_inst,[status(thm)],[])).
% 0.98/1.22 tff(1399,plain,
% 0.98/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.98/1.22 tff(1400,plain,
% 0.98/1.22 (~c2_1(a416)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1399, 138, 1374, 1373, 1383, 1393, 1392, 313, 1382])).
% 0.98/1.22 tff(1401,plain,
% 0.98/1.22 (^[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)) | c1_1(W) | c2_1(W) | (~c3_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) | (~c3_1(W))))),
% 0.98/1.22 inference(bind,[status(th)],[])).
% 0.98/1.22 tff(1402,plain,
% 0.98/1.22 (![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)) | 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)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/1.22 inference(quant_intro,[status(thm)],[1401])).
% 0.98/1.22 tff(1403,plain,
% 0.98/1.22 (![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)) | 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)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1404,plain,
% 0.98/1.22 (^[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)) | (~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)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_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) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_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) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | 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)) | c1_1(W) | (~c3_1(W))) | c2_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) | (~c3_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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | 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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.98/1.22 inference(bind,[status(th)],[])).
% 0.98/1.22 tff(1405,plain,
% 0.98/1.22 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_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)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/1.22 inference(quant_intro,[status(thm)],[1404])).
% 0.98/1.22 tff(1406,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.98/1.22 tff(1407,plain,
% 0.98/1.22 (![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 0.98/1.22 tff(1408,plain,
% 0.98/1.22 (![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1407, 1403])).
% 0.98/1.22 tff(1409,plain,(
% 0.98/1.22 ![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/1.22 inference(skolemize,[status(sab)],[1408])).
% 0.98/1.22 tff(1410,plain,
% 0.98/1.22 (![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1409, 1402])).
% 0.98/1.22 tff(1411,plain,
% 0.98/1.22 (^[U: $i] : refl((hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.98/1.22 inference(bind,[status(th)],[])).
% 0.98/1.22 tff(1412,plain,
% 0.98/1.22 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.98/1.22 inference(quant_intro,[status(thm)],[1411])).
% 0.98/1.22 tff(1413,plain,
% 0.98/1.22 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1414,plain,
% 0.98/1.22 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp3) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp3) <=> (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp3) <=> (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.98/1.22 inference(bind,[status(th)],[])).
% 0.98/1.22 tff(1415,plain,
% 0.98/1.22 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp3) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.98/1.22 inference(quant_intro,[status(thm)],[1414])).
% 0.98/1.22 tff(1416,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.98/1.22 tff(1417,plain,
% 0.98/1.22 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.98/1.22 tff(1418,plain,
% 0.98/1.22 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1417, 1413])).
% 0.98/1.22 tff(1419,plain,(
% 0.98/1.22 ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.98/1.22 inference(skolemize,[status(sab)],[1418])).
% 0.98/1.22 tff(1420,plain,
% 0.98/1.22 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1419, 1412])).
% 0.98/1.22 tff(1421,plain,
% 0.98/1.22 (c3_1(a416)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[667, 1391])).
% 0.98/1.22 tff(1422,plain,
% 0.98/1.22 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1423,plain,
% 0.98/1.22 ((hskp18 | hskp3 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416))) <=> (hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1424,plain,
% 0.98/1.22 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416))))),
% 0.98/1.22 inference(monotonicity,[status(thm)],[1423])).
% 0.98/1.22 tff(1425,plain,
% 0.98/1.22 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.22 inference(transitivity,[status(thm)],[1424, 1422])).
% 0.98/1.22 tff(1426,plain,
% 0.98/1.22 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)))),
% 0.98/1.22 inference(quant_inst,[status(thm)],[])).
% 0.98/1.22 tff(1427,plain,
% 0.98/1.22 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 0.98/1.22 tff(1428,plain,
% 0.98/1.22 (hskp18 | c2_1(a416)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1427, 138, 44, 1421, 1392, 1420])).
% 0.98/1.22 tff(1429,plain,
% 0.98/1.22 (hskp18),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1428, 1400])).
% 0.98/1.22 tff(1430,plain,
% 0.98/1.22 (((~hskp18) | (~c3_1(a440))) <=> ((~hskp18) | (~c3_1(a440)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1431,plain,
% 0.98/1.22 (((~c3_1(a440)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a440)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1432,axiom,((~c3_1(a440)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.98/1.22 tff(1433,plain,
% 0.98/1.22 ((~hskp18) | (~c3_1(a440))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.98/1.22 tff(1434,plain,
% 0.98/1.22 ((~hskp18) | (~c3_1(a440))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1433, 1430])).
% 0.98/1.22 tff(1435,plain,
% 0.98/1.22 (~c3_1(a440)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1434, 1429])).
% 0.98/1.22 tff(1436,plain,
% 0.98/1.22 (((~hskp18) | (~c2_1(a440))) <=> ((~hskp18) | (~c2_1(a440)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1437,plain,
% 0.98/1.22 (((~c2_1(a440)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a440)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1438,axiom,((~c2_1(a440)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.98/1.22 tff(1439,plain,
% 0.98/1.22 ((~hskp18) | (~c2_1(a440))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 0.98/1.22 tff(1440,plain,
% 0.98/1.22 ((~hskp18) | (~c2_1(a440))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1439, 1436])).
% 0.98/1.22 tff(1441,plain,
% 0.98/1.22 (~c2_1(a440)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1440, 1429])).
% 0.98/1.22 tff(1442,plain,
% 0.98/1.22 (c3_1(a408)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1261, 1362])).
% 0.98/1.22 tff(1443,plain,
% 0.98/1.22 (((~hskp18) | c0_1(a440)) <=> ((~hskp18) | c0_1(a440))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1444,axiom,((~hskp18) | c0_1(a440)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.98/1.22 tff(1445,plain,
% 0.98/1.22 ((~hskp18) | c0_1(a440)),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 0.98/1.22 tff(1446,plain,
% 0.98/1.22 ((~hskp18) | c0_1(a440)),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1445, 1443])).
% 0.98/1.22 tff(1447,plain,
% 0.98/1.22 ((~hskp18) | c0_1(a440)),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1446, 1443])).
% 0.98/1.22 tff(1448,plain,
% 0.98/1.22 ((~hskp18) | c0_1(a440)),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1447, 1443])).
% 0.98/1.22 tff(1449,plain,
% 0.98/1.22 ((~hskp18) | c0_1(a440)),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1448, 1443])).
% 0.98/1.22 tff(1450,plain,
% 0.98/1.22 (c0_1(a440)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1449, 1429])).
% 0.98/1.22 tff(1451,plain,
% 0.98/1.22 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1452,plain,
% 0.98/1.22 (((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416))) <=> (c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1453,plain,
% 0.98/1.22 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | (c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440))))),
% 0.98/1.22 inference(monotonicity,[status(thm)],[1452])).
% 0.98/1.22 tff(1454,plain,
% 0.98/1.22 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440)))),
% 0.98/1.22 inference(transitivity,[status(thm)],[1453, 1451])).
% 0.98/1.22 tff(1455,plain,
% 0.98/1.22 ((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))),
% 0.98/1.22 inference(quant_inst,[status(thm)],[])).
% 0.98/1.22 tff(1456,plain,
% 0.98/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 0.98/1.22 tff(1457,plain,
% 0.98/1.22 ($false),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1456, 138, 1450, 1421, 1364, 1442, 1441, 1435, 1392, 1410, 1400, 1371])).
% 0.98/1.22 tff(1458,plain,(hskp1 | hskp3 | (~c0_1(a402)) | c1_1(a402) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.22 tff(1459,plain,
% 0.98/1.22 (hskp1),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1458, 1351, 1350, 93, 1281, 1280, 1282])).
% 0.98/1.22 tff(1460,plain,
% 0.98/1.22 (~c3_1(a401)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[734, 1459])).
% 0.98/1.22 tff(1461,plain,
% 0.98/1.22 (c1_1(a401)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[742, 1459])).
% 0.98/1.22 tff(1462,plain,
% 0.98/1.22 (c0_1(a401)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[750, 1459])).
% 0.98/1.22 tff(1463,plain,
% 0.98/1.22 (hskp20),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[757, 138, 1462, 1461, 1460, 435])).
% 0.98/1.22 tff(1464,plain,
% 0.98/1.22 (c1_1(a449)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[765, 1463])).
% 0.98/1.22 tff(1465,plain,
% 0.98/1.22 (~hskp22),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[822, 1460, 1281, 1461, 1462, 1282, 1280])).
% 0.98/1.22 tff(1466,plain,
% 0.98/1.22 (c3_1(a449)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[830, 1463])).
% 0.98/1.22 tff(1467,plain,
% 0.98/1.22 (~c2_1(a449)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[836, 1463])).
% 0.98/1.22 tff(1468,plain,
% 0.98/1.22 ($false),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[864, 1467, 1466, 1282, 1349, 1465, 1464, 1281, 1280, 93])).
% 0.98/1.22 tff(1469,plain,(c2_1(a403) | c1_1(a402) | c3_1(a403) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.98/1.22 tff(1470,plain,
% 0.98/1.22 (c2_1(a403)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1469, 301, 93, 94, 95, 96, 55])).
% 0.98/1.22 tff(1471,assumption,(c2_1(a403)), introduced(assumption)).
% 0.98/1.22 tff(1472,plain,
% 0.98/1.22 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1473,plain,
% 0.98/1.22 ((hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1474,plain,
% 0.98/1.22 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))))),
% 0.98/1.22 inference(monotonicity,[status(thm)],[1473])).
% 0.98/1.22 tff(1475,plain,
% 0.98/1.22 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 0.98/1.22 inference(transitivity,[status(thm)],[1474, 1472])).
% 0.98/1.22 tff(1476,plain,
% 0.98/1.22 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 0.98/1.22 inference(quant_inst,[status(thm)],[])).
% 0.98/1.22 tff(1477,plain,
% 0.98/1.22 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 0.98/1.22 tff(1478,plain,
% 0.98/1.22 (hskp14),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1477, 138, 95, 94, 303, 1471, 301, 361, 146])).
% 0.98/1.22 tff(1479,plain,
% 0.98/1.22 (~c1_1(a428)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[382, 1478])).
% 0.98/1.22 tff(1480,plain,
% 0.98/1.22 (~c0_1(a428)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[388, 1478])).
% 0.98/1.22 tff(1481,plain,
% 0.98/1.22 (c2_1(a428)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[396, 1478])).
% 0.98/1.22 tff(1482,plain,
% 0.98/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1483,plain,
% 0.98/1.22 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a460) | c0_1(a460) | c2_1(a460)) <=> (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.22 inference(rewrite,[status(thm)],[])).
% 0.98/1.22 tff(1484,plain,
% 0.98/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460))))),
% 0.98/1.22 inference(monotonicity,[status(thm)],[1483])).
% 0.98/1.22 tff(1485,plain,
% 0.98/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460)))),
% 0.98/1.22 inference(transitivity,[status(thm)],[1484, 1482])).
% 0.98/1.22 tff(1486,plain,
% 0.98/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a460) | c0_1(a460) | c2_1(a460))),
% 0.98/1.22 inference(quant_inst,[status(thm)],[])).
% 0.98/1.22 tff(1487,plain,
% 0.98/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460))),
% 0.98/1.22 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 0.98/1.22 tff(1488,plain,
% 0.98/1.22 (c0_1(a460)),
% 0.98/1.22 inference(unit_resolution,[status(thm)],[1487, 138, 218, 1481, 210, 204, 1480, 1479, 313])).
% 0.98/1.22 tff(1489,plain,
% 0.98/1.22 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.98/1.23 inference(rewrite,[status(thm)],[])).
% 0.98/1.23 tff(1490,plain,
% 0.98/1.23 (((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428))) <=> (c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.98/1.23 inference(rewrite,[status(thm)],[])).
% 0.98/1.23 tff(1491,plain,
% 0.98/1.23 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460))))),
% 0.98/1.23 inference(monotonicity,[status(thm)],[1490])).
% 0.98/1.23 tff(1492,plain,
% 0.98/1.23 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.98/1.23 inference(transitivity,[status(thm)],[1491, 1489])).
% 0.98/1.23 tff(1493,plain,
% 0.98/1.23 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))),
% 0.98/1.23 inference(quant_inst,[status(thm)],[])).
% 0.98/1.23 tff(1494,plain,
% 0.98/1.23 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460))),
% 0.98/1.23 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 0.98/1.23 tff(1495,plain,
% 0.98/1.23 (c3_1(a428)),
% 0.98/1.23 inference(unit_resolution,[status(thm)],[1494, 138, 218, 1481, 204, 1479, 811, 1488])).
% 0.98/1.23 tff(1496,plain,
% 0.98/1.23 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.98/1.23 inference(bind,[status(th)],[])).
% 0.98/1.23 tff(1497,plain,
% 0.98/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.23 inference(quant_intro,[status(thm)],[1496])).
% 0.98/1.23 tff(1498,plain,
% 0.98/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.23 inference(rewrite,[status(thm)],[])).
% 0.98/1.23 tff(1499,plain,
% 0.98/1.23 (^[V: $i, U: $i] : 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))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_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))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_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))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_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))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.98/1.23 inference(bind,[status(th)],[])).
% 0.98/1.23 tff(1500,plain,
% 0.98/1.23 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.23 inference(quant_intro,[status(thm)],[1499])).
% 0.98/1.23 tff(1501,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.98/1.23 tff(1502,plain,
% 0.98/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.23 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 0.98/1.23 tff(1503,plain,
% 0.98/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.23 inference(modus_ponens,[status(thm)],[1502, 1498])).
% 0.98/1.23 tff(1504,plain,(
% 0.98/1.23 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.23 inference(skolemize,[status(sab)],[1503])).
% 0.98/1.23 tff(1505,plain,
% 0.98/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.98/1.23 inference(modus_ponens,[status(thm)],[1504, 1497])).
% 0.98/1.23 tff(1506,plain,
% 0.98/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)))),
% 0.98/1.23 inference(rewrite,[status(thm)],[])).
% 0.98/1.23 tff(1507,plain,
% 0.98/1.23 ((hskp1 | (~ndr1_0) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)))),
% 0.98/1.23 inference(rewrite,[status(thm)],[])).
% 0.98/1.23 tff(1508,plain,
% 0.98/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428))))),
% 0.98/1.23 inference(monotonicity,[status(thm)],[1507])).
% 0.98/1.23 tff(1509,plain,
% 0.98/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)))),
% 0.98/1.23 inference(transitivity,[status(thm)],[1508, 1506])).
% 0.98/1.23 tff(1510,plain,
% 0.98/1.23 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 0.98/1.23 inference(quant_inst,[status(thm)],[])).
% 0.98/1.23 tff(1511,plain,
% 0.98/1.23 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428))),
% 0.98/1.23 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 0.98/1.23 tff(1512,plain,
% 0.98/1.23 (hskp1),
% 0.98/1.23 inference(unit_resolution,[status(thm)],[1511, 138, 1481, 1480, 303, 1471, 301, 1505, 1495])).
% 0.98/1.23 tff(1513,plain,
% 0.98/1.23 (~c3_1(a401)),
% 0.98/1.23 inference(unit_resolution,[status(thm)],[734, 1512])).
% 0.98/1.23 tff(1514,plain,
% 0.98/1.23 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.98/1.23 inference(rewrite,[status(thm)],[])).
% 0.98/1.23 tff(1515,plain,
% 0.98/1.23 ((hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428))) <=> (hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1516,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1515])).
% 1.06/1.23 tff(1517,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1516, 1514])).
% 1.06/1.23 tff(1518,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1519,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 1.06/1.23 tff(1520,plain,
% 1.06/1.23 (hskp11),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1519, 138, 218, 1481, 204, 1480, 1036, 1488, 1495])).
% 1.06/1.23 tff(1521,plain,
% 1.06/1.23 (~c2_1(a420)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1142, 1520])).
% 1.06/1.23 tff(1522,plain,
% 1.06/1.23 (~c1_1(a420)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1025, 1520])).
% 1.06/1.23 tff(1523,plain,
% 1.06/1.23 (~c0_1(a420)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1019, 1520])).
% 1.06/1.23 tff(1524,plain,
% 1.06/1.23 (c1_1(a401)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[742, 1512])).
% 1.06/1.23 tff(1525,plain,
% 1.06/1.23 (c0_1(a401)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[750, 1512])).
% 1.06/1.23 tff(1526,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1527,plain,
% 1.06/1.23 ((hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a460) | c3_1(a460) | (~c0_1(a460))) <=> (hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1528,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1527])).
% 1.06/1.23 tff(1529,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1528, 1526])).
% 1.06/1.23 tff(1530,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1531,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.06/1.23 tff(1532,plain,
% 1.06/1.23 (hskp22 | (~c0_1(a460))),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1531, 138, 95, 94, 210, 204, 851, 146])).
% 1.06/1.23 tff(1533,plain,
% 1.06/1.23 (hskp22),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1532, 1488])).
% 1.06/1.23 tff(1534,plain,
% 1.06/1.23 (c2_1(a451)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[783, 1533])).
% 1.06/1.23 tff(1535,plain,
% 1.06/1.23 (c0_1(a451)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[791, 1533])).
% 1.06/1.23 tff(1536,plain,
% 1.06/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1537,plain,
% 1.06/1.23 (((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420)) <=> (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1538,plain,
% 1.06/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1537])).
% 1.06/1.23 tff(1539,plain,
% 1.06/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1538, 1536])).
% 1.06/1.23 tff(1540,plain,
% 1.06/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1541,plain,
% 1.06/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 1.06/1.23 tff(1542,plain,
% 1.06/1.23 (~c3_1(a451)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1541, 138, 1535, 1534, 1525, 1524, 1523, 1522, 1521, 1513, 11])).
% 1.06/1.23 tff(1543,plain,
% 1.06/1.23 (~c1_1(a451)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[775, 1533])).
% 1.06/1.23 tff(1544,plain,
% 1.06/1.23 ($false),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[817, 138, 1534, 1525, 1524, 1543, 1513, 811, 1542])).
% 1.06/1.23 tff(1545,plain,(hskp19 | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.06/1.23 tff(1546,plain,
% 1.06/1.23 (hskp19),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1545, 303, 94, 95, 1470, 301, 96, 55])).
% 1.06/1.23 tff(1547,plain,
% 1.06/1.23 (c1_1(a445)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[413, 1546])).
% 1.06/1.23 tff(1548,plain,
% 1.06/1.23 (~c0_1(a445)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[299, 1546])).
% 1.06/1.23 tff(1549,plain,
% 1.06/1.23 (c3_1(a445)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[422, 1546])).
% 1.06/1.23 tff(1550,plain,
% 1.06/1.23 (((~hskp3) | (~c2_1(a403))) <=> ((~hskp3) | (~c2_1(a403)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1551,plain,
% 1.06/1.23 (((~c2_1(a403)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a403)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1552,axiom,((~c2_1(a403)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.06/1.23 tff(1553,plain,
% 1.06/1.23 ((~hskp3) | (~c2_1(a403))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 1.06/1.23 tff(1554,plain,
% 1.06/1.23 ((~hskp3) | (~c2_1(a403))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1553, 1550])).
% 1.06/1.23 tff(1555,plain,
% 1.06/1.23 (~hskp3),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1554, 1471])).
% 1.06/1.23 tff(1556,plain,
% 1.06/1.23 (~c0_1(a402)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1458, 12, 1555, 93, 425, 424, 436])).
% 1.06/1.23 tff(1557,plain,
% 1.06/1.23 (~hskp2),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[469, 1556])).
% 1.06/1.23 tff(1558,plain,
% 1.06/1.23 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1559,plain,
% 1.06/1.23 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | c0_1(a402)) <=> (hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1560,plain,
% 1.06/1.23 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | c0_1(a402))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0)))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1559])).
% 1.06/1.23 tff(1561,plain,
% 1.06/1.23 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | c0_1(a402))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1560, 1558])).
% 1.06/1.23 tff(1562,plain,
% 1.06/1.23 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | c0_1(a402))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1563,plain,
% 1.06/1.23 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0)),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 1.06/1.23 tff(1564,plain,
% 1.06/1.23 (hskp2 | hskp1 | c0_1(a402) | c2_1(a402)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1563, 138, 93, 33])).
% 1.06/1.23 tff(1565,plain,
% 1.06/1.23 (c2_1(a402)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1564, 1556, 12, 1557])).
% 1.06/1.23 tff(1566,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1567,plain,
% 1.06/1.23 ((hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1568,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1567])).
% 1.06/1.23 tff(1569,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1568, 1566])).
% 1.06/1.23 tff(1570,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1571,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.06/1.23 tff(1572,plain,
% 1.06/1.23 (hskp1 | (~c2_1(a445))),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1571, 138, 425, 424, 303, 1471, 301, 1505])).
% 1.06/1.23 tff(1573,plain,
% 1.06/1.23 (~c2_1(a445)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1572, 12])).
% 1.06/1.23 tff(1574,plain,
% 1.06/1.23 (hskp5 | c2_1(a445)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1360, 138, 1555, 425, 424, 54])).
% 1.06/1.23 tff(1575,plain,
% 1.06/1.23 (hskp5),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1574, 1573])).
% 1.06/1.23 tff(1576,plain,
% 1.06/1.23 (~c0_1(a408)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1253, 1575])).
% 1.06/1.23 tff(1577,plain,
% 1.06/1.23 (c3_1(a408)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1261, 1575])).
% 1.06/1.23 tff(1578,plain,
% 1.06/1.23 (c2_1(a408)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1269, 1575])).
% 1.06/1.23 tff(1579,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1580,plain,
% 1.06/1.24 ((hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1581,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1580])).
% 1.06/1.24 tff(1582,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1581, 1579])).
% 1.06/1.24 tff(1583,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1584,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.06/1.24 tff(1585,plain,
% 1.06/1.24 (c3_1(a402)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1584, 138, 12, 1578, 1577, 1556, 1576, 1565, 1505])).
% 1.06/1.24 tff(1586,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1587,plain,
% 1.06/1.24 ((hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1588,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1587])).
% 1.06/1.24 tff(1589,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1588, 1586])).
% 1.06/1.24 tff(1590,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1591,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 1.06/1.24 tff(1592,plain,
% 1.06/1.24 ($false),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1591, 138, 12, 1556, 303, 1471, 301, 1565, 1505, 1585])).
% 1.06/1.24 tff(1593,plain,(hskp1 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c3_1(a445)) | c0_1(a445) | c1_1(a402) | (~c1_1(a445))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.24 tff(1594,plain,
% 1.06/1.24 (hskp1),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1593, 303, 1470, 301, 1549, 1548, 93, 1547])).
% 1.06/1.24 tff(1595,plain,
% 1.06/1.24 (~c3_1(a401)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[734, 1594])).
% 1.06/1.24 tff(1596,plain,
% 1.06/1.24 (c1_1(a401)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[742, 1594])).
% 1.06/1.24 tff(1597,plain,
% 1.06/1.24 (c0_1(a401)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[750, 1594])).
% 1.06/1.24 tff(1598,plain,
% 1.06/1.24 (~hskp22),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[822, 1595, 1549, 1596, 1597, 1547, 1548])).
% 1.06/1.24 tff(1599,plain,
% 1.06/1.24 (~hskp7),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[914, 1598, 1597, 1596, 1595])).
% 1.06/1.24 tff(1600,plain,
% 1.06/1.24 (hskp20),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[757, 138, 1597, 1596, 1595, 435])).
% 1.06/1.24 tff(1601,plain,
% 1.06/1.24 (c1_1(a449)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[765, 1600])).
% 1.06/1.24 tff(1602,plain,
% 1.06/1.24 (~c2_1(a449)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[836, 1600])).
% 1.06/1.24 tff(1603,plain,
% 1.06/1.24 (c3_1(a449)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[830, 1600])).
% 1.06/1.24 tff(1604,plain,
% 1.06/1.24 (~hskp2),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[864, 1603, 1547, 1602, 1598, 1601, 1549, 1548, 93])).
% 1.06/1.24 tff(1605,plain,
% 1.06/1.24 (~hskp3),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1554, 1470])).
% 1.06/1.24 tff(1606,plain,
% 1.06/1.24 (hskp16),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1315, 138, 1605, 1547, 1549, 1548, 1309])).
% 1.06/1.24 tff(1607,plain,
% 1.06/1.24 (~c3_1(a434)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[938, 1606])).
% 1.06/1.24 tff(1608,plain,
% 1.06/1.24 (c1_1(a434)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[963, 1606])).
% 1.06/1.24 tff(1609,plain,
% 1.06/1.24 (hskp7 | hskp2 | c2_1(a434)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[954, 138, 1608, 1607, 106])).
% 1.06/1.24 tff(1610,plain,
% 1.06/1.24 (c2_1(a434)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1609, 1604, 1599])).
% 1.06/1.24 tff(1611,plain,
% 1.06/1.24 (hskp14),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[991, 1604, 94, 1599, 1596, 1595, 1597, 1606, 96])).
% 1.06/1.24 tff(1612,plain,
% 1.06/1.24 (~c1_1(a428)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[382, 1611])).
% 1.06/1.24 tff(1613,plain,
% 1.06/1.24 ((hskp15 | hskp7 | hskp3) <=> (hskp15 | hskp7 | hskp3)),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1614,plain,
% 1.06/1.24 (((hskp15 | hskp7) | hskp3) <=> (hskp15 | hskp7 | hskp3)),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1615,axiom,((hskp15 | hskp7) | hskp3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 1.06/1.24 tff(1616,plain,
% 1.06/1.24 (hskp15 | hskp7 | hskp3),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 1.06/1.24 tff(1617,plain,
% 1.06/1.24 (hskp15 | hskp7 | hskp3),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1616, 1613])).
% 1.06/1.24 tff(1618,plain,
% 1.06/1.24 (hskp15 | hskp7 | hskp3),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1617, 1613])).
% 1.06/1.24 tff(1619,plain,
% 1.06/1.24 (hskp15 | hskp7 | hskp3),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1618, 1613])).
% 1.06/1.24 tff(1620,plain,
% 1.06/1.24 (hskp15 | hskp7 | hskp3),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1619, 1613])).
% 1.06/1.24 tff(1621,plain,
% 1.06/1.24 (hskp15),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1620, 1599, 1605])).
% 1.06/1.24 tff(1622,plain,
% 1.06/1.24 (((~hskp15) | (~c3_1(a430))) <=> ((~hskp15) | (~c3_1(a430)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1623,plain,
% 1.06/1.24 (((~c3_1(a430)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a430)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1624,axiom,((~c3_1(a430)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.06/1.24 tff(1625,plain,
% 1.06/1.24 ((~hskp15) | (~c3_1(a430))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 1.06/1.24 tff(1626,plain,
% 1.06/1.24 ((~hskp15) | (~c3_1(a430))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1625, 1622])).
% 1.06/1.24 tff(1627,plain,
% 1.06/1.24 (~c3_1(a430)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1626, 1621])).
% 1.06/1.24 tff(1628,plain,
% 1.06/1.24 (~c0_1(a434)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[944, 1606])).
% 1.06/1.24 tff(1629,plain,
% 1.06/1.24 (c2_1(a428)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[396, 1611])).
% 1.06/1.24 tff(1630,plain,
% 1.06/1.24 (((~hskp15) | c2_1(a430)) <=> ((~hskp15) | c2_1(a430))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1631,axiom,((~hskp15) | c2_1(a430)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.06/1.24 tff(1632,plain,
% 1.06/1.24 ((~hskp15) | c2_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 1.06/1.24 tff(1633,plain,
% 1.06/1.24 ((~hskp15) | c2_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1632, 1630])).
% 1.06/1.24 tff(1634,plain,
% 1.06/1.24 ((~hskp15) | c2_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1633, 1630])).
% 1.06/1.24 tff(1635,plain,
% 1.06/1.24 ((~hskp15) | c2_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1634, 1630])).
% 1.06/1.24 tff(1636,plain,
% 1.06/1.24 ((~hskp15) | c2_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1635, 1630])).
% 1.06/1.24 tff(1637,plain,
% 1.06/1.24 (c2_1(a430)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1636, 1621])).
% 1.06/1.24 tff(1638,plain,
% 1.06/1.24 (((~hskp15) | c0_1(a430)) <=> ((~hskp15) | c0_1(a430))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1639,axiom,((~hskp15) | c0_1(a430)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.06/1.24 tff(1640,plain,
% 1.06/1.24 ((~hskp15) | c0_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1639, 1638])).
% 1.06/1.24 tff(1641,plain,
% 1.06/1.24 ((~hskp15) | c0_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1640, 1638])).
% 1.06/1.24 tff(1642,plain,
% 1.06/1.24 ((~hskp15) | c0_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1641, 1638])).
% 1.06/1.24 tff(1643,plain,
% 1.06/1.24 ((~hskp15) | c0_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1642, 1638])).
% 1.06/1.24 tff(1644,plain,
% 1.06/1.24 ((~hskp15) | c0_1(a430)),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1643, 1638])).
% 1.06/1.24 tff(1645,plain,
% 1.06/1.24 (c0_1(a430)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1644, 1621])).
% 1.06/1.24 tff(1646,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1647,plain,
% 1.06/1.24 (((~ndr1_0) | c3_1(a430) | (~c2_1(a430)) | (~c0_1(a430)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1648,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a430) | (~c2_1(a430)) | (~c0_1(a430)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1647])).
% 1.06/1.24 tff(1649,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a430) | (~c2_1(a430)) | (~c0_1(a430)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1648, 1646])).
% 1.06/1.24 tff(1650,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a430) | (~c2_1(a430)) | (~c0_1(a430)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1651,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.06/1.24 tff(1652,plain,
% 1.06/1.24 (~c3_1(a428)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1651, 138, 1608, 1645, 1637, 1629, 1628, 1627, 1612, 647, 1610])).
% 1.06/1.24 tff(1653,plain,
% 1.06/1.24 ($false),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1011, 138, 1629, 1597, 1596, 1612, 1595, 811, 1652])).
% 1.06/1.24 tff(1654,plain,(c0_1(a403) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a402) | c3_1(a403) | (~c1_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.06/1.24 tff(1655,plain,
% 1.06/1.24 (c0_1(a403)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1654, 301, 96, 93, 94, 95, 55])).
% 1.06/1.24 tff(1656,plain,
% 1.06/1.24 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1657,plain,
% 1.06/1.24 ((hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a403)) | (~c1_1(a403)) | (~c0_1(a403))) <=> (hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1658,plain,
% 1.06/1.24 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a403)) | (~c1_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1657])).
% 1.06/1.24 tff(1659,plain,
% 1.06/1.24 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a403)) | (~c1_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1658, 1656])).
% 1.06/1.24 tff(1660,plain,
% 1.06/1.24 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a403)) | (~c1_1(a403)) | (~c0_1(a403)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1661,plain,
% 1.06/1.24 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 1.06/1.24 tff(1662,plain,
% 1.06/1.24 (hskp19 | (~c0_1(a403)) | (~c1_1(a403))),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1661, 138, 55, 1471, 117])).
% 1.06/1.24 tff(1663,plain,
% 1.06/1.24 (~c1_1(a403)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1662, 107, 1176])).
% 1.06/1.24 tff(1664,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1665,plain,
% 1.06/1.24 (((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1666,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1665])).
% 1.06/1.24 tff(1667,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1666, 1664])).
% 1.06/1.24 tff(1668,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1669,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 1.06/1.24 tff(1670,plain,
% 1.06/1.24 (~c0_1(a460)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1669, 138, 218, 204, 1471, 301, 811, 1663])).
% 1.06/1.24 tff(1671,plain,
% 1.06/1.24 (hskp0),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1212, 138, 180, 210, 204, 323, 1670])).
% 1.06/1.24 tff(1672,plain,
% 1.06/1.24 (c2_1(a400)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[338, 1671])).
% 1.06/1.24 tff(1673,plain,
% 1.06/1.24 (c1_1(a400)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[346, 1671])).
% 1.06/1.24 tff(1674,plain,
% 1.06/1.24 (~c0_1(a400)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[350, 138, 55, 107, 1673, 1672, 117])).
% 1.06/1.24 tff(1675,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1676,plain,
% 1.06/1.24 ((hskp9 | (~ndr1_0) | c1_1(a403) | c3_1(a403) | (~c0_1(a403)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460))) <=> (hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1677,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a403) | c3_1(a403) | (~c0_1(a403)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1676])).
% 1.06/1.24 tff(1678,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a403) | c3_1(a403) | (~c0_1(a403)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1677, 1675])).
% 1.06/1.24 tff(1679,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a403) | c3_1(a403) | (~c0_1(a403)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1680,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 1.06/1.24 tff(1681,plain,
% 1.06/1.24 (hskp9),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1680, 138, 218, 204, 1176, 301, 583, 1663, 1670])).
% 1.06/1.24 tff(1682,plain,
% 1.06/1.24 (~c1_1(a416)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[606, 1681])).
% 1.06/1.24 tff(1683,plain,
% 1.06/1.24 (c3_1(a416)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[667, 1681])).
% 1.06/1.24 tff(1684,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1685,plain,
% 1.06/1.24 (((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400))) <=> (c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1686,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1685])).
% 1.06/1.24 tff(1687,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1686, 1684])).
% 1.06/1.24 tff(1688,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1689,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 1.06/1.24 tff(1690,plain,
% 1.06/1.24 (~c2_1(a416)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1689, 138, 1683, 1673, 1672, 1682, 1176, 1471, 301, 647, 1674])).
% 1.06/1.24 tff(1691,plain,
% 1.06/1.24 (~c0_1(a416)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[612, 1681])).
% 1.06/1.24 tff(1692,plain,
% 1.06/1.24 (hskp5),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1247, 138, 1555, 1683, 1691, 54, 1690])).
% 1.06/1.24 tff(1693,plain,
% 1.06/1.24 (~c0_1(a408)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1253, 1692])).
% 1.06/1.24 tff(1694,plain,
% 1.06/1.24 (c3_1(a408)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1261, 1692])).
% 1.06/1.24 tff(1695,plain,
% 1.06/1.24 (c2_1(a408)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1269, 1692])).
% 1.06/1.24 tff(1696,plain,
% 1.06/1.24 ($false),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1276, 138, 218, 1683, 1695, 1694, 210, 1682, 1693, 43, 1670, 1690])).
% 1.06/1.24 tff(1697,plain,(hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | hskp24 | (~c0_1(a405)) | (~c1_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.24 tff(1698,plain,
% 1.06/1.24 (hskp19),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1697, 1655, 1470, 301, 55, 96, 95])).
% 1.06/1.24 tff(1699,plain,
% 1.06/1.24 (~c0_1(a445)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[299, 1698])).
% 1.06/1.24 tff(1700,plain,
% 1.06/1.24 (c3_1(a445)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[422, 1698])).
% 1.06/1.24 tff(1701,plain,
% 1.06/1.24 (c1_1(a445)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[413, 1698])).
% 1.06/1.24 tff(1702,assumption,(~c0_1(a402)), introduced(assumption)).
% 1.06/1.24 tff(1703,plain,
% 1.06/1.24 (~hskp2),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[469, 1702])).
% 1.06/1.24 tff(1704,plain,
% 1.06/1.24 (c2_1(a402)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1564, 1702, 12, 1703])).
% 1.06/1.24 tff(1705,plain,
% 1.06/1.24 (hskp13),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[254, 976, 1703])).
% 1.06/1.24 tff(1706,plain,
% 1.06/1.24 (~c0_1(a427)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[260, 1705])).
% 1.06/1.24 tff(1707,plain,
% 1.06/1.24 (c2_1(a427)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[276, 1705])).
% 1.06/1.24 tff(1708,plain,
% 1.06/1.24 (c1_1(a427)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[284, 1705])).
% 1.06/1.24 tff(1709,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1710,plain,
% 1.06/1.24 (((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1711,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1710])).
% 1.06/1.24 tff(1712,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1711, 1709])).
% 1.06/1.24 tff(1713,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1714,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 1.06/1.24 tff(1715,plain,
% 1.06/1.24 (~c3_1(a402)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1714, 138, 1708, 1707, 1706, 1176, 1471, 301, 93, 1704, 647])).
% 1.06/1.24 tff(1716,plain,
% 1.06/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.06/1.24 inference(bind,[status(th)],[])).
% 1.06/1.24 tff(1717,plain,
% 1.06/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.06/1.24 inference(quant_intro,[status(thm)],[1716])).
% 1.06/1.24 tff(1718,plain,
% 1.06/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1719,plain,
% 1.06/1.24 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_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) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | 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) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | 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) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(1720,plain,
% 1.06/1.25 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[1719])).
% 1.06/1.25 tff(1721,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.06/1.25 tff(1722,plain,
% 1.06/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 1.06/1.25 tff(1723,plain,
% 1.06/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1722, 1718])).
% 1.06/1.25 tff(1724,plain,(
% 1.06/1.25 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.06/1.25 inference(skolemize,[status(sab)],[1723])).
% 1.06/1.25 tff(1725,plain,
% 1.06/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1724, 1717])).
% 1.06/1.25 tff(1726,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1727,plain,
% 1.06/1.25 ((hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1728,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402)))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1727])).
% 1.06/1.25 tff(1729,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1728, 1726])).
% 1.06/1.25 tff(1730,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1731,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402)),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 1.06/1.25 tff(1732,plain,
% 1.06/1.25 (hskp14 | c3_1(a402)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1731, 138, 95, 94, 1702, 1704, 361, 976])).
% 1.06/1.25 tff(1733,plain,
% 1.06/1.25 (hskp14),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1732, 1715])).
% 1.06/1.25 tff(1734,plain,
% 1.06/1.25 (~c1_1(a428)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[382, 1733])).
% 1.06/1.25 tff(1735,plain,
% 1.06/1.25 (~c0_1(a428)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[388, 1733])).
% 1.06/1.25 tff(1736,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1737,plain,
% 1.06/1.25 (((~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c2_1(a402)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a402) | c1_1(a402) | c0_1(a402)) <=> (c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1738,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c2_1(a402)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a402) | c1_1(a402) | c0_1(a402))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1737])).
% 1.06/1.25 tff(1739,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c2_1(a402)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a402) | c1_1(a402) | c0_1(a402))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1738, 1736])).
% 1.06/1.25 tff(1740,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c2_1(a402)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a402) | c1_1(a402) | c0_1(a402))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1741,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 1.06/1.25 tff(1742,plain,
% 1.06/1.25 (~c3_1(a428)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1741, 138, 1702, 1735, 1734, 93, 1704, 1725, 1715])).
% 1.06/1.25 tff(1743,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1744,plain,
% 1.06/1.25 ((hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1745,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1744])).
% 1.06/1.25 tff(1746,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1745, 1743])).
% 1.06/1.25 tff(1747,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1748,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 1.06/1.25 tff(1749,plain,
% 1.06/1.25 (~c3_1(a427)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1748, 138, 12, 1707, 1702, 1706, 1704, 1505, 1715])).
% 1.06/1.25 tff(1750,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1751,plain,
% 1.06/1.25 ((hskp3 | (~ndr1_0) | c3_1(a427) | (~c2_1(a427)) | (~c1_1(a427)) | c1_1(a428) | c0_1(a428) | c3_1(a428)) <=> (hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1752,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a427) | (~c2_1(a427)) | (~c1_1(a427)) | c1_1(a428) | c0_1(a428) | c3_1(a428))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428)))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1751])).
% 1.06/1.25 tff(1753,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a427) | (~c2_1(a427)) | (~c1_1(a427)) | c1_1(a428) | c0_1(a428) | c3_1(a428))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1752, 1750])).
% 1.06/1.25 tff(1754,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a427) | (~c2_1(a427)) | (~c1_1(a427)) | c1_1(a428) | c0_1(a428) | c3_1(a428))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1755,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428)),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 1.06/1.25 tff(1756,plain,
% 1.06/1.25 ($false),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1755, 138, 1555, 1708, 1707, 1735, 1734, 1339, 1749, 1742])).
% 1.06/1.25 tff(1757,plain,(c2_1(a405) | c0_1(a402) | c1_1(a402) | (~c1_1(a405)) | (~c3_1(a405)) | hskp1 | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.25 tff(1758,plain,
% 1.06/1.25 (c2_1(a405)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1757, 1556, 93, 95, 94, 12, 1176, 1471, 301])).
% 1.06/1.25 tff(1759,plain,
% 1.06/1.25 (c0_1(a420) | c2_1(a420)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1045, 138, 1703, 12, 1038, 33])).
% 1.06/1.25 tff(1760,plain,
% 1.06/1.25 (c2_1(a420)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1759, 1037])).
% 1.06/1.25 tff(1761,plain,
% 1.06/1.25 (~hskp11),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1142, 1760])).
% 1.06/1.25 tff(1762,plain,
% 1.06/1.25 (~c2_1(a405)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[890, 1761, 856])).
% 1.06/1.25 tff(1763,plain,
% 1.06/1.25 (hskp13),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[254, 1762, 1703])).
% 1.06/1.25 tff(1764,plain,
% 1.06/1.25 (~c0_1(a427)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[260, 1763])).
% 1.06/1.25 tff(1765,plain,
% 1.06/1.25 (c2_1(a427)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[276, 1763])).
% 1.06/1.25 tff(1766,plain,
% 1.06/1.25 (c1_1(a427)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[284, 1763])).
% 1.06/1.25 tff(1767,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1768,plain,
% 1.06/1.25 (((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a420) | (~c2_1(a420)) | (~c3_1(a420)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1769,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a420) | (~c2_1(a420)) | (~c3_1(a420)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1768])).
% 1.06/1.25 tff(1770,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a420) | (~c2_1(a420)) | (~c3_1(a420)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1769, 1767])).
% 1.06/1.25 tff(1771,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a420) | (~c2_1(a420)) | (~c3_1(a420)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1772,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 1.06/1.25 tff(1773,plain,
% 1.06/1.25 (~c3_1(a420)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1772, 138, 1766, 1765, 1764, 1038, 1760, 1176, 1471, 301, 647])).
% 1.06/1.25 tff(1774,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1775,plain,
% 1.06/1.25 ((hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a420) | c3_1(a420) | (~c2_1(a420))) <=> (hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1776,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a420) | c3_1(a420) | (~c2_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420)))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1775])).
% 1.06/1.25 tff(1777,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a420) | c3_1(a420) | (~c2_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1776, 1774])).
% 1.06/1.25 tff(1778,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a420) | c3_1(a420) | (~c2_1(a420)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1779,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420)),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.06/1.25 tff(1780,plain,
% 1.06/1.25 (hskp14 | c3_1(a420)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1779, 138, 95, 94, 1037, 1760, 361, 1762])).
% 1.06/1.25 tff(1781,plain,
% 1.06/1.25 (hskp14),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1780, 1773])).
% 1.06/1.25 tff(1782,plain,
% 1.06/1.25 (~c1_1(a428)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[382, 1781])).
% 1.06/1.25 tff(1783,plain,
% 1.06/1.25 (~c0_1(a428)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[388, 1781])).
% 1.06/1.25 tff(1784,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1785,plain,
% 1.06/1.25 (((~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a420) | c1_1(a420) | c0_1(a420)) <=> (c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1786,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1785])).
% 1.06/1.25 tff(1787,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1786, 1784])).
% 1.06/1.25 tff(1788,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a420) | c1_1(a420) | c0_1(a420))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1789,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.06/1.25 tff(1790,plain,
% 1.06/1.25 (~c3_1(a428)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1789, 138, 1783, 1782, 1037, 1038, 1760, 1725, 1773])).
% 1.06/1.25 tff(1791,plain,
% 1.06/1.25 (~c3_1(a402)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1714, 138, 1766, 1765, 1764, 1176, 1471, 301, 93, 1704, 647])).
% 1.06/1.25 tff(1792,plain,
% 1.06/1.25 (~c3_1(a427)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1748, 138, 12, 1765, 1702, 1764, 1704, 1505, 1791])).
% 1.06/1.25 tff(1793,plain,
% 1.06/1.25 ($false),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1755, 138, 1555, 1766, 1765, 1783, 1782, 1339, 1792, 1790])).
% 1.06/1.25 tff(1794,plain,(c0_1(a420) | c1_1(a420) | (~c1_1(a405)) | (~c3_1(a405)) | hskp1 | c0_1(a402) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | hskp22 | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.25 tff(1795,plain,
% 1.06/1.25 (c0_1(a420)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1794, 1038, 95, 94, 12, 1556, 1176, 1471, 301, 93, 856, 96])).
% 1.06/1.25 tff(1796,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1797,plain,
% 1.06/1.25 (((~ndr1_0) | c1_1(a420) | (~c3_1(a420)) | (~c0_1(a420)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445))) <=> (c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1798,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a420) | (~c3_1(a420)) | (~c0_1(a420)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1797])).
% 1.06/1.25 tff(1799,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a420) | (~c3_1(a420)) | (~c0_1(a420)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.06/1.25 tff(1800,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a420) | (~c3_1(a420)) | (~c0_1(a420)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1801,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.06/1.26 tff(1802,plain,
% 1.06/1.26 ((~c0_1(a420)) | (~c3_1(a420))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1801, 138, 436, 425, 424, 1038, 480])).
% 1.06/1.26 tff(1803,plain,
% 1.06/1.26 (~c3_1(a420)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1802, 1795])).
% 1.06/1.26 tff(1804,plain,
% 1.06/1.26 (hskp16),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1315, 138, 1555, 436, 425, 424, 1309])).
% 1.06/1.26 tff(1805,plain,
% 1.06/1.26 (~c3_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[938, 1804])).
% 1.06/1.26 tff(1806,plain,
% 1.06/1.26 (~c0_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[944, 1804])).
% 1.06/1.26 tff(1807,plain,
% 1.06/1.26 (c1_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[963, 1804])).
% 1.06/1.26 tff(1808,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1809,plain,
% 1.06/1.26 ((hskp9 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434))) <=> (hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1810,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1809])).
% 1.06/1.26 tff(1811,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1810, 1808])).
% 1.06/1.26 tff(1812,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1813,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1812, 1811])).
% 1.06/1.26 tff(1814,plain,
% 1.06/1.26 (hskp9 | (~c0_1(a420)) | c3_1(a420)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1813, 138, 1807, 1806, 1805, 1038, 583])).
% 1.06/1.26 tff(1815,plain,
% 1.06/1.26 (hskp9),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1814, 1795, 1803])).
% 1.06/1.26 tff(1816,plain,
% 1.06/1.26 (~c1_1(a416)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[606, 1815])).
% 1.06/1.26 tff(1817,plain,
% 1.06/1.26 (~c0_1(a416)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[612, 1815])).
% 1.06/1.26 tff(1818,plain,
% 1.06/1.26 (c2_1(a416)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[619, 138, 1557, 12, 1817, 1816, 33])).
% 1.06/1.26 tff(1819,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1820,plain,
% 1.06/1.26 ((hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1821,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1820])).
% 1.06/1.26 tff(1822,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1821, 1819])).
% 1.06/1.26 tff(1823,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1824,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 1.06/1.26 tff(1825,plain,
% 1.06/1.26 ((~c0_1(a420)) | c3_1(a420) | (~c2_1(a434))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1824, 138, 12, 1807, 1806, 1038, 22])).
% 1.06/1.26 tff(1826,plain,
% 1.06/1.26 (~c2_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1825, 1795, 1803])).
% 1.06/1.26 tff(1827,plain,
% 1.06/1.26 (hskp7 | hskp2 | c2_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[954, 138, 1807, 1805, 106])).
% 1.06/1.26 tff(1828,plain,
% 1.06/1.26 (hskp7),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1827, 1826, 1557])).
% 1.06/1.26 tff(1829,plain,
% 1.06/1.26 (~c3_1(a410)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[230, 1828])).
% 1.06/1.26 tff(1830,plain,
% 1.06/1.26 (c0_1(a410)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[268, 1828])).
% 1.06/1.26 tff(1831,plain,
% 1.06/1.26 (~hskp11),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1019, 1795])).
% 1.06/1.26 tff(1832,plain,
% 1.06/1.26 (c2_1(a410)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[636, 138, 1831, 1557, 1830, 1829, 630])).
% 1.06/1.26 tff(1833,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1834,plain,
% 1.06/1.26 ((hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445))) <=> (hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1835,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1834])).
% 1.06/1.26 tff(1836,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1835, 1833])).
% 1.06/1.26 tff(1837,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1838,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 1.06/1.26 tff(1839,plain,
% 1.06/1.26 ((~c0_1(a420)) | c3_1(a420) | (~c2_1(a445))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1838, 138, 12, 436, 424, 1038, 22])).
% 1.06/1.26 tff(1840,plain,
% 1.06/1.26 (~c2_1(a445)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1839, 1795, 1803])).
% 1.06/1.26 tff(1841,plain,
% 1.06/1.26 (hskp13),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[658, 1840, 1557])).
% 1.06/1.26 tff(1842,plain,
% 1.06/1.26 (~c0_1(a427)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[260, 1841])).
% 1.06/1.26 tff(1843,plain,
% 1.06/1.26 (c3_1(a416)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[667, 1815])).
% 1.06/1.26 tff(1844,plain,
% 1.06/1.26 (c2_1(a427)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[276, 1841])).
% 1.06/1.26 tff(1845,plain,
% 1.06/1.26 (c1_1(a427)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[284, 1841])).
% 1.06/1.26 tff(1846,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[676, 138, 1845, 1844, 1843, 1830, 1842, 1816, 1829, 647, 1832, 1818])).
% 1.06/1.26 tff(1847,plain,(c1_1(a420) | hskp1 | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | hskp22 | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(1848,plain,
% 1.06/1.26 (c1_1(a420)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1847, 856, 436, 425, 424, 95, 94, 1176, 1471, 301, 93, 12, 96])).
% 1.06/1.26 tff(1849,plain,
% 1.06/1.26 (hskp11),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[890, 856, 1758])).
% 1.06/1.26 tff(1850,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1025, 1849, 1848])).
% 1.06/1.26 tff(1851,plain,(hskp22 | (~c0_1(a405)) | (~c3_1(a405)) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a405)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(1852,plain,
% 1.06/1.26 (hskp22),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1851, 12, 94, 436, 425, 424, 95, 1176, 1471, 301, 93, 96])).
% 1.06/1.26 tff(1853,plain,
% 1.06/1.26 (~c1_1(a451)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[775, 1852])).
% 1.06/1.26 tff(1854,plain,
% 1.06/1.26 (c2_1(a451)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[783, 1852])).
% 1.06/1.26 tff(1855,plain,
% 1.06/1.26 (c0_1(a451)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[791, 1852])).
% 1.06/1.26 tff(1856,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1857,plain,
% 1.06/1.26 ((hskp3 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451))) <=> (hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1858,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1857])).
% 1.06/1.26 tff(1859,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1858, 1856])).
% 1.06/1.26 tff(1860,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1861,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 1.06/1.26 tff(1862,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1861, 138, 1555, 96, 94, 1855, 1854, 1853, 1175, 1758])).
% 1.06/1.26 tff(1863,plain,(hskp1 | (~c0_1(a405)) | (~c3_1(a405)) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a405)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(1864,plain,
% 1.06/1.26 (hskp1),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1863, 1701, 94, 96, 1700, 1699, 95, 1655, 1470, 301, 93])).
% 1.06/1.26 tff(1865,plain,
% 1.06/1.26 (~c3_1(a401)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[734, 1864])).
% 1.06/1.26 tff(1866,plain,
% 1.06/1.26 (c1_1(a401)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[742, 1864])).
% 1.06/1.26 tff(1867,plain,
% 1.06/1.26 (c0_1(a401)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[750, 1864])).
% 1.06/1.26 tff(1868,plain,
% 1.06/1.26 (~hskp22),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[822, 1865, 1700, 1866, 1867, 1701, 1699])).
% 1.06/1.26 tff(1869,plain,
% 1.06/1.26 (~hskp7),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[914, 1868, 1867, 1866, 1865])).
% 1.06/1.26 tff(1870,plain,
% 1.06/1.26 (hskp16),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1315, 138, 1605, 1701, 1700, 1699, 1309])).
% 1.06/1.26 tff(1871,plain,
% 1.06/1.26 (~c0_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[944, 1870])).
% 1.06/1.26 tff(1872,plain,
% 1.06/1.26 (~c3_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[938, 1870])).
% 1.06/1.26 tff(1873,plain,
% 1.06/1.26 (hskp20),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[757, 138, 1867, 1866, 1865, 435])).
% 1.06/1.26 tff(1874,plain,
% 1.06/1.26 (c1_1(a449)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[765, 1873])).
% 1.06/1.26 tff(1875,plain,
% 1.06/1.26 (~c2_1(a449)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[836, 1873])).
% 1.06/1.26 tff(1876,plain,
% 1.06/1.26 (c3_1(a449)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[830, 1873])).
% 1.06/1.26 tff(1877,plain,
% 1.06/1.26 (~hskp2),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[864, 1876, 1701, 1875, 1868, 1874, 1700, 1699, 93])).
% 1.06/1.26 tff(1878,plain,
% 1.06/1.26 (c2_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[974, 1877, 94, 1872, 1866, 1871, 1865, 1867, 1869, 96])).
% 1.06/1.26 tff(1879,plain,
% 1.06/1.26 (hskp14),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[991, 1877, 94, 1869, 1866, 1865, 1867, 1870, 96])).
% 1.06/1.26 tff(1880,plain,
% 1.06/1.26 (~c1_1(a428)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[382, 1879])).
% 1.06/1.26 tff(1881,plain,
% 1.06/1.26 (hskp15),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1620, 1869, 1605])).
% 1.06/1.26 tff(1882,plain,
% 1.06/1.26 (~c3_1(a430)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1626, 1881])).
% 1.06/1.26 tff(1883,plain,
% 1.06/1.26 (c2_1(a428)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[396, 1879])).
% 1.06/1.26 tff(1884,plain,
% 1.06/1.26 (c2_1(a430)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1636, 1881])).
% 1.06/1.26 tff(1885,plain,
% 1.06/1.26 (c0_1(a430)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1644, 1881])).
% 1.06/1.26 tff(1886,plain,
% 1.06/1.26 (c1_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[963, 1870])).
% 1.06/1.26 tff(1887,plain,
% 1.06/1.26 (~c3_1(a428)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1651, 138, 1886, 1885, 1884, 1883, 1871, 1882, 1880, 647, 1878])).
% 1.06/1.26 tff(1888,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1011, 138, 1883, 1867, 1866, 1880, 1865, 811, 1887])).
% 1.06/1.26 tff(1889,plain,(c3_1(a403) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a402) | (~c1_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(1890,plain,
% 1.06/1.26 (c3_1(a403)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1889, 93, 96, 94, 95, 55])).
% 1.06/1.26 tff(1891,plain,
% 1.06/1.26 (((~hskp3) | (~c3_1(a403))) <=> ((~hskp3) | (~c3_1(a403)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1892,plain,
% 1.06/1.26 (((~c3_1(a403)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a403)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1893,axiom,((~c3_1(a403)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.06/1.26 tff(1894,plain,
% 1.06/1.26 ((~hskp3) | (~c3_1(a403))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 1.06/1.26 tff(1895,plain,
% 1.06/1.26 ((~hskp3) | (~c3_1(a403))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1894, 1891])).
% 1.06/1.26 tff(1896,plain,
% 1.06/1.26 (~hskp3),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1895, 1890])).
% 1.06/1.26 tff(1897,plain,
% 1.06/1.26 (c3_1(a445)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[422, 294])).
% 1.06/1.26 tff(1898,plain,
% 1.06/1.26 (c1_1(a445)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[413, 294])).
% 1.06/1.26 tff(1899,assumption,(~c3_1(a402)), introduced(assumption)).
% 1.06/1.26 tff(1900,plain,
% 1.06/1.26 (~c0_1(a402)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1458, 424, 44, 93, 12, 425, 436])).
% 1.06/1.26 tff(1901,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1902,plain,
% 1.06/1.26 ((hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | c3_1(a402)) <=> (hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1903,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | c3_1(a402))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1902])).
% 1.06/1.26 tff(1904,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | c3_1(a402))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1903, 1901])).
% 1.06/1.26 tff(1905,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | c3_1(a402))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1906,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 1.06/1.26 tff(1907,plain,
% 1.06/1.26 (c3_1(a402) | (~c2_1(a434))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1906, 138, 44, 1374, 1900, 1383, 93, 1339])).
% 1.06/1.26 tff(1908,plain,
% 1.06/1.26 (~c2_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1907, 1899])).
% 1.06/1.26 tff(1909,plain,
% 1.06/1.26 (hskp7 | c2_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[954, 138, 23, 1374, 1383, 106])).
% 1.06/1.26 tff(1910,plain,
% 1.06/1.26 (hskp7),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1909, 1908])).
% 1.06/1.26 tff(1911,plain,
% 1.06/1.26 (~c3_1(a410)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[230, 1910])).
% 1.06/1.26 tff(1912,plain,
% 1.06/1.26 (~c1_1(a410)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[236, 1910])).
% 1.06/1.26 tff(1913,plain,
% 1.06/1.26 (c2_1(a402)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1564, 1900, 12, 23])).
% 1.06/1.26 tff(1914,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1915,plain,
% 1.06/1.26 ((hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1916,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1915])).
% 1.06/1.26 tff(1917,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.06/1.26 tff(1918,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1919,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.06/1.26 tff(1920,plain,
% 1.06/1.26 (c3_1(a402) | (~c2_1(a445))),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1919, 138, 12, 425, 1900, 424, 1913, 1505])).
% 1.06/1.26 tff(1921,plain,
% 1.06/1.26 (~c2_1(a445)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1920, 1899])).
% 1.06/1.26 tff(1922,plain,
% 1.06/1.26 (hskp13 | c2_1(a445)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[657, 138, 23, 436, 425, 247])).
% 1.06/1.26 tff(1923,plain,
% 1.06/1.26 (hskp13),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1922, 1921])).
% 1.06/1.26 tff(1924,plain,
% 1.06/1.26 (~c0_1(a427)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[260, 1923])).
% 1.06/1.26 tff(1925,plain,
% 1.06/1.26 (c0_1(a410)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[268, 1910])).
% 1.06/1.26 tff(1926,plain,
% 1.06/1.26 (c2_1(a427)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[276, 1923])).
% 1.06/1.26 tff(1927,plain,
% 1.06/1.26 (c1_1(a427)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[284, 1923])).
% 1.06/1.26 tff(1928,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[291, 138, 12, 1927, 1926, 1925, 1924, 1912, 1911, 22])).
% 1.06/1.26 tff(1929,plain,(c3_1(a402) | hskp1 | hskp2 | (~c1_1(a445)) | (~c3_1(a445)) | hskp3 | c1_1(a402) | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(1930,plain,
% 1.06/1.26 (c3_1(a402)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1929, 1898, 12, 23, 1897, 1896, 93, 300])).
% 1.06/1.26 tff(1931,plain,
% 1.06/1.26 (~c0_1(a402)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1458, 300, 1896, 93, 12, 1897, 1898])).
% 1.06/1.26 tff(1932,plain,
% 1.06/1.26 (c2_1(a402)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1564, 1931, 12, 23])).
% 1.06/1.26 tff(1933,plain,
% 1.06/1.26 (hskp16),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1315, 138, 1896, 1898, 1897, 300, 1309])).
% 1.06/1.26 tff(1934,plain,
% 1.06/1.26 (~c3_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[938, 1933])).
% 1.06/1.26 tff(1935,plain,
% 1.06/1.26 (~c0_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[944, 1933])).
% 1.06/1.26 tff(1936,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1937,plain,
% 1.06/1.26 ((hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1938,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1937])).
% 1.06/1.26 tff(1939,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1938, 1936])).
% 1.06/1.26 tff(1940,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1941,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 1.06/1.26 tff(1942,plain,
% 1.06/1.26 (~c2_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1941, 138, 12, 1931, 1935, 1934, 1932, 1505, 1930])).
% 1.06/1.26 tff(1943,plain,
% 1.06/1.26 (c1_1(a434)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[963, 1933])).
% 1.06/1.26 tff(1944,plain,
% 1.06/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1945,plain,
% 1.06/1.27 (((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | (~c2_1(a402)) | c3_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1946,plain,
% 1.06/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | (~c2_1(a402)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1945])).
% 1.06/1.27 tff(1947,plain,
% 1.06/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | (~c2_1(a402)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1946, 1944])).
% 1.06/1.27 tff(1948,plain,
% 1.06/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | (~c2_1(a402)) | c3_1(a434) | c0_1(a434) | c2_1(a434))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1949,plain,
% 1.06/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 1.06/1.27 tff(1950,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1949, 138, 1943, 1931, 1935, 1934, 93, 1932, 313, 1942])).
% 1.06/1.27 tff(1951,plain,(hskp2 | c1_1(a402) | hskp1 | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(1952,plain,
% 1.06/1.27 (hskp2),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1951, 12, 93, 92, 84, 76, 55])).
% 1.06/1.27 tff(1953,plain,
% 1.06/1.27 (~c2_1(a402)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[461, 1952])).
% 1.06/1.27 tff(1954,plain,
% 1.06/1.27 (c0_1(a402)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[469, 1952])).
% 1.06/1.27 tff(1955,assumption,(~c2_1(a402)), introduced(assumption)).
% 1.06/1.27 tff(1956,plain,
% 1.06/1.27 (c3_1(a403)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1889, 93, 92, 76, 84, 55])).
% 1.06/1.27 tff(1957,plain,
% 1.06/1.27 (~hskp3),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1895, 1956])).
% 1.06/1.27 tff(1958,plain,
% 1.06/1.27 (hskp19 | (~c2_1(a405))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[144, 138, 55, 92, 84, 117])).
% 1.06/1.27 tff(1959,plain,
% 1.06/1.27 (~c2_1(a405)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1958, 107])).
% 1.06/1.27 tff(1960,plain,
% 1.06/1.27 (hskp27 | hskp23 | c2_1(a405)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[196, 138, 92, 84, 190])).
% 1.06/1.27 tff(1961,plain,
% 1.06/1.27 (hskp23),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1960, 180, 1959])).
% 1.06/1.27 tff(1962,plain,
% 1.06/1.27 (c1_1(a460)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[217, 1961])).
% 1.06/1.27 tff(1963,plain,
% 1.06/1.27 (~c3_1(a460)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[203, 1961])).
% 1.06/1.27 tff(1964,plain,
% 1.06/1.27 (~c2_1(a460)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[209, 1961])).
% 1.06/1.27 tff(1965,plain,
% 1.06/1.27 (~c3_1(a451)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1198, 138, 44, 792, 784, 776, 1175])).
% 1.06/1.27 tff(1966,assumption,(~c3_1(a460)), introduced(assumption)).
% 1.06/1.27 tff(1967,assumption,(c1_1(a460)), introduced(assumption)).
% 1.06/1.27 tff(1968,plain,
% 1.06/1.27 (~c0_1(a460)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1205, 138, 1967, 784, 1966, 776, 811, 1965])).
% 1.06/1.27 tff(1969,assumption,(~c2_1(a460)), introduced(assumption)).
% 1.06/1.27 tff(1970,assumption,(~hskp27), introduced(assumption)).
% 1.06/1.27 tff(1971,plain,
% 1.06/1.27 (hskp0 | c0_1(a460)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1212, 138, 1970, 1969, 1966, 323])).
% 1.06/1.27 tff(1972,plain,
% 1.06/1.27 (hskp0),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1971, 1968])).
% 1.06/1.27 tff(1973,plain,
% 1.06/1.27 (~c3_1(a400)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[366, 1972])).
% 1.06/1.27 tff(1974,plain,
% 1.06/1.27 (c1_1(a400)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[346, 1972])).
% 1.06/1.27 tff(1975,plain,
% 1.06/1.27 (~c0_1(a400)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1222, 138, 784, 1974, 776, 1973, 811, 1965])).
% 1.06/1.27 tff(1976,plain,
% 1.06/1.27 (c2_1(a400)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[338, 1972])).
% 1.06/1.27 tff(1977,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1978,plain,
% 1.06/1.27 ((hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400))) <=> (hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1979,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1978])).
% 1.06/1.27 tff(1980,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1979, 1977])).
% 1.06/1.27 tff(1981,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1982,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 1.06/1.27 tff(1983,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1982, 138, 12, 792, 1974, 1976, 776, 22, 1975, 1965])).
% 1.06/1.27 tff(1984,plain,((~hskp22) | hskp1 | hskp27 | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(1985,plain,
% 1.06/1.27 (~hskp22),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1984, 180, 12, 1964, 1963, 1962, 1957])).
% 1.06/1.27 tff(1986,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1987,plain,
% 1.06/1.27 ((hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1988,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1987])).
% 1.06/1.27 tff(1989,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1988, 1986])).
% 1.06/1.27 tff(1990,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1991,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 1.06/1.27 tff(1992,plain,
% 1.06/1.27 (hskp22 | c3_1(a402)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1991, 138, 84, 76, 1352, 1955, 851, 1959])).
% 1.06/1.27 tff(1993,plain,
% 1.06/1.27 (c3_1(a402)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1992, 1985])).
% 1.06/1.27 tff(1994,plain,
% 1.06/1.27 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1995,plain,
% 1.06/1.27 ((hskp18 | hskp3 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402))) <=> (hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1996,plain,
% 1.06/1.27 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1995])).
% 1.06/1.27 tff(1997,plain,
% 1.06/1.27 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1996, 1994])).
% 1.06/1.27 tff(1998,plain,
% 1.06/1.27 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1999,plain,
% 1.06/1.27 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 1.06/1.27 tff(2000,plain,
% 1.06/1.27 (hskp18 | hskp3 | c2_1(a402) | (~c3_1(a402))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1999, 138, 93, 1420])).
% 1.06/1.27 tff(2001,plain,
% 1.06/1.27 (hskp18),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[2000, 1993, 1957, 1955])).
% 1.06/1.27 tff(2002,plain,
% 1.06/1.27 (~c3_1(a440)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1434, 2001])).
% 1.06/1.27 tff(2003,plain,
% 1.06/1.27 (~c2_1(a440)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1440, 2001])).
% 1.06/1.27 tff(2004,plain,
% 1.06/1.27 (^[U: $i] : refl((hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(2005,plain,
% 1.06/1.27 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[2004])).
% 1.06/1.27 tff(2006,plain,
% 1.06/1.27 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2007,plain,
% 1.06/1.27 (^[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)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp21) <=> ((hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite(((hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp21) <=> (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(2008,plain,
% 1.06/1.27 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp21) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[2007])).
% 1.06/1.27 tff(2009,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.06/1.27 tff(2010,plain,
% 1.06/1.27 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 1.06/1.27 tff(2011,plain,
% 1.06/1.27 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2010, 2006])).
% 1.06/1.27 tff(2012,plain,(
% 1.06/1.27 ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.27 inference(skolemize,[status(sab)],[2011])).
% 1.06/1.27 tff(2013,plain,
% 1.06/1.27 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2012, 2005])).
% 1.06/1.27 tff(2014,plain,
% 1.06/1.27 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2015,plain,
% 1.06/1.27 ((hskp21 | hskp20 | (~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402))) <=> (hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2016,plain,
% 1.06/1.27 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[2015])).
% 1.06/1.27 tff(2017,plain,
% 1.06/1.27 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[2016, 2014])).
% 1.06/1.27 tff(2018,plain,
% 1.06/1.27 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(2019,plain,
% 1.06/1.27 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 1.06/1.27 tff(2020,plain,
% 1.06/1.27 (hskp20 | (~c3_1(a402)) | (~c0_1(a402))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[2019, 138, 56, 93, 2013])).
% 1.06/1.27 tff(2021,plain,
% 1.06/1.27 (hskp20),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[2020, 1993, 1352])).
% 1.06/1.27 tff(2022,plain,
% 1.06/1.27 (~c2_1(a449)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[836, 2021])).
% 1.06/1.27 tff(2023,plain,
% 1.06/1.27 (c0_1(a440)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1449, 2001])).
% 1.06/1.27 tff(2024,plain,
% 1.06/1.27 (c3_1(a449)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[830, 2021])).
% 1.06/1.27 tff(2025,plain,
% 1.06/1.27 (c1_1(a449)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[765, 2021])).
% 1.06/1.27 tff(2026,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2027,plain,
% 1.06/1.27 ((hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a440) | c3_1(a440) | (~c0_1(a440))) <=> (hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2028,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[2027])).
% 1.06/1.27 tff(2029,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[2028, 2026])).
% 1.06/1.27 tff(2030,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(2031,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 1.06/1.27 tff(2032,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[2031, 138, 1985, 2025, 2024, 2023, 2022, 2003, 2002, 851])).
% 1.06/1.27 tff(2033,plain,(hskp19 | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | hskp21 | hskp1 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(2034,plain,
% 1.06/1.27 (hskp19),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[2033, 1954, 93, 12, 56, 1953, 55])).
% 1.06/1.27 tff(2035,plain,
% 1.06/1.27 (c1_1(a445)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[413, 2034])).
% 1.06/1.27 tff(2036,plain,
% 1.06/1.27 (c3_1(a445)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[422, 2034])).
% 1.06/1.27 tff(2037,plain,
% 1.06/1.27 (~c0_1(a445)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[299, 2034])).
% 1.06/1.27 tff(2038,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1458, 2037, 2036, 1957, 93, 12, 1954, 2035])).
% 1.06/1.27 tff(2039,plain,(hskp1 | c1_1(a402) | hskp21 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(2040,plain,
% 1.06/1.27 (hskp1),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[2039, 93, 56, 55])).
% 1.06/1.27 tff(2041,plain,
% 1.06/1.27 (~c3_1(a401)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[734, 2040])).
% 1.06/1.27 tff(2042,plain,
% 1.06/1.27 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(2043,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[2042])).
% 1.06/1.27 tff(2044,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2045,plain,
% 1.06/1.27 (^[V: $i, U: $i] : 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)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(2046,plain,
% 1.06/1.27 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[2045])).
% 1.06/1.27 tff(2047,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.06/1.27 tff(2048,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 1.06/1.27 tff(2049,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2048, 2044])).
% 1.06/1.27 tff(2050,plain,(
% 1.06/1.27 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.06/1.27 inference(skolemize,[status(sab)],[2049])).
% 1.06/1.27 tff(2051,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2050, 2043])).
% 1.06/1.27 tff(2052,plain,
% 1.06/1.27 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2053,plain,
% 1.06/1.27 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | (~c3_1(a403))) <=> (hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2054,plain,
% 1.06/1.27 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0)))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[2053])).
% 1.06/1.27 tff(2055,plain,
% 1.06/1.27 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.06/1.27 inference(transitivity,[status(thm)],[2054, 2052])).
% 1.06/1.27 tff(2056,plain,
% 1.06/1.27 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(2057,plain,
% 1.06/1.27 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0)),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.06/1.27 tff(2058,plain,
% 1.06/1.27 (hskp5 | c0_1(a403) | c2_1(a403)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[2057, 138, 1896, 1890, 54])).
% 1.06/1.27 tff(2059,plain,
% 1.06/1.27 (hskp5),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[2058, 302, 303])).
% 1.06/1.27 tff(2060,plain,
% 1.06/1.27 (~c0_1(a408)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1253, 2059])).
% 1.06/1.27 tff(2061,plain,
% 1.06/1.27 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(2062,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[2061])).
% 1.06/1.27 tff(2063,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(2064,plain,
% 1.06/1.27 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(2065,plain,
% 1.06/1.27 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[2064])).
% 1.06/1.27 tff(2066,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.06/1.27 tff(2067,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 1.06/1.28 tff(2068,plain,
% 1.06/1.28 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2067, 2063])).
% 1.06/1.28 tff(2069,plain,(
% 1.06/1.28 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.06/1.28 inference(skolemize,[status(sab)],[2068])).
% 1.06/1.28 tff(2070,plain,
% 1.06/1.28 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2069, 2062])).
% 1.06/1.28 tff(2071,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2072,plain,
% 1.06/1.28 ((hskp10 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403))) <=> (hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2073,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))))),
% 1.06/1.28 inference(monotonicity,[status(thm)],[2072])).
% 1.06/1.28 tff(2074,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.06/1.28 inference(transitivity,[status(thm)],[2073, 2071])).
% 1.06/1.28 tff(2075,plain,
% 1.06/1.28 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))),
% 1.06/1.28 inference(quant_inst,[status(thm)],[])).
% 1.06/1.28 tff(2076,plain,
% 1.06/1.28 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.06/1.28 tff(2077,plain,
% 1.06/1.28 (hskp10),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2076, 138, 95, 94, 303, 302, 1890, 2070, 146])).
% 1.06/1.28 tff(2078,plain,
% 1.06/1.28 (((~hskp10) | (~c2_1(a418))) <=> ((~hskp10) | (~c2_1(a418)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2079,plain,
% 1.06/1.28 (((~c2_1(a418)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a418)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2080,axiom,((~c2_1(a418)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.06/1.28 tff(2081,plain,
% 1.06/1.28 ((~hskp10) | (~c2_1(a418))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 1.06/1.28 tff(2082,plain,
% 1.06/1.28 ((~hskp10) | (~c2_1(a418))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2081, 2078])).
% 1.06/1.28 tff(2083,plain,
% 1.06/1.28 (~c2_1(a418)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2082, 2077])).
% 1.06/1.28 tff(2084,plain,
% 1.06/1.28 (((~hskp10) | (~c0_1(a418))) <=> ((~hskp10) | (~c0_1(a418)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2085,plain,
% 1.06/1.28 (((~c0_1(a418)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a418)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2086,axiom,((~c0_1(a418)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.06/1.28 tff(2087,plain,
% 1.06/1.28 ((~hskp10) | (~c0_1(a418))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 1.06/1.28 tff(2088,plain,
% 1.06/1.28 ((~hskp10) | (~c0_1(a418))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2087, 2084])).
% 1.06/1.28 tff(2089,plain,
% 1.06/1.28 (~c0_1(a418)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2088, 2077])).
% 1.06/1.28 tff(2090,plain,
% 1.06/1.28 (c3_1(a408)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[1261, 2059])).
% 1.06/1.28 tff(2091,plain,
% 1.06/1.28 (c2_1(a408)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[1269, 2059])).
% 1.06/1.28 tff(2092,plain,
% 1.06/1.28 (((~hskp10) | c1_1(a418)) <=> ((~hskp10) | c1_1(a418))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2093,axiom,((~hskp10) | c1_1(a418)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.06/1.28 tff(2094,plain,
% 1.06/1.28 ((~hskp10) | c1_1(a418)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 1.06/1.28 tff(2095,plain,
% 1.06/1.28 ((~hskp10) | c1_1(a418)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2094, 2092])).
% 1.06/1.28 tff(2096,plain,
% 1.06/1.28 ((~hskp10) | c1_1(a418)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2095, 2092])).
% 1.06/1.28 tff(2097,plain,
% 1.06/1.28 ((~hskp10) | c1_1(a418)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2096, 2092])).
% 1.06/1.28 tff(2098,plain,
% 1.06/1.28 ((~hskp10) | c1_1(a418)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2097, 2092])).
% 1.06/1.28 tff(2099,plain,
% 1.06/1.28 (c1_1(a418)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2098, 2077])).
% 1.06/1.28 tff(2100,plain,
% 1.06/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2101,plain,
% 1.06/1.28 (((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418))) <=> (c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2102,plain,
% 1.06/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418))))),
% 1.06/1.28 inference(monotonicity,[status(thm)],[2101])).
% 1.06/1.28 tff(2103,plain,
% 1.06/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)))),
% 1.06/1.28 inference(transitivity,[status(thm)],[2102, 2100])).
% 1.06/1.28 tff(2104,plain,
% 1.06/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))),
% 1.06/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(2105,plain,
% 1.11/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 1.11/1.28 tff(2106,plain,
% 1.11/1.28 (c1_1(a403)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2105, 138, 2099, 2091, 2090, 2089, 2083, 2060, 302, 1890, 43])).
% 1.11/1.28 tff(2107,plain,
% 1.11/1.28 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2108,plain,
% 1.11/1.28 ((hskp16 | hskp3 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403))) <=> (hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2109,plain,
% 1.11/1.28 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[2108])).
% 1.11/1.28 tff(2110,plain,
% 1.11/1.28 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[2109, 2107])).
% 1.11/1.28 tff(2111,plain,
% 1.11/1.28 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(2112,plain,
% 1.11/1.28 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2111, 2110])).
% 1.11/1.28 tff(2113,plain,
% 1.11/1.28 (hskp16 | c0_1(a403) | (~c1_1(a403))),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2112, 138, 1896, 1890, 1309])).
% 1.11/1.28 tff(2114,plain,
% 1.11/1.28 (hskp16),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2113, 2106, 303])).
% 1.11/1.28 tff(2115,plain,
% 1.11/1.28 (~c3_1(a434)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[938, 2114])).
% 1.11/1.28 tff(2116,plain,
% 1.11/1.28 (~c0_1(a434)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[944, 2114])).
% 1.11/1.28 tff(2117,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2118,plain,
% 1.11/1.28 ((hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2119,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[2118])).
% 1.11/1.28 tff(2120,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[2119, 2117])).
% 1.11/1.28 tff(2121,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(2122,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 1.11/1.28 tff(2123,plain,
% 1.11/1.28 (~c2_1(a434)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2122, 138, 12, 2091, 2090, 2116, 2115, 2060, 1505])).
% 1.11/1.28 tff(2124,plain,
% 1.11/1.28 (^[U: $i] : refl((hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.11/1.28 inference(bind,[status(th)],[])).
% 1.11/1.28 tff(2125,plain,
% 1.11/1.28 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.28 inference(quant_intro,[status(thm)],[2124])).
% 1.11/1.28 tff(2126,plain,
% 1.11/1.28 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2127,plain,
% 1.11/1.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp9) <=> ((hskp27 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp9))), rewrite(((hskp27 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.11/1.28 inference(bind,[status(th)],[])).
% 1.11/1.28 tff(2128,plain,
% 1.11/1.28 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp9) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.28 inference(quant_intro,[status(thm)],[2127])).
% 1.11/1.28 tff(2129,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.11/1.28 tff(2130,plain,
% 1.11/1.28 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 1.11/1.28 tff(2131,plain,
% 1.11/1.28 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2130, 2126])).
% 1.11/1.28 tff(2132,plain,(
% 1.11/1.28 ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.28 inference(skolemize,[status(sab)],[2131])).
% 1.11/1.28 tff(2133,plain,
% 1.11/1.28 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2132, 2125])).
% 1.11/1.28 tff(2134,plain,
% 1.11/1.28 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2135,plain,
% 1.11/1.28 ((hskp27 | hskp9 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403))) <=> (hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2136,plain,
% 1.11/1.28 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[2135])).
% 1.11/1.28 tff(2137,plain,
% 1.11/1.28 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[2136, 2134])).
% 1.11/1.28 tff(2138,plain,
% 1.11/1.28 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(2139,plain,
% 1.11/1.28 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 1.11/1.28 tff(2140,plain,
% 1.11/1.28 (hskp27 | hskp9 | c0_1(a403) | (~c1_1(a403))),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2139, 138, 1890, 2133])).
% 1.11/1.28 tff(2141,plain,
% 1.11/1.28 (hskp9),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2140, 2106, 303, 180])).
% 1.11/1.28 tff(2142,plain,
% 1.11/1.28 (~c1_1(a416)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[606, 2141])).
% 1.11/1.28 tff(2143,plain,
% 1.11/1.28 (~c0_1(a416)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[612, 2141])).
% 1.11/1.28 tff(2144,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2145,plain,
% 1.11/1.28 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2146,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[2145])).
% 1.11/1.28 tff(2147,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[2146, 2144])).
% 1.11/1.28 tff(2148,plain,
% 1.11/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(2149,plain,
% 1.11/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 1.11/1.28 tff(2150,plain,
% 1.11/1.28 ((~c2_1(a416)) | c2_1(a434)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2149, 138, 218, 210, 204, 2116, 2115, 2143, 2142, 313])).
% 1.11/1.28 tff(2151,plain,
% 1.11/1.28 (~c2_1(a416)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2150, 2123])).
% 1.11/1.28 tff(2152,plain,
% 1.11/1.28 (hskp2 | c2_1(a416)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[619, 138, 12, 2143, 2142, 33])).
% 1.11/1.28 tff(2153,plain,
% 1.11/1.28 (hskp2),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2152, 2151])).
% 1.11/1.28 tff(2154,plain,
% 1.11/1.28 (c0_1(a402)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[469, 2153])).
% 1.11/1.28 tff(2155,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2156,plain,
% 1.11/1.28 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a403) | (~c3_1(a403)) | (~c1_1(a403))) <=> (c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2157,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a403) | (~c3_1(a403)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[2156])).
% 1.11/1.28 tff(2158,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a403) | (~c3_1(a403)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[2157, 2155])).
% 1.11/1.28 tff(2159,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a403) | (~c3_1(a403)) | (~c1_1(a403)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(2160,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.11/1.28 tff(2161,plain,
% 1.11/1.28 ((~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2160, 138, 303, 1890, 93, 480])).
% 1.11/1.28 tff(2162,plain,
% 1.11/1.28 (~c3_1(a402)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2161, 2154, 2106])).
% 1.11/1.28 tff(2163,plain,
% 1.11/1.28 (hskp1 | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a408))),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1370, 138, 2091, 2060, 93, 22])).
% 1.11/1.28 tff(2164,plain,
% 1.11/1.28 (~c1_1(a408)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2163, 2162, 12, 2154])).
% 1.11/1.28 tff(2165,plain,
% 1.11/1.28 (c1_1(a434)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[963, 2114])).
% 1.11/1.28 tff(2166,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2167,plain,
% 1.11/1.28 (((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)) | c3_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(2168,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[2167])).
% 1.11/1.28 tff(2169,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[2168, 2166])).
% 1.11/1.28 tff(2170,plain,
% 1.11/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)) | c3_1(a434) | c0_1(a434) | c2_1(a434))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(2171,plain,
% 1.11/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[2170, 2169])).
% 1.11/1.28 tff(2172,plain,
% 1.11/1.28 ($false),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2171, 138, 2165, 2091, 2116, 2115, 2060, 313, 2123, 2164])).
% 1.11/1.28 tff(2173,plain,(hskp19 | hskp1 | c1_1(a402) | c0_1(a403) | c2_1(a403) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.28 tff(2174,plain,
% 1.11/1.28 (hskp19),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[2173, 12, 93, 303, 302, 95, 94, 96, 55])).
% 1.11/1.28 tff(2175,plain,
% 1.11/1.28 (c1_1(a445)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[413, 2174])).
% 1.11/1.28 tff(2176,plain,
% 1.11/1.28 (~c0_1(a445)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[299, 2174])).
% 1.11/1.28 tff(2177,plain,
% 1.11/1.28 (c3_1(a445)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[422, 2174])).
% 1.11/1.29 tff(2178,plain,
% 1.11/1.29 (~c0_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1458, 2177, 1896, 93, 12, 2176, 2175])).
% 1.11/1.29 tff(2179,plain,
% 1.11/1.29 (~hskp2),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[469, 2178])).
% 1.11/1.29 tff(2180,plain,
% 1.11/1.29 (c2_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1564, 2178, 12, 2179])).
% 1.11/1.29 tff(2181,plain,
% 1.11/1.29 (c3_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1584, 138, 12, 2091, 2090, 2178, 2060, 2180, 1505])).
% 1.11/1.29 tff(2182,plain,
% 1.11/1.29 (hskp2 | hskp1 | c2_1(a403) | c1_1(a403)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[454, 138, 303, 33])).
% 1.11/1.29 tff(2183,plain,
% 1.11/1.29 (c1_1(a403)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2182, 2179, 302, 12])).
% 1.11/1.29 tff(2184,plain,
% 1.11/1.29 (hskp16),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2113, 2183, 303])).
% 1.11/1.29 tff(2185,plain,
% 1.11/1.29 (~c3_1(a434)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[938, 2184])).
% 1.11/1.29 tff(2186,plain,
% 1.11/1.29 (~c0_1(a434)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[944, 2184])).
% 1.11/1.29 tff(2187,plain,
% 1.11/1.29 (~c2_1(a434)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1941, 138, 12, 2178, 2186, 2185, 2180, 1505, 2181])).
% 1.11/1.29 tff(2188,plain,
% 1.11/1.29 (c1_1(a434)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[963, 2184])).
% 1.11/1.29 tff(2189,plain,
% 1.11/1.29 (hskp7 | c2_1(a434)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[954, 138, 2179, 2188, 2185, 106])).
% 1.11/1.29 tff(2190,plain,
% 1.11/1.29 (hskp7),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2189, 2187])).
% 1.11/1.29 tff(2191,plain,
% 1.11/1.29 (~c3_1(a410)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[230, 2190])).
% 1.11/1.29 tff(2192,plain,
% 1.11/1.29 (~c1_1(a410)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[236, 2190])).
% 1.11/1.29 tff(2193,plain,
% 1.11/1.29 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2194,plain,
% 1.11/1.29 ((hskp13 | hskp2 | (~ndr1_0) | c2_1(a403) | (~c1_1(a403)) | (~c3_1(a403))) <=> (hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2195,plain,
% 1.11/1.29 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2194])).
% 1.11/1.29 tff(2196,plain,
% 1.11/1.29 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[2195, 2193])).
% 1.11/1.29 tff(2197,plain,
% 1.11/1.29 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(2198,plain,
% 1.11/1.29 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 1.11/1.29 tff(2199,plain,
% 1.11/1.29 (hskp13 | hskp2 | c2_1(a403) | (~c1_1(a403))),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2198, 138, 1890, 247])).
% 1.11/1.29 tff(2200,plain,
% 1.11/1.29 (hskp13),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2199, 2183, 302, 2179])).
% 1.11/1.29 tff(2201,plain,
% 1.11/1.29 (~c0_1(a427)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[260, 2200])).
% 1.11/1.29 tff(2202,plain,
% 1.11/1.29 (c0_1(a410)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[268, 2190])).
% 1.11/1.29 tff(2203,plain,
% 1.11/1.29 (c2_1(a427)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[276, 2200])).
% 1.11/1.29 tff(2204,plain,
% 1.11/1.29 (c1_1(a427)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[284, 2200])).
% 1.11/1.29 tff(2205,plain,
% 1.11/1.29 ($false),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[291, 138, 12, 2204, 2203, 2202, 2201, 2192, 2191, 22])).
% 1.11/1.29 tff(2206,plain,(hskp1 | c2_1(a403) | c0_1(a403) | c1_1(a402) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.29 tff(2207,plain,
% 1.11/1.29 (hskp1),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2206, 302, 303, 93, 95, 94, 96, 55])).
% 1.11/1.29 tff(2208,plain,
% 1.11/1.29 (~c3_1(a401)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[734, 2207])).
% 1.11/1.29 tff(2209,plain,
% 1.11/1.29 (c1_1(a401)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[742, 2207])).
% 1.11/1.29 tff(2210,plain,
% 1.11/1.29 (c0_1(a401)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[750, 2207])).
% 1.11/1.29 tff(2211,plain,
% 1.11/1.29 (hskp20),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[757, 138, 2210, 2209, 2208, 435])).
% 1.11/1.29 tff(2212,plain,
% 1.11/1.29 (~c2_1(a449)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[836, 2211])).
% 1.11/1.29 tff(2213,plain,
% 1.11/1.29 (c3_1(a449)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[830, 2211])).
% 1.11/1.29 tff(2214,plain,
% 1.11/1.29 (c1_1(a449)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[765, 2211])).
% 1.11/1.29 tff(2215,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2216,plain,
% 1.11/1.29 ((hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403))) <=> (hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2217,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2216])).
% 1.11/1.29 tff(2218,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[2217, 2215])).
% 1.11/1.29 tff(2219,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(2220,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 1.11/1.29 tff(2221,plain,
% 1.11/1.29 (hskp10),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2220, 138, 2214, 2213, 2212, 303, 302, 1890, 2070])).
% 1.11/1.29 tff(2222,plain,
% 1.11/1.29 (~c2_1(a418)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2082, 2221])).
% 1.11/1.29 tff(2223,plain,
% 1.11/1.29 (~c0_1(a418)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2088, 2221])).
% 1.11/1.29 tff(2224,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2225,plain,
% 1.11/1.29 ((hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408))) <=> (hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2226,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2225])).
% 1.11/1.29 tff(2227,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[2226, 2224])).
% 1.11/1.29 tff(2228,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(2229,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 1.11/1.29 tff(2230,plain,
% 1.11/1.29 (hskp11),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2229, 138, 2091, 2090, 2210, 2209, 2060, 2208, 1036])).
% 1.11/1.29 tff(2231,plain,
% 1.11/1.29 (~c2_1(a420)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1142, 2230])).
% 1.11/1.29 tff(2232,plain,
% 1.11/1.29 (~c1_1(a420)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1025, 2230])).
% 1.11/1.29 tff(2233,plain,
% 1.11/1.29 (c1_1(a418)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2098, 2221])).
% 1.11/1.29 tff(2234,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2235,plain,
% 1.11/1.29 (((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418))) <=> (c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2236,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2235])).
% 1.11/1.29 tff(2237,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[2236, 2234])).
% 1.11/1.29 tff(2238,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(2239,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 1.11/1.29 tff(2240,plain,
% 1.11/1.29 (~c3_1(a420)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2239, 138, 2233, 2091, 2090, 2232, 2231, 2223, 2222, 2060, 43])).
% 1.11/1.29 tff(2241,plain,
% 1.11/1.29 (~c0_1(a420)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1019, 2230])).
% 1.11/1.29 tff(2242,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2243,plain,
% 1.11/1.29 ((hskp0 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a420) | c1_1(a420) | c0_1(a420)) <=> (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2244,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2243])).
% 1.11/1.29 tff(2245,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[2244, 2242])).
% 1.11/1.29 tff(2246,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a420) | c1_1(a420) | c0_1(a420))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(2247,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 1.11/1.29 tff(2248,plain,
% 1.11/1.29 (hskp0),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2247, 138, 2091, 2090, 2241, 2232, 2231, 2060, 2051])).
% 1.11/1.29 tff(2249,plain,
% 1.11/1.29 (~c3_1(a400)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[366, 2248])).
% 1.11/1.29 tff(2250,plain,
% 1.11/1.29 (c2_1(a400)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[338, 2248])).
% 1.11/1.29 tff(2251,plain,
% 1.11/1.29 (c1_1(a400)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[346, 2248])).
% 1.11/1.29 tff(2252,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2253,plain,
% 1.11/1.29 ((hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a420) | c0_1(a420) | c3_1(a420)) <=> (hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2254,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a420) | c0_1(a420) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420)))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2253])).
% 1.11/1.29 tff(2255,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a420) | c0_1(a420) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420))),
% 1.11/1.29 inference(transitivity,[status(thm)],[2254, 2252])).
% 1.11/1.29 tff(2256,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a420) | c0_1(a420) | c3_1(a420))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(2257,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 1.11/1.29 tff(2258,plain,
% 1.11/1.29 ($false),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2257, 138, 1896, 2251, 2250, 2241, 2232, 2249, 1339, 2240])).
% 1.11/1.29 tff(2259,plain,(c2_1(a403) | c0_1(a403) | c1_1(a402) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.29 tff(2260,plain,
% 1.11/1.29 (c2_1(a403)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2259, 303, 93, 95, 94, 96, 55])).
% 1.11/1.29 tff(2261,plain,
% 1.11/1.29 (~c0_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1458, 1897, 1896, 93, 12, 300, 1898])).
% 1.11/1.29 tff(2262,plain,
% 1.11/1.29 (c2_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1564, 2261, 12, 23])).
% 1.11/1.29 tff(2263,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2264,plain,
% 1.11/1.29 ((hskp1 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2265,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402)))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2264])).
% 1.11/1.29 tff(2266,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402))),
% 1.11/1.29 inference(transitivity,[status(thm)],[2265, 2263])).
% 1.11/1.29 tff(2267,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(2268,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 1.11/1.29 tff(2269,plain,
% 1.11/1.29 (c3_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2268, 138, 12, 2261, 303, 2260, 1890, 2262, 1505])).
% 1.11/1.29 tff(2270,plain,
% 1.11/1.29 (~c2_1(a434)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1941, 138, 12, 2261, 1935, 1934, 2262, 1505, 2269])).
% 1.11/1.29 tff(2271,plain,
% 1.11/1.29 ($false),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1949, 138, 1943, 2261, 1935, 1934, 93, 2262, 313, 2270])).
% 1.11/1.29 tff(2272,plain,(hskp2 | c1_1(a402) | hskp1 | c0_1(a403) | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.29 tff(2273,plain,
% 1.11/1.29 (hskp2),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2272, 12, 93, 303, 96, 95, 94, 55])).
% 1.11/1.29 tff(2274,plain,
% 1.11/1.29 (c0_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[469, 2273])).
% 1.11/1.29 tff(2275,plain,
% 1.11/1.29 (~c2_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[461, 2273])).
% 1.11/1.29 tff(2276,assumption,(c3_1(a402)), introduced(assumption)).
% 1.11/1.29 tff(2277,assumption,(c3_1(a403)), introduced(assumption)).
% 1.11/1.29 tff(2278,plain,
% 1.11/1.29 ((~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2160, 138, 303, 2277, 93, 480])).
% 1.11/1.29 tff(2279,plain,
% 1.11/1.29 (~c1_1(a403)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2278, 2276, 1352])).
% 1.11/1.29 tff(2280,plain,
% 1.11/1.29 (~hskp3),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1895, 2277])).
% 1.11/1.29 tff(2281,plain,
% 1.11/1.29 (hskp18),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2000, 2276, 2280, 1955])).
% 1.11/1.29 tff(2282,plain,
% 1.11/1.29 (~c3_1(a440)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1434, 2281])).
% 1.11/1.29 tff(2283,plain,
% 1.11/1.29 (~c2_1(a440)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1440, 2281])).
% 1.11/1.29 tff(2284,plain,
% 1.11/1.29 (c0_1(a440)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1449, 2281])).
% 1.11/1.29 tff(2285,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | (c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2286,plain,
% 1.11/1.29 (((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402))) <=> (c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2287,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | (c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2286])).
% 1.11/1.29 tff(2288,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[2287, 2285])).
% 1.11/1.29 tff(2289,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(2290,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 1.11/1.29 tff(2291,plain,
% 1.11/1.29 ($false),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2290, 138, 2284, 2283, 2282, 1471, 2277, 93, 1955, 1410, 2276, 2279])).
% 1.11/1.29 tff(2292,plain,((~c3_1(a402)) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)) | c0_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.29 tff(2293,plain,
% 1.11/1.29 (~c3_1(a402)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[2292, 2275, 1890, 93, 2260, 2274, 303])).
% 1.11/1.29 tff(2294,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2295,plain,
% 1.11/1.29 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | (~c2_1(a403)) | (~c1_1(a403))) <=> (hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(2296,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | (~c2_1(a403)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[2295])).
% 1.11/1.30 tff(2297,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | (~c2_1(a403)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2296, 2294])).
% 1.11/1.30 tff(2298,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | (~c2_1(a403)) | (~c1_1(a403)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2299,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.11/1.30 tff(2300,plain,
% 1.11/1.30 (hskp1 | (~c2_1(a403)) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2299, 138, 303, 93, 22])).
% 1.11/1.30 tff(2301,plain,
% 1.11/1.30 (~c1_1(a403)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2300, 2293, 2260, 12, 2274])).
% 1.11/1.30 tff(2302,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2303,plain,
% 1.11/1.30 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a403) | c0_1(a403) | (~c2_1(a403)) | c3_1(a460) | c0_1(a460) | c2_1(a460)) <=> (c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2304,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a403) | c0_1(a403) | (~c2_1(a403)) | c3_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[2303])).
% 1.11/1.30 tff(2305,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a403) | c0_1(a403) | (~c2_1(a403)) | c3_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2304, 2302])).
% 1.11/1.30 tff(2306,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a403) | c0_1(a403) | (~c2_1(a403)) | c3_1(a460) | c0_1(a460) | c2_1(a460))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2307,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 1.11/1.30 tff(2308,plain,
% 1.11/1.30 (c0_1(a460)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2307, 138, 218, 210, 204, 303, 1471, 313, 448])).
% 1.11/1.30 tff(2309,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2310,plain,
% 1.11/1.30 ((hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403))) <=> (hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2311,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[2310])).
% 1.11/1.30 tff(2312,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2311, 2309])).
% 1.11/1.30 tff(2313,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2314,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 1.11/1.30 tff(2315,plain,
% 1.11/1.30 (hskp11),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2314, 138, 218, 204, 303, 1471, 2277, 1036, 2308])).
% 1.11/1.30 tff(2316,plain,
% 1.11/1.30 (~c2_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1142, 2315])).
% 1.11/1.30 tff(2317,plain,
% 1.11/1.30 (~c1_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1025, 2315])).
% 1.11/1.30 tff(2318,plain,
% 1.11/1.30 (~c0_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1019, 2315])).
% 1.11/1.30 tff(2319,plain,
% 1.11/1.30 (hskp22),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1991, 138, 95, 94, 1352, 1955, 851, 146, 1899])).
% 1.11/1.30 tff(2320,plain,
% 1.11/1.30 (c2_1(a451)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[783, 2319])).
% 1.11/1.30 tff(2321,plain,
% 1.11/1.30 (c0_1(a451)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[791, 2319])).
% 1.11/1.30 tff(2322,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2323,plain,
% 1.11/1.30 (((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a420) | c0_1(a420) | c2_1(a420)) <=> (c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2324,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[2323])).
% 1.11/1.30 tff(2325,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2324, 2322])).
% 1.11/1.30 tff(2326,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a420) | c0_1(a420) | c2_1(a420))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2327,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 1.11/1.30 tff(2328,plain,
% 1.11/1.30 (~c3_1(a451)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2327, 138, 218, 2321, 2320, 204, 2318, 2317, 2316, 11, 2308])).
% 1.11/1.30 tff(2329,plain,
% 1.11/1.30 (~c1_1(a451)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[775, 2319])).
% 1.11/1.30 tff(2330,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1205, 138, 218, 2320, 204, 2329, 811, 2308, 2328])).
% 1.11/1.30 tff(2331,plain,(hskp19 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a403) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a402)) | c2_1(a402) | c3_1(a402) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(2332,plain,
% 1.11/1.30 (hskp19),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2331, 2301, 2260, 1890, 303, 95, 94, 2274, 2275, 2293, 96, 55])).
% 1.11/1.30 tff(2333,plain,
% 1.11/1.30 (c1_1(a445)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[413, 2332])).
% 1.11/1.30 tff(2334,plain,
% 1.11/1.30 (c3_1(a445)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[422, 2332])).
% 1.11/1.30 tff(2335,plain,
% 1.11/1.30 (~c0_1(a445)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[299, 2332])).
% 1.11/1.30 tff(2336,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1458, 2335, 2334, 1896, 93, 12, 2274, 2333])).
% 1.11/1.30 tff(2337,plain,(hskp1 | c1_1(a402) | c0_1(a403) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(2338,plain,
% 1.11/1.30 (hskp1),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2337, 303, 93, 95, 94, 96, 55])).
% 1.11/1.30 tff(2339,plain,
% 1.11/1.30 (~c3_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[734, 2338])).
% 1.11/1.30 tff(2340,plain,
% 1.11/1.30 (c1_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[742, 2338])).
% 1.11/1.30 tff(2341,plain,
% 1.11/1.30 (c0_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[750, 2338])).
% 1.11/1.30 tff(2342,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2343,plain,
% 1.11/1.30 ((hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403))) <=> (hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2344,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[2343])).
% 1.11/1.30 tff(2345,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2344, 2342])).
% 1.11/1.30 tff(2346,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2347,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 1.11/1.30 tff(2348,plain,
% 1.11/1.30 (hskp11),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2347, 138, 2341, 2340, 303, 2260, 1890, 2339, 1036])).
% 1.11/1.30 tff(2349,plain,
% 1.11/1.30 (~c2_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1142, 2348])).
% 1.11/1.30 tff(2350,plain,
% 1.11/1.30 (~c1_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1025, 2348])).
% 1.11/1.30 tff(2351,plain,
% 1.11/1.30 (~c0_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1019, 2348])).
% 1.11/1.30 tff(2352,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2353,plain,
% 1.11/1.30 ((hskp0 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c2_1(a420) | c1_1(a420) | c0_1(a420)) <=> (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2354,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0)))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[2353])).
% 1.11/1.30 tff(2355,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2354, 2352])).
% 1.11/1.30 tff(2356,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c2_1(a420) | c1_1(a420) | c0_1(a420))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2357,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.11/1.30 tff(2358,plain,
% 1.11/1.30 (hskp0),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2357, 138, 2351, 2350, 2349, 303, 2260, 1890, 2051])).
% 1.11/1.30 tff(2359,plain,
% 1.11/1.30 (~c3_1(a400)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[366, 2358])).
% 1.11/1.30 tff(2360,plain,
% 1.11/1.30 (c2_1(a400)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[338, 2358])).
% 1.11/1.30 tff(2361,plain,
% 1.11/1.30 (c1_1(a400)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[346, 2358])).
% 1.11/1.30 tff(2362,plain,
% 1.11/1.30 (c3_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2257, 138, 1896, 2361, 2360, 2351, 2350, 2359, 1339])).
% 1.11/1.30 tff(2363,plain,
% 1.11/1.30 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2364,plain,
% 1.11/1.30 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a420) | c0_1(a420) | (~c3_1(a420))) <=> (hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2365,plain,
% 1.11/1.30 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[2364])).
% 1.11/1.30 tff(2366,plain,
% 1.11/1.30 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2365, 2363])).
% 1.11/1.30 tff(2367,plain,
% 1.11/1.30 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2368,plain,
% 1.11/1.30 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 1.11/1.30 tff(2369,plain,
% 1.11/1.30 (hskp5 | (~c3_1(a420))),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2368, 138, 1896, 2351, 2349, 54])).
% 1.11/1.30 tff(2370,plain,
% 1.11/1.30 (hskp5),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2369, 2362])).
% 1.11/1.30 tff(2371,plain,
% 1.11/1.30 (~c0_1(a408)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1253, 2370])).
% 1.11/1.30 tff(2372,plain,
% 1.11/1.30 (hskp20),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[757, 138, 2341, 2340, 2339, 435])).
% 1.11/1.30 tff(2373,plain,
% 1.11/1.30 (~c2_1(a449)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[836, 2372])).
% 1.11/1.30 tff(2374,plain,
% 1.11/1.30 (c3_1(a449)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[830, 2372])).
% 1.11/1.30 tff(2375,plain,
% 1.11/1.30 (c1_1(a449)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[765, 2372])).
% 1.11/1.30 tff(2376,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2377,plain,
% 1.11/1.30 ((hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a420) | c0_1(a420) | (~c3_1(a420))) <=> (hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2378,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[2377])).
% 1.11/1.30 tff(2379,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2378, 2376])).
% 1.11/1.30 tff(2380,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2381,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 1.11/1.30 tff(2382,plain,
% 1.11/1.30 (hskp10 | (~c3_1(a420))),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2381, 138, 2375, 2374, 2373, 2351, 2349, 2070])).
% 1.11/1.30 tff(2383,plain,
% 1.11/1.30 (hskp10),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2382, 2362])).
% 1.11/1.30 tff(2384,plain,
% 1.11/1.30 (~c2_1(a418)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2082, 2383])).
% 1.11/1.30 tff(2385,plain,
% 1.11/1.30 (~c0_1(a418)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2088, 2383])).
% 1.11/1.30 tff(2386,plain,
% 1.11/1.30 (c3_1(a408)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1261, 2370])).
% 1.11/1.30 tff(2387,plain,
% 1.11/1.30 (c2_1(a408)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1269, 2370])).
% 1.11/1.30 tff(2388,plain,
% 1.11/1.30 (c1_1(a418)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2098, 2383])).
% 1.11/1.30 tff(2389,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2239, 138, 2388, 2387, 2386, 2350, 2349, 2385, 2384, 2371, 43, 2362])).
% 1.11/1.30 tff(2390,plain,(c0_1(a403) | c1_1(a402) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(2391,plain,
% 1.11/1.30 (c0_1(a403)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2390, 93, 84, 76, 92, 55])).
% 1.11/1.30 tff(2392,plain,
% 1.11/1.30 (c3_1(a402)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1929, 23, 12, 1898, 1897, 1896, 93, 300])).
% 1.11/1.30 tff(2393,plain,
% 1.11/1.30 ((~c3_1(a402)) | (~c2_1(a434))),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1941, 138, 12, 1931, 1935, 1934, 1932, 1505])).
% 1.11/1.30 tff(2394,plain,
% 1.11/1.30 (~c2_1(a434)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2393, 2392])).
% 1.11/1.30 tff(2395,plain,
% 1.11/1.30 (hskp7 | c2_1(a434)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[954, 138, 23, 1943, 1934, 106])).
% 1.11/1.30 tff(2396,plain,
% 1.11/1.30 (hskp7),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2395, 2394])).
% 1.11/1.30 tff(2397,plain,
% 1.11/1.30 (~c3_1(a410)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[230, 2396])).
% 1.11/1.30 tff(2398,plain,
% 1.11/1.30 (~c1_1(a410)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[236, 2396])).
% 1.11/1.30 tff(2399,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2400,plain,
% 1.11/1.30 (((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c2_1(a434) | (~c1_1(a434))) <=> (c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2401,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[2400])).
% 1.11/1.30 tff(2402,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[2401, 2399])).
% 1.11/1.30 tff(2403,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c2_1(a434) | (~c1_1(a434)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2404,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.11/1.30 tff(2405,plain,
% 1.11/1.30 ((~c3_1(a402)) | c1_1(a403) | c2_1(a434)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2404, 138, 1943, 1931, 1935, 302, 1890, 1932, 43])).
% 1.11/1.30 tff(2406,plain,
% 1.11/1.30 (c1_1(a403)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2405, 2394, 2392])).
% 1.11/1.30 tff(2407,plain,
% 1.11/1.30 (hskp13),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2199, 2406, 302, 23])).
% 1.11/1.30 tff(2408,plain,
% 1.11/1.30 (~c0_1(a427)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[260, 2407])).
% 1.11/1.30 tff(2409,plain,
% 1.11/1.30 (c0_1(a410)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[268, 2396])).
% 1.11/1.30 tff(2410,plain,
% 1.11/1.30 (c2_1(a427)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[276, 2407])).
% 1.11/1.30 tff(2411,plain,
% 1.11/1.30 (c1_1(a427)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[284, 2407])).
% 1.11/1.30 tff(2412,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[291, 138, 12, 2411, 2410, 2409, 2408, 2398, 2397, 22])).
% 1.11/1.30 tff(2413,plain,(hskp2 | hskp1 | c2_1(a403) | c1_1(a402) | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(2414,plain,
% 1.11/1.30 (hskp2),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2413, 12, 302, 93, 92, 84, 76, 55])).
% 1.11/1.30 tff(2415,plain,
% 1.11/1.30 (c0_1(a402)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[469, 2414])).
% 1.11/1.30 tff(2416,plain,
% 1.11/1.30 (~c2_1(a402)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[461, 2414])).
% 1.11/1.30 tff(2417,plain,
% 1.11/1.30 (hskp19),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2033, 2416, 93, 2415, 56, 12, 55])).
% 1.11/1.30 tff(2418,plain,
% 1.11/1.30 (c1_1(a445)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[413, 2417])).
% 1.11/1.30 tff(2419,plain,
% 1.11/1.30 (c3_1(a445)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[422, 2417])).
% 1.11/1.30 tff(2420,plain,
% 1.11/1.30 (~c0_1(a445)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[299, 2417])).
% 1.11/1.30 tff(2421,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1458, 2420, 2419, 1957, 93, 12, 2415, 2418])).
% 1.11/1.30 tff(2422,plain,(hskp1 | c1_1(a402) | hskp21 | hskp24 | c2_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(2423,plain,
% 1.11/1.30 (hskp1),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2422, 302, 56, 55, 93])).
% 1.11/1.30 tff(2424,plain,
% 1.11/1.30 (~c3_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[734, 2423])).
% 1.11/1.30 tff(2425,plain,
% 1.11/1.30 (c1_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[742, 2423])).
% 1.11/1.30 tff(2426,plain,
% 1.11/1.30 (c0_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[750, 2423])).
% 1.11/1.30 tff(2427,assumption,(~c2_1(a401)), introduced(assumption)).
% 1.11/1.30 tff(2428,plain,
% 1.11/1.30 (hskp11 | hskp2 | c2_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[871, 138, 767, 768, 630])).
% 1.11/1.30 tff(2429,plain,
% 1.11/1.30 (hskp11),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2428, 2427, 23])).
% 1.11/1.30 tff(2430,plain,
% 1.11/1.30 (~c2_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1142, 2429])).
% 1.11/1.30 tff(2431,plain,
% 1.11/1.30 (~c1_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1025, 2429])).
% 1.11/1.30 tff(2432,plain,
% 1.11/1.30 (~c0_1(a420)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1019, 2429])).
% 1.11/1.30 tff(2433,plain,
% 1.11/1.30 (hskp7 | hskp2 | c2_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1105, 138, 769, 768, 106])).
% 1.11/1.30 tff(2434,plain,
% 1.11/1.30 (hskp7),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2433, 2427, 23])).
% 1.11/1.30 tff(2435,plain,
% 1.11/1.30 (hskp22),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[914, 2434, 767, 769, 768])).
% 1.11/1.30 tff(2436,plain,
% 1.11/1.30 (c2_1(a451)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[783, 2435])).
% 1.11/1.30 tff(2437,plain,
% 1.11/1.30 (c0_1(a451)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[791, 2435])).
% 1.11/1.30 tff(2438,plain,
% 1.11/1.30 (~c3_1(a451)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1541, 138, 2437, 2436, 767, 769, 2432, 2431, 2430, 768, 11])).
% 1.11/1.30 tff(2439,plain,
% 1.11/1.30 (~c1_1(a451)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[775, 2435])).
% 1.11/1.30 tff(2440,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[817, 138, 2436, 767, 769, 2439, 768, 811, 2438])).
% 1.11/1.30 tff(2441,plain,(c2_1(a401) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(2442,plain,
% 1.11/1.30 (c2_1(a401)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2441, 23, 769, 768, 767])).
% 1.11/1.30 tff(2443,plain,
% 1.11/1.30 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(2444,plain,
% 1.11/1.30 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(2445,plain,
% 1.11/1.30 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)) | (~c0_1(a401))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 1.11/1.30 tff(2446,plain,
% 1.11/1.30 (hskp19 | (~c2_1(a401))),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[2445, 138, 55, 767, 769, 117])).
% 1.11/1.31 tff(2447,plain,
% 1.11/1.31 (hskp19),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2446, 2442])).
% 1.11/1.31 tff(2448,plain,
% 1.11/1.31 (~c0_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[299, 2447])).
% 1.11/1.31 tff(2449,plain,
% 1.11/1.31 (c1_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[413, 2447])).
% 1.11/1.31 tff(2450,plain,
% 1.11/1.31 (c3_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[422, 2447])).
% 1.11/1.31 tff(2451,plain,
% 1.11/1.31 (~hskp22),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[822, 2450, 768, 769, 767, 2449, 2448])).
% 1.11/1.31 tff(2452,plain,
% 1.11/1.31 (~hskp7),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[914, 2451, 767, 769, 768])).
% 1.11/1.31 tff(2453,plain,
% 1.11/1.31 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2454,plain,
% 1.11/1.31 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a403) | (~c3_1(a403)) | (~c0_1(a403))) <=> (hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2455,plain,
% 1.11/1.31 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a403) | (~c3_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0)))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[2454])).
% 1.11/1.31 tff(2456,plain,
% 1.11/1.31 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a403) | (~c3_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.31 inference(transitivity,[status(thm)],[2455, 2453])).
% 1.11/1.31 tff(2457,plain,
% 1.11/1.31 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a403) | (~c3_1(a403)) | (~c0_1(a403)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(2458,plain,
% 1.11/1.31 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 1.11/1.31 tff(2459,plain,
% 1.11/1.31 (hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2458, 138, 2277, 925])).
% 1.11/1.31 tff(2460,plain,
% 1.11/1.31 (hskp16),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2459, 2452, 1176, 302])).
% 1.11/1.31 tff(2461,plain,
% 1.11/1.31 (~c0_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[944, 2460])).
% 1.11/1.31 tff(2462,plain,
% 1.11/1.31 (~c3_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[938, 2460])).
% 1.11/1.31 tff(2463,plain,
% 1.11/1.31 (c2_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[974, 2462, 94, 767, 769, 2461, 768, 2452, 23, 96])).
% 1.11/1.31 tff(2464,plain,
% 1.11/1.31 (hskp14),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[991, 2452, 94, 23, 769, 768, 767, 2460, 96])).
% 1.11/1.31 tff(2465,plain,
% 1.11/1.31 (~c1_1(a428)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[382, 2464])).
% 1.11/1.31 tff(2466,plain,
% 1.11/1.31 (hskp15),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1620, 2452, 2280])).
% 1.11/1.31 tff(2467,plain,
% 1.11/1.31 (~c3_1(a430)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1626, 2466])).
% 1.11/1.31 tff(2468,plain,
% 1.11/1.31 (c2_1(a428)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[396, 2464])).
% 1.11/1.31 tff(2469,plain,
% 1.11/1.31 (c2_1(a430)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1636, 2466])).
% 1.11/1.31 tff(2470,plain,
% 1.11/1.31 (c0_1(a430)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1644, 2466])).
% 1.11/1.31 tff(2471,plain,
% 1.11/1.31 (c1_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[963, 2460])).
% 1.11/1.31 tff(2472,plain,
% 1.11/1.31 (~c3_1(a428)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1651, 138, 2471, 2470, 2469, 2468, 2461, 2467, 2465, 647, 2463])).
% 1.11/1.31 tff(2473,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1011, 138, 2468, 767, 769, 2465, 768, 811, 2472])).
% 1.11/1.31 tff(2474,plain,(hskp2 | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | (~c3_1(a405)) | (~c0_1(a405)) | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2475,plain,
% 1.11/1.31 (hskp2),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2474, 2426, 2425, 2424, 76, 92, 2391, 302, 1956, 55])).
% 1.11/1.31 tff(2476,plain,
% 1.11/1.31 (~c2_1(a402)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[461, 2475])).
% 1.11/1.31 tff(2477,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[817, 138, 784, 767, 769, 776, 768, 811, 1965])).
% 1.11/1.31 tff(2478,plain,((~hskp22) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2479,plain,
% 1.11/1.31 (~hskp22),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2478, 2426, 2425, 2424, 1957])).
% 1.11/1.31 tff(2480,plain,
% 1.11/1.31 (hskp20),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[757, 138, 2426, 2425, 2424, 435])).
% 1.11/1.31 tff(2481,plain,
% 1.11/1.31 (~c2_1(a449)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[836, 2480])).
% 1.11/1.31 tff(2482,plain,
% 1.11/1.31 (c0_1(a402)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[469, 2475])).
% 1.11/1.31 tff(2483,plain,
% 1.11/1.31 (c3_1(a449)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[830, 2480])).
% 1.11/1.31 tff(2484,plain,
% 1.11/1.31 (c1_1(a449)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[765, 2480])).
% 1.11/1.31 tff(2485,plain,
% 1.11/1.31 (hskp22 | c3_1(a402)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[862, 138, 2484, 2483, 2482, 2481, 2476, 851])).
% 1.11/1.31 tff(2486,plain,
% 1.11/1.31 (c3_1(a402)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2485, 2479])).
% 1.11/1.31 tff(2487,plain,
% 1.11/1.31 (hskp18),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2000, 2486, 1957, 2476])).
% 1.11/1.31 tff(2488,plain,
% 1.11/1.31 (~c3_1(a440)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1434, 2487])).
% 1.11/1.31 tff(2489,plain,
% 1.11/1.31 (~c2_1(a440)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1440, 2487])).
% 1.11/1.31 tff(2490,plain,
% 1.11/1.31 (c0_1(a440)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1449, 2487])).
% 1.11/1.31 tff(2491,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2031, 138, 2479, 2484, 2483, 2490, 2481, 2489, 2488, 851])).
% 1.11/1.31 tff(2492,plain,(c2_1(a403) | c1_1(a402) | hskp24 | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2493,plain,
% 1.11/1.31 (c2_1(a403)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2492, 93, 55, 56])).
% 1.11/1.31 tff(2494,plain,
% 1.11/1.31 (c1_1(a401)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[742, 2040])).
% 1.11/1.31 tff(2495,plain,
% 1.11/1.31 (c0_1(a401)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[750, 2040])).
% 1.11/1.31 tff(2496,plain,
% 1.11/1.31 (~hskp22),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2478, 2495, 2494, 2041, 1957])).
% 1.11/1.31 tff(2497,plain,
% 1.11/1.31 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2498,plain,
% 1.11/1.31 ((hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403))) <=> (hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2499,plain,
% 1.11/1.31 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0)))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[2498])).
% 1.11/1.31 tff(2500,plain,
% 1.11/1.31 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.11/1.31 inference(transitivity,[status(thm)],[2499, 2497])).
% 1.11/1.31 tff(2501,plain,
% 1.11/1.31 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(2502,plain,
% 1.11/1.31 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2501, 2500])).
% 1.11/1.31 tff(2503,plain,
% 1.11/1.31 (hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403))),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2502, 138, 1956, 883])).
% 1.11/1.31 tff(2504,plain,
% 1.11/1.31 (hskp11),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2503, 2496, 2391, 2493])).
% 1.11/1.31 tff(2505,plain,
% 1.11/1.31 (~c2_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1142, 2504])).
% 1.11/1.31 tff(2506,plain,
% 1.11/1.31 (~c1_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1025, 2504])).
% 1.11/1.31 tff(2507,plain,
% 1.11/1.31 (~c0_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1019, 2504])).
% 1.11/1.31 tff(2508,plain,
% 1.11/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2509,plain,
% 1.11/1.31 (((~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420)) <=> (c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2510,plain,
% 1.11/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[2509])).
% 1.11/1.31 tff(2511,plain,
% 1.11/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[2510, 2508])).
% 1.11/1.31 tff(2512,plain,
% 1.11/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(2513,plain,
% 1.11/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 1.11/1.31 tff(2514,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2513, 138, 2495, 2494, 2507, 2506, 2505, 2391, 2493, 1956, 2041, 11])).
% 1.11/1.31 tff(2515,plain,(c1_1(a402) | hskp21 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2516,plain,
% 1.11/1.31 (c1_1(a402)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2515, 56, 55])).
% 1.11/1.31 tff(2517,plain,
% 1.11/1.31 (((~hskp2) | (~c1_1(a402))) <=> ((~hskp2) | (~c1_1(a402)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2518,plain,
% 1.11/1.31 (((~c1_1(a402)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a402)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2519,axiom,((~c1_1(a402)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.11/1.31 tff(2520,plain,
% 1.11/1.31 ((~hskp2) | (~c1_1(a402))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 1.11/1.31 tff(2521,plain,
% 1.11/1.31 ((~hskp2) | (~c1_1(a402))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2520, 2517])).
% 1.11/1.31 tff(2522,plain,
% 1.11/1.31 (~hskp2),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2521, 2516])).
% 1.11/1.31 tff(2523,plain,
% 1.11/1.31 (hskp19),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[293, 12, 23, 96, 95, 94, 55])).
% 1.11/1.31 tff(2524,plain,
% 1.11/1.31 (c1_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[413, 2523])).
% 1.11/1.31 tff(2525,plain,
% 1.11/1.31 (~c0_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[299, 2523])).
% 1.11/1.31 tff(2526,plain,
% 1.11/1.31 (c3_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[422, 2523])).
% 1.11/1.31 tff(2527,plain,
% 1.11/1.31 (hskp16 | hskp3),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1315, 138, 436, 425, 424, 1309])).
% 1.11/1.31 tff(2528,plain,
% 1.11/1.31 (hskp16),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2527, 44])).
% 1.11/1.31 tff(2529,plain,
% 1.11/1.31 (~c3_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[938, 2528])).
% 1.11/1.31 tff(2530,plain,
% 1.11/1.31 (~c0_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[944, 2528])).
% 1.11/1.31 tff(2531,plain,
% 1.11/1.31 (c1_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[963, 2528])).
% 1.11/1.31 tff(2532,assumption,(c1_1(a434)), introduced(assumption)).
% 1.11/1.31 tff(2533,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2534,plain,
% 1.11/1.31 ((hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2535,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[2534])).
% 1.11/1.31 tff(2536,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[2535, 2533])).
% 1.11/1.31 tff(2537,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(2538,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 1.11/1.31 tff(2539,plain,
% 1.11/1.31 (~c2_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2538, 138, 12, 2532, 904, 966, 894, 893, 22])).
% 1.11/1.31 tff(2540,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2541,plain,
% 1.11/1.31 ((hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434))) <=> (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2542,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[2541])).
% 1.11/1.31 tff(2543,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[2542, 2540])).
% 1.11/1.31 tff(2544,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(2545,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2544, 2543])).
% 1.11/1.31 tff(2546,plain,
% 1.11/1.31 (hskp9),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2545, 138, 2532, 904, 966, 948, 894, 893, 583])).
% 1.11/1.31 tff(2547,plain,
% 1.11/1.31 (~c1_1(a416)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[606, 2546])).
% 1.11/1.31 tff(2548,plain,
% 1.11/1.31 (~c0_1(a416)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[612, 2546])).
% 1.11/1.31 tff(2549,plain,
% 1.11/1.31 (~c2_1(a416)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1399, 138, 2532, 966, 948, 2548, 2547, 313, 2539])).
% 1.11/1.31 tff(2550,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[619, 138, 23, 12, 2548, 2547, 33, 2549])).
% 1.11/1.31 tff(2551,plain,((~hskp7) | hskp2 | hskp1 | (~c1_1(a434)) | c0_1(a434) | c3_1(a434)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2552,plain,
% 1.11/1.31 (~hskp7),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2551, 2531, 12, 23, 2530, 2529])).
% 1.11/1.31 tff(2553,plain,
% 1.11/1.31 (hskp7 | c2_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[954, 138, 23, 2531, 2529, 106])).
% 1.11/1.31 tff(2554,plain,
% 1.11/1.31 (c2_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2553, 2552])).
% 1.11/1.31 tff(2555,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2556,plain,
% 1.11/1.31 ((hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2557,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[2556])).
% 1.11/1.31 tff(2558,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[2557, 2555])).
% 1.11/1.31 tff(2559,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(2560,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 1.11/1.31 tff(2561,plain,
% 1.11/1.31 ((~c2_1(a434)) | (~c2_1(a445))),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2560, 138, 12, 425, 424, 2530, 2529, 1505])).
% 1.11/1.31 tff(2562,plain,
% 1.11/1.31 (~c2_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2561, 2554])).
% 1.11/1.31 tff(2563,plain,
% 1.11/1.31 (hskp5 | hskp3 | c2_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1360, 138, 425, 424, 54])).
% 1.11/1.31 tff(2564,plain,
% 1.11/1.31 (hskp5),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2563, 2562, 44])).
% 1.11/1.31 tff(2565,plain,
% 1.11/1.31 (~c0_1(a408)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1253, 2564])).
% 1.11/1.31 tff(2566,plain,
% 1.11/1.31 (hskp13),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1922, 2562])).
% 1.11/1.31 tff(2567,plain,
% 1.11/1.31 (~c0_1(a427)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[260, 2566])).
% 1.11/1.31 tff(2568,plain,
% 1.11/1.31 (c3_1(a408)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1261, 2564])).
% 1.11/1.31 tff(2569,plain,
% 1.11/1.31 (c2_1(a408)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1269, 2564])).
% 1.11/1.31 tff(2570,plain,
% 1.11/1.31 (c2_1(a427)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[276, 2566])).
% 1.11/1.31 tff(2571,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2572,plain,
% 1.11/1.31 ((hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427))) <=> (hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2573,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427)))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[2572])).
% 1.11/1.31 tff(2574,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427))),
% 1.11/1.31 inference(transitivity,[status(thm)],[2573, 2571])).
% 1.11/1.31 tff(2575,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(2576,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 1.11/1.31 tff(2577,plain,
% 1.11/1.31 (c3_1(a427)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2576, 138, 12, 2570, 2569, 2568, 2567, 2565, 1505])).
% 1.11/1.31 tff(2578,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2579,plain,
% 1.11/1.31 ((hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2580,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[2579])).
% 1.11/1.31 tff(2581,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[2580, 2578])).
% 1.11/1.31 tff(2582,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(2583,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2582, 2581])).
% 1.11/1.31 tff(2584,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2583, 138, 12, 2570, 2530, 2529, 2567, 1505, 2554, 2577])).
% 1.11/1.31 tff(2585,plain,(hskp3 | hskp1 | (~c3_1(a445)) | c0_1(a445) | hskp2 | (~c1_1(a445))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2586,plain,
% 1.11/1.31 (hskp3),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2585, 12, 2526, 2525, 23, 2524])).
% 1.11/1.31 tff(2587,plain,
% 1.11/1.31 (~c0_1(a403)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1191, 2586])).
% 1.11/1.31 tff(2588,plain,
% 1.11/1.31 (~c3_1(a403)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1895, 2586])).
% 1.11/1.31 tff(2589,plain,
% 1.11/1.31 (~c2_1(a403)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1554, 2586])).
% 1.11/1.31 tff(2590,plain,
% 1.11/1.31 (c1_1(a403)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[454, 138, 23, 12, 2587, 2589, 33])).
% 1.11/1.31 tff(2591,plain,
% 1.11/1.31 (hskp11),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[678, 2590, 23, 2526, 2524, 2589, 2588, 2525, 2587, 12])).
% 1.11/1.31 tff(2592,plain,
% 1.11/1.31 (~c2_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1142, 2591])).
% 1.11/1.31 tff(2593,plain,
% 1.11/1.31 (~c1_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1025, 2591])).
% 1.11/1.31 tff(2594,plain,
% 1.11/1.31 (~c0_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1019, 2591])).
% 1.11/1.31 tff(2595,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1045, 138, 23, 12, 2594, 2593, 2592, 33])).
% 1.11/1.31 tff(2596,plain,(hskp1 | hskp2 | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2597,plain,
% 1.11/1.31 (hskp1),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2596, 2522, 92, 84, 76, 55])).
% 1.11/1.31 tff(2598,plain,
% 1.11/1.31 (c0_1(a401)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[750, 2597])).
% 1.11/1.31 tff(2599,plain,
% 1.11/1.31 (~c3_1(a401)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[734, 2597])).
% 1.11/1.31 tff(2600,plain,
% 1.11/1.31 (c1_1(a401)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[742, 2597])).
% 1.11/1.31 tff(2601,plain,
% 1.11/1.31 (c2_1(a401)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2441, 2600, 2522, 2599, 2598])).
% 1.11/1.31 tff(2602,plain,
% 1.11/1.31 (hskp19),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2445, 138, 55, 2598, 2600, 117, 2601])).
% 1.11/1.31 tff(2603,plain,
% 1.11/1.31 (~c0_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[299, 2602])).
% 1.11/1.31 tff(2604,plain,
% 1.11/1.31 (c1_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[413, 2602])).
% 1.11/1.31 tff(2605,plain,
% 1.11/1.31 (c3_1(a445)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[422, 2602])).
% 1.11/1.31 tff(2606,plain,
% 1.11/1.31 (~hskp22),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[822, 2605, 2599, 2600, 2598, 2604, 2603])).
% 1.11/1.31 tff(2607,plain,
% 1.11/1.31 (~hskp7),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[914, 2606, 2598, 2600, 2599])).
% 1.11/1.31 tff(2608,plain,
% 1.11/1.31 (hskp11),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[890, 1108, 856])).
% 1.11/1.31 tff(2609,plain,
% 1.11/1.31 (~c1_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1025, 2608])).
% 1.11/1.31 tff(2610,plain,
% 1.11/1.31 (~c0_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1019, 2608])).
% 1.11/1.31 tff(2611,plain,
% 1.11/1.31 (~c2_1(a420)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1142, 2608])).
% 1.11/1.31 tff(2612,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1116, 2611, 2610, 94, 96, 769, 1108, 2609, 767, 768])).
% 1.11/1.31 tff(2613,plain,((~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a401) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2614,plain,
% 1.11/1.31 (~c2_1(a405)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2613, 76, 92, 2600, 2598, 2599, 2606])).
% 1.11/1.31 tff(2615,plain,
% 1.11/1.31 (hskp16 | hskp7 | c2_1(a405)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[931, 138, 92, 76, 925])).
% 1.11/1.31 tff(2616,plain,
% 1.11/1.31 (hskp16),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2615, 2614, 2607])).
% 1.11/1.31 tff(2617,plain,
% 1.11/1.31 (~c3_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[938, 2616])).
% 1.11/1.31 tff(2618,plain,
% 1.11/1.31 (~c0_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[944, 2616])).
% 1.11/1.31 tff(2619,plain,
% 1.11/1.31 (c2_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[974, 2618, 76, 2598, 2600, 2617, 2599, 2607, 2522, 92])).
% 1.11/1.31 tff(2620,plain,
% 1.11/1.31 (hskp14),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[994, 2614, 92, 76, 2522, 2600, 2599, 2598, 2607])).
% 1.11/1.31 tff(2621,plain,
% 1.11/1.31 (~c1_1(a428)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[382, 2620])).
% 1.11/1.31 tff(2622,plain,
% 1.11/1.31 (c2_1(a428)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[396, 2620])).
% 1.11/1.31 tff(2623,plain,
% 1.11/1.31 (c1_1(a434)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[963, 2616])).
% 1.11/1.31 tff(2624,plain,
% 1.11/1.31 (~c3_1(a428)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1004, 138, 2623, 2622, 2598, 2618, 2621, 2599, 647, 2619, 2601])).
% 1.11/1.31 tff(2625,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1011, 138, 2622, 2598, 2600, 2621, 2599, 811, 2624])).
% 1.11/1.31 tff(2626,plain,(hskp21 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(2627,plain,
% 1.11/1.31 (hskp21),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2626, 55])).
% 1.11/1.31 tff(2628,plain,
% 1.11/1.31 (((~hskp21) | (~c3_1(a450))) <=> ((~hskp21) | (~c3_1(a450)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2629,plain,
% 1.11/1.31 (((~c3_1(a450)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a450)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2630,axiom,((~c3_1(a450)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.11/1.31 tff(2631,plain,
% 1.11/1.31 ((~hskp21) | (~c3_1(a450))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2630, 2629])).
% 1.11/1.31 tff(2632,plain,
% 1.11/1.31 ((~hskp21) | (~c3_1(a450))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2631, 2628])).
% 1.11/1.31 tff(2633,plain,
% 1.11/1.31 (~c3_1(a450)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2632, 2627])).
% 1.11/1.31 tff(2634,plain,
% 1.11/1.31 (((~hskp21) | (~c1_1(a450))) <=> ((~hskp21) | (~c1_1(a450)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2635,plain,
% 1.11/1.31 (((~c1_1(a450)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a450)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2636,axiom,((~c1_1(a450)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.11/1.31 tff(2637,plain,
% 1.11/1.31 ((~hskp21) | (~c1_1(a450))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2636, 2635])).
% 1.11/1.31 tff(2638,plain,
% 1.11/1.31 ((~hskp21) | (~c1_1(a450))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[2637, 2634])).
% 1.11/1.31 tff(2639,plain,
% 1.11/1.31 (~c1_1(a450)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[2638, 2627])).
% 1.11/1.31 tff(2640,plain,
% 1.11/1.31 (((~hskp21) | (~c0_1(a450))) <=> ((~hskp21) | (~c0_1(a450)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2641,plain,
% 1.11/1.31 (((~c0_1(a450)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a450)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(2642,axiom,((~c0_1(a450)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.11/1.31 tff(2643,plain,
% 1.11/1.32 ((~hskp21) | (~c0_1(a450))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 1.11/1.32 tff(2644,plain,
% 1.11/1.32 ((~hskp21) | (~c0_1(a450))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2643, 2640])).
% 1.11/1.32 tff(2645,plain,
% 1.11/1.32 (~c0_1(a450)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2644, 2627])).
% 1.11/1.32 tff(2646,assumption,(~hskp25), introduced(assumption)).
% 1.11/1.32 tff(2647,plain,
% 1.11/1.32 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.11/1.32 inference(bind,[status(th)],[])).
% 1.11/1.32 tff(2648,plain,
% 1.11/1.32 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.11/1.32 inference(quant_intro,[status(thm)],[2647])).
% 1.11/1.32 tff(2649,plain,
% 1.11/1.32 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2650,plain,
% 1.11/1.32 (^[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)) | hskp25) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp25))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) | hskp3) <=> ((hskp25 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite(((hskp25 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.11/1.32 inference(bind,[status(th)],[])).
% 1.11/1.32 tff(2651,plain,
% 1.11/1.32 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) | hskp3) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.11/1.32 inference(quant_intro,[status(thm)],[2650])).
% 1.11/1.32 tff(2652,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.11/1.32 tff(2653,plain,
% 1.11/1.32 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 1.11/1.32 tff(2654,plain,
% 1.11/1.32 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2653, 2649])).
% 1.11/1.32 tff(2655,plain,(
% 1.11/1.32 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.11/1.32 inference(skolemize,[status(sab)],[2654])).
% 1.11/1.32 tff(2656,plain,
% 1.11/1.32 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2655, 2648])).
% 1.11/1.32 tff(2657,plain,
% 1.11/1.32 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2658,plain,
% 1.11/1.32 ((hskp25 | hskp3 | (~ndr1_0) | c1_1(a450) | c0_1(a450) | (~c2_1(a450))) <=> (hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2659,plain,
% 1.11/1.32 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2658])).
% 1.11/1.32 tff(2660,plain,
% 1.11/1.32 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2659, 2657])).
% 1.11/1.32 tff(2661,plain,
% 1.11/1.32 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2662,plain,
% 1.11/1.32 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 1.11/1.32 tff(2663,plain,
% 1.11/1.32 (hskp25 | hskp3 | (~c2_1(a450))),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2662, 138, 2645, 2639, 2656])).
% 1.11/1.32 tff(2664,plain,
% 1.11/1.32 (~c2_1(a450)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2663, 44, 2646])).
% 1.11/1.32 tff(2665,assumption,(hskp0), introduced(assumption)).
% 1.11/1.32 tff(2666,plain,
% 1.11/1.32 (~c3_1(a400)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[366, 2665])).
% 1.11/1.32 tff(2667,assumption,(~c3_1(a450)), introduced(assumption)).
% 1.11/1.32 tff(2668,assumption,(~c1_1(a450)), introduced(assumption)).
% 1.11/1.32 tff(2669,assumption,(~c0_1(a450)), introduced(assumption)).
% 1.11/1.32 tff(2670,plain,
% 1.11/1.32 (c2_1(a400)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[338, 2665])).
% 1.11/1.32 tff(2671,plain,
% 1.11/1.32 (c1_1(a400)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[346, 2665])).
% 1.11/1.32 tff(2672,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2673,plain,
% 1.11/1.32 ((hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a450) | c0_1(a450) | c3_1(a450)) <=> (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2674,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2673])).
% 1.11/1.32 tff(2675,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2674, 2672])).
% 1.11/1.32 tff(2676,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a450) | c0_1(a450) | c3_1(a450))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2677,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 1.11/1.32 tff(2678,plain,
% 1.11/1.32 ($false),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2677, 138, 44, 2671, 2670, 2669, 2668, 2667, 2666, 1339])).
% 1.11/1.32 tff(2679,plain,((~hskp0) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.32 tff(2680,plain,
% 1.11/1.32 (~hskp0),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2679, 44, 2645, 2639, 2633])).
% 1.11/1.32 tff(2681,plain,
% 1.11/1.32 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2682,plain,
% 1.11/1.32 ((hskp27 | hskp0 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | c3_1(a450)) <=> (hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2683,plain,
% 1.11/1.32 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450)))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2682])).
% 1.11/1.32 tff(2684,plain,
% 1.11/1.32 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2683, 2681])).
% 1.11/1.32 tff(2685,plain,
% 1.11/1.32 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | c3_1(a450))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2686,plain,
% 1.11/1.32 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2685, 2684])).
% 1.11/1.32 tff(2687,plain,
% 1.11/1.32 (hskp27 | hskp0 | c2_1(a450)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2686, 138, 2645, 2633, 323])).
% 1.11/1.32 tff(2688,plain,
% 1.11/1.32 (hskp27),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2687, 2680, 2664])).
% 1.11/1.32 tff(2689,plain,
% 1.11/1.32 (hskp19),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[179, 2688, 55])).
% 1.11/1.32 tff(2690,plain,
% 1.11/1.32 (c1_1(a445)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[413, 2689])).
% 1.11/1.32 tff(2691,plain,
% 1.11/1.32 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2692,plain,
% 1.11/1.32 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a450) | c1_1(a450) | c0_1(a450)) <=> (hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2693,plain,
% 1.11/1.32 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a450) | c1_1(a450) | c0_1(a450))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450)))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2692])).
% 1.11/1.32 tff(2694,plain,
% 1.11/1.32 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a450) | c1_1(a450) | c0_1(a450))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2693, 2691])).
% 1.11/1.32 tff(2695,plain,
% 1.11/1.32 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a450) | c1_1(a450) | c0_1(a450))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2696,plain,
% 1.11/1.32 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2695, 2694])).
% 1.11/1.32 tff(2697,plain,
% 1.11/1.32 (hskp2 | hskp1 | c2_1(a450)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2696, 138, 2669, 2668, 33])).
% 1.11/1.32 tff(2698,plain,
% 1.11/1.32 (c2_1(a450)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2697, 23, 12])).
% 1.11/1.32 tff(2699,plain,
% 1.11/1.32 (hskp25 | hskp3 | (~c2_1(a450))),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2662, 138, 2669, 2668, 2656])).
% 1.11/1.32 tff(2700,plain,
% 1.11/1.32 (hskp3),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2699, 2698, 2646])).
% 1.11/1.32 tff(2701,plain,
% 1.11/1.32 (~c3_1(a403)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1895, 2700])).
% 1.11/1.32 tff(2702,plain,
% 1.11/1.32 (~c2_1(a403)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1554, 2700])).
% 1.11/1.32 tff(2703,plain,
% 1.11/1.32 (~c0_1(a403)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1191, 2700])).
% 1.11/1.32 tff(2704,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2705,plain,
% 1.11/1.32 (((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)) | c3_1(a403) | c0_1(a403) | c2_1(a403)) <=> (c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2706,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2705])).
% 1.11/1.32 tff(2707,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2706, 2704])).
% 1.11/1.32 tff(2708,plain,
% 1.11/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)) | c3_1(a403) | c0_1(a403) | c2_1(a403))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2709,plain,
% 1.11/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2708, 2707])).
% 1.11/1.32 tff(2710,plain,
% 1.11/1.32 (~c1_1(a403)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2709, 138, 2669, 2668, 2703, 2702, 2701, 313, 2698])).
% 1.11/1.32 tff(2711,plain,
% 1.11/1.32 ($false),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[454, 138, 23, 12, 2703, 2702, 33, 2710])).
% 1.11/1.32 tff(2712,plain,(hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.11/1.32 tff(2713,plain,
% 1.11/1.32 (hskp2),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2712, 2646, 2645, 2639, 12])).
% 1.11/1.32 tff(2714,plain,
% 1.11/1.32 (c0_1(a402)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[469, 2713])).
% 1.11/1.32 tff(2715,plain,
% 1.11/1.32 (~c1_1(a402)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2521, 2713])).
% 1.11/1.32 tff(2716,plain,
% 1.11/1.32 (c3_1(a445)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[422, 2689])).
% 1.11/1.32 tff(2717,plain,
% 1.11/1.32 (~c0_1(a445)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[299, 2689])).
% 1.11/1.32 tff(2718,plain,
% 1.11/1.32 ($false),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1458, 2717, 2716, 2715, 44, 12, 2714, 2690])).
% 1.11/1.32 tff(2719,plain,(hskp3 | hskp1 | hskp24 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.11/1.32 tff(2720,plain,
% 1.11/1.32 (hskp3),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2719, 2646, 55, 12])).
% 1.11/1.32 tff(2721,plain,
% 1.11/1.32 (~c3_1(a403)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1895, 2720])).
% 1.11/1.32 tff(2722,plain,
% 1.11/1.32 (~c2_1(a403)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1554, 2720])).
% 1.11/1.32 tff(2723,plain,
% 1.11/1.32 (~c0_1(a403)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1191, 2720])).
% 1.11/1.32 tff(2724,plain,
% 1.11/1.32 (~c2_1(a402)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[461, 2713])).
% 1.11/1.32 tff(2725,plain,
% 1.11/1.32 (hskp27 | hskp0),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[329, 138, 303, 302, 301, 323])).
% 1.11/1.32 tff(2726,plain,
% 1.11/1.32 (hskp0),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2725, 180])).
% 1.11/1.32 tff(2727,plain,
% 1.11/1.32 (c2_1(a400)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[338, 2726])).
% 1.11/1.32 tff(2728,plain,
% 1.11/1.32 (c1_1(a400)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[346, 2726])).
% 1.11/1.32 tff(2729,plain,
% 1.11/1.32 (~c0_1(a400)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[350, 138, 55, 107, 2728, 2727, 117])).
% 1.11/1.32 tff(2730,plain,
% 1.11/1.32 (c3_1(a402)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[569, 138, 12, 1352, 2728, 2727, 93, 22, 2729])).
% 1.11/1.32 tff(2731,plain,
% 1.11/1.32 (~c3_1(a400)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[366, 2726])).
% 1.11/1.32 tff(2732,plain,
% 1.11/1.32 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.11/1.32 inference(bind,[status(th)],[])).
% 1.11/1.32 tff(2733,plain,
% 1.11/1.32 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/1.32 inference(quant_intro,[status(thm)],[2732])).
% 1.11/1.32 tff(2734,plain,
% 1.11/1.32 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2735,plain,
% 1.11/1.32 (^[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)) | c0_1(V) | c3_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) | c3_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)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_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)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.11/1.32 inference(bind,[status(th)],[])).
% 1.11/1.32 tff(2736,plain,
% 1.11/1.32 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/1.32 inference(quant_intro,[status(thm)],[2735])).
% 1.11/1.32 tff(2737,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)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.11/1.32 tff(2738,plain,
% 1.11/1.32 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2737, 2736])).
% 1.11/1.32 tff(2739,plain,
% 1.11/1.32 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2738, 2734])).
% 1.11/1.32 tff(2740,plain,(
% 1.11/1.32 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/1.32 inference(skolemize,[status(sab)],[2739])).
% 1.11/1.32 tff(2741,plain,
% 1.11/1.32 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2740, 2733])).
% 1.11/1.32 tff(2742,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2743,plain,
% 1.11/1.32 ((hskp9 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400))) <=> (hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2744,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2743])).
% 1.11/1.32 tff(2745,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2744, 2742])).
% 1.11/1.32 tff(2746,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2747,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 1.11/1.32 tff(2748,plain,
% 1.11/1.32 (hskp9),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2747, 138, 1352, 2727, 93, 1955, 2731, 2741, 2729])).
% 1.11/1.32 tff(2749,plain,
% 1.11/1.32 (~c1_1(a416)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[606, 2748])).
% 1.11/1.32 tff(2750,plain,
% 1.11/1.32 (~c0_1(a416)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[612, 2748])).
% 1.11/1.32 tff(2751,plain,
% 1.11/1.32 (c3_1(a416)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[667, 2748])).
% 1.11/1.32 tff(2752,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2753,plain,
% 1.11/1.32 (((~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416))) <=> (c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2754,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2753])).
% 1.11/1.32 tff(2755,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2754, 2752])).
% 1.11/1.32 tff(2756,plain,
% 1.11/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2757,plain,
% 1.11/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 1.11/1.32 tff(2758,plain,
% 1.11/1.32 ($false),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2757, 138, 2751, 2727, 2750, 2749, 93, 1955, 2731, 718, 2729, 2730])).
% 1.11/1.32 tff(2759,plain,(hskp19 | c1_1(a402) | c2_1(a402) | (~c0_1(a402)) | hskp1 | hskp24 | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.32 tff(2760,plain,
% 1.11/1.32 (hskp19),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2759, 2715, 2724, 2714, 12, 55, 2723, 2722, 2721])).
% 1.11/1.32 tff(2761,plain,
% 1.11/1.32 (c1_1(a445)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[413, 2760])).
% 1.11/1.32 tff(2762,plain,
% 1.11/1.32 (~c0_1(a445)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[299, 2760])).
% 1.11/1.32 tff(2763,plain,
% 1.11/1.32 (c3_1(a445)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[422, 2760])).
% 1.11/1.32 tff(2764,plain,
% 1.11/1.32 (hskp11),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[728, 2763, 2715, 2722, 12, 2723, 2721, 2762, 2761])).
% 1.11/1.32 tff(2765,plain,
% 1.11/1.32 (~c2_1(a420)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1142, 2764])).
% 1.11/1.32 tff(2766,plain,
% 1.11/1.32 (~c0_1(a420)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1019, 2764])).
% 1.11/1.32 tff(2767,plain,
% 1.11/1.32 (~c1_1(a420)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1025, 2764])).
% 1.11/1.32 tff(2768,plain,
% 1.11/1.32 ($false),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1088, 2767, 2766, 2715, 2723, 2761, 2762, 2763, 12, 2765, 2722, 2721])).
% 1.11/1.32 tff(2769,plain,(hskp25 | hskp1 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.32 tff(2770,plain,
% 1.11/1.32 (hskp25),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2769, 12, 55])).
% 1.11/1.32 tff(2771,plain,
% 1.11/1.32 (c1_1(a405)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[83, 2770])).
% 1.11/1.32 tff(2772,plain,
% 1.11/1.32 (c3_1(a405)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[75, 2770])).
% 1.11/1.32 tff(2773,plain,
% 1.11/1.32 (c0_1(a405)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[91, 2770])).
% 1.11/1.32 tff(2774,plain,
% 1.11/1.32 (hskp2),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2596, 2773, 12, 2771, 2772, 55])).
% 1.11/1.32 tff(2775,plain,
% 1.11/1.32 (~c1_1(a402)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2521, 2774])).
% 1.11/1.32 tff(2776,plain,
% 1.11/1.32 (c3_1(a403)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1889, 2775, 2773, 2772, 2771, 55])).
% 1.11/1.32 tff(2777,plain,
% 1.11/1.32 (~hskp3),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1895, 2776])).
% 1.11/1.32 tff(2778,plain,
% 1.11/1.32 (~hskp0),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2679, 2777, 2645, 2639, 2633])).
% 1.11/1.32 tff(2779,plain,
% 1.11/1.32 (c2_1(a450)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2687, 180, 2778])).
% 1.11/1.32 tff(2780,plain,
% 1.11/1.32 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.11/1.32 inference(bind,[status(th)],[])).
% 1.11/1.32 tff(2781,plain,
% 1.11/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/1.32 inference(quant_intro,[status(thm)],[2780])).
% 1.11/1.32 tff(2782,plain,
% 1.11/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2783,plain,
% 1.11/1.32 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.11/1.33 inference(bind,[status(th)],[])).
% 1.11/1.33 tff(2784,plain,
% 1.11/1.33 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/1.33 inference(quant_intro,[status(thm)],[2783])).
% 1.11/1.33 tff(2785,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.11/1.33 tff(2786,plain,
% 1.11/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 1.11/1.33 tff(2787,plain,
% 1.11/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2786, 2782])).
% 1.11/1.33 tff(2788,plain,(
% 1.11/1.33 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/1.33 inference(skolemize,[status(sab)],[2787])).
% 1.11/1.33 tff(2789,plain,
% 1.11/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2788, 2781])).
% 1.11/1.33 tff(2790,plain,
% 1.11/1.33 (~c2_1(a402)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[461, 2774])).
% 1.11/1.33 tff(2791,plain,
% 1.11/1.33 (c0_1(a402)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[469, 2774])).
% 1.11/1.33 tff(2792,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2793,plain,
% 1.11/1.33 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450))) <=> (c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2794,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2793])).
% 1.11/1.33 tff(2795,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2794, 2792])).
% 1.11/1.33 tff(2796,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2797,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2796, 2795])).
% 1.11/1.33 tff(2798,plain,
% 1.11/1.33 ((~c3_1(a402)) | (~c2_1(a450))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2797, 138, 2791, 2645, 2639, 2775, 2790, 2789])).
% 1.11/1.33 tff(2799,plain,
% 1.11/1.33 (~c3_1(a402)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2798, 2779])).
% 1.11/1.33 tff(2800,plain,
% 1.11/1.33 (hskp19 | (~c2_1(a405))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[144, 138, 55, 2773, 2771, 117])).
% 1.11/1.33 tff(2801,plain,
% 1.11/1.33 (~c2_1(a405)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2800, 107])).
% 1.11/1.33 tff(2802,plain,
% 1.11/1.33 (hskp27 | hskp23 | c2_1(a405)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[196, 138, 2773, 2771, 190])).
% 1.11/1.33 tff(2803,plain,
% 1.11/1.33 (hskp23),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2802, 180, 2801])).
% 1.11/1.33 tff(2804,plain,
% 1.11/1.33 (c1_1(a460)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[217, 2803])).
% 1.11/1.33 tff(2805,plain,
% 1.11/1.33 (~c3_1(a460)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[203, 2803])).
% 1.11/1.33 tff(2806,plain,
% 1.11/1.33 (~c2_1(a460)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[209, 2803])).
% 1.11/1.33 tff(2807,plain,
% 1.11/1.33 (~hskp22),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1984, 2806, 12, 180, 2805, 2804, 2777])).
% 1.11/1.33 tff(2808,plain,
% 1.11/1.33 ($false),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1991, 138, 2807, 2771, 2772, 2791, 2790, 851, 2801, 2799])).
% 1.11/1.33 tff(2809,plain,(hskp19 | hskp1 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.33 tff(2810,plain,
% 1.11/1.33 (hskp19),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2809, 12, 55])).
% 1.11/1.33 tff(2811,plain,
% 1.11/1.33 (c1_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[413, 2810])).
% 1.11/1.33 tff(2812,plain,
% 1.11/1.33 (c3_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[422, 2810])).
% 1.11/1.33 tff(2813,plain,
% 1.11/1.33 (~c0_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[299, 2810])).
% 1.11/1.33 tff(2814,plain,
% 1.11/1.33 ($false),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1458, 2813, 2812, 2775, 2777, 12, 2791, 2811])).
% 1.11/1.33 tff(2815,plain,(hskp1 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.33 tff(2816,plain,
% 1.11/1.33 (hskp1),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2815, 55])).
% 1.11/1.33 tff(2817,plain,
% 1.11/1.33 (c0_1(a401)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[750, 2816])).
% 1.11/1.33 tff(2818,plain,
% 1.11/1.33 (~c3_1(a401)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[734, 2816])).
% 1.11/1.33 tff(2819,plain,
% 1.11/1.33 (c1_1(a401)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[742, 2816])).
% 1.11/1.33 tff(2820,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2821,plain,
% 1.11/1.33 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c3_1(a450) | (~c2_1(a450))) <=> (c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2822,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c3_1(a450) | (~c2_1(a450)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2821])).
% 1.11/1.33 tff(2823,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c3_1(a450) | (~c2_1(a450)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2822, 2820])).
% 1.11/1.33 tff(2824,plain,
% 1.11/1.33 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c3_1(a450) | (~c2_1(a450)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2825,plain,
% 1.11/1.33 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2824, 2823])).
% 1.11/1.33 tff(2826,plain,
% 1.11/1.33 (~c2_1(a450)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2825, 138, 2817, 2819, 2639, 2633, 2818, 811])).
% 1.11/1.33 tff(2827,assumption,(~c2_1(a450)), introduced(assumption)).
% 1.11/1.33 tff(2828,assumption,(hskp28), introduced(assumption)).
% 1.11/1.33 tff(2829,plain,
% 1.11/1.33 (((~hskp28) | c3_1(a414)) <=> ((~hskp28) | c3_1(a414))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2830,axiom,((~hskp28) | c3_1(a414)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.11/1.33 tff(2831,plain,
% 1.11/1.33 ((~hskp28) | c3_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2830, 2829])).
% 1.11/1.33 tff(2832,plain,
% 1.11/1.33 ((~hskp28) | c3_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2831, 2829])).
% 1.11/1.33 tff(2833,plain,
% 1.11/1.33 ((~hskp28) | c3_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2832, 2829])).
% 1.11/1.33 tff(2834,plain,
% 1.11/1.33 ((~hskp28) | c3_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2833, 2829])).
% 1.11/1.33 tff(2835,plain,
% 1.11/1.33 ((~hskp28) | c3_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2834, 2829])).
% 1.11/1.33 tff(2836,plain,
% 1.11/1.33 (c3_1(a414)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2835, 2828])).
% 1.11/1.33 tff(2837,plain,
% 1.11/1.33 (((~hskp28) | c2_1(a414)) <=> ((~hskp28) | c2_1(a414))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2838,axiom,((~hskp28) | c2_1(a414)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.11/1.33 tff(2839,plain,
% 1.11/1.33 ((~hskp28) | c2_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 1.11/1.33 tff(2840,plain,
% 1.11/1.33 ((~hskp28) | c2_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2839, 2837])).
% 1.11/1.33 tff(2841,plain,
% 1.11/1.33 ((~hskp28) | c2_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2840, 2837])).
% 1.11/1.33 tff(2842,plain,
% 1.11/1.33 ((~hskp28) | c2_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2841, 2837])).
% 1.11/1.33 tff(2843,plain,
% 1.11/1.33 ((~hskp28) | c2_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2842, 2837])).
% 1.11/1.33 tff(2844,plain,
% 1.11/1.33 (c2_1(a414)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2843, 2828])).
% 1.11/1.33 tff(2845,plain,
% 1.11/1.33 (((~hskp28) | c0_1(a414)) <=> ((~hskp28) | c0_1(a414))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2846,axiom,((~hskp28) | c0_1(a414)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.11/1.33 tff(2847,plain,
% 1.11/1.33 ((~hskp28) | c0_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 1.11/1.33 tff(2848,plain,
% 1.11/1.33 ((~hskp28) | c0_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2847, 2845])).
% 1.11/1.33 tff(2849,plain,
% 1.11/1.33 ((~hskp28) | c0_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2848, 2845])).
% 1.11/1.33 tff(2850,plain,
% 1.11/1.33 ((~hskp28) | c0_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2849, 2845])).
% 1.11/1.33 tff(2851,plain,
% 1.11/1.33 ((~hskp28) | c0_1(a414)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2850, 2845])).
% 1.11/1.33 tff(2852,plain,
% 1.11/1.33 (c0_1(a414)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2851, 2828])).
% 1.11/1.33 tff(2853,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2854,plain,
% 1.11/1.33 (((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c0_1(a450) | c2_1(a450)) <=> (c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2855,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c0_1(a450) | c2_1(a450))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450)))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2854])).
% 1.11/1.33 tff(2856,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c0_1(a450) | c2_1(a450))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2855, 2853])).
% 1.11/1.33 tff(2857,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c0_1(a450) | c2_1(a450))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2858,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2857, 2856])).
% 1.11/1.33 tff(2859,plain,
% 1.11/1.33 ($false),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2858, 138, 2852, 2844, 2836, 767, 769, 2669, 2668, 768, 11, 2827])).
% 1.11/1.33 tff(2860,plain,((~hskp28) | (~c0_1(a401)) | (~c1_1(a401)) | c0_1(a450) | c1_1(a450) | c3_1(a401) | c2_1(a450)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.33 tff(2861,plain,
% 1.11/1.33 (~hskp28),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2860, 2817, 2819, 2645, 2639, 2818, 2826])).
% 1.11/1.33 tff(2862,plain,
% 1.11/1.33 (^[U: $i] : refl((hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.11/1.33 inference(bind,[status(th)],[])).
% 1.11/1.33 tff(2863,plain,
% 1.11/1.33 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.33 inference(quant_intro,[status(thm)],[2862])).
% 1.11/1.33 tff(2864,plain,
% 1.11/1.33 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2865,plain,
% 1.11/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp28) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp28))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp28) <=> (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp28) <=> (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.11/1.33 inference(bind,[status(th)],[])).
% 1.11/1.33 tff(2866,plain,
% 1.11/1.33 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp28) <=> ![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.33 inference(quant_intro,[status(thm)],[2865])).
% 1.11/1.33 tff(2867,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.11/1.33 tff(2868,plain,
% 1.11/1.33 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2867, 2866])).
% 1.11/1.33 tff(2869,plain,
% 1.11/1.33 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2868, 2864])).
% 1.11/1.33 tff(2870,plain,(
% 1.11/1.33 ![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.33 inference(skolemize,[status(sab)],[2869])).
% 1.11/1.33 tff(2871,plain,
% 1.11/1.33 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2870, 2863])).
% 1.11/1.33 tff(2872,plain,
% 1.11/1.33 (hskp20),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[757, 138, 2817, 2819, 2818, 435])).
% 1.11/1.33 tff(2873,plain,
% 1.11/1.33 (~c2_1(a449)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[836, 2872])).
% 1.11/1.33 tff(2874,plain,
% 1.11/1.33 (c3_1(a449)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[830, 2872])).
% 1.11/1.33 tff(2875,plain,
% 1.11/1.33 (c1_1(a449)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[765, 2872])).
% 1.11/1.33 tff(2876,plain,
% 1.11/1.33 (((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2877,plain,
% 1.11/1.33 ((hskp28 | hskp25 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449))) <=> (hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2878,plain,
% 1.11/1.33 (((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))) <=> ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2877])).
% 1.11/1.33 tff(2879,plain,
% 1.11/1.33 (((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))) <=> ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2878, 2876])).
% 1.11/1.33 tff(2880,plain,
% 1.11/1.33 ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2881,plain,
% 1.11/1.33 ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 1.11/1.33 tff(2882,plain,
% 1.11/1.33 (hskp28 | hskp25),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2881, 138, 2875, 2874, 2873, 2871])).
% 1.11/1.33 tff(2883,plain,
% 1.11/1.33 (hskp25),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2882, 2861])).
% 1.11/1.33 tff(2884,plain,
% 1.11/1.33 (c0_1(a405)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[91, 2883])).
% 1.11/1.33 tff(2885,plain,
% 1.11/1.33 (c1_1(a405)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[83, 2883])).
% 1.11/1.33 tff(2886,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2887,plain,
% 1.11/1.33 ((hskp3 | (~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c1_1(a401)) | c1_1(a450) | c0_1(a450) | c3_1(a450)) <=> (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2888,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c1_1(a401)) | c1_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2887])).
% 1.11/1.33 tff(2889,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c1_1(a401)) | c1_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2888, 2886])).
% 1.11/1.33 tff(2890,plain,
% 1.11/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c1_1(a401)) | c1_1(a450) | c0_1(a450) | c3_1(a450))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2891,plain,
% 1.11/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 1.11/1.33 tff(2892,plain,
% 1.11/1.33 (hskp3 | (~c2_1(a401))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2891, 138, 2819, 2645, 2639, 2633, 2818, 1339])).
% 1.11/1.33 tff(2893,plain,
% 1.11/1.33 (~c2_1(a401)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2892, 44])).
% 1.11/1.33 tff(2894,plain,
% 1.11/1.33 (hskp2),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2441, 2893, 2819, 2818, 2817])).
% 1.11/1.33 tff(2895,plain,
% 1.11/1.33 (~c1_1(a402)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2521, 2894])).
% 1.11/1.33 tff(2896,plain,
% 1.11/1.33 (hskp27),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2687, 2680, 2826])).
% 1.11/1.33 tff(2897,plain,
% 1.11/1.33 (hskp19),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[179, 2896, 55])).
% 1.11/1.33 tff(2898,plain,
% 1.11/1.33 (~c0_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[299, 2897])).
% 1.11/1.33 tff(2899,plain,
% 1.11/1.33 (~hskp22),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2478, 44, 2819, 2818, 2817])).
% 1.11/1.33 tff(2900,plain,
% 1.11/1.33 (c1_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[413, 2897])).
% 1.11/1.33 tff(2901,plain,
% 1.11/1.33 (c3_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[422, 2897])).
% 1.11/1.33 tff(2902,plain,
% 1.11/1.33 ($false),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[864, 2901, 2900, 2874, 2899, 2894, 2875, 2873, 2898, 2895])).
% 1.11/1.33 tff(2903,plain,(hskp3 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.33 tff(2904,plain,
% 1.11/1.33 (hskp3),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2903, 55])).
% 1.11/1.33 tff(2905,plain,
% 1.11/1.33 (~c3_1(a403)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1895, 2904])).
% 1.11/1.33 tff(2906,plain,
% 1.11/1.33 (~c2_1(a403)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1554, 2904])).
% 1.11/1.33 tff(2907,plain,
% 1.11/1.33 (c3_1(a405)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[75, 2883])).
% 1.11/1.33 tff(2908,plain,
% 1.11/1.33 (c1_1(a402)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1469, 2907, 2906, 2905, 2885, 2884, 55])).
% 1.11/1.33 tff(2909,plain,
% 1.11/1.33 (~hskp2),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2521, 2908])).
% 1.11/1.33 tff(2910,plain,
% 1.11/1.33 (c2_1(a401)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2441, 2909, 2819, 2818, 2817])).
% 1.11/1.33 tff(2911,plain,
% 1.11/1.33 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2912,plain,
% 1.11/1.33 ((hskp13 | hskp2 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449))) <=> (hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2913,plain,
% 1.11/1.33 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2912])).
% 1.11/1.33 tff(2914,plain,
% 1.11/1.33 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2913, 2911])).
% 1.11/1.33 tff(2915,plain,
% 1.11/1.33 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2916,plain,
% 1.11/1.33 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 1.11/1.33 tff(2917,plain,
% 1.11/1.33 (hskp13 | hskp2),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2916, 138, 2875, 2874, 2873, 247])).
% 1.11/1.33 tff(2918,plain,
% 1.11/1.33 (hskp13),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2917, 2909])).
% 1.11/1.33 tff(2919,plain,
% 1.11/1.33 (~c0_1(a427)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[260, 2918])).
% 1.11/1.33 tff(2920,plain,
% 1.11/1.33 (~c0_1(a403)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1191, 2904])).
% 1.11/1.33 tff(2921,plain,
% 1.11/1.33 (hskp19),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[405, 2884, 2920, 2906, 2905, 2885, 2907, 55])).
% 1.11/1.33 tff(2922,plain,
% 1.11/1.33 (~c0_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[299, 2921])).
% 1.11/1.33 tff(2923,plain,
% 1.11/1.33 (c1_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[413, 2921])).
% 1.11/1.33 tff(2924,plain,
% 1.11/1.33 (c3_1(a445)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[422, 2921])).
% 1.11/1.33 tff(2925,plain,
% 1.11/1.33 (~hskp22),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[822, 2924, 2818, 2819, 2817, 2923, 2922])).
% 1.11/1.33 tff(2926,plain,
% 1.11/1.33 (~c2_1(a405)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2613, 2925, 2884, 2819, 2817, 2818, 2907])).
% 1.11/1.33 tff(2927,plain,
% 1.11/1.33 (~hskp7),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[914, 2925, 2817, 2819, 2818])).
% 1.11/1.33 tff(2928,plain,
% 1.11/1.33 (hskp14),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[994, 2927, 2884, 2907, 2817, 2819, 2818, 2909, 2926])).
% 1.11/1.33 tff(2929,plain,
% 1.11/1.33 (~c1_1(a428)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[382, 2928])).
% 1.11/1.33 tff(2930,plain,
% 1.11/1.33 (c2_1(a427)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[276, 2918])).
% 1.11/1.33 tff(2931,plain,
% 1.11/1.33 (c1_1(a427)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[284, 2918])).
% 1.11/1.33 tff(2932,plain,
% 1.11/1.33 (c2_1(a428)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[396, 2928])).
% 1.11/1.33 tff(2933,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2934,plain,
% 1.11/1.33 (((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2935,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2934])).
% 1.11/1.33 tff(2936,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2935, 2933])).
% 1.11/1.33 tff(2937,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2938,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.11/1.33 tff(2939,plain,
% 1.11/1.33 (~c3_1(a428)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2938, 138, 2932, 2931, 2930, 2817, 2929, 2919, 2818, 647, 2910])).
% 1.11/1.34 tff(2940,plain,
% 1.11/1.34 ($false),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[1011, 138, 2932, 2817, 2819, 2929, 2818, 811, 2939])).
% 1.11/1.34 tff(2941,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 1.11/1.34 tff(2942,plain,
% 1.11/1.34 (((~hskp24) | (~c2_1(a477))) <=> ((~hskp24) | (~c2_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2943,plain,
% 1.11/1.34 (((~c2_1(a477)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2944,axiom,((~c2_1(a477)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.11/1.34 tff(2945,plain,
% 1.11/1.34 ((~hskp24) | (~c2_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2944, 2943])).
% 1.11/1.34 tff(2946,plain,
% 1.11/1.34 ((~hskp24) | (~c2_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2945, 2942])).
% 1.11/1.34 tff(2947,plain,
% 1.11/1.34 (~c2_1(a477)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2946, 2941])).
% 1.11/1.34 tff(2948,plain,
% 1.11/1.34 (((~hskp24) | (~c0_1(a477))) <=> ((~hskp24) | (~c0_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2949,plain,
% 1.11/1.34 (((~c0_1(a477)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2950,axiom,((~c0_1(a477)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.11/1.34 tff(2951,plain,
% 1.11/1.34 ((~hskp24) | (~c0_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2950, 2949])).
% 1.11/1.34 tff(2952,plain,
% 1.11/1.34 ((~hskp24) | (~c0_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2951, 2948])).
% 1.11/1.34 tff(2953,plain,
% 1.11/1.34 (~c0_1(a477)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2952, 2941])).
% 1.11/1.34 tff(2954,plain,
% 1.11/1.34 (((~hskp24) | c3_1(a477)) <=> ((~hskp24) | c3_1(a477))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2955,axiom,((~hskp24) | c3_1(a477)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.11/1.34 tff(2956,plain,
% 1.11/1.34 ((~hskp24) | c3_1(a477)),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2955, 2954])).
% 1.11/1.34 tff(2957,plain,
% 1.11/1.34 ((~hskp24) | c3_1(a477)),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2956, 2954])).
% 1.11/1.34 tff(2958,plain,
% 1.11/1.34 ((~hskp24) | c3_1(a477)),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2957, 2954])).
% 1.11/1.34 tff(2959,plain,
% 1.11/1.34 ((~hskp24) | c3_1(a477)),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2958, 2954])).
% 1.11/1.34 tff(2960,plain,
% 1.11/1.34 ((~hskp24) | c3_1(a477)),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2959, 2954])).
% 1.11/1.34 tff(2961,plain,
% 1.11/1.34 (c3_1(a477)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2960, 2941])).
% 1.11/1.34 tff(2962,plain,
% 1.11/1.34 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2963,plain,
% 1.11/1.34 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2964,plain,
% 1.11/1.34 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477))))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[2963])).
% 1.11/1.34 tff(2965,plain,
% 1.11/1.34 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)))),
% 1.11/1.34 inference(transitivity,[status(thm)],[2964, 2962])).
% 1.11/1.34 tff(2966,plain,
% 1.11/1.34 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(2967,plain,
% 1.11/1.34 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2966, 2965])).
% 1.11/1.34 tff(2968,plain,
% 1.11/1.34 (hskp5 | hskp3),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2967, 138, 2961, 2953, 2947, 54])).
% 1.11/1.34 tff(2969,plain,
% 1.11/1.34 (hskp5),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2968, 44])).
% 1.11/1.34 tff(2970,plain,
% 1.11/1.34 (~c0_1(a408)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[1253, 2969])).
% 1.11/1.34 tff(2971,plain,
% 1.11/1.34 (c3_1(a408)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[1261, 2969])).
% 1.11/1.34 tff(2972,plain,
% 1.11/1.34 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2973,plain,
% 1.11/1.34 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | c0_1(a477)) <=> (hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2974,plain,
% 1.11/1.34 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | c0_1(a477))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477)))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[2973])).
% 1.11/1.34 tff(2975,plain,
% 1.11/1.34 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | c0_1(a477))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477))),
% 1.11/1.34 inference(transitivity,[status(thm)],[2974, 2972])).
% 1.11/1.34 tff(2976,plain,
% 1.11/1.34 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | c0_1(a477))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(2977,plain,
% 1.11/1.34 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477)),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2976, 2975])).
% 1.11/1.34 tff(2978,plain,
% 1.11/1.34 (hskp2 | hskp1 | c1_1(a477)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2977, 138, 2953, 2947, 33])).
% 1.11/1.34 tff(2979,plain,
% 1.11/1.34 (c1_1(a477)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2978, 23, 12])).
% 1.11/1.34 tff(2980,plain,
% 1.11/1.34 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2981,plain,
% 1.11/1.34 ((hskp16 | hskp3 | (~ndr1_0) | c0_1(a477) | (~c1_1(a477)) | (~c3_1(a477))) <=> (hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(2982,plain,
% 1.11/1.34 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[2981])).
% 1.11/1.34 tff(2983,plain,
% 1.11/1.34 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.11/1.34 inference(transitivity,[status(thm)],[2982, 2980])).
% 1.11/1.34 tff(2984,plain,
% 1.11/1.34 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(2985,plain,
% 1.11/1.34 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 1.11/1.34 tff(2986,plain,
% 1.11/1.34 (hskp16 | hskp3 | (~c1_1(a477))),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2985, 138, 2961, 2953, 1309])).
% 1.11/1.34 tff(2987,plain,
% 1.11/1.34 (hskp16),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2986, 2979, 44])).
% 1.11/1.34 tff(2988,plain,
% 1.11/1.34 (~c3_1(a434)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[938, 2987])).
% 1.11/1.34 tff(2989,plain,
% 1.11/1.34 (c1_1(a434)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[963, 2987])).
% 1.11/1.34 tff(2990,plain,
% 1.11/1.34 (~c0_1(a434)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[944, 2987])).
% 1.11/1.34 tff(2991,plain,
% 1.11/1.34 (~hskp7),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2551, 2990, 12, 23, 2989, 2988])).
% 1.11/1.34 tff(2992,plain,
% 1.11/1.34 (c2_1(a434)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[954, 138, 2991, 23, 2989, 2988, 106])).
% 1.11/1.34 tff(2993,plain,
% 1.11/1.34 (c2_1(a408)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[1269, 2969])).
% 1.11/1.34 tff(2994,plain,
% 1.11/1.34 ($false),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2122, 138, 12, 2993, 2971, 2990, 2988, 2970, 1505, 2992])).
% 1.11/1.34 tff(2995,plain,(hskp2 | hskp1 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.11/1.34 tff(2996,plain,
% 1.11/1.34 (hskp2),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2995, 12, 44])).
% 1.11/1.34 tff(2997,plain,
% 1.11/1.34 (~c1_1(a402)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[2521, 2996])).
% 1.11/1.34 tff(2998,plain,
% 1.11/1.34 (c0_1(a402)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[469, 2996])).
% 1.11/1.34 tff(2999,assumption,(c1_1(a408)), introduced(assumption)).
% 1.11/1.34 tff(3000,assumption,(~c0_1(a408)), introduced(assumption)).
% 1.11/1.34 tff(3001,assumption,(c3_1(a408)), introduced(assumption)).
% 1.11/1.34 tff(3002,plain,
% 1.11/1.34 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3003,plain,
% 1.11/1.34 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a408) | (~c3_1(a408)) | (~c1_1(a408))) <=> (c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3004,plain,
% 1.11/1.34 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a408) | (~c3_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408))))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[3003])).
% 1.11/1.34 tff(3005,plain,
% 1.11/1.34 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a408) | (~c3_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408)))),
% 1.11/1.34 inference(transitivity,[status(thm)],[3004, 3002])).
% 1.11/1.34 tff(3006,plain,
% 1.11/1.34 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a408) | (~c3_1(a408)) | (~c1_1(a408)))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(3007,plain,
% 1.11/1.34 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 1.11/1.34 tff(3008,plain,
% 1.11/1.34 ((~c3_1(a402)) | (~c1_1(a408))),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3007, 138, 3001, 1352, 3000, 93, 480])).
% 1.11/1.34 tff(3009,plain,
% 1.11/1.34 (~c3_1(a402)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3008, 2999])).
% 1.11/1.34 tff(3010,assumption,(c2_1(a408)), introduced(assumption)).
% 1.11/1.34 tff(3011,plain,
% 1.11/1.34 (c3_1(a402) | (~c1_1(a408))),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[1370, 138, 12, 3010, 1352, 3000, 93, 22])).
% 1.11/1.34 tff(3012,plain,
% 1.11/1.34 ($false),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3011, 3009, 2999])).
% 1.11/1.34 tff(3013,plain,((~c1_1(a408)) | hskp1 | (~c2_1(a408)) | (~c0_1(a402)) | c0_1(a408) | c1_1(a402) | (~c3_1(a408))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.34 tff(3014,plain,
% 1.11/1.34 (~c1_1(a408)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3013, 12, 2993, 2998, 2970, 2997, 2971])).
% 1.11/1.34 tff(3015,plain,
% 1.11/1.34 (~c2_1(a402)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[461, 2996])).
% 1.11/1.34 tff(3016,plain,
% 1.11/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3017,plain,
% 1.11/1.34 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408))) <=> (c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3018,plain,
% 1.11/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408)))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[3017])).
% 1.11/1.34 tff(3019,plain,
% 1.11/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408))),
% 1.11/1.34 inference(transitivity,[status(thm)],[3018, 3016])).
% 1.11/1.34 tff(3020,plain,
% 1.11/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(3021,plain,
% 1.11/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408)),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 1.11/1.34 tff(3022,plain,
% 1.11/1.34 (~c3_1(a402)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3021, 138, 2993, 2998, 2970, 2997, 3015, 2789, 3014])).
% 1.11/1.34 tff(3023,assumption,(~c1_1(a408)), introduced(assumption)).
% 1.11/1.34 tff(3024,plain,
% 1.11/1.34 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3025,plain,
% 1.11/1.34 ((hskp18 | hskp3 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477))) <=> (hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3026,plain,
% 1.11/1.34 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477))))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[3025])).
% 1.11/1.34 tff(3027,plain,
% 1.11/1.34 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(transitivity,[status(thm)],[3026, 3024])).
% 1.11/1.34 tff(3028,plain,
% 1.11/1.34 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(3029,plain,
% 1.11/1.34 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[3028, 3027])).
% 1.11/1.34 tff(3030,plain,
% 1.11/1.34 (hskp18 | hskp3 | c1_1(a477)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3029, 138, 2961, 2947, 1420])).
% 1.11/1.34 tff(3031,plain,
% 1.11/1.34 (hskp18),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3030, 1, 44])).
% 1.11/1.34 tff(3032,plain,
% 1.11/1.34 (~c3_1(a440)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[1434, 3031])).
% 1.11/1.34 tff(3033,plain,
% 1.11/1.34 (~c2_1(a440)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[1440, 3031])).
% 1.11/1.34 tff(3034,plain,
% 1.11/1.34 (c0_1(a440)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[1449, 3031])).
% 1.11/1.34 tff(3035,plain,
% 1.11/1.34 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3036,plain,
% 1.11/1.34 (((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477))) <=> (c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3037,plain,
% 1.11/1.34 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | (c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477))))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[3036])).
% 1.11/1.34 tff(3038,plain,
% 1.11/1.34 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(transitivity,[status(thm)],[3037, 3035])).
% 1.11/1.34 tff(3039,plain,
% 1.11/1.34 ((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(3040,plain,
% 1.11/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 1.11/1.34 tff(3041,plain,
% 1.11/1.34 ($false),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3040, 138, 2961, 3034, 2993, 2971, 2947, 3033, 3032, 1410, 1, 3023])).
% 1.11/1.34 tff(3042,plain,(c1_1(a477) | c1_1(a408) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.11/1.34 tff(3043,plain,
% 1.11/1.34 (c1_1(a477)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3042, 3014, 44])).
% 1.11/1.34 tff(3044,plain,
% 1.11/1.34 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3045,plain,
% 1.11/1.34 ((hskp22 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3046,plain,
% 1.11/1.34 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[3045])).
% 1.11/1.34 tff(3047,plain,
% 1.11/1.34 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.11/1.34 inference(transitivity,[status(thm)],[3046, 3044])).
% 1.11/1.34 tff(3048,plain,
% 1.11/1.34 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(3049,plain,
% 1.11/1.34 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 1.11/1.34 tff(3050,plain,
% 1.11/1.34 (hskp22 | c3_1(a402) | (~c1_1(a477))),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3049, 138, 2961, 2998, 2947, 3015, 851])).
% 1.11/1.34 tff(3051,plain,
% 1.11/1.34 (hskp22),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[3050, 3043, 3022])).
% 1.11/1.34 tff(3052,plain,
% 1.11/1.34 (~c1_1(a451)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[775, 3051])).
% 1.11/1.34 tff(3053,plain,
% 1.11/1.34 (c0_1(a451)),
% 1.11/1.34 inference(unit_resolution,[status(thm)],[791, 3051])).
% 1.11/1.34 tff(3054,plain,
% 1.11/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3055,plain,
% 1.11/1.34 (((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408))) <=> (c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.11/1.34 inference(rewrite,[status(thm)],[])).
% 1.11/1.34 tff(3056,plain,
% 1.11/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451))))),
% 1.11/1.34 inference(monotonicity,[status(thm)],[3055])).
% 1.11/1.34 tff(3057,plain,
% 1.11/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.11/1.34 inference(transitivity,[status(thm)],[3056, 3054])).
% 1.11/1.34 tff(3058,plain,
% 1.11/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))),
% 1.11/1.34 inference(quant_inst,[status(thm)],[])).
% 1.11/1.34 tff(3059,plain,
% 1.11/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.11/1.34 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 1.11/1.34 tff(3060,plain,
% 1.11/1.34 (~c3_1(a451)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3059, 138, 3053, 2993, 2998, 3052, 2970, 2997, 3015, 2789, 3014])).
% 1.18/1.35 tff(3061,plain,
% 1.18/1.35 (hskp16),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2986, 3043, 44])).
% 1.18/1.35 tff(3062,plain,
% 1.18/1.35 (~c0_1(a434)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[944, 3061])).
% 1.18/1.35 tff(3063,plain,
% 1.18/1.35 (c1_1(a434)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[963, 3061])).
% 1.18/1.35 tff(3064,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3065,plain,
% 1.18/1.35 ((hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3066,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[3065])).
% 1.18/1.35 tff(3067,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[3066, 3064])).
% 1.18/1.35 tff(3068,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(3069,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3068, 3067])).
% 1.18/1.35 tff(3070,plain,
% 1.18/1.35 (~c2_1(a434)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3069, 138, 12, 3053, 3063, 3052, 3062, 22, 3060])).
% 1.18/1.35 tff(3071,plain,
% 1.18/1.35 (~c3_1(a434)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[938, 3061])).
% 1.18/1.35 tff(3072,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2171, 138, 3063, 2993, 3062, 3071, 2970, 313, 3070, 3014])).
% 1.18/1.35 tff(3073,plain,(hskp1 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(3074,plain,
% 1.18/1.35 (hskp1),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3073, 44])).
% 1.18/1.35 tff(3075,plain,
% 1.18/1.35 (~c3_1(a401)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[734, 3074])).
% 1.18/1.35 tff(3076,plain,
% 1.18/1.35 (c1_1(a401)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[742, 3074])).
% 1.18/1.35 tff(3077,plain,
% 1.18/1.35 (c0_1(a401)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[750, 3074])).
% 1.18/1.35 tff(3078,plain,
% 1.18/1.35 (hskp20),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[757, 138, 3077, 3076, 3075, 435])).
% 1.18/1.35 tff(3079,plain,
% 1.18/1.35 (~c2_1(a449)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[836, 3078])).
% 1.18/1.35 tff(3080,plain,
% 1.18/1.35 (c3_1(a449)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[830, 3078])).
% 1.18/1.35 tff(3081,plain,
% 1.18/1.35 (c1_1(a449)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[765, 3078])).
% 1.18/1.35 tff(3082,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3083,plain,
% 1.18/1.35 ((hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3084,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[3083])).
% 1.18/1.35 tff(3085,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[3084, 3082])).
% 1.18/1.35 tff(3086,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(3087,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3086, 3085])).
% 1.18/1.35 tff(3088,plain,
% 1.18/1.35 (hskp10),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3087, 138, 2961, 3081, 3080, 2953, 2947, 3079, 2070])).
% 1.18/1.35 tff(3089,plain,
% 1.18/1.35 (~c2_1(a418)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2082, 3088])).
% 1.18/1.35 tff(3090,plain,
% 1.18/1.35 (~c0_1(a418)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2088, 3088])).
% 1.18/1.35 tff(3091,plain,
% 1.18/1.35 (hskp11),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2229, 138, 2993, 2971, 3077, 3076, 2970, 3075, 1036])).
% 1.18/1.35 tff(3092,plain,
% 1.18/1.35 (~c2_1(a420)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1142, 3091])).
% 1.18/1.35 tff(3093,plain,
% 1.18/1.35 (~c1_1(a420)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1025, 3091])).
% 1.18/1.35 tff(3094,plain,
% 1.18/1.35 (c1_1(a418)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2098, 3088])).
% 1.18/1.35 tff(3095,plain,
% 1.18/1.35 (~c3_1(a420)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2239, 138, 3094, 2993, 2971, 3093, 3092, 3090, 3089, 2970, 43])).
% 1.18/1.35 tff(3096,plain,
% 1.18/1.35 (~c0_1(a420)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1019, 3091])).
% 1.18/1.35 tff(3097,plain,
% 1.18/1.35 (hskp0),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2247, 138, 2993, 2971, 3096, 3093, 3092, 2970, 2051])).
% 1.18/1.35 tff(3098,plain,
% 1.18/1.35 (~c3_1(a400)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[366, 3097])).
% 1.18/1.35 tff(3099,plain,
% 1.18/1.35 (c2_1(a400)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[338, 3097])).
% 1.18/1.35 tff(3100,plain,
% 1.18/1.35 (c1_1(a400)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[346, 3097])).
% 1.18/1.35 tff(3101,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2257, 138, 44, 3100, 3099, 3096, 3093, 3098, 1339, 3095])).
% 1.18/1.35 tff(3102,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(3103,plain,
% 1.18/1.35 (~c2_1(a403)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1554, 3102])).
% 1.18/1.35 tff(3104,plain,
% 1.18/1.35 (~c0_1(a403)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1191, 3102])).
% 1.18/1.35 tff(3105,plain,
% 1.18/1.35 (hskp2 | hskp1 | c1_1(a403)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[454, 138, 3104, 3103, 33])).
% 1.18/1.35 tff(3106,plain,
% 1.18/1.35 (c1_1(a403)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3105, 23, 12])).
% 1.18/1.35 tff(3107,plain,
% 1.18/1.35 (~c3_1(a403)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1895, 3102])).
% 1.18/1.35 tff(3108,plain,
% 1.18/1.35 (hskp7 | hskp2 | (~c1_1(a403))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[589, 138, 3103, 3107, 106])).
% 1.18/1.35 tff(3109,plain,
% 1.18/1.35 (hskp7),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3108, 23, 3106])).
% 1.18/1.35 tff(3110,plain,
% 1.18/1.35 (~c3_1(a410)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[230, 3109])).
% 1.18/1.35 tff(3111,plain,
% 1.18/1.35 (~c1_1(a410)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[236, 3109])).
% 1.18/1.35 tff(3112,plain,
% 1.18/1.35 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3113,plain,
% 1.18/1.35 ((hskp13 | hskp2 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477))) <=> (hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3114,plain,
% 1.18/1.35 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[3113])).
% 1.18/1.35 tff(3115,plain,
% 1.18/1.35 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[3114, 3112])).
% 1.18/1.35 tff(3116,plain,
% 1.18/1.35 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(3117,plain,
% 1.18/1.35 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 1.18/1.35 tff(3118,plain,
% 1.18/1.35 (hskp13 | hskp2 | (~c1_1(a477))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3117, 138, 2961, 2947, 247])).
% 1.18/1.35 tff(3119,plain,
% 1.18/1.35 (hskp13),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3118, 23, 2979])).
% 1.18/1.35 tff(3120,plain,
% 1.18/1.35 (~c0_1(a427)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[260, 3119])).
% 1.18/1.35 tff(3121,plain,
% 1.18/1.35 (c0_1(a410)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[268, 3109])).
% 1.18/1.35 tff(3122,plain,
% 1.18/1.35 (c2_1(a427)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[276, 3119])).
% 1.18/1.35 tff(3123,plain,
% 1.18/1.35 (c1_1(a427)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[284, 3119])).
% 1.18/1.35 tff(3124,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[291, 138, 12, 3123, 3122, 3121, 3120, 3111, 3110, 22])).
% 1.18/1.35 tff(3125,plain,(hskp2 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(3126,plain,
% 1.18/1.35 (hskp2),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3125, 12])).
% 1.18/1.35 tff(3127,plain,
% 1.18/1.35 (~c1_1(a402)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2521, 3126])).
% 1.18/1.35 tff(3128,plain,
% 1.18/1.35 (c0_1(a402)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[469, 3126])).
% 1.18/1.35 tff(3129,assumption,(hskp19), introduced(assumption)).
% 1.18/1.35 tff(3130,plain,
% 1.18/1.35 (c1_1(a445)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[413, 3129])).
% 1.18/1.35 tff(3131,plain,
% 1.18/1.35 (~c0_1(a445)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[299, 3129])).
% 1.18/1.35 tff(3132,plain,
% 1.18/1.35 (c3_1(a445)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[422, 3129])).
% 1.18/1.35 tff(3133,plain,
% 1.18/1.35 (hskp11),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[728, 3132, 12, 3127, 3103, 3104, 3107, 3131, 3130])).
% 1.18/1.35 tff(3134,plain,
% 1.18/1.35 (~c2_1(a420)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1142, 3133])).
% 1.18/1.35 tff(3135,plain,
% 1.18/1.35 (~c0_1(a420)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1019, 3133])).
% 1.18/1.35 tff(3136,plain,
% 1.18/1.35 (~c1_1(a420)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1025, 3133])).
% 1.18/1.35 tff(3137,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1088, 3136, 3135, 3104, 3127, 3130, 3131, 3132, 12, 3134, 3103, 3107])).
% 1.18/1.35 tff(3138,plain,((~hskp19) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(3139,plain,
% 1.18/1.35 (~hskp19),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3138, 12])).
% 1.18/1.35 tff(3140,plain,
% 1.18/1.35 (~c2_1(a402)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[461, 3126])).
% 1.18/1.35 tff(3141,assumption,(~hskp16), introduced(assumption)).
% 1.18/1.35 tff(3142,plain,
% 1.18/1.35 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3143,plain,
% 1.18/1.35 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a402) | (~c3_1(a402)) | (~c0_1(a402))) <=> (hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3144,plain,
% 1.18/1.35 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[3143])).
% 1.18/1.35 tff(3145,plain,
% 1.18/1.35 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[3144, 3142])).
% 1.18/1.35 tff(3146,plain,
% 1.18/1.35 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(3147,plain,
% 1.18/1.35 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 1.18/1.35 tff(3148,plain,
% 1.18/1.35 (hskp16 | hskp7 | (~c3_1(a402))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3147, 138, 3128, 3140, 925])).
% 1.18/1.35 tff(3149,plain,
% 1.18/1.35 (~c3_1(a402)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3148, 3141, 947])).
% 1.18/1.35 tff(3150,plain,
% 1.18/1.35 (hskp12 | c3_1(a402)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[504, 138, 12, 3128, 3127, 498])).
% 1.18/1.35 tff(3151,plain,
% 1.18/1.35 (hskp12),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3150, 3149])).
% 1.18/1.35 tff(3152,plain,
% 1.18/1.35 (~c2_1(a426)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[511, 3151])).
% 1.18/1.35 tff(3153,plain,
% 1.18/1.35 (c0_1(a426)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[555, 3151])).
% 1.18/1.35 tff(3154,plain,
% 1.18/1.35 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3155,plain,
% 1.18/1.35 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a426) | (~c3_1(a426)) | (~c0_1(a426))) <=> (hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3156,plain,
% 1.18/1.35 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a426) | (~c3_1(a426)) | (~c0_1(a426)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[3155])).
% 1.18/1.35 tff(3157,plain,
% 1.18/1.35 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a426) | (~c3_1(a426)) | (~c0_1(a426)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[3156, 3154])).
% 1.18/1.35 tff(3158,plain,
% 1.18/1.35 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a426) | (~c3_1(a426)) | (~c0_1(a426)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(3159,plain,
% 1.18/1.35 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 1.18/1.35 tff(3160,plain,
% 1.18/1.35 (~c3_1(a426)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3159, 138, 3141, 947, 3153, 3152, 925])).
% 1.18/1.35 tff(3161,plain,
% 1.18/1.35 (hskp22 | c3_1(a402) | (~c1_1(a477))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3049, 138, 2961, 3128, 2947, 3140, 851])).
% 1.18/1.35 tff(3162,plain,
% 1.18/1.35 (~c1_1(a477)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3161, 3149, 856])).
% 1.18/1.35 tff(3163,plain,
% 1.18/1.35 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.18/1.35 inference(bind,[status(th)],[])).
% 1.18/1.35 tff(3164,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.18/1.35 inference(quant_intro,[status(thm)],[3163])).
% 1.18/1.35 tff(3165,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3166,plain,
% 1.18/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_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) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.18/1.35 inference(bind,[status(th)],[])).
% 1.18/1.35 tff(3167,plain,
% 1.18/1.35 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.18/1.35 inference(quant_intro,[status(thm)],[3166])).
% 1.18/1.35 tff(3168,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.18/1.35 tff(3169,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3168, 3167])).
% 1.18/1.35 tff(3170,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3169, 3165])).
% 1.18/1.35 tff(3171,plain,(
% 1.18/1.35 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.18/1.35 inference(skolemize,[status(sab)],[3170])).
% 1.18/1.35 tff(3172,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3171, 3164])).
% 1.18/1.35 tff(3173,plain,
% 1.18/1.35 (c1_1(a426)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[547, 3151])).
% 1.18/1.35 tff(3174,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3175,plain,
% 1.18/1.35 ((hskp7 | (~ndr1_0) | c2_1(a426) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3176,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a426) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[3175])).
% 1.18/1.35 tff(3177,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a426) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[3176, 3174])).
% 1.18/1.35 tff(3178,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a426) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(3179,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3178, 3177])).
% 1.18/1.35 tff(3180,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3179, 138, 947, 2961, 3173, 2953, 3152, 3172, 3162, 3160])).
% 1.18/1.35 tff(3181,plain,(hskp16 | hskp7 | hskp22 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(3182,plain,
% 1.18/1.35 (hskp16),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3181, 947, 856, 12])).
% 1.18/1.35 tff(3183,plain,
% 1.18/1.35 (~c0_1(a434)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[944, 3182])).
% 1.18/1.35 tff(3184,assumption,(c1_1(a477)), introduced(assumption)).
% 1.18/1.35 tff(3185,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3186,plain,
% 1.18/1.35 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477))) <=> (c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(3187,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[3186])).
% 1.18/1.35 tff(3188,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[3187, 3185])).
% 1.18/1.35 tff(3189,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(3190,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 1.18/1.35 tff(3191,plain,
% 1.18/1.35 ((~c3_1(a402)) | (~c1_1(a477))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3190, 138, 2961, 1352, 2953, 93, 480])).
% 1.18/1.35 tff(3192,plain,
% 1.18/1.35 (~c3_1(a402)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3191, 3184])).
% 1.18/1.35 tff(3193,plain,
% 1.18/1.35 (hskp22 | c3_1(a402) | (~c1_1(a477))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3049, 138, 2961, 1352, 2947, 1955, 851])).
% 1.18/1.35 tff(3194,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3193, 3192, 3184, 856])).
% 1.18/1.35 tff(3195,plain,((~c1_1(a477)) | hskp22 | (~c0_1(a402)) | c2_1(a402) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(3196,plain,
% 1.18/1.35 (~c1_1(a477)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[3195, 856, 3128, 3140, 3127])).
% 1.18/1.35 tff(3197,plain,
% 1.18/1.35 (c1_1(a434)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[963, 3182])).
% 1.18/1.36 tff(3198,plain,
% 1.18/1.36 (~c3_1(a434)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[938, 3182])).
% 1.18/1.36 tff(3199,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3200,plain,
% 1.18/1.36 (((~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3201,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[3200])).
% 1.18/1.36 tff(3202,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[3201, 3199])).
% 1.18/1.36 tff(3203,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(3204,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3203, 3202])).
% 1.18/1.36 tff(3205,plain,
% 1.18/1.36 (~c2_1(a434)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3204, 138, 2961, 2953, 2947, 966, 948, 718, 1])).
% 1.18/1.36 tff(3206,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3207,plain,
% 1.18/1.36 ((hskp7 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3208,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[3207])).
% 1.18/1.36 tff(3209,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[3208, 3206])).
% 1.18/1.36 tff(3210,plain,
% 1.18/1.36 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(3211,plain,
% 1.18/1.36 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 1.18/1.36 tff(3212,plain,
% 1.18/1.36 ($false),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3211, 138, 947, 2961, 2532, 2953, 948, 3172, 3205, 1])).
% 1.18/1.36 tff(3213,plain,(c1_1(a477) | hskp7 | (~c1_1(a434)) | c3_1(a434) | c0_1(a434)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.36 tff(3214,plain,
% 1.18/1.36 ($false),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3213, 3198, 3197, 3196, 947, 3183])).
% 1.18/1.36 tff(3215,plain,(hskp7 | hskp22 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.18/1.36 tff(3216,plain,
% 1.18/1.36 (hskp7),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3215, 856, 12])).
% 1.18/1.36 tff(3217,plain,
% 1.18/1.36 (~c3_1(a410)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[230, 3216])).
% 1.18/1.36 tff(3218,plain,
% 1.18/1.36 (~c1_1(a410)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[236, 3216])).
% 1.18/1.36 tff(3219,plain,
% 1.18/1.36 (c0_1(a410)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[268, 3216])).
% 1.18/1.36 tff(3220,plain,
% 1.18/1.36 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3221,plain,
% 1.18/1.36 ((hskp12 | hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410))) <=> (hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3222,plain,
% 1.18/1.36 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[3221])).
% 1.18/1.36 tff(3223,plain,
% 1.18/1.36 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[3222, 3220])).
% 1.18/1.36 tff(3224,plain,
% 1.18/1.36 ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(3225,plain,
% 1.18/1.36 ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3224, 3223])).
% 1.18/1.36 tff(3226,plain,
% 1.18/1.36 (hskp12),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3225, 138, 12, 3219, 3218, 3217, 498])).
% 1.18/1.36 tff(3227,plain,
% 1.18/1.36 (~c2_1(a426)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[511, 3226])).
% 1.18/1.36 tff(3228,plain,
% 1.18/1.36 (c1_1(a426)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[547, 3226])).
% 1.18/1.36 tff(3229,plain,
% 1.18/1.36 (c0_1(a426)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[555, 3226])).
% 1.18/1.36 tff(3230,plain,
% 1.18/1.36 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.18/1.36 inference(bind,[status(th)],[])).
% 1.18/1.36 tff(3231,plain,
% 1.18/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.18/1.36 inference(quant_intro,[status(thm)],[3230])).
% 1.18/1.36 tff(3232,plain,
% 1.18/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3233,plain,
% 1.18/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.18/1.36 inference(bind,[status(th)],[])).
% 1.18/1.36 tff(3234,plain,
% 1.18/1.36 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.18/1.36 inference(quant_intro,[status(thm)],[3233])).
% 1.18/1.36 tff(3235,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.18/1.36 tff(3236,plain,
% 1.18/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 1.18/1.36 tff(3237,plain,
% 1.18/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3236, 3232])).
% 1.18/1.36 tff(3238,plain,(
% 1.18/1.36 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.18/1.36 inference(skolemize,[status(sab)],[3237])).
% 1.18/1.36 tff(3239,plain,
% 1.18/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3238, 3231])).
% 1.18/1.36 tff(3240,assumption,(~c3_1(a426)), introduced(assumption)).
% 1.18/1.36 tff(3241,assumption,(c1_1(a426)), introduced(assumption)).
% 1.18/1.36 tff(3242,assumption,(c0_1(a426)), introduced(assumption)).
% 1.18/1.36 tff(3243,plain,
% 1.18/1.36 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3244,plain,
% 1.18/1.36 ((hskp20 | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | (~c0_1(a426))) <=> (hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3245,plain,
% 1.18/1.36 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | (~c0_1(a426)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[3244])).
% 1.18/1.36 tff(3246,plain,
% 1.18/1.36 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | (~c0_1(a426)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[3245, 3243])).
% 1.18/1.36 tff(3247,plain,
% 1.18/1.36 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | (~c0_1(a426)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(3248,plain,
% 1.18/1.36 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3247, 3246])).
% 1.18/1.36 tff(3249,plain,
% 1.18/1.36 (hskp20 | c3_1(a426)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3248, 138, 3242, 3241, 435])).
% 1.18/1.36 tff(3250,plain,
% 1.18/1.36 (hskp20),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3249, 3240])).
% 1.18/1.36 tff(3251,plain,
% 1.18/1.36 (~c2_1(a449)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[836, 3250])).
% 1.18/1.36 tff(3252,plain,
% 1.18/1.36 (c3_1(a449)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[830, 3250])).
% 1.18/1.36 tff(3253,plain,
% 1.18/1.36 (c1_1(a449)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[765, 3250])).
% 1.18/1.36 tff(3254,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3255,plain,
% 1.18/1.36 ((hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a426) | c3_1(a426) | (~c0_1(a426))) <=> (hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3256,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a426) | c3_1(a426) | (~c0_1(a426)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[3255])).
% 1.18/1.36 tff(3257,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a426) | c3_1(a426) | (~c0_1(a426)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[3256, 3254])).
% 1.18/1.36 tff(3258,plain,
% 1.18/1.36 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a426) | c3_1(a426) | (~c0_1(a426)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(3259,plain,
% 1.18/1.36 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 1.18/1.36 tff(3260,plain,
% 1.18/1.36 ($false),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3259, 138, 856, 3253, 3252, 3242, 3251, 1049, 851, 3240])).
% 1.18/1.36 tff(3261,plain,(c3_1(a426) | hskp22 | (~c0_1(a426)) | c2_1(a426) | (~c1_1(a426))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.36 tff(3262,plain,
% 1.18/1.36 (c3_1(a426)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3261, 3228, 3229, 3227, 856])).
% 1.18/1.36 tff(3263,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3264,plain,
% 1.18/1.36 ((hskp10 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(3265,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[3264])).
% 1.18/1.36 tff(3266,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[3265, 3263])).
% 1.18/1.36 tff(3267,plain,
% 1.18/1.36 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(3268,plain,
% 1.18/1.36 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[3267, 3266])).
% 1.18/1.36 tff(3269,plain,
% 1.18/1.36 (hskp10),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[3268, 138, 2961, 3228, 2953, 2947, 3227, 2070, 3262])).
% 1.18/1.36 tff(3270,plain,
% 1.18/1.36 (~c2_1(a418)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2082, 3269])).
% 1.18/1.36 tff(3271,plain,
% 1.18/1.36 (~c0_1(a418)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2088, 3269])).
% 1.18/1.36 tff(3272,plain,
% 1.18/1.36 (c1_1(a418)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2098, 3269])).
% 1.18/1.36 tff(3273,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(3274,plain,
% 1.20/1.36 ((hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a418) | c0_1(a418) | (~c1_1(a418))) <=> (hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(3275,plain,
% 1.20/1.36 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a418) | c0_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[3274])).
% 1.20/1.36 tff(3276,plain,
% 1.20/1.36 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a418) | c0_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.36 inference(transitivity,[status(thm)],[3275, 3273])).
% 1.20/1.36 tff(3277,plain,
% 1.20/1.36 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a418) | c0_1(a418) | (~c1_1(a418)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(3278,plain,
% 1.20/1.36 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[3277, 3276])).
% 1.20/1.36 tff(3279,plain,
% 1.20/1.36 (hskp28),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[3278, 138, 2961, 3272, 2947, 3271, 3270, 3239, 1])).
% 1.20/1.36 tff(3280,plain,
% 1.20/1.36 (c2_1(a414)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[2843, 3279])).
% 1.20/1.36 tff(3281,plain,
% 1.20/1.36 (c0_1(a414)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[2851, 3279])).
% 1.20/1.36 tff(3282,plain,
% 1.20/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(3283,plain,
% 1.20/1.36 (((~ndr1_0) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402))) <=> (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(3284,plain,
% 1.20/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[3283])).
% 1.20/1.36 tff(3285,plain,
% 1.20/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)))),
% 1.20/1.36 inference(transitivity,[status(thm)],[3284, 3282])).
% 1.20/1.36 tff(3286,plain,
% 1.20/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(3287,plain,
% 1.20/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[3286, 3285])).
% 1.20/1.36 tff(3288,plain,
% 1.20/1.36 (~c1_1(a414)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[3287, 138, 3281, 3280, 3229, 3228, 3128, 3227, 3127, 3140, 447])).
% 1.20/1.36 tff(3289,plain,
% 1.20/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(3290,plain,
% 1.20/1.36 ((hskp22 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(3291,plain,
% 1.20/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[3290])).
% 1.20/1.36 tff(3292,plain,
% 1.20/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3291, 3289])).
% 1.20/1.37 tff(3293,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(3294,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3293, 3292])).
% 1.20/1.37 tff(3295,plain,
% 1.20/1.37 (c3_1(a402)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3294, 138, 856, 3228, 3128, 3227, 3140, 851, 3262])).
% 1.20/1.37 tff(3296,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3297,plain,
% 1.20/1.37 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a418) | (~c3_1(a418)) | (~c1_1(a418))) <=> (c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3298,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a418) | (~c3_1(a418)) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[3297])).
% 1.20/1.37 tff(3299,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a418) | (~c3_1(a418)) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3298, 3296])).
% 1.20/1.37 tff(3300,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a418) | (~c3_1(a418)) | (~c1_1(a418)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(3301,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 1.20/1.37 tff(3302,plain,
% 1.20/1.37 (~c3_1(a418)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3301, 138, 3272, 3128, 3271, 3127, 480, 3295])).
% 1.20/1.37 tff(3303,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3304,plain,
% 1.20/1.37 ((hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a418) | c3_1(a418) | (~c1_1(a418))) <=> (hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3305,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a418) | c3_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[3304])).
% 1.20/1.37 tff(3306,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a418) | c3_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3305, 3303])).
% 1.20/1.37 tff(3307,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a418) | c3_1(a418) | (~c1_1(a418)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(3308,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3307, 3306])).
% 1.20/1.37 tff(3309,plain,
% 1.20/1.37 (hskp9),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3308, 138, 3272, 3219, 3271, 3218, 3217, 583, 3302])).
% 1.20/1.37 tff(3310,plain,
% 1.20/1.37 (~c1_1(a416)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[606, 3309])).
% 1.20/1.37 tff(3311,plain,
% 1.20/1.37 (~c0_1(a416)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[612, 3309])).
% 1.20/1.37 tff(3312,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3313,plain,
% 1.20/1.37 (((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a418) | c0_1(a418) | c2_1(a418)) <=> (c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3314,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a418) | c0_1(a418) | c2_1(a418))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[3313])).
% 1.20/1.37 tff(3315,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a418) | c0_1(a418) | c2_1(a418))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3314, 3312])).
% 1.20/1.37 tff(3316,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a418) | c0_1(a418) | c2_1(a418))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(3317,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3316, 3315])).
% 1.20/1.37 tff(3318,plain,
% 1.20/1.37 (~c2_1(a416)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3317, 138, 3272, 3271, 3270, 3311, 3310, 313, 3302])).
% 1.20/1.37 tff(3319,plain,
% 1.20/1.37 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.20/1.37 inference(bind,[status(th)],[])).
% 1.20/1.37 tff(3320,plain,
% 1.20/1.37 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.37 inference(quant_intro,[status(thm)],[3319])).
% 1.20/1.37 tff(3321,plain,
% 1.20/1.37 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3322,plain,
% 1.20/1.37 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.20/1.37 inference(bind,[status(th)],[])).
% 1.20/1.37 tff(3323,plain,
% 1.20/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.37 inference(quant_intro,[status(thm)],[3322])).
% 1.20/1.37 tff(3324,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.20/1.37 tff(3325,plain,
% 1.20/1.37 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3324, 3323])).
% 1.20/1.37 tff(3326,plain,
% 1.20/1.37 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3325, 3321])).
% 1.20/1.37 tff(3327,plain,(
% 1.20/1.37 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.37 inference(skolemize,[status(sab)],[3326])).
% 1.20/1.37 tff(3328,plain,
% 1.20/1.37 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3327, 3320])).
% 1.20/1.37 tff(3329,plain,
% 1.20/1.37 (c3_1(a414)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[2835, 3279])).
% 1.20/1.37 tff(3330,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3331,plain,
% 1.20/1.37 ((hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410))) <=> (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3332,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[3331])).
% 1.20/1.37 tff(3333,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3332, 3330])).
% 1.20/1.37 tff(3334,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(3335,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 1.20/1.37 tff(3336,plain,
% 1.20/1.37 (~c2_1(a410)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3335, 138, 3139, 3281, 3280, 3329, 3218, 3217, 3328])).
% 1.20/1.37 tff(3337,plain,
% 1.20/1.37 (c3_1(a416)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[667, 3309])).
% 1.20/1.37 tff(3338,plain,
% 1.20/1.37 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3339,plain,
% 1.20/1.37 (((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416))) <=> (c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3340,plain,
% 1.20/1.37 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | (c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[3339])).
% 1.20/1.37 tff(3341,plain,
% 1.20/1.37 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3340, 3338])).
% 1.20/1.37 tff(3342,plain,
% 1.20/1.37 ((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(3343,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3342, 3341])).
% 1.20/1.37 tff(3344,plain,
% 1.20/1.37 ($false),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3343, 138, 3280, 3329, 3337, 3219, 3310, 3217, 1410, 3336, 3318, 3288])).
% 1.20/1.37 tff(3345,plain,(hskp22 | c1_1(a477) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.20/1.37 tff(3346,plain,
% 1.20/1.37 (hskp22),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3345, 1, 12])).
% 1.20/1.37 tff(3347,plain,
% 1.20/1.37 (~c1_1(a451)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[775, 3346])).
% 1.20/1.37 tff(3348,plain,
% 1.20/1.37 (c2_1(a451)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[783, 3346])).
% 1.20/1.37 tff(3349,assumption,(~c3_1(a451)), introduced(assumption)).
% 1.20/1.37 tff(3350,assumption,(c2_1(a451)), introduced(assumption)).
% 1.20/1.37 tff(3351,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3352,plain,
% 1.20/1.37 (((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)) | c3_1(a403) | c1_1(a403) | c0_1(a403)) <=> (c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3353,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[3352])).
% 1.20/1.37 tff(3354,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3353, 3351])).
% 1.20/1.37 tff(3355,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)) | c3_1(a403) | c1_1(a403) | c0_1(a403))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(3356,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 1.20/1.37 tff(3357,plain,
% 1.20/1.37 (c1_1(a403) | c3_1(a451)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3356, 138, 2961, 3350, 2953, 793, 3104, 3107, 1725, 1])).
% 1.20/1.37 tff(3358,plain,
% 1.20/1.37 (c1_1(a403)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3357, 3349])).
% 1.20/1.37 tff(3359,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3360,plain,
% 1.20/1.37 ((hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a403) | c0_1(a403) | (~c1_1(a403))) <=> (hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3361,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a403) | c0_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[3360])).
% 1.20/1.37 tff(3362,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a403) | c0_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3361, 3359])).
% 1.20/1.37 tff(3363,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a403) | c0_1(a403) | (~c1_1(a403)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(3364,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[3363, 3362])).
% 1.20/1.37 tff(3365,plain,
% 1.20/1.37 (hskp28 | (~c1_1(a403)) | c1_1(a477)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3364, 138, 2961, 2947, 3104, 3103, 3239])).
% 1.20/1.37 tff(3366,plain,
% 1.20/1.37 (hskp28),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[3365, 3358, 1])).
% 1.20/1.37 tff(3367,plain,
% 1.20/1.37 (c3_1(a414)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[2835, 3366])).
% 1.20/1.37 tff(3368,plain,
% 1.20/1.37 (c2_1(a414)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[2843, 3366])).
% 1.20/1.37 tff(3369,plain,
% 1.20/1.37 (c0_1(a414)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[2851, 3366])).
% 1.20/1.37 tff(3370,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3371,plain,
% 1.20/1.37 ((hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451))) <=> (hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(3372,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451)))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[3371])).
% 1.20/1.37 tff(3373,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.37 inference(transitivity,[status(thm)],[3372, 3370])).
% 1.20/1.37 tff(3374,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(3375,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3374, 3373])).
% 1.20/1.38 tff(3376,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3375, 138, 107, 3369, 3368, 3367, 3350, 793, 3328, 3349])).
% 1.20/1.38 tff(3377,plain,(c3_1(a451) | hskp19 | (~c2_1(a451)) | c1_1(a451) | c1_1(a477)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(3378,plain,
% 1.20/1.38 (c3_1(a451)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3377, 3348, 1, 3347, 3139])).
% 1.20/1.38 tff(3379,plain,
% 1.20/1.38 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.20/1.38 inference(bind,[status(th)],[])).
% 1.20/1.38 tff(3380,plain,
% 1.20/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.20/1.38 inference(quant_intro,[status(thm)],[3379])).
% 1.20/1.38 tff(3381,plain,
% 1.20/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3382,plain,
% 1.20/1.38 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.20/1.38 inference(bind,[status(th)],[])).
% 1.20/1.38 tff(3383,plain,
% 1.20/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.20/1.38 inference(quant_intro,[status(thm)],[3382])).
% 1.20/1.38 tff(3384,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.20/1.38 tff(3385,plain,
% 1.20/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 1.20/1.38 tff(3386,plain,
% 1.20/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3385, 3381])).
% 1.20/1.38 tff(3387,plain,(
% 1.20/1.38 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.20/1.38 inference(skolemize,[status(sab)],[3386])).
% 1.20/1.38 tff(3388,plain,
% 1.20/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3387, 3380])).
% 1.20/1.38 tff(3389,plain,
% 1.20/1.38 (c0_1(a451)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[791, 3346])).
% 1.20/1.38 tff(3390,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3391,plain,
% 1.20/1.38 ((hskp4 | (~ndr1_0) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c2_1(a477) | c1_1(a477) | (~c3_1(a477))) <=> (hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3392,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[3391])).
% 1.20/1.38 tff(3393,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[3392, 3390])).
% 1.20/1.38 tff(3394,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(3395,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3394, 3393])).
% 1.20/1.38 tff(3396,plain,
% 1.20/1.38 (hskp4),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3395, 138, 2961, 3389, 3348, 2947, 3347, 3388, 1])).
% 1.20/1.38 tff(3397,plain,
% 1.20/1.38 (((~hskp4) | (~c2_1(a404))) <=> ((~hskp4) | (~c2_1(a404)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3398,plain,
% 1.20/1.38 (((~c2_1(a404)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a404)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3399,axiom,((~c2_1(a404)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.20/1.38 tff(3400,plain,
% 1.20/1.38 ((~hskp4) | (~c2_1(a404))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3399, 3398])).
% 1.20/1.38 tff(3401,plain,
% 1.20/1.38 ((~hskp4) | (~c2_1(a404))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3400, 3397])).
% 1.20/1.38 tff(3402,plain,
% 1.20/1.38 (~c2_1(a404)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3401, 3396])).
% 1.20/1.38 tff(3403,plain,
% 1.20/1.38 (((~hskp4) | c3_1(a404)) <=> ((~hskp4) | c3_1(a404))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3404,axiom,((~hskp4) | c3_1(a404)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.20/1.38 tff(3405,plain,
% 1.20/1.38 ((~hskp4) | c3_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 1.20/1.38 tff(3406,plain,
% 1.20/1.38 ((~hskp4) | c3_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3405, 3403])).
% 1.20/1.38 tff(3407,plain,
% 1.20/1.38 ((~hskp4) | c3_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3406, 3403])).
% 1.20/1.38 tff(3408,plain,
% 1.20/1.38 ((~hskp4) | c3_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3407, 3403])).
% 1.20/1.38 tff(3409,plain,
% 1.20/1.38 ((~hskp4) | c3_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3408, 3403])).
% 1.20/1.38 tff(3410,plain,
% 1.20/1.38 (c3_1(a404)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3409, 3396])).
% 1.20/1.38 tff(3411,plain,
% 1.20/1.38 (((~hskp4) | c0_1(a404)) <=> ((~hskp4) | c0_1(a404))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3412,axiom,((~hskp4) | c0_1(a404)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.20/1.38 tff(3413,plain,
% 1.20/1.38 ((~hskp4) | c0_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 1.20/1.38 tff(3414,plain,
% 1.20/1.38 ((~hskp4) | c0_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3413, 3411])).
% 1.20/1.38 tff(3415,plain,
% 1.20/1.38 ((~hskp4) | c0_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3414, 3411])).
% 1.20/1.38 tff(3416,plain,
% 1.20/1.38 ((~hskp4) | c0_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3415, 3411])).
% 1.20/1.38 tff(3417,plain,
% 1.20/1.38 ((~hskp4) | c0_1(a404)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3416, 3411])).
% 1.20/1.38 tff(3418,plain,
% 1.20/1.38 (c0_1(a404)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3417, 3396])).
% 1.20/1.38 tff(3419,assumption,(~c2_1(a404)), introduced(assumption)).
% 1.20/1.38 tff(3420,assumption,(c3_1(a404)), introduced(assumption)).
% 1.20/1.38 tff(3421,assumption,(c0_1(a404)), introduced(assumption)).
% 1.20/1.38 tff(3422,plain,
% 1.20/1.38 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3423,plain,
% 1.20/1.38 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a404) | (~c3_1(a404)) | (~c0_1(a404))) <=> (hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3424,plain,
% 1.20/1.38 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a404) | (~c3_1(a404)) | (~c0_1(a404)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[3423])).
% 1.20/1.38 tff(3425,plain,
% 1.20/1.38 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a404) | (~c3_1(a404)) | (~c0_1(a404)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[3424, 3422])).
% 1.20/1.38 tff(3426,plain,
% 1.20/1.38 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a404) | (~c3_1(a404)) | (~c0_1(a404)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(3427,plain,
% 1.20/1.38 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3426, 3425])).
% 1.20/1.38 tff(3428,plain,
% 1.20/1.38 (hskp16 | hskp7),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3427, 138, 3421, 3420, 3419, 925])).
% 1.20/1.38 tff(3429,plain,
% 1.20/1.38 (hskp16),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3428, 947])).
% 1.20/1.38 tff(3430,plain,
% 1.20/1.38 (~c0_1(a434)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[944, 3429])).
% 1.20/1.38 tff(3431,plain,
% 1.20/1.38 (c1_1(a434)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[963, 3429])).
% 1.20/1.38 tff(3432,plain,
% 1.20/1.38 (~c3_1(a434)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[938, 3429])).
% 1.20/1.38 tff(3433,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3213, 3432, 3431, 1, 947, 3430])).
% 1.20/1.38 tff(3434,plain,(hskp7 | c1_1(a477) | (~c0_1(a404)) | (~c3_1(a404)) | c2_1(a404)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(3435,plain,
% 1.20/1.38 (hskp7),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3434, 3418, 1, 3410, 3402])).
% 1.20/1.38 tff(3436,plain,
% 1.20/1.38 (~c3_1(a410)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[230, 3435])).
% 1.20/1.38 tff(3437,plain,
% 1.20/1.38 (~c1_1(a410)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[236, 3435])).
% 1.20/1.38 tff(3438,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3439,plain,
% 1.20/1.38 ((hskp19 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410))) <=> (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3440,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[3439])).
% 1.20/1.38 tff(3441,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[3440, 3438])).
% 1.20/1.38 tff(3442,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(3443,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3442, 3441])).
% 1.20/1.38 tff(3444,plain,
% 1.20/1.38 (~c2_1(a410)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3443, 138, 3139, 3389, 3348, 3437, 3436, 3328, 3378])).
% 1.20/1.38 tff(3445,plain,
% 1.20/1.38 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3446,plain,
% 1.20/1.38 (((~ndr1_0) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477))) <=> (c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3447,plain,
% 1.20/1.38 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | (c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[3446])).
% 1.20/1.38 tff(3448,plain,
% 1.20/1.38 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[3447, 3445])).
% 1.20/1.38 tff(3449,plain,
% 1.20/1.38 ((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(3450,plain,
% 1.20/1.38 ((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3449, 3448])).
% 1.20/1.38 tff(3451,plain,
% 1.20/1.38 (c3_1(a402)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3450, 138, 2961, 3348, 3128, 2947, 3347, 3140, 1410, 1, 3378])).
% 1.20/1.38 tff(3452,plain,
% 1.20/1.38 (c0_1(a410)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[268, 3435])).
% 1.20/1.38 tff(3453,plain,
% 1.20/1.38 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3454,plain,
% 1.20/1.38 (((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402))) <=> (c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3455,plain,
% 1.20/1.38 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | (c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[3454])).
% 1.20/1.38 tff(3456,plain,
% 1.20/1.38 (((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~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) | (~c3_1(W)))) | c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[3455, 3453])).
% 1.20/1.38 tff(3457,plain,
% 1.20/1.38 ((~![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)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(3458,plain,
% 1.20/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3457, 3456])).
% 1.20/1.38 tff(3459,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3458, 138, 3348, 3452, 3347, 3436, 3127, 3140, 1410, 3451, 3378, 3444])).
% 1.20/1.38 tff(3460,plain,(c1_1(a477) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(3461,plain,
% 1.20/1.38 (c1_1(a477)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3460, 12])).
% 1.20/1.38 tff(3462,plain,
% 1.20/1.38 (hskp22),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3195, 3461, 3128, 3140, 3127])).
% 1.20/1.38 tff(3463,plain,
% 1.20/1.38 (~c1_1(a451)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[775, 3462])).
% 1.20/1.38 tff(3464,plain,
% 1.20/1.38 (c0_1(a451)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[791, 3462])).
% 1.20/1.38 tff(3465,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3466,plain,
% 1.20/1.38 (((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477))) <=> (c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3467,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[3466])).
% 1.20/1.38 tff(3468,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[3467, 3465])).
% 1.20/1.38 tff(3469,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(3470,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 1.20/1.38 tff(3471,plain,
% 1.20/1.38 (~c3_1(a451)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3470, 138, 2961, 3464, 2953, 3463, 480, 3461])).
% 1.20/1.38 tff(3472,plain,
% 1.20/1.38 (c2_1(a451)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[783, 3462])).
% 1.20/1.38 tff(3473,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3375, 138, 107, 2852, 2844, 2836, 3350, 793, 3328, 3349])).
% 1.20/1.38 tff(3474,plain,((~hskp28) | hskp19 | (~c2_1(a451)) | c1_1(a451) | c3_1(a451)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(3475,plain,
% 1.20/1.38 (~hskp28),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3474, 3139, 3472, 3463, 3471])).
% 1.20/1.38 tff(3476,assumption,(~hskp9), introduced(assumption)).
% 1.20/1.38 tff(3477,plain,
% 1.20/1.38 (hskp9 | c3_1(a402) | (~c1_1(a403))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[687, 138, 1352, 3104, 3107, 93, 583])).
% 1.20/1.38 tff(3478,plain,
% 1.20/1.38 (~c1_1(a403)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3477, 3476, 3192])).
% 1.20/1.38 tff(3479,plain,
% 1.20/1.38 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.20/1.38 inference(bind,[status(th)],[])).
% 1.20/1.38 tff(3480,plain,
% 1.20/1.38 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.20/1.38 inference(quant_intro,[status(thm)],[3479])).
% 1.20/1.38 tff(3481,plain,
% 1.20/1.38 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3482,plain,
% 1.20/1.38 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.20/1.38 inference(bind,[status(th)],[])).
% 1.20/1.38 tff(3483,plain,
% 1.20/1.38 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.20/1.38 inference(quant_intro,[status(thm)],[3482])).
% 1.20/1.38 tff(3484,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.20/1.38 tff(3485,plain,
% 1.20/1.38 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3484, 3483])).
% 1.20/1.38 tff(3486,plain,
% 1.20/1.38 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3485, 3481])).
% 1.20/1.38 tff(3487,plain,(
% 1.20/1.38 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.20/1.38 inference(skolemize,[status(sab)],[3486])).
% 1.20/1.38 tff(3488,plain,
% 1.20/1.38 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3487, 3480])).
% 1.20/1.38 tff(3489,plain,
% 1.20/1.38 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3490,plain,
% 1.20/1.38 ((hskp9 | hskp8 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c1_1(a477))) <=> (hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3491,plain,
% 1.20/1.38 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[3490])).
% 1.20/1.38 tff(3492,plain,
% 1.20/1.38 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[3491, 3489])).
% 1.20/1.38 tff(3493,plain,
% 1.20/1.38 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(3494,plain,
% 1.20/1.38 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 1.20/1.38 tff(3495,plain,
% 1.20/1.38 (hskp9 | hskp8 | (~c1_1(a477))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3494, 138, 2953, 2947, 3488])).
% 1.20/1.38 tff(3496,plain,
% 1.20/1.38 (hskp8),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3495, 3476, 3184])).
% 1.20/1.38 tff(3497,plain,
% 1.20/1.38 (((~hskp8) | (~c1_1(a415))) <=> ((~hskp8) | (~c1_1(a415)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3498,plain,
% 1.20/1.38 (((~c1_1(a415)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a415)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3499,axiom,((~c1_1(a415)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.20/1.38 tff(3500,plain,
% 1.20/1.38 ((~hskp8) | (~c1_1(a415))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3499, 3498])).
% 1.20/1.38 tff(3501,plain,
% 1.20/1.38 ((~hskp8) | (~c1_1(a415))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3500, 3497])).
% 1.20/1.38 tff(3502,plain,
% 1.20/1.38 (~c1_1(a415)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[3501, 3496])).
% 1.20/1.38 tff(3503,plain,
% 1.20/1.38 (((~hskp8) | c3_1(a415)) <=> ((~hskp8) | c3_1(a415))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(3504,axiom,((~hskp8) | c3_1(a415)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.20/1.38 tff(3505,plain,
% 1.20/1.38 ((~hskp8) | c3_1(a415)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3504, 3503])).
% 1.20/1.38 tff(3506,plain,
% 1.20/1.38 ((~hskp8) | c3_1(a415)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3505, 3503])).
% 1.20/1.38 tff(3507,plain,
% 1.20/1.38 ((~hskp8) | c3_1(a415)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3506, 3503])).
% 1.20/1.38 tff(3508,plain,
% 1.20/1.38 ((~hskp8) | c3_1(a415)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3507, 3503])).
% 1.20/1.38 tff(3509,plain,
% 1.20/1.38 ((~hskp8) | c3_1(a415)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[3508, 3503])).
% 1.20/1.39 tff(3510,plain,
% 1.20/1.39 (c3_1(a415)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3509, 3496])).
% 1.20/1.39 tff(3511,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3512,plain,
% 1.20/1.39 (((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a403) | c1_1(a403) | c0_1(a403)) <=> (c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3513,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451)))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[3512])).
% 1.20/1.39 tff(3514,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(transitivity,[status(thm)],[3513, 3511])).
% 1.20/1.39 tff(3515,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a403) | c1_1(a403) | c0_1(a403))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(3516,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3515, 3514])).
% 1.20/1.39 tff(3517,plain,
% 1.20/1.39 (c0_1(a415)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3516, 138, 3350, 3510, 793, 3502, 3104, 3107, 1725, 3478, 3349])).
% 1.20/1.39 tff(3518,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3519,plain,
% 1.20/1.39 (((~ndr1_0) | c1_1(a415) | (~c3_1(a415)) | (~c0_1(a415)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477))) <=> (c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3520,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a415) | (~c3_1(a415)) | (~c0_1(a415)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[3519])).
% 1.20/1.39 tff(3521,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a415) | (~c3_1(a415)) | (~c0_1(a415)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[3520, 3518])).
% 1.20/1.39 tff(3522,plain,
% 1.20/1.39 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a415) | (~c3_1(a415)) | (~c0_1(a415)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(3523,plain,
% 1.20/1.39 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3522, 3521])).
% 1.20/1.39 tff(3524,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3523, 138, 2961, 3510, 2953, 3502, 480, 3184, 3517])).
% 1.20/1.39 tff(3525,plain,(hskp9 | (~c1_1(a477)) | (~c2_1(a451)) | c1_1(a451) | c3_1(a451) | (~c0_1(a402)) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(3526,plain,
% 1.20/1.39 (hskp9),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3525, 3461, 3472, 3463, 3471, 3128, 3127])).
% 1.20/1.39 tff(3527,plain,
% 1.20/1.39 (~c0_1(a416)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[612, 3526])).
% 1.20/1.39 tff(3528,plain,
% 1.20/1.39 (~c1_1(a416)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[606, 3526])).
% 1.20/1.39 tff(3529,assumption,(~c0_1(a416)), introduced(assumption)).
% 1.20/1.39 tff(3530,assumption,(~c1_1(a416)), introduced(assumption)).
% 1.20/1.39 tff(3531,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3532,plain,
% 1.20/1.39 (((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)) | c3_1(a403) | c1_1(a403) | c0_1(a403)) <=> (c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3533,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451)))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[3532])).
% 1.20/1.39 tff(3534,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(transitivity,[status(thm)],[3533, 3531])).
% 1.20/1.39 tff(3535,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)) | c3_1(a403) | c1_1(a403) | c0_1(a403))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(3536,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3535, 3534])).
% 1.20/1.39 tff(3537,plain,
% 1.20/1.39 (c1_1(a403) | (~c3_1(a416))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3536, 138, 3350, 793, 3529, 3530, 3104, 3107, 1725, 3349])).
% 1.20/1.39 tff(3538,plain,
% 1.20/1.39 (~c3_1(a416)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3537, 3478])).
% 1.20/1.39 tff(3539,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3540,plain,
% 1.20/1.39 (((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a416) | c1_1(a416) | c0_1(a416)) <=> (c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3541,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a416) | c1_1(a416) | c0_1(a416))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451)))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[3540])).
% 1.20/1.39 tff(3542,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a416) | c1_1(a416) | c0_1(a416))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.20/1.39 inference(transitivity,[status(thm)],[3541, 3539])).
% 1.20/1.39 tff(3543,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a416) | c1_1(a416) | c0_1(a416))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(3544,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3543, 3542])).
% 1.20/1.39 tff(3545,plain,
% 1.20/1.39 (c0_1(a415)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3544, 138, 3350, 3538, 3510, 793, 3529, 3530, 3502, 1725, 3349])).
% 1.20/1.39 tff(3546,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3523, 138, 2961, 3510, 2953, 3502, 480, 3184, 3545])).
% 1.20/1.39 tff(3547,plain,(hskp9 | (~c1_1(a477)) | (~c2_1(a451)) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c3_1(a451) | (~c0_1(a402)) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(3548,plain,
% 1.20/1.39 (hskp9),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3547, 3529, 3350, 793, 3530, 3184, 3349, 1352, 93])).
% 1.20/1.39 tff(3549,plain,
% 1.20/1.39 (c3_1(a416)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[667, 3548])).
% 1.20/1.39 tff(3550,plain,
% 1.20/1.39 (c0_1(a416) | c1_1(a403) | (~c3_1(a416))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3536, 138, 3350, 793, 3530, 3104, 3107, 1725, 3349])).
% 1.20/1.39 tff(3551,plain,
% 1.20/1.39 (c1_1(a403)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3550, 3549, 3529])).
% 1.20/1.39 tff(3552,plain,
% 1.20/1.39 (c0_1(a416) | (~c1_1(a403)) | (~c2_1(a416))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[697, 138, 3530, 3104, 3103, 3107, 313])).
% 1.20/1.39 tff(3553,plain,
% 1.20/1.39 (~c2_1(a416)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3552, 3551, 3529])).
% 1.20/1.39 tff(3554,assumption,(~hskp28), introduced(assumption)).
% 1.20/1.39 tff(3555,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3556,plain,
% 1.20/1.39 ((hskp28 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c2_1(a477) | c0_1(a477) | (~c1_1(a477))) <=> (hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3557,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[3556])).
% 1.20/1.39 tff(3558,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[3557, 3555])).
% 1.20/1.39 tff(3559,plain,
% 1.20/1.39 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(3560,plain,
% 1.20/1.39 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3559, 3558])).
% 1.20/1.39 tff(3561,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3560, 3554, 138, 3549, 2953, 2947, 3530, 3239, 3184, 3553])).
% 1.20/1.39 tff(3562,plain,(c0_1(a416) | hskp28 | c1_1(a416) | (~c1_1(a477)) | (~c2_1(a451)) | c1_1(a451) | c3_1(a451) | (~c0_1(a402)) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(3563,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3562, 3528, 3527, 3475, 3461, 3472, 3463, 3471, 3128, 3127])).
% 1.20/1.39 tff(3564,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(3565,plain,
% 1.20/1.39 (~c3_1(a401)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[734, 3564])).
% 1.20/1.39 tff(3566,plain,
% 1.20/1.39 (c1_1(a401)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[742, 3564])).
% 1.20/1.39 tff(3567,plain,
% 1.20/1.39 (c0_1(a401)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[750, 3564])).
% 1.20/1.39 tff(3568,plain,
% 1.20/1.39 (hskp20),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[757, 138, 3567, 3566, 3565, 435])).
% 1.20/1.39 tff(3569,plain,
% 1.20/1.39 (~c2_1(a449)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[836, 3568])).
% 1.20/1.39 tff(3570,plain,
% 1.20/1.39 (c3_1(a449)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[830, 3568])).
% 1.20/1.39 tff(3571,plain,
% 1.20/1.39 (c1_1(a449)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[765, 3568])).
% 1.20/1.39 tff(3572,plain,
% 1.20/1.39 (hskp10),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3087, 138, 2961, 3571, 3570, 2953, 2947, 3569, 2070])).
% 1.20/1.39 tff(3573,plain,
% 1.20/1.39 (~c2_1(a418)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[2082, 3572])).
% 1.20/1.39 tff(3574,plain,
% 1.20/1.39 (~c0_1(a418)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[2088, 3572])).
% 1.20/1.39 tff(3575,plain,
% 1.20/1.39 (c1_1(a418)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[2098, 3572])).
% 1.20/1.39 tff(3576,plain,
% 1.20/1.39 (hskp28 | c1_1(a477)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3278, 138, 2961, 3575, 2947, 3574, 3573, 3239])).
% 1.20/1.39 tff(3577,plain,
% 1.20/1.39 (hskp28),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3576, 1])).
% 1.20/1.39 tff(3578,plain,
% 1.20/1.39 (c3_1(a414)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[2835, 3577])).
% 1.20/1.39 tff(3579,plain,
% 1.20/1.39 (c2_1(a414)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[2843, 3577])).
% 1.20/1.39 tff(3580,plain,
% 1.20/1.39 (c0_1(a414)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[2851, 3577])).
% 1.20/1.39 tff(3581,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3582,plain,
% 1.20/1.39 (((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a477) | c0_1(a477) | c2_1(a477)) <=> (c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3583,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a477) | c0_1(a477) | c2_1(a477))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477)))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[3582])).
% 1.20/1.39 tff(3584,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a477) | c0_1(a477) | c2_1(a477))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477))),
% 1.20/1.39 inference(transitivity,[status(thm)],[3583, 3581])).
% 1.20/1.39 tff(3585,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a477) | c0_1(a477) | c2_1(a477))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(3586,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3585, 3584])).
% 1.20/1.39 tff(3587,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3586, 138, 3580, 3579, 3578, 3567, 3566, 2953, 2947, 3565, 11, 1])).
% 1.20/1.39 tff(3588,plain,(c1_1(a477)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(3589,plain,
% 1.20/1.39 (c2_1(a401)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[2441, 23, 3566, 3565, 3567])).
% 1.20/1.39 tff(3590,plain,
% 1.20/1.39 (hskp13),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3118, 23, 3588])).
% 1.20/1.39 tff(3591,plain,
% 1.20/1.39 (~c0_1(a427)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[260, 3590])).
% 1.20/1.39 tff(3592,plain,
% 1.20/1.39 (c2_1(a427)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[276, 3590])).
% 1.20/1.39 tff(3593,plain,
% 1.20/1.39 (c1_1(a427)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[284, 3590])).
% 1.20/1.39 tff(3594,assumption,(c2_1(a401)), introduced(assumption)).
% 1.20/1.39 tff(3595,assumption,(hskp8), introduced(assumption)).
% 1.20/1.39 tff(3596,plain,
% 1.20/1.39 (~c1_1(a415)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3501, 3595])).
% 1.20/1.39 tff(3597,assumption,(~c0_1(a427)), introduced(assumption)).
% 1.20/1.39 tff(3598,plain,
% 1.20/1.39 (c3_1(a415)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3509, 3595])).
% 1.20/1.39 tff(3599,plain,
% 1.20/1.39 (((~hskp8) | c2_1(a415)) <=> ((~hskp8) | c2_1(a415))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3600,axiom,((~hskp8) | c2_1(a415)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.20/1.39 tff(3601,plain,
% 1.20/1.39 ((~hskp8) | c2_1(a415)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3600, 3599])).
% 1.20/1.39 tff(3602,plain,
% 1.20/1.39 ((~hskp8) | c2_1(a415)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3601, 3599])).
% 1.20/1.39 tff(3603,plain,
% 1.20/1.39 ((~hskp8) | c2_1(a415)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3602, 3599])).
% 1.20/1.39 tff(3604,plain,
% 1.20/1.39 ((~hskp8) | c2_1(a415)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3603, 3599])).
% 1.20/1.39 tff(3605,plain,
% 1.20/1.39 ((~hskp8) | c2_1(a415)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3604, 3599])).
% 1.20/1.39 tff(3606,plain,
% 1.20/1.39 (c2_1(a415)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3605, 3595])).
% 1.20/1.39 tff(3607,assumption,(c2_1(a427)), introduced(assumption)).
% 1.20/1.39 tff(3608,assumption,(c1_1(a427)), introduced(assumption)).
% 1.20/1.39 tff(3609,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3610,plain,
% 1.20/1.39 (((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a415) | (~c2_1(a415)) | (~c3_1(a415)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3611,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a415) | (~c2_1(a415)) | (~c3_1(a415)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[3610])).
% 1.20/1.39 tff(3612,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a415) | (~c2_1(a415)) | (~c3_1(a415)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[3611, 3609])).
% 1.20/1.39 tff(3613,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a415) | (~c2_1(a415)) | (~c3_1(a415)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(3614,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[3613, 3612])).
% 1.20/1.39 tff(3615,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3614, 138, 3608, 3607, 3606, 3598, 3567, 3597, 3596, 3565, 647, 3594])).
% 1.20/1.39 tff(3616,plain,((~hskp8) | (~c1_1(a427)) | (~c2_1(a427)) | c0_1(a427) | (~c2_1(a401))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(3617,plain,
% 1.20/1.39 (~hskp8),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3616, 3593, 3592, 3591, 3589])).
% 1.20/1.39 tff(3618,plain,
% 1.20/1.39 (hskp9),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[3495, 3617, 3588])).
% 1.20/1.39 tff(3619,plain,
% 1.20/1.39 (~c1_1(a416)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[606, 3618])).
% 1.20/1.39 tff(3620,plain,
% 1.20/1.39 (c3_1(a416)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[667, 3618])).
% 1.20/1.39 tff(3621,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3622,plain,
% 1.20/1.39 (((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(3623,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[3622])).
% 1.20/1.39 tff(3624,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[3623, 3621])).
% 1.20/1.40 tff(3625,plain,
% 1.20/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(3626,plain,
% 1.20/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[3625, 3624])).
% 1.20/1.40 tff(3627,plain,
% 1.20/1.40 (~c2_1(a416)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[3626, 138, 3593, 3592, 3620, 3567, 3591, 3619, 3565, 647, 3589])).
% 1.20/1.40 tff(3628,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(3629,plain,
% 1.20/1.40 (((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a477) | c2_1(a477) | (~c1_1(a477))) <=> (c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(3630,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a477) | c2_1(a477) | (~c1_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[3629])).
% 1.20/1.40 tff(3631,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a477) | c2_1(a477) | (~c1_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[3630, 3628])).
% 1.20/1.40 tff(3632,plain,
% 1.20/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a477) | c2_1(a477) | (~c1_1(a477)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(3633,plain,
% 1.20/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[3632, 3631])).
% 1.20/1.40 tff(3634,plain,
% 1.20/1.40 (~c3_1(a427)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[3633, 138, 3592, 3620, 2953, 2947, 3591, 3619, 43, 3588, 3627])).
% 1.20/1.40 tff(3635,plain,
% 1.20/1.40 (~c0_1(a416)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[612, 3618])).
% 1.20/1.40 tff(3636,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(3637,plain,
% 1.20/1.40 (((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416))) <=> (c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(3638,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427)))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[3637])).
% 1.20/1.40 tff(3639,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427))),
% 1.20/1.40 inference(transitivity,[status(thm)],[3638, 3636])).
% 1.20/1.40 tff(3640,plain,
% 1.20/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(3641,plain,
% 1.20/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[3640, 3639])).
% 1.20/1.40 tff(3642,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[3641, 138, 3592, 3620, 3591, 3635, 3619, 718, 3634, 3627])).
% 1.20/1.40 tff(3643,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(3644,plain,
% 1.20/1.40 (~c1_1(a402)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[2521, 3643])).
% 1.20/1.40 tff(3645,plain,
% 1.20/1.40 (c0_1(a402)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[469, 3643])).
% 1.20/1.40 tff(3646,plain,
% 1.20/1.40 (~c2_1(a402)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[461, 3643])).
% 1.20/1.40 tff(3647,plain,
% 1.20/1.40 (hskp22),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[3195, 3646, 3588, 3645, 3644])).
% 1.20/1.40 tff(3648,plain,
% 1.20/1.40 (~c1_1(a451)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[775, 3647])).
% 1.20/1.40 tff(3649,plain,
% 1.20/1.40 (c0_1(a451)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[791, 3647])).
% 1.20/1.40 tff(3650,plain,
% 1.20/1.40 (~c3_1(a451)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[3470, 138, 2961, 3649, 2953, 3648, 480, 3588])).
% 1.20/1.40 tff(3651,plain,
% 1.20/1.40 (c2_1(a451)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[783, 3647])).
% 1.20/1.40 tff(3652,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[817, 138, 3651, 3567, 3566, 3648, 3565, 811, 3650])).
% 1.20/1.40 % SZS output end Proof
% 1.20/1.40 % E exiting
%------------------------------------------------------------------------------