%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN436-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:39:05 AM UTC 2025
% Result : Unsatisfiable 0.88s 1.05s
% Output : Proof 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN436-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:36:57 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.88/1.05 % SZS status Unsatisfiable
% 0.88/1.05 % SZS output start Proof
% 0.88/1.05 tff(c1_1_type, type, (
% 0.88/1.05 c1_1: $i > $o)).
% 0.88/1.05 tff(a22_type, type, (
% 0.88/1.05 a22: $i)).
% 0.88/1.05 tff(a33_type, type, (
% 0.88/1.05 a33: $i)).
% 0.88/1.05 tff(c3_1_type, type, (
% 0.88/1.05 c3_1: $i > $o)).
% 0.88/1.05 tff(a31_type, type, (
% 0.88/1.05 a31: $i)).
% 0.88/1.05 tff(c2_1_type, type, (
% 0.88/1.05 c2_1: $i > $o)).
% 0.88/1.05 tff(hskp17_type, type, (
% 0.88/1.05 hskp17: $o)).
% 0.88/1.05 tff(c0_1_type, type, (
% 0.88/1.05 c0_1: $i > $o)).
% 0.88/1.05 tff(a3_type, type, (
% 0.88/1.05 a3: $i)).
% 0.88/1.05 tff(hskp11_type, type, (
% 0.88/1.05 hskp11: $o)).
% 0.88/1.05 tff(a24_type, type, (
% 0.88/1.05 a24: $i)).
% 0.88/1.05 tff(hskp14_type, type, (
% 0.88/1.05 hskp14: $o)).
% 0.88/1.05 tff(hskp8_type, type, (
% 0.88/1.05 hskp8: $o)).
% 0.88/1.05 tff(hskp9_type, type, (
% 0.88/1.05 hskp9: $o)).
% 0.88/1.05 tff(a16_type, type, (
% 0.88/1.05 a16: $i)).
% 0.88/1.05 tff(a4_type, type, (
% 0.88/1.05 a4: $i)).
% 0.88/1.05 tff(hskp4_type, type, (
% 0.88/1.05 hskp4: $o)).
% 0.88/1.05 tff(a5_type, type, (
% 0.88/1.05 a5: $i)).
% 0.88/1.05 tff(ndr1_0_type, type, (
% 0.88/1.05 ndr1_0: $o)).
% 0.88/1.05 tff(hskp3_type, type, (
% 0.88/1.05 hskp3: $o)).
% 0.88/1.05 tff(hskp2_type, type, (
% 0.88/1.05 hskp2: $o)).
% 0.88/1.05 tff(a37_type, type, (
% 0.88/1.05 a37: $i)).
% 0.88/1.05 tff(a30_type, type, (
% 0.88/1.05 a30: $i)).
% 0.88/1.05 tff(hskp16_type, type, (
% 0.88/1.05 hskp16: $o)).
% 0.88/1.05 tff(a25_type, type, (
% 0.88/1.05 a25: $i)).
% 0.88/1.05 tff(a32_type, type, (
% 0.88/1.05 a32: $i)).
% 0.88/1.05 tff(hskp18_type, type, (
% 0.88/1.05 hskp18: $o)).
% 0.88/1.05 tff(a6_type, type, (
% 0.88/1.05 a6: $i)).
% 0.88/1.05 tff(a15_type, type, (
% 0.88/1.05 a15: $i)).
% 0.88/1.05 tff(hskp24_type, type, (
% 0.88/1.05 hskp24: $o)).
% 0.88/1.05 tff(hskp13_type, type, (
% 0.88/1.05 hskp13: $o)).
% 0.88/1.05 tff(a10_type, type, (
% 0.88/1.05 a10: $i)).
% 0.88/1.05 tff(hskp26_type, type, (
% 0.88/1.05 hskp26: $o)).
% 0.88/1.05 tff(a14_type, type, (
% 0.88/1.05 a14: $i)).
% 0.88/1.05 tff(hskp7_type, type, (
% 0.88/1.05 hskp7: $o)).
% 0.88/1.05 tff(hskp0_type, type, (
% 0.88/1.05 hskp0: $o)).
% 0.88/1.05 tff(hskp25_type, type, (
% 0.88/1.05 hskp25: $o)).
% 0.88/1.05 tff(hskp21_type, type, (
% 0.88/1.05 hskp21: $o)).
% 0.88/1.05 tff(a1_type, type, (
% 0.88/1.05 a1: $i)).
% 0.88/1.05 tff(hskp23_type, type, (
% 0.88/1.05 hskp23: $o)).
% 0.88/1.05 tff(a53_type, type, (
% 0.88/1.05 a53: $i)).
% 0.88/1.05 tff(hskp27_type, type, (
% 0.88/1.05 hskp27: $o)).
% 0.88/1.05 tff(a11_type, type, (
% 0.88/1.05 a11: $i)).
% 0.88/1.05 tff(hskp19_type, type, (
% 0.88/1.05 hskp19: $o)).
% 0.88/1.05 tff(a42_type, type, (
% 0.88/1.05 a42: $i)).
% 0.88/1.05 tff(a9_type, type, (
% 0.88/1.05 a9: $i)).
% 0.88/1.05 tff(hskp6_type, type, (
% 0.88/1.05 hskp6: $o)).
% 0.88/1.05 tff(a19_type, type, (
% 0.88/1.05 a19: $i)).
% 0.88/1.05 tff(a18_type, type, (
% 0.88/1.05 a18: $i)).
% 0.88/1.05 tff(hskp10_type, type, (
% 0.88/1.05 hskp10: $o)).
% 0.88/1.05 tff(hskp20_type, type, (
% 0.88/1.05 hskp20: $o)).
% 0.88/1.05 tff(a8_type, type, (
% 0.88/1.05 a8: $i)).
% 0.88/1.05 tff(a2_type, type, (
% 0.88/1.05 a2: $i)).
% 0.88/1.05 tff(hskp1_type, type, (
% 0.88/1.05 hskp1: $o)).
% 0.88/1.05 tff(hskp5_type, type, (
% 0.88/1.05 hskp5: $o)).
% 0.88/1.05 tff(a7_type, type, (
% 0.88/1.05 a7: $i)).
% 0.88/1.05 tff(a21_type, type, (
% 0.88/1.05 a21: $i)).
% 0.88/1.05 tff(hskp12_type, type, (
% 0.88/1.05 hskp12: $o)).
% 0.88/1.05 tff(hskp15_type, type, (
% 0.88/1.05 hskp15: $o)).
% 0.88/1.05 tff(hskp22_type, type, (
% 0.88/1.05 hskp22: $o)).
% 0.88/1.05 tff(a45_type, type, (
% 0.88/1.05 a45: $i)).
% 0.88/1.05 tff(1,assumption,(~c0_1(a3)), introduced(assumption)).
% 0.88/1.05 tff(2,assumption,(~c3_1(a16)), introduced(assumption)).
% 0.88/1.05 tff(3,assumption,(~c1_1(a16)), introduced(assumption)).
% 0.88/1.05 tff(4,plain,
% 0.88/1.05 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(5,plain,
% 0.88/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_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)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[4])).
% 0.88/1.05 tff(6,plain,
% 0.88/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_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)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(7,plain,
% 0.88/1.05 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(8,plain,
% 0.88/1.05 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[7])).
% 0.88/1.05 tff(9,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.88/1.05 tff(10,plain,
% 0.88/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.88/1.05 tff(11,plain,
% 0.88/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.88/1.05 tff(12,plain,(
% 0.88/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.88/1.05 inference(skolemize,[status(sab)],[11])).
% 0.88/1.05 tff(13,plain,
% 0.88/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.88/1.05 tff(14,plain,
% 0.88/1.05 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(15,plain,
% 0.88/1.05 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[14])).
% 0.88/1.05 tff(16,plain,
% 0.88/1.05 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(17,plain,
% 0.88/1.05 (^[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) | (~c2_1(U)) | c0_1(U))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) | hskp3))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))))),
% 0.88/1.05 inference(bind,[status(th)],[])).
% 0.88/1.05 tff(18,plain,
% 0.88/1.05 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.88/1.05 inference(quant_intro,[status(thm)],[17])).
% 0.88/1.05 tff(19,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.88/1.05 tff(20,plain,
% 0.88/1.05 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.88/1.05 tff(21,plain,
% 0.88/1.05 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.88/1.05 tff(22,plain,(
% 0.88/1.05 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.88/1.05 inference(skolemize,[status(sab)],[21])).
% 0.88/1.05 tff(23,plain,
% 0.88/1.05 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.88/1.05 tff(24,assumption,(~c2_1(a16)), introduced(assumption)).
% 0.88/1.06 tff(25,plain,
% 0.88/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(26,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[25])).
% 0.88/1.06 tff(27,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(28,plain,
% 0.88/1.06 (^[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)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(29,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[28])).
% 0.88/1.06 tff(30,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.88/1.06 tff(31,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.88/1.06 tff(32,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.88/1.06 tff(33,plain,(
% 0.88/1.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(skolemize,[status(sab)],[32])).
% 0.88/1.06 tff(34,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.88/1.06 tff(35,assumption,(~c0_1(a16)), introduced(assumption)).
% 0.88/1.06 tff(36,plain,
% 0.88/1.06 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(37,plain,
% 0.88/1.06 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[36])).
% 0.88/1.06 tff(38,plain,
% 0.88/1.06 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(39,plain,
% 0.88/1.06 (^[V: $i, U: $i] : 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)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(40,plain,
% 0.88/1.06 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[39])).
% 0.88/1.06 tff(41,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.88/1.06 tff(42,plain,
% 0.88/1.06 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.88/1.06 tff(43,plain,
% 0.88/1.06 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.88/1.06 tff(44,plain,(
% 0.88/1.06 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.88/1.06 inference(skolemize,[status(sab)],[43])).
% 0.88/1.06 tff(45,plain,
% 0.88/1.06 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.88/1.06 tff(46,plain,
% 0.88/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(47,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[46])).
% 0.88/1.06 tff(48,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(49,plain,
% 0.88/1.06 (^[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)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_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) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_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) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(50,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[49])).
% 0.88/1.06 tff(51,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.88/1.06 tff(52,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.88/1.06 tff(53,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.88/1.06 tff(54,plain,(
% 0.88/1.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(skolemize,[status(sab)],[53])).
% 0.88/1.06 tff(55,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.88/1.06 tff(56,plain,
% 0.88/1.06 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(57,plain,
% 0.88/1.06 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[56])).
% 0.88/1.06 tff(58,plain,
% 0.88/1.06 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(59,plain,
% 0.88/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(60,plain,
% 0.88/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[59])).
% 0.88/1.06 tff(61,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.88/1.06 tff(62,plain,
% 0.88/1.06 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.88/1.06 tff(63,plain,
% 0.88/1.06 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.88/1.06 tff(64,plain,(
% 0.88/1.06 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(skolemize,[status(sab)],[63])).
% 0.88/1.06 tff(65,plain,
% 0.88/1.06 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.88/1.06 tff(66,assumption,(hskp17), introduced(assumption)).
% 0.88/1.06 tff(67,plain,
% 0.88/1.06 (((~hskp17) | (~c1_1(a31))) <=> ((~hskp17) | (~c1_1(a31)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(68,plain,
% 0.88/1.06 (((~c1_1(a31)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a31)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(69,axiom,((~c1_1(a31)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.88/1.06 tff(70,plain,
% 0.88/1.06 ((~hskp17) | (~c1_1(a31))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.88/1.06 tff(71,plain,
% 0.88/1.06 ((~hskp17) | (~c1_1(a31))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.88/1.06 tff(72,plain,
% 0.88/1.06 (~c1_1(a31)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[71, 66])).
% 0.88/1.06 tff(73,assumption,(~hskp24), introduced(assumption)).
% 0.88/1.06 tff(74,plain,
% 0.88/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(75,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[74])).
% 0.88/1.06 tff(76,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(77,plain,
% 0.88/1.06 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(78,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[77])).
% 0.88/1.06 tff(79,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.88/1.06 tff(80,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.88/1.06 tff(81,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.88/1.06 tff(82,plain,(
% 0.88/1.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(skolemize,[status(sab)],[81])).
% 0.88/1.06 tff(83,plain,
% 0.88/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.88/1.06 tff(84,assumption,(~hskp26), introduced(assumption)).
% 0.88/1.06 tff(85,plain,
% 0.88/1.06 (^[U: $i] : refl((hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(86,plain,
% 0.88/1.06 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[85])).
% 0.88/1.06 tff(87,plain,
% 0.88/1.06 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(88,plain,
% 0.88/1.06 (^[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) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp16) <=> ((hskp26 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp16))), rewrite(((hskp26 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp16) <=> (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp16) <=> (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(89,plain,
% 0.88/1.06 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp16) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[88])).
% 0.88/1.06 tff(90,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.88/1.06 tff(91,plain,
% 0.88/1.06 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.88/1.06 tff(92,plain,
% 0.88/1.06 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.88/1.06 tff(93,plain,(
% 0.88/1.06 ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.88/1.06 inference(skolemize,[status(sab)],[92])).
% 0.88/1.06 tff(94,plain,
% 0.88/1.06 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.88/1.06 tff(95,plain,
% 0.88/1.06 (^[U: $i] : refl((hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(96,plain,
% 0.88/1.06 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[95])).
% 0.88/1.06 tff(97,plain,
% 0.88/1.06 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(98,plain,
% 0.88/1.06 (^[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)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp24) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp24))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp24) <=> (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp24) <=> (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.88/1.06 inference(bind,[status(th)],[])).
% 0.88/1.06 tff(99,plain,
% 0.88/1.06 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp24) <=> ![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.88/1.06 inference(quant_intro,[status(thm)],[98])).
% 0.88/1.06 tff(100,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.88/1.06 tff(101,plain,
% 0.88/1.06 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.88/1.06 tff(102,plain,
% 0.88/1.06 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.88/1.06 tff(103,plain,(
% 0.88/1.06 ![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.88/1.06 inference(skolemize,[status(sab)],[102])).
% 0.88/1.06 tff(104,plain,
% 0.88/1.06 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.88/1.06 tff(105,assumption,(~hskp9), introduced(assumption)).
% 0.88/1.06 tff(106,assumption,(hskp4), introduced(assumption)).
% 0.88/1.06 tff(107,plain,
% 0.88/1.06 (((~hskp4) | (~c2_1(a6))) <=> ((~hskp4) | (~c2_1(a6)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(108,plain,
% 0.88/1.06 (((~c2_1(a6)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a6)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(109,axiom,((~c2_1(a6)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.88/1.06 tff(110,plain,
% 0.88/1.06 ((~hskp4) | (~c2_1(a6))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.88/1.06 tff(111,plain,
% 0.88/1.06 ((~hskp4) | (~c2_1(a6))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[110, 107])).
% 0.88/1.06 tff(112,plain,
% 0.88/1.06 (~c2_1(a6)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[111, 106])).
% 0.88/1.06 tff(113,plain,
% 0.88/1.06 (((~hskp4) | c3_1(a6)) <=> ((~hskp4) | c3_1(a6))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(114,axiom,((~hskp4) | c3_1(a6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.88/1.06 tff(115,plain,
% 0.88/1.06 ((~hskp4) | c3_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.88/1.06 tff(116,plain,
% 0.88/1.06 ((~hskp4) | c3_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[115, 113])).
% 0.88/1.06 tff(117,plain,
% 0.88/1.06 ((~hskp4) | c3_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.88/1.06 tff(118,plain,
% 0.88/1.06 ((~hskp4) | c3_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.88/1.06 tff(119,plain,
% 0.88/1.06 ((~hskp4) | c3_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[118, 113])).
% 0.88/1.06 tff(120,plain,
% 0.88/1.06 (c3_1(a6)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[119, 106])).
% 0.88/1.06 tff(121,plain,
% 0.88/1.06 (((~hskp4) | c1_1(a6)) <=> ((~hskp4) | c1_1(a6))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(122,axiom,((~hskp4) | c1_1(a6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.88/1.06 tff(123,plain,
% 0.88/1.06 ((~hskp4) | c1_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.88/1.06 tff(124,plain,
% 0.88/1.06 ((~hskp4) | c1_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[123, 121])).
% 0.88/1.06 tff(125,plain,
% 0.88/1.06 ((~hskp4) | c1_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.88/1.06 tff(126,plain,
% 0.88/1.06 ((~hskp4) | c1_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.88/1.06 tff(127,plain,
% 0.88/1.06 ((~hskp4) | c1_1(a6)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[126, 121])).
% 0.88/1.06 tff(128,plain,
% 0.88/1.06 (c1_1(a6)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[127, 106])).
% 0.88/1.06 tff(129,assumption,(~ndr1_0), introduced(assumption)).
% 0.88/1.06 tff(130,plain,
% 0.88/1.06 ((ndr1_0 | (~hskp17)) <=> (ndr1_0 | (~hskp17))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(131,plain,
% 0.88/1.06 (((~hskp17) | ndr1_0) <=> (ndr1_0 | (~hskp17))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(132,axiom,((~hskp17) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause11')).
% 0.88/1.06 tff(133,plain,
% 0.88/1.06 (ndr1_0 | (~hskp17)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.88/1.06 tff(134,plain,
% 0.88/1.06 (ndr1_0 | (~hskp17)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.88/1.06 tff(135,plain,
% 0.88/1.06 (~hskp17),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[134, 129])).
% 0.88/1.06 tff(136,plain,
% 0.88/1.06 ((ndr1_0 | (~hskp25)) <=> (ndr1_0 | (~hskp25))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(137,plain,
% 0.88/1.06 (((~hskp25) | ndr1_0) <=> (ndr1_0 | (~hskp25))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(138,axiom,((~hskp25) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.88/1.06 tff(139,plain,
% 0.88/1.06 (ndr1_0 | (~hskp25)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.88/1.06 tff(140,plain,
% 0.88/1.06 (ndr1_0 | (~hskp25)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[139, 136])).
% 0.88/1.06 tff(141,plain,
% 0.88/1.06 (~hskp25),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[140, 129])).
% 0.88/1.06 tff(142,plain,
% 0.88/1.06 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(143,plain,
% 0.88/1.06 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(144,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.88/1.06 tff(145,plain,
% 0.88/1.06 (ndr1_0 | (~hskp21)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.88/1.06 tff(146,plain,
% 0.88/1.06 (ndr1_0 | (~hskp21)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[145, 142])).
% 0.88/1.06 tff(147,plain,
% 0.88/1.06 (~hskp21),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[146, 129])).
% 0.88/1.06 tff(148,plain,
% 0.88/1.06 ((hskp25 | hskp21 | hskp17) <=> (hskp25 | hskp21 | hskp17)),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(149,plain,
% 0.88/1.06 (((hskp25 | hskp17) | hskp21) <=> (hskp25 | hskp21 | hskp17)),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(150,plain,
% 0.88/1.06 ((hskp25 | hskp17) <=> (hskp25 | hskp17)),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(151,plain,
% 0.88/1.06 (((hskp25 | hskp17) | hskp21) <=> ((hskp25 | hskp17) | hskp21)),
% 0.88/1.06 inference(monotonicity,[status(thm)],[150])).
% 0.88/1.06 tff(152,plain,
% 0.88/1.06 (((hskp25 | hskp17) | hskp21) <=> (hskp25 | hskp21 | hskp17)),
% 0.88/1.06 inference(transitivity,[status(thm)],[151, 149])).
% 0.88/1.06 tff(153,axiom,((hskp25 | hskp17) | hskp21), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause29')).
% 0.88/1.06 tff(154,plain,
% 0.88/1.06 (hskp25 | hskp21 | hskp17),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.88/1.06 tff(155,plain,
% 0.88/1.06 (hskp25 | hskp21 | hskp17),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[154, 148])).
% 0.88/1.06 tff(156,plain,
% 0.88/1.06 (hskp25 | hskp21 | hskp17),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.88/1.06 tff(157,plain,
% 0.88/1.06 (hskp25 | hskp21 | hskp17),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[156, 148])).
% 0.88/1.07 tff(158,plain,
% 0.88/1.07 (hskp25 | hskp21 | hskp17),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[157, 148])).
% 0.88/1.07 tff(159,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[158, 147, 141, 135])).
% 0.88/1.07 tff(160,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(161,plain,
% 0.88/1.07 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(162,plain,
% 0.88/1.07 ((hskp24 | hskp9 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6))) <=> (hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(163,plain,
% 0.88/1.07 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[162])).
% 0.88/1.07 tff(164,plain,
% 0.88/1.07 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[163, 161])).
% 0.88/1.07 tff(165,plain,
% 0.88/1.07 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(166,plain,
% 0.88/1.07 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.88/1.07 tff(167,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[166, 160, 73, 105, 128, 120, 112, 104])).
% 0.88/1.07 tff(168,plain,((~hskp4) | hskp24 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(169,plain,
% 0.88/1.07 (~hskp4),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[168, 105, 73])).
% 0.88/1.07 tff(170,assumption,(hskp8), introduced(assumption)).
% 0.88/1.07 tff(171,plain,
% 0.88/1.07 (((~hskp8) | (~c2_1(a15))) <=> ((~hskp8) | (~c2_1(a15)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(172,plain,
% 0.88/1.07 (((~c2_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a15)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(173,axiom,((~c2_1(a15)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.88/1.07 tff(174,plain,
% 0.88/1.07 ((~hskp8) | (~c2_1(a15))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.88/1.07 tff(175,plain,
% 0.88/1.07 ((~hskp8) | (~c2_1(a15))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[174, 171])).
% 0.88/1.07 tff(176,plain,
% 0.88/1.07 (~c2_1(a15)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[175, 170])).
% 0.88/1.07 tff(177,plain,
% 0.88/1.07 (((~hskp8) | c0_1(a15)) <=> ((~hskp8) | c0_1(a15))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(178,axiom,((~hskp8) | c0_1(a15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.88/1.07 tff(179,plain,
% 0.88/1.07 ((~hskp8) | c0_1(a15)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.88/1.07 tff(180,plain,
% 0.88/1.07 ((~hskp8) | c0_1(a15)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[179, 177])).
% 0.88/1.07 tff(181,plain,
% 0.88/1.07 ((~hskp8) | c0_1(a15)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[180, 177])).
% 0.88/1.07 tff(182,plain,
% 0.88/1.07 ((~hskp8) | c0_1(a15)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.88/1.07 tff(183,plain,
% 0.88/1.07 ((~hskp8) | c0_1(a15)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[182, 177])).
% 0.88/1.07 tff(184,plain,
% 0.88/1.07 (c0_1(a15)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[183, 170])).
% 0.88/1.07 tff(185,plain,
% 0.88/1.07 (((~hskp8) | (~c1_1(a15))) <=> ((~hskp8) | (~c1_1(a15)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(186,plain,
% 0.88/1.07 (((~c1_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a15)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(187,axiom,((~c1_1(a15)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.88/1.07 tff(188,plain,
% 0.88/1.07 ((~hskp8) | (~c1_1(a15))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.88/1.07 tff(189,plain,
% 0.88/1.07 ((~hskp8) | (~c1_1(a15))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[188, 185])).
% 0.88/1.07 tff(190,plain,
% 0.88/1.07 (~c1_1(a15)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[189, 170])).
% 0.88/1.07 tff(191,assumption,(~c2_1(a15)), introduced(assumption)).
% 0.88/1.07 tff(192,assumption,(c0_1(a15)), introduced(assumption)).
% 0.88/1.07 tff(193,assumption,(~hskp4), introduced(assumption)).
% 0.88/1.07 tff(194,assumption,(~c1_1(a15)), introduced(assumption)).
% 0.88/1.07 tff(195,assumption,(hskp23), introduced(assumption)).
% 0.88/1.07 tff(196,plain,
% 0.88/1.07 (((~hskp23) | (~c1_1(a53))) <=> ((~hskp23) | (~c1_1(a53)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(197,plain,
% 0.88/1.07 (((~c1_1(a53)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a53)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(198,axiom,((~c1_1(a53)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.88/1.07 tff(199,plain,
% 0.88/1.07 ((~hskp23) | (~c1_1(a53))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.88/1.07 tff(200,plain,
% 0.88/1.07 ((~hskp23) | (~c1_1(a53))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[199, 196])).
% 0.88/1.07 tff(201,plain,
% 0.88/1.07 (~c1_1(a53)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[200, 195])).
% 0.88/1.07 tff(202,plain,
% 0.88/1.07 (((~hskp23) | (~c0_1(a53))) <=> ((~hskp23) | (~c0_1(a53)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(203,plain,
% 0.88/1.07 (((~c0_1(a53)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a53)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(204,axiom,((~c0_1(a53)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.88/1.07 tff(205,plain,
% 0.88/1.07 ((~hskp23) | (~c0_1(a53))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.88/1.07 tff(206,plain,
% 0.88/1.07 ((~hskp23) | (~c0_1(a53))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[205, 202])).
% 0.88/1.07 tff(207,plain,
% 0.88/1.07 (~c0_1(a53)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[206, 195])).
% 0.88/1.07 tff(208,plain,
% 0.88/1.07 (((~hskp23) | c3_1(a53)) <=> ((~hskp23) | c3_1(a53))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(209,axiom,((~hskp23) | c3_1(a53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.88/1.07 tff(210,plain,
% 0.88/1.07 ((~hskp23) | c3_1(a53)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.88/1.07 tff(211,plain,
% 0.88/1.07 ((~hskp23) | c3_1(a53)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[210, 208])).
% 0.88/1.07 tff(212,plain,
% 0.88/1.07 ((~hskp23) | c3_1(a53)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[211, 208])).
% 0.88/1.07 tff(213,plain,
% 0.88/1.07 ((~hskp23) | c3_1(a53)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.88/1.07 tff(214,plain,
% 0.88/1.07 ((~hskp23) | c3_1(a53)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[213, 208])).
% 0.88/1.07 tff(215,plain,
% 0.88/1.07 (c3_1(a53)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[214, 195])).
% 0.88/1.07 tff(216,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(217,plain,
% 0.88/1.07 ((hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53))) <=> (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(218,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[217])).
% 0.88/1.07 tff(219,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[218, 216])).
% 0.88/1.07 tff(220,plain,
% 0.88/1.07 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(221,plain,
% 0.88/1.07 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.88/1.07 tff(222,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[221, 160, 193, 215, 192, 207, 201, 194, 191, 65])).
% 0.88/1.07 tff(223,plain,((~hskp23) | hskp4 | (~c0_1(a15)) | c1_1(a15) | c2_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(224,plain,
% 0.88/1.07 (~hskp23),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[223, 194, 193, 192, 191])).
% 0.88/1.07 tff(225,plain,
% 0.88/1.07 ((hskp24 | hskp23 | hskp0) <=> (hskp24 | hskp23 | hskp0)),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(226,plain,
% 0.88/1.07 (((hskp24 | hskp23) | hskp0) <=> (hskp24 | hskp23 | hskp0)),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(227,plain,
% 0.88/1.07 ((hskp24 | hskp23) <=> (hskp24 | hskp23)),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(228,plain,
% 0.88/1.07 (((hskp24 | hskp23) | hskp0) <=> ((hskp24 | hskp23) | hskp0)),
% 0.88/1.07 inference(monotonicity,[status(thm)],[227])).
% 0.88/1.07 tff(229,plain,
% 0.88/1.07 (((hskp24 | hskp23) | hskp0) <=> (hskp24 | hskp23 | hskp0)),
% 0.88/1.07 inference(transitivity,[status(thm)],[228, 226])).
% 0.88/1.07 tff(230,axiom,((hskp24 | hskp23) | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.88/1.07 tff(231,plain,
% 0.88/1.07 (hskp24 | hskp23 | hskp0),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.88/1.07 tff(232,plain,
% 0.88/1.07 (hskp24 | hskp23 | hskp0),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[231, 225])).
% 0.88/1.07 tff(233,plain,
% 0.88/1.07 (hskp24 | hskp23 | hskp0),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.88/1.07 tff(234,plain,
% 0.88/1.07 (hskp24 | hskp23 | hskp0),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[233, 225])).
% 0.88/1.07 tff(235,plain,
% 0.88/1.07 (hskp24 | hskp23 | hskp0),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[234, 225])).
% 0.88/1.07 tff(236,plain,
% 0.88/1.07 (hskp0),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[235, 73, 224])).
% 0.88/1.07 tff(237,plain,
% 0.88/1.07 (((~hskp0) | (~c2_1(a1))) <=> ((~hskp0) | (~c2_1(a1)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(238,plain,
% 0.88/1.07 (((~c2_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(239,axiom,((~c2_1(a1)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.88/1.07 tff(240,plain,
% 0.88/1.07 ((~hskp0) | (~c2_1(a1))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.88/1.07 tff(241,plain,
% 0.88/1.07 ((~hskp0) | (~c2_1(a1))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[240, 237])).
% 0.88/1.07 tff(242,plain,
% 0.88/1.07 (~c2_1(a1)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[241, 236])).
% 0.88/1.07 tff(243,plain,
% 0.88/1.07 (((~hskp0) | c3_1(a1)) <=> ((~hskp0) | c3_1(a1))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(244,axiom,((~hskp0) | c3_1(a1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.88/1.07 tff(245,plain,
% 0.88/1.07 ((~hskp0) | c3_1(a1)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.88/1.07 tff(246,plain,
% 0.88/1.07 ((~hskp0) | c3_1(a1)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[245, 243])).
% 0.88/1.07 tff(247,plain,
% 0.88/1.07 ((~hskp0) | c3_1(a1)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[246, 243])).
% 0.88/1.07 tff(248,plain,
% 0.88/1.07 ((~hskp0) | c3_1(a1)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.88/1.07 tff(249,plain,
% 0.88/1.07 ((~hskp0) | c3_1(a1)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[248, 243])).
% 0.88/1.07 tff(250,plain,
% 0.88/1.07 (c3_1(a1)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[249, 236])).
% 0.88/1.07 tff(251,plain,
% 0.88/1.07 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(252,plain,
% 0.88/1.07 ((hskp24 | hskp9 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1))) <=> (hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(253,plain,
% 0.88/1.07 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[252])).
% 0.88/1.07 tff(254,plain,
% 0.88/1.07 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[253, 251])).
% 0.88/1.07 tff(255,plain,
% 0.88/1.07 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(256,plain,
% 0.88/1.07 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.88/1.07 tff(257,plain,
% 0.88/1.07 (~c1_1(a1)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[256, 160, 73, 105, 250, 242, 104])).
% 0.88/1.07 tff(258,plain,
% 0.88/1.07 (((~hskp0) | (~c0_1(a1))) <=> ((~hskp0) | (~c0_1(a1)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(259,plain,
% 0.88/1.07 (((~c0_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(260,axiom,((~c0_1(a1)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.88/1.07 tff(261,plain,
% 0.88/1.07 ((~hskp0) | (~c0_1(a1))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.88/1.07 tff(262,plain,
% 0.88/1.07 ((~hskp0) | (~c0_1(a1))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[261, 258])).
% 0.88/1.07 tff(263,plain,
% 0.88/1.07 (~c0_1(a1)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[262, 236])).
% 0.88/1.07 tff(264,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(265,plain,
% 0.88/1.07 ((hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1))) <=> (hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(266,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[265])).
% 0.88/1.07 tff(267,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[266, 264])).
% 0.88/1.07 tff(268,plain,
% 0.88/1.07 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(269,plain,
% 0.88/1.07 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.88/1.07 tff(270,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[269, 160, 193, 192, 250, 194, 191, 263, 65, 257])).
% 0.88/1.07 tff(271,plain,(hskp24 | hskp4 | (~c0_1(a15)) | c1_1(a15) | c2_1(a15) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(272,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[271, 190, 184, 105, 73, 176, 169])).
% 0.88/1.07 tff(273,plain,((~hskp8) | hskp9 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(274,plain,
% 0.88/1.07 (~hskp8),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[273, 105, 73])).
% 0.88/1.07 tff(275,plain,
% 0.88/1.07 ((hskp17 | hskp8 | hskp4) <=> (hskp17 | hskp8 | hskp4)),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(276,plain,
% 0.88/1.07 (((hskp17 | hskp8) | hskp4) <=> (hskp17 | hskp8 | hskp4)),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(277,axiom,((hskp17 | hskp8) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.88/1.07 tff(278,plain,
% 0.88/1.07 (hskp17 | hskp8 | hskp4),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.88/1.07 tff(279,plain,
% 0.88/1.07 (hskp17 | hskp8 | hskp4),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[278, 275])).
% 0.88/1.07 tff(280,plain,
% 0.88/1.07 (hskp17 | hskp8 | hskp4),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.88/1.07 tff(281,plain,
% 0.88/1.07 (hskp17 | hskp8 | hskp4),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[280, 275])).
% 0.88/1.07 tff(282,plain,
% 0.88/1.07 (hskp17 | hskp8 | hskp4),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[281, 275])).
% 0.88/1.07 tff(283,plain,
% 0.88/1.07 (hskp17),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[282, 274, 169])).
% 0.88/1.07 tff(284,plain,
% 0.88/1.07 (((~hskp17) | c0_1(a31)) <=> ((~hskp17) | c0_1(a31))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(285,axiom,((~hskp17) | c0_1(a31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.88/1.07 tff(286,plain,
% 0.88/1.07 ((~hskp17) | c0_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.88/1.07 tff(287,plain,
% 0.88/1.07 ((~hskp17) | c0_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[286, 284])).
% 0.88/1.07 tff(288,plain,
% 0.88/1.07 ((~hskp17) | c0_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[287, 284])).
% 0.88/1.07 tff(289,plain,
% 0.88/1.07 ((~hskp17) | c0_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[288, 284])).
% 0.88/1.07 tff(290,plain,
% 0.88/1.07 ((~hskp17) | c0_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[289, 284])).
% 0.88/1.07 tff(291,plain,
% 0.88/1.07 (c0_1(a31)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[290, 283])).
% 0.88/1.07 tff(292,plain,
% 0.88/1.07 (((~hskp17) | c2_1(a31)) <=> ((~hskp17) | c2_1(a31))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(293,axiom,((~hskp17) | c2_1(a31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.88/1.07 tff(294,plain,
% 0.88/1.07 ((~hskp17) | c2_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.88/1.07 tff(295,plain,
% 0.88/1.07 ((~hskp17) | c2_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[294, 292])).
% 0.88/1.07 tff(296,plain,
% 0.88/1.07 ((~hskp17) | c2_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[295, 292])).
% 0.88/1.07 tff(297,plain,
% 0.88/1.07 ((~hskp17) | c2_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[296, 292])).
% 0.88/1.07 tff(298,plain,
% 0.88/1.07 ((~hskp17) | c2_1(a31)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[297, 292])).
% 0.88/1.07 tff(299,plain,
% 0.88/1.07 (c2_1(a31)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[298, 283])).
% 0.88/1.07 tff(300,plain,
% 0.88/1.07 (~c1_1(a31)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[71, 283])).
% 0.88/1.07 tff(301,assumption,(c0_1(a31)), introduced(assumption)).
% 0.88/1.07 tff(302,assumption,(c2_1(a31)), introduced(assumption)).
% 0.88/1.07 tff(303,plain,
% 0.88/1.07 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.88/1.07 inference(bind,[status(th)],[])).
% 0.88/1.07 tff(304,plain,
% 0.88/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.88/1.07 inference(quant_intro,[status(thm)],[303])).
% 0.88/1.07 tff(305,plain,
% 0.88/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(306,plain,
% 0.88/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.88/1.07 inference(bind,[status(th)],[])).
% 0.88/1.07 tff(307,plain,
% 0.88/1.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.88/1.07 inference(quant_intro,[status(thm)],[306])).
% 0.88/1.07 tff(308,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.88/1.07 tff(309,plain,
% 0.88/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.88/1.07 tff(310,plain,
% 0.88/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[309, 305])).
% 0.88/1.07 tff(311,plain,(
% 0.88/1.07 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.88/1.07 inference(skolemize,[status(sab)],[310])).
% 0.88/1.07 tff(312,plain,
% 0.88/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[311, 304])).
% 0.88/1.07 tff(313,assumption,(~c1_1(a31)), introduced(assumption)).
% 0.88/1.07 tff(314,assumption,(~hskp0), introduced(assumption)).
% 0.88/1.07 tff(315,plain,
% 0.88/1.07 (hskp23),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[235, 314, 73])).
% 0.88/1.07 tff(316,plain,
% 0.88/1.07 (~c1_1(a53)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[200, 315])).
% 0.88/1.07 tff(317,plain,
% 0.88/1.07 (~c0_1(a53)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[206, 315])).
% 0.88/1.07 tff(318,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(319,plain,
% 0.88/1.07 ((hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | c2_1(a53)) <=> (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(320,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53)))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[319])).
% 0.88/1.07 tff(321,plain,
% 0.88/1.07 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53))),
% 0.88/1.07 inference(transitivity,[status(thm)],[320, 318])).
% 0.88/1.07 tff(322,plain,
% 0.88/1.07 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | c2_1(a53))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(323,plain,
% 0.88/1.07 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.88/1.07 tff(324,plain,
% 0.88/1.07 (c2_1(a53)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[323, 160, 314, 301, 302, 317, 316, 313, 312])).
% 0.88/1.07 tff(325,plain,
% 0.88/1.07 (c3_1(a53)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[214, 315])).
% 0.88/1.07 tff(326,assumption,(hskp3), introduced(assumption)).
% 0.88/1.07 tff(327,plain,
% 0.88/1.07 (((~hskp3) | (~c2_1(a5))) <=> ((~hskp3) | (~c2_1(a5)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(328,plain,
% 0.88/1.07 (((~c2_1(a5)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a5)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(329,axiom,((~c2_1(a5)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.88/1.07 tff(330,plain,
% 0.88/1.07 ((~hskp3) | (~c2_1(a5))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.88/1.07 tff(331,plain,
% 0.88/1.07 ((~hskp3) | (~c2_1(a5))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[330, 327])).
% 0.88/1.07 tff(332,plain,
% 0.88/1.07 (~c2_1(a5)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[331, 326])).
% 0.88/1.07 tff(333,plain,
% 0.88/1.07 (((~hskp3) | (~c1_1(a5))) <=> ((~hskp3) | (~c1_1(a5)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(334,plain,
% 0.88/1.08 (((~c1_1(a5)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a5)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(335,axiom,((~c1_1(a5)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.88/1.08 tff(336,plain,
% 0.88/1.08 ((~hskp3) | (~c1_1(a5))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.88/1.08 tff(337,plain,
% 0.88/1.08 ((~hskp3) | (~c1_1(a5))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[336, 333])).
% 0.88/1.08 tff(338,plain,
% 0.88/1.08 (~c1_1(a5)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[337, 326])).
% 0.88/1.08 tff(339,assumption,(~c1_1(a53)), introduced(assumption)).
% 0.88/1.08 tff(340,assumption,(~c0_1(a53)), introduced(assumption)).
% 0.88/1.08 tff(341,assumption,(c3_1(a53)), introduced(assumption)).
% 0.88/1.08 tff(342,plain,
% 0.88/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(343,plain,
% 0.88/1.08 ((hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53))) <=> (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(344,plain,
% 0.88/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[343])).
% 0.88/1.08 tff(345,plain,
% 0.88/1.08 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53)))),
% 0.88/1.08 inference(transitivity,[status(thm)],[344, 342])).
% 0.88/1.08 tff(346,plain,
% 0.88/1.08 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(347,plain,
% 0.88/1.08 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.88/1.08 tff(348,plain,
% 0.88/1.08 (~c0_1(a5)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[347, 160, 193, 341, 340, 339, 338, 332, 65])).
% 0.88/1.08 tff(349,plain,
% 0.88/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(350,plain,
% 0.88/1.08 ((hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a5) | c0_1(a5) | c2_1(a5)) <=> (hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(351,plain,
% 0.88/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a5) | c0_1(a5) | c2_1(a5))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[350])).
% 0.88/1.08 tff(352,plain,
% 0.88/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a5) | c0_1(a5) | c2_1(a5))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31)))),
% 0.88/1.08 inference(transitivity,[status(thm)],[351, 349])).
% 0.88/1.08 tff(353,plain,
% 0.88/1.08 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a5) | c0_1(a5) | c2_1(a5))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(354,plain,
% 0.88/1.08 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.88/1.08 tff(355,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[354, 160, 314, 301, 302, 313, 338, 332, 312, 348])).
% 0.88/1.08 tff(356,plain,((~hskp3) | hskp0 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | hskp4 | (~c3_1(a53)) | c0_1(a53) | c1_1(a53)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(357,plain,
% 0.88/1.08 (~hskp3),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[356, 314, 301, 302, 313, 193, 325, 317, 316])).
% 0.88/1.08 tff(358,plain,
% 0.88/1.08 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(359,plain,
% 0.88/1.08 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | c0_1(a53)) <=> (hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(360,plain,
% 0.88/1.08 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | c0_1(a53))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[359])).
% 0.88/1.08 tff(361,plain,
% 0.88/1.08 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | c0_1(a53))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53)))),
% 0.88/1.08 inference(transitivity,[status(thm)],[360, 358])).
% 0.88/1.08 tff(362,plain,
% 0.88/1.08 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | c0_1(a53))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(363,plain,
% 0.88/1.08 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.88/1.08 tff(364,plain,
% 0.88/1.08 (hskp3 | hskp2 | (~c2_1(a53))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[363, 160, 317, 316, 23])).
% 0.88/1.08 tff(365,plain,
% 0.88/1.08 (hskp2),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[364, 357, 324])).
% 0.88/1.08 tff(366,plain,
% 0.88/1.08 (((~hskp2) | (~c3_1(a4))) <=> ((~hskp2) | (~c3_1(a4)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(367,plain,
% 0.88/1.08 (((~c3_1(a4)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a4)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(368,axiom,((~c3_1(a4)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.88/1.08 tff(369,plain,
% 0.88/1.08 ((~hskp2) | (~c3_1(a4))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.88/1.08 tff(370,plain,
% 0.88/1.08 ((~hskp2) | (~c3_1(a4))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[369, 366])).
% 0.88/1.08 tff(371,plain,
% 0.88/1.08 (~c3_1(a4)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[370, 365])).
% 0.88/1.08 tff(372,plain,
% 0.88/1.08 (((~hskp2) | c1_1(a4)) <=> ((~hskp2) | c1_1(a4))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(373,axiom,((~hskp2) | c1_1(a4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.88/1.08 tff(374,plain,
% 0.88/1.08 ((~hskp2) | c1_1(a4)),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.88/1.08 tff(375,plain,
% 0.88/1.08 ((~hskp2) | c1_1(a4)),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[374, 372])).
% 0.88/1.08 tff(376,plain,
% 0.88/1.08 ((~hskp2) | c1_1(a4)),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[375, 372])).
% 0.88/1.08 tff(377,plain,
% 0.88/1.08 ((~hskp2) | c1_1(a4)),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[376, 372])).
% 0.88/1.08 tff(378,plain,
% 0.88/1.08 ((~hskp2) | c1_1(a4)),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[377, 372])).
% 0.88/1.08 tff(379,plain,
% 0.88/1.08 (c1_1(a4)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[378, 365])).
% 0.88/1.08 tff(380,plain,
% 0.88/1.08 (((~hskp2) | (~c2_1(a4))) <=> ((~hskp2) | (~c2_1(a4)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(381,plain,
% 0.88/1.08 (((~c2_1(a4)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a4)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(382,axiom,((~c2_1(a4)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.88/1.08 tff(383,plain,
% 0.88/1.08 ((~hskp2) | (~c2_1(a4))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.88/1.08 tff(384,plain,
% 0.88/1.08 ((~hskp2) | (~c2_1(a4))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[383, 380])).
% 0.88/1.08 tff(385,plain,
% 0.88/1.08 (~c2_1(a4)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[384, 365])).
% 0.88/1.08 tff(386,assumption,(c2_1(a53)), introduced(assumption)).
% 0.88/1.08 tff(387,assumption,(~c3_1(a4)), introduced(assumption)).
% 0.88/1.08 tff(388,assumption,(c1_1(a4)), introduced(assumption)).
% 0.88/1.08 tff(389,plain,
% 0.88/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(390,plain,
% 0.88/1.08 (((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(391,plain,
% 0.88/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[390])).
% 0.88/1.08 tff(392,plain,
% 0.88/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 0.88/1.08 inference(transitivity,[status(thm)],[391, 389])).
% 0.88/1.08 tff(393,plain,
% 0.88/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(394,plain,
% 0.88/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.88/1.08 tff(395,plain,
% 0.88/1.08 (c0_1(a4) | (~c2_1(a53))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[394, 160, 341, 388, 340, 339, 387, 83])).
% 0.88/1.08 tff(396,plain,
% 0.88/1.08 (c0_1(a4)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[395, 386])).
% 0.88/1.08 tff(397,plain,
% 0.88/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.88/1.08 inference(bind,[status(th)],[])).
% 0.88/1.08 tff(398,plain,
% 0.88/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.88/1.08 inference(quant_intro,[status(thm)],[397])).
% 0.88/1.08 tff(399,plain,
% 0.88/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(400,plain,
% 0.88/1.08 (^[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)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(401,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[400])).
% 0.92/1.08 tff(402,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.92/1.08 tff(403,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.92/1.08 tff(404,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[403, 399])).
% 0.92/1.08 tff(405,plain,(
% 0.92/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.92/1.08 inference(skolemize,[status(sab)],[404])).
% 0.92/1.08 tff(406,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[405, 398])).
% 0.92/1.08 tff(407,assumption,(~c2_1(a4)), introduced(assumption)).
% 0.92/1.08 tff(408,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(409,plain,
% 0.92/1.08 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4))) <=> (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(410,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[409])).
% 0.92/1.08 tff(411,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 0.92/1.08 inference(transitivity,[status(thm)],[410, 408])).
% 0.92/1.08 tff(412,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(413,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.92/1.08 tff(414,plain,
% 0.92/1.08 ((~c0_1(a4)) | (~c3_1(a31))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[413, 160, 301, 302, 388, 407, 387, 406])).
% 0.92/1.08 tff(415,plain,
% 0.92/1.08 (~c3_1(a31)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[414, 396])).
% 0.92/1.08 tff(416,plain,
% 0.92/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(417,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[416])).
% 0.92/1.08 tff(418,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(419,plain,
% 0.92/1.08 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(420,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[419])).
% 0.92/1.08 tff(421,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.92/1.08 tff(422,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.92/1.08 tff(423,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[422, 418])).
% 0.92/1.08 tff(424,plain,(
% 0.92/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(skolemize,[status(sab)],[423])).
% 0.92/1.08 tff(425,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[424, 417])).
% 0.92/1.08 tff(426,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(427,plain,
% 0.92/1.08 (((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(428,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[427])).
% 0.92/1.08 tff(429,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53)))),
% 0.92/1.08 inference(transitivity,[status(thm)],[428, 426])).
% 0.92/1.08 tff(430,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(431,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.92/1.08 tff(432,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[431, 160, 301, 388, 340, 339, 313, 407, 387, 425, 415, 386])).
% 0.92/1.08 tff(433,plain,((~c2_1(a53)) | (~c0_1(a31)) | (~c1_1(a4)) | c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~c2_1(a31)) | (~c3_1(a53))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(434,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[433, 385, 379, 325, 317, 316, 313, 324, 371, 302, 301])).
% 0.92/1.09 tff(435,plain,(hskp0 | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | hskp4 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(436,plain,
% 0.92/1.09 (hskp0),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[435, 300, 299, 291, 169, 73])).
% 0.92/1.09 tff(437,assumption,(hskp0), introduced(assumption)).
% 0.92/1.09 tff(438,plain,
% 0.92/1.09 (~c2_1(a1)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[241, 437])).
% 0.92/1.09 tff(439,plain,
% 0.92/1.09 (~c0_1(a1)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[262, 437])).
% 0.92/1.09 tff(440,assumption,(hskp13), introduced(assumption)).
% 0.92/1.09 tff(441,plain,
% 0.92/1.09 (c3_1(a1)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[249, 437])).
% 0.92/1.09 tff(442,assumption,(~c1_1(a1)), introduced(assumption)).
% 0.92/1.09 tff(443,assumption,(~c2_1(a1)), introduced(assumption)).
% 0.92/1.09 tff(444,assumption,(~c0_1(a1)), introduced(assumption)).
% 0.92/1.09 tff(445,plain,
% 0.92/1.09 (((~hskp13) | (~c3_1(a22))) <=> ((~hskp13) | (~c3_1(a22)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(446,plain,
% 0.92/1.09 (((~c3_1(a22)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a22)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(447,axiom,((~c3_1(a22)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.92/1.09 tff(448,plain,
% 0.92/1.09 ((~hskp13) | (~c3_1(a22))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.92/1.09 tff(449,plain,
% 0.92/1.09 ((~hskp13) | (~c3_1(a22))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[448, 445])).
% 0.92/1.09 tff(450,plain,
% 0.92/1.09 (~c3_1(a22)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[449, 440])).
% 0.92/1.09 tff(451,plain,
% 0.92/1.09 (((~hskp13) | (~c2_1(a22))) <=> ((~hskp13) | (~c2_1(a22)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(452,plain,
% 0.92/1.09 (((~c2_1(a22)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a22)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(453,axiom,((~c2_1(a22)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.92/1.09 tff(454,plain,
% 0.92/1.09 ((~hskp13) | (~c2_1(a22))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.92/1.09 tff(455,plain,
% 0.92/1.09 ((~hskp13) | (~c2_1(a22))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[454, 451])).
% 0.92/1.09 tff(456,plain,
% 0.92/1.09 (~c2_1(a22)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[455, 440])).
% 0.92/1.09 tff(457,plain,
% 0.92/1.09 (((~hskp13) | (~c0_1(a22))) <=> ((~hskp13) | (~c0_1(a22)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(458,plain,
% 0.92/1.09 (((~c0_1(a22)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a22)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(459,axiom,((~c0_1(a22)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.92/1.09 tff(460,plain,
% 0.92/1.09 ((~hskp13) | (~c0_1(a22))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.92/1.09 tff(461,plain,
% 0.92/1.09 ((~hskp13) | (~c0_1(a22))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[460, 457])).
% 0.92/1.09 tff(462,plain,
% 0.92/1.09 (~c0_1(a22)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[461, 440])).
% 0.92/1.09 tff(463,assumption,(c3_1(a1)), introduced(assumption)).
% 0.92/1.09 tff(464,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(465,plain,
% 0.92/1.09 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a22) | c0_1(a22) | c2_1(a22) | c2_1(a1) | c1_1(a1) | c0_1(a1)) <=> (c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(466,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a22) | c0_1(a22) | c2_1(a22) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[465])).
% 0.92/1.09 tff(467,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a22) | c0_1(a22) | c2_1(a22) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[466, 464])).
% 0.92/1.09 tff(468,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a22) | c0_1(a22) | c2_1(a22) | c2_1(a1) | c1_1(a1) | c0_1(a1))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(469,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.92/1.09 tff(470,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[469, 160, 463, 462, 456, 450, 444, 443, 55, 442])).
% 0.92/1.09 tff(471,plain,((~hskp13) | (~c3_1(a1)) | c0_1(a1) | c2_1(a1) | c1_1(a1)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(472,plain,
% 0.92/1.09 (c1_1(a1)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[471, 441, 440, 439, 438])).
% 0.92/1.09 tff(473,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[256, 160, 73, 105, 441, 438, 104, 472])).
% 0.92/1.09 tff(474,plain,((~hskp0) | hskp24 | hskp9 | (~hskp13)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(475,plain,
% 0.92/1.09 (~hskp13),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[474, 436, 73, 105])).
% 0.92/1.09 tff(476,plain,
% 0.92/1.09 ((hskp13 | hskp9 | hskp7) <=> (hskp13 | hskp9 | hskp7)),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(477,plain,
% 0.92/1.09 (((hskp7 | hskp9) | hskp13) <=> (hskp13 | hskp9 | hskp7)),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(478,axiom,((hskp7 | hskp9) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.92/1.09 tff(479,plain,
% 0.92/1.09 (hskp13 | hskp9 | hskp7),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.92/1.09 tff(480,plain,
% 0.92/1.09 (hskp13 | hskp9 | hskp7),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[479, 476])).
% 0.92/1.09 tff(481,plain,
% 0.92/1.09 (hskp13 | hskp9 | hskp7),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[480, 476])).
% 0.92/1.09 tff(482,plain,
% 0.92/1.09 (hskp13 | hskp9 | hskp7),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[481, 476])).
% 0.92/1.09 tff(483,plain,
% 0.92/1.09 (hskp13 | hskp9 | hskp7),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[482, 476])).
% 0.92/1.09 tff(484,plain,
% 0.92/1.09 (hskp7),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[483, 475, 105])).
% 0.92/1.09 tff(485,plain,
% 0.92/1.09 (((~hskp7) | (~c2_1(a14))) <=> ((~hskp7) | (~c2_1(a14)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(486,plain,
% 0.92/1.09 (((~c2_1(a14)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a14)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(487,axiom,((~c2_1(a14)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.92/1.09 tff(488,plain,
% 0.92/1.09 ((~hskp7) | (~c2_1(a14))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.92/1.09 tff(489,plain,
% 0.92/1.09 ((~hskp7) | (~c2_1(a14))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[488, 485])).
% 0.92/1.09 tff(490,plain,
% 0.92/1.09 (~c2_1(a14)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[489, 484])).
% 0.92/1.09 tff(491,plain,
% 0.92/1.09 (((~hskp7) | c3_1(a14)) <=> ((~hskp7) | c3_1(a14))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(492,axiom,((~hskp7) | c3_1(a14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.92/1.09 tff(493,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.92/1.09 tff(494,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[493, 491])).
% 0.92/1.09 tff(495,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[494, 491])).
% 0.92/1.09 tff(496,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[495, 491])).
% 0.92/1.09 tff(497,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[496, 491])).
% 0.92/1.09 tff(498,plain,
% 0.92/1.09 (c3_1(a14)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[497, 484])).
% 0.92/1.09 tff(499,plain,
% 0.92/1.09 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(500,plain,
% 0.92/1.09 ((hskp24 | hskp9 | (~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14))) <=> (hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(501,plain,
% 0.92/1.09 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[500])).
% 0.92/1.09 tff(502,plain,
% 0.92/1.09 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[501, 499])).
% 0.92/1.09 tff(503,plain,
% 0.92/1.09 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(504,plain,
% 0.92/1.09 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.92/1.09 tff(505,plain,
% 0.92/1.09 (~c1_1(a14)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[504, 160, 73, 105, 498, 490, 104])).
% 0.92/1.09 tff(506,plain,
% 0.92/1.09 (~c2_1(a1)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[241, 436])).
% 0.92/1.09 tff(507,plain,
% 0.92/1.09 (c3_1(a1)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[249, 436])).
% 0.92/1.09 tff(508,plain,
% 0.92/1.09 (~c1_1(a1)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[256, 160, 73, 105, 507, 506, 104])).
% 0.92/1.09 tff(509,plain,
% 0.92/1.09 (~c0_1(a1)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[262, 436])).
% 0.92/1.09 tff(510,plain,
% 0.92/1.09 (((~hskp7) | c0_1(a14)) <=> ((~hskp7) | c0_1(a14))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(511,axiom,((~hskp7) | c0_1(a14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.92/1.09 tff(512,plain,
% 0.92/1.09 ((~hskp7) | c0_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.92/1.09 tff(513,plain,
% 0.92/1.09 ((~hskp7) | c0_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[512, 510])).
% 0.92/1.09 tff(514,plain,
% 0.92/1.09 ((~hskp7) | c0_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[513, 510])).
% 0.92/1.09 tff(515,plain,
% 0.92/1.09 ((~hskp7) | c0_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[514, 510])).
% 0.92/1.09 tff(516,plain,
% 0.92/1.09 ((~hskp7) | c0_1(a14)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[515, 510])).
% 0.92/1.09 tff(517,plain,
% 0.92/1.09 (c0_1(a14)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[516, 484])).
% 0.92/1.09 tff(518,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(519,plain,
% 0.92/1.09 ((hskp4 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1))) <=> (hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(520,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[519])).
% 0.92/1.09 tff(521,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[520, 518])).
% 0.92/1.09 tff(522,plain,
% 0.92/1.09 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(523,plain,
% 0.92/1.09 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.92/1.09 tff(524,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[523, 160, 169, 517, 507, 490, 509, 65, 508, 505])).
% 0.92/1.09 tff(525,plain,(hskp9 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(526,plain,
% 0.92/1.09 (hskp9),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[525, 73])).
% 0.92/1.09 tff(527,plain,
% 0.92/1.09 (((~hskp9) | (~c3_1(a16))) <=> ((~hskp9) | (~c3_1(a16)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(528,plain,
% 0.92/1.09 (((~c3_1(a16)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a16)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(529,axiom,((~c3_1(a16)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.92/1.09 tff(530,plain,
% 0.92/1.09 ((~hskp9) | (~c3_1(a16))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.92/1.09 tff(531,plain,
% 0.92/1.09 ((~hskp9) | (~c3_1(a16))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[530, 527])).
% 0.92/1.09 tff(532,plain,
% 0.92/1.09 (~c3_1(a16)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[531, 526])).
% 0.92/1.09 tff(533,plain,
% 0.92/1.09 (((~hskp9) | (~c2_1(a16))) <=> ((~hskp9) | (~c2_1(a16)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(534,plain,
% 0.92/1.09 (((~c2_1(a16)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a16)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(535,axiom,((~c2_1(a16)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.92/1.09 tff(536,plain,
% 0.92/1.09 ((~hskp9) | (~c2_1(a16))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.92/1.09 tff(537,plain,
% 0.92/1.09 ((~hskp9) | (~c2_1(a16))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[536, 533])).
% 0.92/1.09 tff(538,plain,
% 0.92/1.09 (~c2_1(a16)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[537, 526])).
% 0.92/1.09 tff(539,plain,
% 0.92/1.09 (((~hskp9) | c0_1(a16)) <=> ((~hskp9) | c0_1(a16))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(540,axiom,((~hskp9) | c0_1(a16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.92/1.09 tff(541,plain,
% 0.92/1.09 ((~hskp9) | c0_1(a16)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[540, 539])).
% 0.92/1.09 tff(542,plain,
% 0.92/1.09 ((~hskp9) | c0_1(a16)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[541, 539])).
% 0.92/1.09 tff(543,plain,
% 0.92/1.09 ((~hskp9) | c0_1(a16)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[542, 539])).
% 0.92/1.09 tff(544,plain,
% 0.92/1.09 ((~hskp9) | c0_1(a16)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[543, 539])).
% 0.92/1.09 tff(545,plain,
% 0.92/1.09 ((~hskp9) | c0_1(a16)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[544, 539])).
% 0.92/1.09 tff(546,plain,
% 0.92/1.09 (c0_1(a16)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[545, 526])).
% 0.92/1.09 tff(547,plain,
% 0.92/1.09 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(548,plain,
% 0.92/1.09 ((hskp26 | hskp16 | (~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c0_1(a16))) <=> (hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(549,plain,
% 0.92/1.09 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[548])).
% 0.92/1.09 tff(550,plain,
% 0.92/1.09 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[549, 547])).
% 0.92/1.09 tff(551,plain,
% 0.92/1.09 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c0_1(a16)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(552,plain,
% 0.92/1.09 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.92/1.09 tff(553,plain,
% 0.92/1.09 (hskp26 | hskp16),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[552, 160, 546, 538, 532, 94])).
% 0.92/1.09 tff(554,plain,
% 0.92/1.09 (hskp16),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[553, 84])).
% 0.92/1.09 tff(555,plain,
% 0.92/1.09 (((~hskp16) | c1_1(a30)) <=> ((~hskp16) | c1_1(a30))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(556,axiom,((~hskp16) | c1_1(a30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.92/1.09 tff(557,plain,
% 0.92/1.09 ((~hskp16) | c1_1(a30)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.92/1.09 tff(558,plain,
% 0.92/1.09 ((~hskp16) | c1_1(a30)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[557, 555])).
% 0.92/1.09 tff(559,plain,
% 0.92/1.09 ((~hskp16) | c1_1(a30)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[558, 555])).
% 0.92/1.09 tff(560,plain,
% 0.92/1.09 ((~hskp16) | c1_1(a30)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[559, 555])).
% 0.92/1.09 tff(561,plain,
% 0.92/1.09 ((~hskp16) | c1_1(a30)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[560, 555])).
% 0.92/1.09 tff(562,plain,
% 0.92/1.09 (c1_1(a30)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[561, 554])).
% 0.92/1.09 tff(563,plain,
% 0.92/1.09 (((~hskp16) | (~c2_1(a30))) <=> ((~hskp16) | (~c2_1(a30)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(564,plain,
% 0.92/1.09 (((~c2_1(a30)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a30)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(565,axiom,((~c2_1(a30)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.92/1.09 tff(566,plain,
% 0.92/1.09 ((~hskp16) | (~c2_1(a30))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.92/1.09 tff(567,plain,
% 0.92/1.09 ((~hskp16) | (~c2_1(a30))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[566, 563])).
% 0.92/1.09 tff(568,plain,
% 0.92/1.09 (~c2_1(a30)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[567, 554])).
% 0.92/1.09 tff(569,plain,
% 0.92/1.09 (((~hskp16) | (~c0_1(a30))) <=> ((~hskp16) | (~c0_1(a30)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(570,plain,
% 0.92/1.09 (((~c0_1(a30)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a30)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(571,axiom,((~c0_1(a30)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.92/1.09 tff(572,plain,
% 0.92/1.09 ((~hskp16) | (~c0_1(a30))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.92/1.09 tff(573,plain,
% 0.92/1.09 ((~hskp16) | (~c0_1(a30))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[572, 569])).
% 0.92/1.09 tff(574,plain,
% 0.92/1.09 (~c0_1(a30)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[573, 554])).
% 0.92/1.09 tff(575,plain,
% 0.92/1.09 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(576,plain,
% 0.92/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[575])).
% 0.92/1.09 tff(577,plain,
% 0.92/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(578,plain,
% 0.92/1.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(579,plain,
% 0.92/1.09 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[578])).
% 0.92/1.09 tff(580,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.92/1.09 tff(581,plain,
% 0.92/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.92/1.09 tff(582,plain,
% 0.92/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[581, 577])).
% 0.92/1.09 tff(583,plain,(
% 0.92/1.09 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[582])).
% 0.92/1.09 tff(584,plain,
% 0.92/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[583, 576])).
% 0.92/1.09 tff(585,assumption,(~c0_1(a30)), introduced(assumption)).
% 0.92/1.09 tff(586,assumption,(c1_1(a30)), introduced(assumption)).
% 0.92/1.09 tff(587,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(588,plain,
% 0.92/1.09 ((hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(589,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[588])).
% 0.92/1.09 tff(590,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[589, 587])).
% 0.92/1.09 tff(591,plain,
% 0.92/1.09 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(592,plain,
% 0.92/1.09 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.92/1.09 tff(593,plain,
% 0.92/1.09 (hskp4 | (~c3_1(a30))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[592, 160, 586, 546, 585, 532, 584, 3])).
% 0.92/1.09 tff(594,plain,
% 0.92/1.09 (~c3_1(a30)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[593, 193])).
% 0.92/1.09 tff(595,assumption,(~hskp17), introduced(assumption)).
% 0.92/1.09 tff(596,plain,
% 0.92/1.09 (hskp8),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[282, 193, 595])).
% 0.92/1.09 tff(597,plain,
% 0.92/1.09 (~c2_1(a15)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[175, 596])).
% 0.92/1.09 tff(598,plain,
% 0.92/1.09 (c0_1(a15)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[183, 596])).
% 0.92/1.09 tff(599,plain,
% 0.92/1.09 (~c1_1(a15)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[189, 596])).
% 0.92/1.09 tff(600,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[223, 599, 598, 193, 195, 597])).
% 0.92/1.09 tff(601,plain,(hskp4 | (~hskp23) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(602,plain,
% 0.92/1.09 (hskp4),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[601, 315, 595])).
% 0.92/1.09 tff(603,plain,
% 0.92/1.09 (~c2_1(a6)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[111, 602])).
% 0.92/1.09 tff(604,plain,
% 0.92/1.09 (c3_1(a6)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[119, 602])).
% 0.92/1.09 tff(605,plain,
% 0.92/1.09 (c1_1(a6)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[127, 602])).
% 0.92/1.09 tff(606,assumption,(~hskp2), introduced(assumption)).
% 0.92/1.09 tff(607,assumption,(~hskp14), introduced(assumption)).
% 0.92/1.09 tff(608,assumption,(hskp26), introduced(assumption)).
% 0.92/1.09 tff(609,plain,
% 0.92/1.09 (((~hskp26) | c0_1(a10)) <=> ((~hskp26) | c0_1(a10))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(610,axiom,((~hskp26) | c0_1(a10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.92/1.09 tff(611,plain,
% 0.92/1.09 ((~hskp26) | c0_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.92/1.09 tff(612,plain,
% 0.92/1.09 ((~hskp26) | c0_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[611, 609])).
% 0.92/1.09 tff(613,plain,
% 0.92/1.09 ((~hskp26) | c0_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[612, 609])).
% 0.92/1.09 tff(614,plain,
% 0.92/1.09 ((~hskp26) | c0_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[613, 609])).
% 0.92/1.09 tff(615,plain,
% 0.92/1.09 ((~hskp26) | c0_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[614, 609])).
% 0.92/1.09 tff(616,plain,
% 0.92/1.09 (c0_1(a10)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[615, 608])).
% 0.92/1.09 tff(617,assumption,(hskp9), introduced(assumption)).
% 0.92/1.09 tff(618,plain,
% 0.92/1.09 (((~hskp26) | c2_1(a10)) <=> ((~hskp26) | c2_1(a10))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(619,axiom,((~hskp26) | c2_1(a10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.92/1.09 tff(620,plain,
% 0.92/1.09 ((~hskp26) | c2_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.92/1.09 tff(621,plain,
% 0.92/1.09 ((~hskp26) | c2_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[620, 618])).
% 0.92/1.09 tff(622,plain,
% 0.92/1.09 ((~hskp26) | c2_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[621, 618])).
% 0.92/1.09 tff(623,plain,
% 0.92/1.09 ((~hskp26) | c2_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[622, 618])).
% 0.92/1.09 tff(624,plain,
% 0.92/1.09 ((~hskp26) | c2_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[623, 618])).
% 0.92/1.09 tff(625,plain,
% 0.92/1.09 (c2_1(a10)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[624, 608])).
% 0.92/1.09 tff(626,plain,
% 0.92/1.09 (((~hskp26) | c3_1(a10)) <=> ((~hskp26) | c3_1(a10))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(627,axiom,((~hskp26) | c3_1(a10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.92/1.09 tff(628,plain,
% 0.92/1.09 ((~hskp26) | c3_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.92/1.09 tff(629,plain,
% 0.92/1.09 ((~hskp26) | c3_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[628, 626])).
% 0.92/1.09 tff(630,plain,
% 0.92/1.09 ((~hskp26) | c3_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[629, 626])).
% 0.92/1.09 tff(631,plain,
% 0.92/1.09 ((~hskp26) | c3_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[630, 626])).
% 0.92/1.09 tff(632,plain,
% 0.92/1.09 ((~hskp26) | c3_1(a10)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[631, 626])).
% 0.92/1.09 tff(633,plain,
% 0.92/1.09 (c3_1(a10)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[632, 608])).
% 0.92/1.09 tff(634,plain,
% 0.92/1.09 (^[U: $i] : refl((hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(635,plain,
% 0.92/1.09 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[634])).
% 0.92/1.09 tff(636,plain,
% 0.92/1.09 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(637,plain,
% 0.92/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp14) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp14))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp14) <=> (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp14) <=> (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(638,plain,
% 0.92/1.10 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp14) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[637])).
% 0.92/1.10 tff(639,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.92/1.10 tff(640,plain,
% 0.92/1.10 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.92/1.10 tff(641,plain,
% 0.92/1.10 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[640, 636])).
% 0.92/1.10 tff(642,plain,(
% 0.92/1.10 ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[641])).
% 0.92/1.10 tff(643,plain,
% 0.92/1.10 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[642, 635])).
% 0.92/1.10 tff(644,plain,
% 0.92/1.10 (~c2_1(a16)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[537, 617])).
% 0.92/1.10 tff(645,plain,
% 0.92/1.10 (c0_1(a16)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[545, 617])).
% 0.92/1.10 tff(646,plain,
% 0.92/1.10 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(647,plain,
% 0.92/1.10 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16))) <=> (hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(648,plain,
% 0.92/1.10 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[647])).
% 0.92/1.10 tff(649,plain,
% 0.92/1.10 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[648, 646])).
% 0.92/1.10 tff(650,plain,
% 0.92/1.10 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(651,plain,
% 0.92/1.10 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.92/1.10 tff(652,plain,
% 0.92/1.10 (c1_1(a16)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[651, 160, 607, 606, 645, 644, 643])).
% 0.92/1.10 tff(653,plain,
% 0.92/1.10 (~c3_1(a16)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[531, 617])).
% 0.92/1.10 tff(654,assumption,(c3_1(a10)), introduced(assumption)).
% 0.92/1.10 tff(655,assumption,(c2_1(a10)), introduced(assumption)).
% 0.92/1.10 tff(656,assumption,(c0_1(a10)), introduced(assumption)).
% 0.92/1.10 tff(657,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(658,plain,
% 0.92/1.10 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(659,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[658])).
% 0.92/1.10 tff(660,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[659, 657])).
% 0.92/1.10 tff(661,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(662,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.92/1.10 tff(663,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[662, 160, 656, 655, 654, 645, 644, 653, 406, 652])).
% 0.92/1.10 tff(664,plain,((~hskp9) | (~c0_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(665,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[664, 633, 625, 617, 606, 607, 616])).
% 0.92/1.10 tff(666,plain,((~hskp26) | (~hskp9) | hskp2 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(667,plain,
% 0.92/1.10 (~hskp26),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[666, 607, 606, 526])).
% 0.92/1.10 tff(668,assumption,(c0_1(a16)), introduced(assumption)).
% 0.92/1.10 tff(669,plain,
% 0.92/1.10 (hskp14 | hskp2 | c1_1(a16)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[651, 160, 668, 24, 643])).
% 0.92/1.10 tff(670,plain,
% 0.92/1.10 (c1_1(a16)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[669, 607, 606])).
% 0.92/1.10 tff(671,assumption,(~c2_1(a6)), introduced(assumption)).
% 0.92/1.10 tff(672,assumption,(c3_1(a6)), introduced(assumption)).
% 0.92/1.10 tff(673,assumption,(c1_1(a6)), introduced(assumption)).
% 0.92/1.10 tff(674,assumption,(~hskp18), introduced(assumption)).
% 0.92/1.10 tff(675,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(676,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[675])).
% 0.92/1.10 tff(677,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(678,plain,
% 0.92/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp18) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp18))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp18) <=> (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp18) <=> (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(679,plain,
% 0.92/1.10 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp18) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[678])).
% 0.92/1.10 tff(680,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.92/1.10 tff(681,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.92/1.10 tff(682,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[681, 677])).
% 0.92/1.10 tff(683,plain,(
% 0.92/1.10 ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[682])).
% 0.92/1.10 tff(684,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[683, 676])).
% 0.92/1.10 tff(685,assumption,(hskp27), introduced(assumption)).
% 0.92/1.10 tff(686,plain,
% 0.92/1.10 (((~hskp27) | c3_1(a11)) <=> ((~hskp27) | c3_1(a11))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(687,axiom,((~hskp27) | c3_1(a11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.92/1.10 tff(688,plain,
% 0.92/1.10 ((~hskp27) | c3_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.92/1.10 tff(689,plain,
% 0.92/1.10 ((~hskp27) | c3_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[688, 686])).
% 0.92/1.10 tff(690,plain,
% 0.92/1.10 ((~hskp27) | c3_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[689, 686])).
% 0.92/1.10 tff(691,plain,
% 0.92/1.10 ((~hskp27) | c3_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[690, 686])).
% 0.92/1.10 tff(692,plain,
% 0.92/1.10 ((~hskp27) | c3_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[691, 686])).
% 0.92/1.10 tff(693,plain,
% 0.92/1.10 (c3_1(a11)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[692, 685])).
% 0.92/1.10 tff(694,plain,
% 0.92/1.10 (((~hskp27) | c0_1(a11)) <=> ((~hskp27) | c0_1(a11))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(695,axiom,((~hskp27) | c0_1(a11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.92/1.10 tff(696,plain,
% 0.92/1.10 ((~hskp27) | c0_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.92/1.10 tff(697,plain,
% 0.92/1.10 ((~hskp27) | c0_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[696, 694])).
% 0.92/1.10 tff(698,plain,
% 0.92/1.10 ((~hskp27) | c0_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[697, 694])).
% 0.92/1.10 tff(699,plain,
% 0.92/1.10 ((~hskp27) | c0_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[698, 694])).
% 0.92/1.10 tff(700,plain,
% 0.92/1.10 ((~hskp27) | c0_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[699, 694])).
% 0.92/1.10 tff(701,plain,
% 0.92/1.10 (c0_1(a11)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[700, 685])).
% 0.92/1.10 tff(702,plain,
% 0.92/1.10 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(703,plain,
% 0.92/1.10 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a11) | (~c0_1(a11)) | (~c3_1(a11))) <=> (hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(704,plain,
% 0.92/1.10 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a11) | (~c0_1(a11)) | (~c3_1(a11)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[703])).
% 0.92/1.10 tff(705,plain,
% 0.92/1.10 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a11) | (~c0_1(a11)) | (~c3_1(a11)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11))),
% 0.92/1.10 inference(transitivity,[status(thm)],[704, 702])).
% 0.92/1.10 tff(706,plain,
% 0.92/1.10 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a11) | (~c0_1(a11)) | (~c3_1(a11)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(707,plain,
% 0.92/1.10 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.92/1.10 tff(708,plain,
% 0.92/1.10 (c2_1(a11)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[707, 160, 674, 595, 701, 693, 684])).
% 0.92/1.10 tff(709,assumption,(c1_1(a16)), introduced(assumption)).
% 0.92/1.10 tff(710,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(711,plain,
% 0.92/1.10 (((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(712,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[711])).
% 0.92/1.10 tff(713,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[712, 710])).
% 0.92/1.10 tff(714,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(715,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.92/1.10 tff(716,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[715, 160, 701, 693, 668, 24, 2, 406, 709, 708])).
% 0.92/1.10 tff(717,plain,((~hskp27) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | hskp18 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(718,plain,
% 0.92/1.10 (~hskp27),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[717, 674, 24, 2, 670, 668, 595])).
% 0.92/1.10 tff(719,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(720,plain,
% 0.92/1.10 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[719])).
% 0.92/1.10 tff(721,plain,
% 0.92/1.10 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(722,plain,
% 0.92/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp26) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp26))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp26) <=> (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp26) <=> (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(723,plain,
% 0.92/1.10 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp26) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[722])).
% 0.92/1.10 tff(724,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.92/1.10 tff(725,plain,
% 0.92/1.10 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.92/1.10 tff(726,plain,
% 0.92/1.10 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[725, 721])).
% 0.92/1.10 tff(727,plain,(
% 0.92/1.10 ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[726])).
% 0.92/1.10 tff(728,plain,
% 0.92/1.10 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[727, 720])).
% 0.92/1.10 tff(729,assumption,(~hskp3), introduced(assumption)).
% 0.92/1.10 tff(730,assumption,(hskp21), introduced(assumption)).
% 0.92/1.10 tff(731,plain,
% 0.92/1.10 (((~hskp21) | c3_1(a42)) <=> ((~hskp21) | c3_1(a42))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(732,axiom,((~hskp21) | c3_1(a42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.92/1.10 tff(733,plain,
% 0.92/1.10 ((~hskp21) | c3_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.92/1.10 tff(734,plain,
% 0.92/1.10 ((~hskp21) | c3_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[733, 731])).
% 0.92/1.10 tff(735,plain,
% 0.92/1.10 ((~hskp21) | c3_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[734, 731])).
% 0.92/1.10 tff(736,plain,
% 0.92/1.10 ((~hskp21) | c3_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[735, 731])).
% 0.92/1.10 tff(737,plain,
% 0.92/1.10 ((~hskp21) | c3_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[736, 731])).
% 0.92/1.10 tff(738,plain,
% 0.92/1.10 (c3_1(a42)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[737, 730])).
% 0.92/1.10 tff(739,plain,
% 0.92/1.10 (((~hskp21) | c2_1(a42)) <=> ((~hskp21) | c2_1(a42))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(740,axiom,((~hskp21) | c2_1(a42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.92/1.10 tff(741,plain,
% 0.92/1.10 ((~hskp21) | c2_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.92/1.10 tff(742,plain,
% 0.92/1.10 ((~hskp21) | c2_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[741, 739])).
% 0.92/1.10 tff(743,plain,
% 0.92/1.10 ((~hskp21) | c2_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[742, 739])).
% 0.92/1.10 tff(744,plain,
% 0.92/1.10 ((~hskp21) | c2_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[743, 739])).
% 0.92/1.10 tff(745,plain,
% 0.92/1.10 ((~hskp21) | c2_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[744, 739])).
% 0.92/1.10 tff(746,plain,
% 0.92/1.10 (c2_1(a42)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[745, 730])).
% 0.92/1.10 tff(747,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(748,plain,
% 0.92/1.10 (((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(749,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[748])).
% 0.92/1.10 tff(750,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[749, 747])).
% 0.92/1.10 tff(751,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(752,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[751, 750])).
% 0.92/1.10 tff(753,plain,
% 0.92/1.10 (~c0_1(a42)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[752, 160, 746, 738, 668, 24, 2, 406, 709])).
% 0.92/1.10 tff(754,plain,
% 0.92/1.10 (((~hskp21) | (~c1_1(a42))) <=> ((~hskp21) | (~c1_1(a42)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(755,plain,
% 0.92/1.10 (((~c1_1(a42)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a42)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(756,axiom,((~c1_1(a42)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.92/1.10 tff(757,plain,
% 0.92/1.10 ((~hskp21) | (~c1_1(a42))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.92/1.10 tff(758,plain,
% 0.92/1.10 ((~hskp21) | (~c1_1(a42))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[757, 754])).
% 0.92/1.10 tff(759,plain,
% 0.92/1.10 (~c1_1(a42)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[758, 730])).
% 0.92/1.10 tff(760,plain,
% 0.92/1.10 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(761,plain,
% 0.92/1.10 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | c0_1(a42)) <=> (hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(762,plain,
% 0.92/1.10 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | c0_1(a42))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[761])).
% 0.92/1.10 tff(763,plain,
% 0.92/1.10 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | c0_1(a42))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42))),
% 0.92/1.10 inference(transitivity,[status(thm)],[762, 760])).
% 0.92/1.10 tff(764,plain,
% 0.92/1.10 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | c0_1(a42))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(765,plain,
% 0.92/1.10 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[764, 763])).
% 0.92/1.10 tff(766,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[765, 160, 729, 606, 746, 759, 23, 753])).
% 0.92/1.10 tff(767,plain,((~hskp21) | hskp3 | hskp2 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(768,plain,
% 0.92/1.10 (~hskp21),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[767, 729, 606, 668, 24, 2, 709])).
% 0.92/1.10 tff(769,plain,
% 0.92/1.10 (hskp25),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[158, 768, 595])).
% 0.92/1.10 tff(770,plain,
% 0.92/1.10 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(771,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[770])).
% 0.92/1.10 tff(772,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(773,plain,
% 0.92/1.10 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(774,plain,
% 0.92/1.10 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[773])).
% 0.92/1.10 tff(775,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.92/1.11 tff(776,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.92/1.11 tff(777,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[776, 772])).
% 0.92/1.11 tff(778,plain,(
% 0.92/1.11 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[777])).
% 0.92/1.11 tff(779,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[778, 771])).
% 0.92/1.11 tff(780,assumption,(hskp25), introduced(assumption)).
% 0.92/1.11 tff(781,plain,
% 0.92/1.11 (((~hskp25) | c2_1(a9)) <=> ((~hskp25) | c2_1(a9))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(782,axiom,((~hskp25) | c2_1(a9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.92/1.11 tff(783,plain,
% 0.92/1.11 ((~hskp25) | c2_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.92/1.11 tff(784,plain,
% 0.92/1.11 ((~hskp25) | c2_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[783, 781])).
% 0.92/1.11 tff(785,plain,
% 0.92/1.11 ((~hskp25) | c2_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[784, 781])).
% 0.92/1.11 tff(786,plain,
% 0.92/1.11 ((~hskp25) | c2_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[785, 781])).
% 0.92/1.11 tff(787,plain,
% 0.92/1.11 ((~hskp25) | c2_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[786, 781])).
% 0.92/1.11 tff(788,plain,
% 0.92/1.11 (c2_1(a9)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[787, 780])).
% 0.92/1.11 tff(789,plain,
% 0.92/1.11 (((~hskp25) | c1_1(a9)) <=> ((~hskp25) | c1_1(a9))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(790,axiom,((~hskp25) | c1_1(a9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.92/1.11 tff(791,plain,
% 0.92/1.11 ((~hskp25) | c1_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.92/1.11 tff(792,plain,
% 0.92/1.11 ((~hskp25) | c1_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[791, 789])).
% 0.92/1.11 tff(793,plain,
% 0.92/1.11 ((~hskp25) | c1_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[792, 789])).
% 0.92/1.11 tff(794,plain,
% 0.92/1.11 ((~hskp25) | c1_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[793, 789])).
% 0.92/1.11 tff(795,plain,
% 0.92/1.11 ((~hskp25) | c1_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[794, 789])).
% 0.92/1.11 tff(796,plain,
% 0.92/1.11 (c1_1(a9)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[795, 780])).
% 0.92/1.11 tff(797,plain,
% 0.92/1.11 (((~hskp25) | c0_1(a9)) <=> ((~hskp25) | c0_1(a9))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(798,axiom,((~hskp25) | c0_1(a9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.92/1.11 tff(799,plain,
% 0.92/1.11 ((~hskp25) | c0_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[798, 797])).
% 0.92/1.11 tff(800,plain,
% 0.92/1.11 ((~hskp25) | c0_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[799, 797])).
% 0.92/1.11 tff(801,plain,
% 0.92/1.11 ((~hskp25) | c0_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[800, 797])).
% 0.92/1.11 tff(802,plain,
% 0.92/1.11 ((~hskp25) | c0_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[801, 797])).
% 0.92/1.11 tff(803,plain,
% 0.92/1.11 ((~hskp25) | c0_1(a9)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[802, 797])).
% 0.92/1.11 tff(804,plain,
% 0.92/1.11 (c0_1(a9)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[803, 780])).
% 0.92/1.11 tff(805,assumption,(~hskp19), introduced(assumption)).
% 0.92/1.11 tff(806,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(807,plain,
% 0.92/1.11 ((hskp19 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6))) <=> (hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(808,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[807])).
% 0.92/1.11 tff(809,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[808, 806])).
% 0.92/1.11 tff(810,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(811,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.92/1.11 tff(812,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[811, 160, 805, 804, 796, 788, 673, 672, 671, 779])).
% 0.92/1.11 tff(813,plain,((~hskp25) | hskp19 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(814,plain,
% 0.92/1.11 (hskp19),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[813, 769, 673, 672, 671])).
% 0.92/1.11 tff(815,plain,
% 0.92/1.11 (((~hskp19) | (~c0_1(a33))) <=> ((~hskp19) | (~c0_1(a33)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(816,plain,
% 0.92/1.11 (((~c0_1(a33)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a33)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(817,axiom,((~c0_1(a33)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.92/1.11 tff(818,plain,
% 0.92/1.11 ((~hskp19) | (~c0_1(a33))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.92/1.11 tff(819,plain,
% 0.92/1.11 ((~hskp19) | (~c0_1(a33))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[818, 815])).
% 0.92/1.11 tff(820,plain,
% 0.92/1.11 (~c0_1(a33)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[819, 814])).
% 0.92/1.11 tff(821,plain,
% 0.92/1.11 (((~hskp19) | c2_1(a33)) <=> ((~hskp19) | c2_1(a33))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(822,axiom,((~hskp19) | c2_1(a33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.92/1.11 tff(823,plain,
% 0.92/1.11 ((~hskp19) | c2_1(a33)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.92/1.11 tff(824,plain,
% 0.92/1.11 ((~hskp19) | c2_1(a33)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[823, 821])).
% 0.92/1.11 tff(825,plain,
% 0.92/1.11 ((~hskp19) | c2_1(a33)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[824, 821])).
% 0.92/1.11 tff(826,plain,
% 0.92/1.11 ((~hskp19) | c2_1(a33)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[825, 821])).
% 0.92/1.11 tff(827,plain,
% 0.92/1.11 ((~hskp19) | c2_1(a33)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[826, 821])).
% 0.92/1.11 tff(828,plain,
% 0.92/1.11 (c2_1(a33)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[827, 814])).
% 0.92/1.11 tff(829,assumption,(~hskp27), introduced(assumption)).
% 0.92/1.11 tff(830,plain,
% 0.92/1.11 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(831,plain,
% 0.92/1.11 ((hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33))) <=> (hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(832,plain,
% 0.92/1.11 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[831])).
% 0.92/1.11 tff(833,plain,
% 0.92/1.11 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[832, 830])).
% 0.92/1.11 tff(834,plain,
% 0.92/1.11 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(835,plain,
% 0.92/1.11 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.92/1.11 tff(836,plain,
% 0.92/1.11 (~c1_1(a33)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[835, 829, 160, 84, 828, 820, 728])).
% 0.92/1.11 tff(837,plain,
% 0.92/1.11 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(838,plain,
% 0.92/1.11 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | c0_1(a33)) <=> (hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(839,plain,
% 0.92/1.11 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | c0_1(a33))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33)))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[838])).
% 0.92/1.11 tff(840,plain,
% 0.92/1.11 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | c0_1(a33))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33))),
% 0.92/1.11 inference(transitivity,[status(thm)],[839, 837])).
% 0.92/1.11 tff(841,plain,
% 0.92/1.11 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | c0_1(a33))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(842,plain,
% 0.92/1.11 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.92/1.11 tff(843,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[842, 160, 729, 606, 828, 820, 23, 836])).
% 0.92/1.11 tff(844,plain,(hskp3 | hskp2 | hskp27 | hskp26 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | hskp17 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(845,plain,
% 0.92/1.11 (hskp3),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[844, 718, 606, 84, 673, 672, 671, 595, 668, 24, 2, 670])).
% 0.92/1.11 tff(846,plain,
% 0.92/1.11 (~c2_1(a5)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[331, 845])).
% 0.92/1.11 tff(847,plain,
% 0.92/1.11 (~c1_1(a5)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[337, 845])).
% 0.92/1.11 tff(848,plain,
% 0.92/1.11 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(849,plain,
% 0.92/1.11 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5))) <=> (hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(850,plain,
% 0.92/1.11 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[849])).
% 0.92/1.11 tff(851,plain,
% 0.92/1.11 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[850, 848])).
% 0.92/1.11 tff(852,plain,
% 0.92/1.11 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(853,plain,
% 0.92/1.11 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.92/1.11 tff(854,plain,
% 0.92/1.11 (~c0_1(a5)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[853, 160, 607, 606, 847, 846, 643])).
% 0.92/1.11 tff(855,plain,
% 0.92/1.11 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(856,plain,
% 0.92/1.11 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a6) | (~c0_1(a6)) | (~c3_1(a6))) <=> (hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(857,plain,
% 0.92/1.11 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a6) | (~c0_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[856])).
% 0.92/1.11 tff(858,plain,
% 0.92/1.11 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a6) | (~c0_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[857, 855])).
% 0.92/1.11 tff(859,plain,
% 0.92/1.11 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a6) | (~c0_1(a6)) | (~c3_1(a6)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(860,plain,
% 0.92/1.11 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[859, 858])).
% 0.92/1.11 tff(861,plain,
% 0.92/1.11 (hskp18 | (~c0_1(a6))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[860, 160, 595, 672, 671, 684])).
% 0.92/1.11 tff(862,plain,
% 0.92/1.11 (~c0_1(a6)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[861, 674])).
% 0.92/1.11 tff(863,plain,
% 0.92/1.11 (((~hskp3) | (~c3_1(a5))) <=> ((~hskp3) | (~c3_1(a5)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(864,plain,
% 0.92/1.11 (((~c3_1(a5)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a5)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(865,axiom,((~c3_1(a5)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.92/1.11 tff(866,plain,
% 0.92/1.11 ((~hskp3) | (~c3_1(a5))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.92/1.11 tff(867,plain,
% 0.92/1.11 ((~hskp3) | (~c3_1(a5))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[866, 863])).
% 0.92/1.11 tff(868,plain,
% 0.92/1.11 (~c3_1(a5)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[867, 845])).
% 0.92/1.11 tff(869,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(870,plain,
% 0.92/1.11 (((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5)) <=> (c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(871,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6)))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[870])).
% 0.92/1.11 tff(872,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6))),
% 0.92/1.11 inference(transitivity,[status(thm)],[871, 869])).
% 0.92/1.11 tff(873,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(874,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.92/1.11 tff(875,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[874, 160, 672, 671, 847, 846, 868, 55, 862, 854])).
% 0.92/1.11 tff(876,plain,(hskp18 | (~c3_1(a6)) | c2_1(a6) | hskp14 | hskp2 | hskp26 | (~c1_1(a6)) | hskp17 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(877,plain,
% 0.92/1.11 (hskp18),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[876, 607, 603, 604, 606, 667, 605, 595, 546, 538, 532])).
% 0.92/1.11 tff(878,plain,
% 0.92/1.11 (((~hskp18) | (~c1_1(a32))) <=> ((~hskp18) | (~c1_1(a32)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(879,plain,
% 0.92/1.11 (((~c1_1(a32)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a32)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(880,axiom,((~c1_1(a32)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.92/1.11 tff(881,plain,
% 0.92/1.11 ((~hskp18) | (~c1_1(a32))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.92/1.11 tff(882,plain,
% 0.92/1.11 ((~hskp18) | (~c1_1(a32))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[881, 878])).
% 0.92/1.11 tff(883,plain,
% 0.92/1.11 (~c1_1(a32)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[882, 877])).
% 0.92/1.11 tff(884,plain,
% 0.92/1.11 (((~hskp18) | (~c3_1(a32))) <=> ((~hskp18) | (~c3_1(a32)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(885,plain,
% 0.92/1.11 (((~c3_1(a32)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a32)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(886,axiom,((~c3_1(a32)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.92/1.11 tff(887,plain,
% 0.92/1.11 ((~hskp18) | (~c3_1(a32))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.92/1.11 tff(888,plain,
% 0.92/1.11 ((~hskp18) | (~c3_1(a32))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[887, 884])).
% 0.92/1.11 tff(889,plain,
% 0.92/1.11 (~c3_1(a32)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[888, 877])).
% 0.92/1.11 tff(890,plain,
% 0.92/1.11 (hskp14 | hskp2 | c1_1(a16)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[651, 160, 546, 538, 643])).
% 0.92/1.11 tff(891,plain,
% 0.92/1.11 (c1_1(a16)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[890, 607, 606])).
% 0.92/1.11 tff(892,plain,
% 0.92/1.11 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(893,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[892])).
% 0.92/1.11 tff(894,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(895,plain,
% 0.92/1.11 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(896,plain,
% 0.92/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[895])).
% 0.92/1.11 tff(897,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.92/1.11 tff(898,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.92/1.11 tff(899,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[898, 894])).
% 0.92/1.11 tff(900,plain,(
% 0.92/1.11 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.11 inference(skolemize,[status(sab)],[899])).
% 0.92/1.11 tff(901,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[900, 893])).
% 0.92/1.11 tff(902,assumption,(~c3_1(a32)), introduced(assumption)).
% 0.92/1.11 tff(903,assumption,(~c1_1(a32)), introduced(assumption)).
% 0.92/1.11 tff(904,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(905,plain,
% 0.92/1.11 ((hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(906,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[905])).
% 0.92/1.11 tff(907,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[906, 904])).
% 0.92/1.11 tff(908,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(909,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.92/1.11 tff(910,plain,
% 0.92/1.11 (c0_1(a32)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[909, 160, 73, 546, 903, 902, 532, 901, 891])).
% 0.92/1.11 tff(911,plain,
% 0.92/1.11 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(912,plain,
% 0.92/1.11 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a32) | c2_1(a32) | (~c0_1(a32))) <=> (hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(913,plain,
% 0.92/1.11 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a32) | c2_1(a32) | (~c0_1(a32)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[912])).
% 0.92/1.12 tff(914,plain,
% 0.92/1.12 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a32) | c2_1(a32) | (~c0_1(a32)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32))),
% 0.92/1.12 inference(transitivity,[status(thm)],[913, 911])).
% 0.92/1.12 tff(915,plain,
% 0.92/1.12 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a32) | c2_1(a32) | (~c0_1(a32)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(916,plain,
% 0.92/1.12 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[915, 914])).
% 0.92/1.12 tff(917,plain,
% 0.92/1.12 ((~c0_1(a32)) | c2_1(a32)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[916, 160, 607, 606, 903, 643])).
% 0.92/1.12 tff(918,plain,
% 0.92/1.12 (c2_1(a32)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[917, 910])).
% 0.92/1.12 tff(919,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(920,plain,
% 0.92/1.12 (((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(921,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[920])).
% 0.92/1.12 tff(922,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[921, 919])).
% 0.92/1.12 tff(923,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(924,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.92/1.12 tff(925,plain,
% 0.92/1.12 ((~c0_1(a32)) | (~c2_1(a53))),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[924, 160, 317, 316, 903, 902, 538, 532, 425, 891])).
% 0.92/1.12 tff(926,plain,
% 0.92/1.12 (~c2_1(a53)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[925, 910])).
% 0.92/1.12 tff(927,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(928,plain,
% 0.92/1.12 ((hskp0 | (~ndr1_0) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | c2_1(a53)) <=> (hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(929,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[928])).
% 0.92/1.12 tff(930,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53))),
% 0.92/1.12 inference(transitivity,[status(thm)],[929, 927])).
% 0.92/1.12 tff(931,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | c2_1(a53))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(932,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.92/1.12 tff(933,plain,
% 0.92/1.12 ((~c0_1(a32)) | (~c2_1(a32)) | c2_1(a53)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[932, 160, 314, 317, 316, 903, 312])).
% 0.92/1.12 tff(934,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[933, 926, 918, 910])).
% 0.92/1.12 tff(935,plain,(c3_1(a32) | hskp0 | c1_1(a32) | hskp14 | hskp2 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(936,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[935, 889, 883, 314, 607, 606, 73])).
% 0.92/1.12 tff(937,plain,(hskp14 | hskp0 | hskp2 | hskp24 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(938,plain,
% 0.92/1.12 (hskp14),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[937, 606, 314, 73, 595])).
% 0.92/1.12 tff(939,plain,
% 0.92/1.12 (((~hskp14) | (~c1_1(a24))) <=> ((~hskp14) | (~c1_1(a24)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(940,plain,
% 0.92/1.12 (((~c1_1(a24)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a24)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(941,axiom,((~c1_1(a24)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.92/1.12 tff(942,plain,
% 0.92/1.12 ((~hskp14) | (~c1_1(a24))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.92/1.12 tff(943,plain,
% 0.92/1.12 ((~hskp14) | (~c1_1(a24))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[942, 939])).
% 0.92/1.12 tff(944,plain,
% 0.92/1.12 (~c1_1(a24)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[943, 938])).
% 0.92/1.12 tff(945,plain,
% 0.92/1.12 (((~hskp14) | (~c0_1(a24))) <=> ((~hskp14) | (~c0_1(a24)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(946,plain,
% 0.92/1.12 (((~c0_1(a24)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a24)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(947,axiom,((~c0_1(a24)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.92/1.12 tff(948,plain,
% 0.92/1.12 ((~hskp14) | (~c0_1(a24))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[947, 946])).
% 0.92/1.12 tff(949,plain,
% 0.92/1.12 ((~hskp14) | (~c0_1(a24))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[948, 945])).
% 0.92/1.12 tff(950,plain,
% 0.92/1.12 (~c0_1(a24)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[949, 938])).
% 0.92/1.12 tff(951,plain,
% 0.92/1.12 (((~hskp14) | c2_1(a24)) <=> ((~hskp14) | c2_1(a24))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(952,axiom,((~hskp14) | c2_1(a24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.92/1.12 tff(953,plain,
% 0.92/1.12 ((~hskp14) | c2_1(a24)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.92/1.12 tff(954,plain,
% 0.92/1.12 ((~hskp14) | c2_1(a24)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[953, 951])).
% 0.92/1.12 tff(955,plain,
% 0.92/1.12 ((~hskp14) | c2_1(a24)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[954, 951])).
% 0.92/1.12 tff(956,plain,
% 0.92/1.12 ((~hskp14) | c2_1(a24)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[955, 951])).
% 0.92/1.12 tff(957,plain,
% 0.92/1.12 ((~hskp14) | c2_1(a24)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[956, 951])).
% 0.92/1.12 tff(958,plain,
% 0.92/1.12 (c2_1(a24)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[957, 938])).
% 0.92/1.12 tff(959,plain,
% 0.92/1.12 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(960,plain,
% 0.92/1.12 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | c0_1(a24)) <=> (hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(961,plain,
% 0.92/1.12 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[960])).
% 0.92/1.12 tff(962,plain,
% 0.92/1.12 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[961, 959])).
% 0.92/1.12 tff(963,plain,
% 0.92/1.12 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | c0_1(a24))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(964,plain,
% 0.92/1.12 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.92/1.12 tff(965,plain,
% 0.92/1.12 (hskp3),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[964, 160, 606, 958, 950, 944, 23])).
% 0.92/1.12 tff(966,plain,
% 0.92/1.12 (~c3_1(a5)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[867, 965])).
% 0.92/1.12 tff(967,plain,
% 0.92/1.12 (~c1_1(a5)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[337, 965])).
% 0.92/1.12 tff(968,assumption,(~c3_1(a5)), introduced(assumption)).
% 0.92/1.12 tff(969,assumption,(~c1_1(a5)), introduced(assumption)).
% 0.92/1.12 tff(970,assumption,(~c1_1(a24)), introduced(assumption)).
% 0.92/1.12 tff(971,assumption,(~c0_1(a24)), introduced(assumption)).
% 0.92/1.12 tff(972,assumption,(c2_1(a24)), introduced(assumption)).
% 0.92/1.12 tff(973,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(974,plain,
% 0.92/1.12 (((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(975,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[974])).
% 0.92/1.12 tff(976,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[975, 973])).
% 0.92/1.12 tff(977,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(978,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[977, 976])).
% 0.92/1.12 tff(979,plain,
% 0.92/1.12 ((~c0_1(a5)) | (~c1_1(a16))),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[978, 160, 972, 971, 970, 538, 532, 969, 968, 425])).
% 0.92/1.12 tff(980,plain,
% 0.92/1.12 (~c0_1(a5)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[979, 709])).
% 0.92/1.12 tff(981,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(982,plain,
% 0.92/1.12 ((hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | c0_1(a5)) <=> (hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(983,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[982])).
% 0.92/1.12 tff(984,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[983, 981])).
% 0.92/1.12 tff(985,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | c0_1(a5))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(986,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.92/1.12 tff(987,plain,
% 0.92/1.12 (c0_1(a5) | (~c1_1(a16))),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[986, 160, 73, 546, 532, 969, 968, 901])).
% 0.92/1.12 tff(988,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[987, 980, 709])).
% 0.92/1.12 tff(989,plain,((~c1_1(a16)) | hskp24 | c1_1(a5) | c3_1(a5) | (~c2_1(a24)) | c0_1(a24) | c1_1(a24)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(990,plain,
% 0.92/1.12 (~c1_1(a16)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[989, 967, 73, 966, 958, 950, 944])).
% 0.92/1.12 tff(991,plain,
% 0.92/1.12 (~c2_1(a5)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[331, 965])).
% 0.92/1.12 tff(992,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(993,plain,
% 0.92/1.12 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a5) | c0_1(a5) | c3_1(a5)) <=> (c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(994,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a5) | c0_1(a5) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[993])).
% 0.92/1.12 tff(995,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a5) | c0_1(a5) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[994, 992])).
% 0.92/1.12 tff(996,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a5) | c0_1(a5) | c3_1(a5))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(997,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[996, 995])).
% 0.92/1.12 tff(998,plain,
% 0.92/1.12 (c0_1(a5) | c1_1(a16)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[997, 160, 546, 605, 604, 532, 603, 991, 966, 13])).
% 0.92/1.12 tff(999,plain,
% 0.92/1.12 (c0_1(a5)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[998, 990])).
% 0.92/1.12 tff(1000,plain,
% 0.92/1.12 (hskp26 | hskp16),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[552, 160, 668, 24, 2, 94])).
% 0.92/1.12 tff(1001,plain,
% 0.92/1.12 (hskp16),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1000, 84])).
% 0.92/1.12 tff(1002,plain,
% 0.92/1.12 (~c2_1(a30)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[567, 1001])).
% 0.92/1.12 tff(1003,plain,
% 0.92/1.12 (c1_1(a30)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[561, 1001])).
% 0.92/1.12 tff(1004,plain,
% 0.92/1.12 (~c0_1(a30)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[573, 1001])).
% 0.92/1.12 tff(1005,assumption,(~c2_1(a30)), introduced(assumption)).
% 0.92/1.12 tff(1006,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1007,plain,
% 0.92/1.12 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a30) | c0_1(a30) | c3_1(a30)) <=> (c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1008,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1007])).
% 0.92/1.12 tff(1009,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30))),
% 0.92/1.12 inference(transitivity,[status(thm)],[1008, 1006])).
% 0.92/1.12 tff(1010,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a30) | c0_1(a30) | c3_1(a30))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(1011,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.92/1.12 tff(1012,plain,
% 0.92/1.12 (c1_1(a16) | c3_1(a30)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1011, 160, 668, 673, 672, 585, 1005, 2, 671, 13])).
% 0.92/1.12 tff(1013,plain,
% 0.92/1.12 (c3_1(a30)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1012, 3])).
% 0.92/1.12 tff(1014,plain,
% 0.92/1.12 (^[U: $i] : refl((hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) <=> (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(1015,plain,
% 0.92/1.12 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[1014])).
% 0.92/1.12 tff(1016,plain,
% 0.92/1.12 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1017,plain,
% 0.92/1.12 (^[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) | (~c2_1(U)) | c0_1(U))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_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) | c3_1(U) | (~c2_1(U)) | c0_1(U))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) | hskp26) <=> ((hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) | hskp26))), rewrite(((hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) | hskp26) <=> (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) | hskp26) <=> (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(1018,plain,
% 0.92/1.12 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) | hskp26) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[1017])).
% 0.92/1.12 tff(1019,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.92/1.12 tff(1020,plain,
% 0.92/1.12 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 0.92/1.12 tff(1021,plain,
% 0.92/1.12 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1020, 1016])).
% 0.92/1.12 tff(1022,plain,(
% 0.92/1.12 ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.92/1.12 inference(skolemize,[status(sab)],[1021])).
% 0.92/1.12 tff(1023,plain,
% 0.92/1.12 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1022, 1015])).
% 0.92/1.12 tff(1024,assumption,(~hskp25), introduced(assumption)).
% 0.92/1.12 tff(1025,plain,
% 0.92/1.12 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1026,plain,
% 0.92/1.12 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24)) <=> (hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1027,plain,
% 0.92/1.12 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1026])).
% 0.92/1.12 tff(1028,plain,
% 0.92/1.12 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1027, 1025])).
% 0.92/1.13 tff(1029,plain,
% 0.92/1.13 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1030,plain,
% 0.92/1.13 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.92/1.13 tff(1031,plain,
% 0.92/1.13 (hskp26 | hskp25 | c3_1(a24)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1030, 160, 972, 971, 1023])).
% 0.92/1.13 tff(1032,plain,
% 0.92/1.13 (c3_1(a24)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1031, 1024, 84])).
% 0.92/1.13 tff(1033,plain,
% 0.92/1.13 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(1034,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[1033])).
% 0.92/1.13 tff(1035,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1036,plain,
% 0.92/1.13 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(1037,plain,
% 0.92/1.13 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_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) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[1036])).
% 0.92/1.13 tff(1038,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.92/1.13 tff(1039,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.92/1.13 tff(1040,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1039, 1035])).
% 0.92/1.13 tff(1041,plain,(
% 0.92/1.13 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.13 inference(skolemize,[status(sab)],[1040])).
% 0.92/1.13 tff(1042,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1041, 1034])).
% 0.92/1.13 tff(1043,assumption,(c3_1(a30)), introduced(assumption)).
% 0.92/1.13 tff(1044,plain,
% 0.92/1.13 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(1045,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[1044])).
% 0.92/1.13 tff(1046,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1047,plain,
% 0.92/1.13 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(1048,plain,
% 0.92/1.13 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[1047])).
% 0.92/1.13 tff(1049,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.92/1.13 tff(1050,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.92/1.13 tff(1051,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1050, 1046])).
% 0.92/1.13 tff(1052,plain,(
% 0.92/1.13 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.13 inference(skolemize,[status(sab)],[1051])).
% 0.92/1.13 tff(1053,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1052, 1045])).
% 0.92/1.13 tff(1054,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1055,plain,
% 0.92/1.13 ((hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1056,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1055])).
% 0.92/1.13 tff(1057,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1056, 1054])).
% 0.92/1.13 tff(1058,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1059,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.92/1.13 tff(1060,plain,
% 0.92/1.13 (hskp10 | (~c3_1(a24)) | (~c3_1(a30))),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1059, 160, 586, 972, 585, 970, 1053])).
% 0.92/1.13 tff(1061,plain,
% 0.92/1.13 (hskp10),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1060, 1032, 1043])).
% 0.92/1.13 tff(1062,plain,
% 0.92/1.13 (((~hskp10) | (~c3_1(a18))) <=> ((~hskp10) | (~c3_1(a18)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1063,plain,
% 0.92/1.13 (((~c3_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a18)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1064,axiom,((~c3_1(a18)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.92/1.13 tff(1065,plain,
% 0.92/1.13 ((~hskp10) | (~c3_1(a18))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.92/1.13 tff(1066,plain,
% 0.92/1.13 ((~hskp10) | (~c3_1(a18))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1065, 1062])).
% 0.92/1.13 tff(1067,plain,
% 0.92/1.13 (~c3_1(a18)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1066, 1061])).
% 0.92/1.13 tff(1068,plain,
% 0.92/1.13 (((~hskp10) | c2_1(a18)) <=> ((~hskp10) | c2_1(a18))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1069,axiom,((~hskp10) | c2_1(a18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.92/1.13 tff(1070,plain,
% 0.92/1.13 ((~hskp10) | c2_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 0.92/1.13 tff(1071,plain,
% 0.92/1.13 ((~hskp10) | c2_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1070, 1068])).
% 0.92/1.13 tff(1072,plain,
% 0.92/1.13 ((~hskp10) | c2_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1071, 1068])).
% 0.92/1.13 tff(1073,plain,
% 0.92/1.13 ((~hskp10) | c2_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1072, 1068])).
% 0.92/1.13 tff(1074,plain,
% 0.92/1.13 ((~hskp10) | c2_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1073, 1068])).
% 0.92/1.13 tff(1075,plain,
% 0.92/1.13 (c2_1(a18)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1074, 1061])).
% 0.92/1.13 tff(1076,plain,
% 0.92/1.13 (((~hskp10) | c0_1(a18)) <=> ((~hskp10) | c0_1(a18))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1077,axiom,((~hskp10) | c0_1(a18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.92/1.13 tff(1078,plain,
% 0.92/1.13 ((~hskp10) | c0_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.92/1.13 tff(1079,plain,
% 0.92/1.13 ((~hskp10) | c0_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1078, 1076])).
% 0.92/1.13 tff(1080,plain,
% 0.92/1.13 ((~hskp10) | c0_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1079, 1076])).
% 0.92/1.13 tff(1081,plain,
% 0.92/1.13 ((~hskp10) | c0_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1080, 1076])).
% 0.92/1.13 tff(1082,plain,
% 0.92/1.13 ((~hskp10) | c0_1(a18)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1081, 1076])).
% 0.92/1.13 tff(1083,plain,
% 0.92/1.13 (c0_1(a18)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1082, 1061])).
% 0.92/1.13 tff(1084,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1085,plain,
% 0.92/1.13 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24))) <=> (hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1086,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1085])).
% 0.92/1.13 tff(1087,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1086, 1084])).
% 0.92/1.13 tff(1088,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1089,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.92/1.13 tff(1090,plain,
% 0.92/1.13 (hskp11),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1089, 160, 972, 1083, 1075, 971, 1067, 1042, 1032])).
% 0.92/1.13 tff(1091,plain,
% 0.92/1.13 (((~hskp11) | (~c3_1(a19))) <=> ((~hskp11) | (~c3_1(a19)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1092,plain,
% 0.92/1.13 (((~c3_1(a19)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a19)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1093,axiom,((~c3_1(a19)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.92/1.13 tff(1094,plain,
% 0.92/1.13 ((~hskp11) | (~c3_1(a19))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 0.92/1.13 tff(1095,plain,
% 0.92/1.13 ((~hskp11) | (~c3_1(a19))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1094, 1091])).
% 0.92/1.13 tff(1096,plain,
% 0.92/1.13 (~c3_1(a19)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1095, 1090])).
% 0.92/1.13 tff(1097,plain,
% 0.92/1.13 (((~hskp11) | c2_1(a19)) <=> ((~hskp11) | c2_1(a19))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1098,axiom,((~hskp11) | c2_1(a19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.92/1.13 tff(1099,plain,
% 0.92/1.13 ((~hskp11) | c2_1(a19)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.92/1.13 tff(1100,plain,
% 0.92/1.13 ((~hskp11) | c2_1(a19)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1099, 1097])).
% 0.92/1.13 tff(1101,plain,
% 0.92/1.13 ((~hskp11) | c2_1(a19)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1100, 1097])).
% 0.92/1.13 tff(1102,plain,
% 0.92/1.13 ((~hskp11) | c2_1(a19)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1101, 1097])).
% 0.92/1.13 tff(1103,plain,
% 0.92/1.13 ((~hskp11) | c2_1(a19)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1102, 1097])).
% 0.92/1.13 tff(1104,plain,
% 0.92/1.13 (c2_1(a19)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1103, 1090])).
% 0.92/1.13 tff(1105,plain,
% 0.92/1.13 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1106,plain,
% 0.92/1.13 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | c0_1(a19)) <=> (hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1107,plain,
% 0.92/1.13 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | c0_1(a19))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1106])).
% 0.92/1.13 tff(1108,plain,
% 0.92/1.13 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | c0_1(a19))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1107, 1105])).
% 0.92/1.13 tff(1109,plain,
% 0.92/1.13 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | c0_1(a19))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1110,plain,
% 0.92/1.13 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.92/1.13 tff(1111,plain,
% 0.92/1.13 (c0_1(a19)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1110, 160, 84, 1024, 1104, 1096, 1023])).
% 0.92/1.13 tff(1112,plain,
% 0.92/1.13 (((~hskp11) | (~c1_1(a19))) <=> ((~hskp11) | (~c1_1(a19)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1113,plain,
% 0.92/1.13 (((~c1_1(a19)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a19)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1114,axiom,((~c1_1(a19)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.92/1.13 tff(1115,plain,
% 0.92/1.13 ((~hskp11) | (~c1_1(a19))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.92/1.13 tff(1116,plain,
% 0.92/1.13 ((~hskp11) | (~c1_1(a19))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1115, 1112])).
% 0.92/1.13 tff(1117,plain,
% 0.92/1.13 (~c1_1(a19)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1116, 1090])).
% 0.92/1.13 tff(1118,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1119,plain,
% 0.92/1.13 ((hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a53) | c0_1(a53) | c2_1(a53)) <=> (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1120,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1119])).
% 0.92/1.13 tff(1121,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1120, 1118])).
% 0.92/1.13 tff(1122,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a53) | c0_1(a53) | c2_1(a53))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1123,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.92/1.13 tff(1124,plain,
% 0.92/1.13 (c2_1(a53)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1123, 160, 314, 1104, 340, 339, 1117, 312, 1111])).
% 0.92/1.13 tff(1125,plain,
% 0.92/1.13 (^[U: $i] : refl((hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(1126,plain,
% 0.92/1.13 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[1125])).
% 0.92/1.13 tff(1127,plain,
% 0.92/1.13 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1128,plain,
% 0.92/1.13 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp20) <=> ((hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp20) <=> (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(1129,plain,
% 0.92/1.13 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp20) <=> ![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[1128])).
% 0.92/1.13 tff(1130,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.92/1.13 tff(1131,plain,
% 0.92/1.13 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 0.92/1.13 tff(1132,plain,
% 0.92/1.13 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1131, 1127])).
% 0.92/1.13 tff(1133,plain,(
% 0.92/1.13 ![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(skolemize,[status(sab)],[1132])).
% 0.92/1.13 tff(1134,plain,
% 0.92/1.13 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1133, 1126])).
% 0.92/1.13 tff(1135,plain,
% 0.92/1.13 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1136,plain,
% 0.92/1.13 ((hskp26 | hskp20 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18))) <=> (hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1137,plain,
% 0.92/1.13 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1136])).
% 0.92/1.14 tff(1138,plain,
% 0.92/1.14 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1137, 1135])).
% 0.92/1.14 tff(1139,plain,
% 0.92/1.14 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1140,plain,
% 0.92/1.14 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 0.92/1.14 tff(1141,plain,
% 0.92/1.14 (hskp20),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1140, 160, 84, 1083, 1075, 1067, 1134])).
% 0.92/1.14 tff(1142,plain,
% 0.92/1.14 (((~hskp20) | (~c3_1(a37))) <=> ((~hskp20) | (~c3_1(a37)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1143,plain,
% 0.92/1.14 (((~c3_1(a37)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a37)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1144,axiom,((~c3_1(a37)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.92/1.14 tff(1145,plain,
% 0.92/1.14 ((~hskp20) | (~c3_1(a37))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 0.92/1.14 tff(1146,plain,
% 0.92/1.14 ((~hskp20) | (~c3_1(a37))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1145, 1142])).
% 0.92/1.14 tff(1147,plain,
% 0.92/1.14 (~c3_1(a37)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1146, 1141])).
% 0.92/1.14 tff(1148,plain,
% 0.92/1.14 (((~hskp20) | (~c0_1(a37))) <=> ((~hskp20) | (~c0_1(a37)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1149,plain,
% 0.92/1.14 (((~c0_1(a37)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a37)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1150,axiom,((~c0_1(a37)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.92/1.14 tff(1151,plain,
% 0.92/1.14 ((~hskp20) | (~c0_1(a37))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 0.92/1.14 tff(1152,plain,
% 0.92/1.14 ((~hskp20) | (~c0_1(a37))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1151, 1148])).
% 0.92/1.14 tff(1153,plain,
% 0.92/1.14 (~c0_1(a37)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1152, 1141])).
% 0.92/1.14 tff(1154,plain,
% 0.92/1.14 (((~hskp20) | c1_1(a37)) <=> ((~hskp20) | c1_1(a37))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1155,axiom,((~hskp20) | c1_1(a37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.92/1.14 tff(1156,plain,
% 0.92/1.14 ((~hskp20) | c1_1(a37)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 0.92/1.14 tff(1157,plain,
% 0.92/1.14 ((~hskp20) | c1_1(a37)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1156, 1154])).
% 0.92/1.14 tff(1158,plain,
% 0.92/1.14 ((~hskp20) | c1_1(a37)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1157, 1154])).
% 0.92/1.14 tff(1159,plain,
% 0.92/1.14 ((~hskp20) | c1_1(a37)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1158, 1154])).
% 0.92/1.14 tff(1160,plain,
% 0.92/1.14 ((~hskp20) | c1_1(a37)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1159, 1154])).
% 0.92/1.14 tff(1161,plain,
% 0.92/1.14 (c1_1(a37)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1160, 1141])).
% 0.92/1.14 tff(1162,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1163,plain,
% 0.92/1.14 (((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1164,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1163])).
% 0.92/1.14 tff(1165,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1164, 1162])).
% 0.92/1.14 tff(1166,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1167,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.92/1.14 tff(1168,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1167, 160, 341, 1161, 340, 339, 1153, 1147, 83, 1124])).
% 0.92/1.14 tff(1169,plain,(hskp25 | (~c3_1(a53)) | c0_1(a53) | c1_1(a53) | hskp0 | hskp26 | (~c2_1(a24)) | c0_1(a24) | (~c3_1(a30)) | (~c1_1(a30)) | c0_1(a30) | c1_1(a24)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(1170,plain,
% 0.92/1.14 (hskp25),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1169, 1013, 340, 339, 314, 84, 972, 971, 341, 586, 585, 970])).
% 0.92/1.14 tff(1171,plain,
% 0.92/1.14 (c1_1(a9)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[795, 1170])).
% 0.92/1.14 tff(1172,plain,
% 0.92/1.14 (c2_1(a9)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[787, 1170])).
% 0.92/1.14 tff(1173,plain,
% 0.92/1.14 (c0_1(a9)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[803, 1170])).
% 0.92/1.14 tff(1174,assumption,(~hskp6), introduced(assumption)).
% 0.92/1.14 tff(1175,plain,
% 0.92/1.14 (^[U: $i] : refl((hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1176,plain,
% 0.92/1.14 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1175])).
% 0.92/1.14 tff(1177,plain,
% 0.92/1.14 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1178,plain,
% 0.92/1.14 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp26) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp26))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp26) <=> (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp26) <=> (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1179,plain,
% 0.92/1.14 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp26) <=> ![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1178])).
% 0.92/1.14 tff(1180,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.92/1.14 tff(1181,plain,
% 0.92/1.14 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.92/1.14 tff(1182,plain,
% 0.92/1.14 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1181, 1177])).
% 0.92/1.14 tff(1183,plain,(
% 0.92/1.14 ![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.92/1.14 inference(skolemize,[status(sab)],[1182])).
% 0.92/1.14 tff(1184,plain,
% 0.92/1.14 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1183, 1176])).
% 0.92/1.14 tff(1185,plain,
% 0.92/1.14 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1186,plain,
% 0.92/1.14 ((hskp26 | hskp6 | (~ndr1_0) | c3_1(a24) | c1_1(a24) | (~c2_1(a24))) <=> (hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1187,plain,
% 0.92/1.14 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24)))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1186])).
% 0.92/1.14 tff(1188,plain,
% 0.92/1.14 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.92/1.14 tff(1189,plain,
% 0.92/1.14 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1190,plain,
% 0.92/1.14 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.92/1.14 tff(1191,plain,
% 0.92/1.14 (hskp26 | hskp6 | c3_1(a24)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1190, 160, 972, 970, 1184])).
% 0.92/1.14 tff(1192,plain,
% 0.92/1.14 (c3_1(a24)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1191, 1174, 84])).
% 0.92/1.14 tff(1193,plain,
% 0.92/1.14 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1194,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1193])).
% 0.92/1.14 tff(1195,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1196,plain,
% 0.92/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1197,plain,
% 0.92/1.14 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1196])).
% 0.92/1.14 tff(1198,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.92/1.14 tff(1199,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.92/1.14 tff(1200,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 0.92/1.14 tff(1201,plain,(
% 0.92/1.14 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.14 inference(skolemize,[status(sab)],[1200])).
% 0.92/1.14 tff(1202,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1201, 1194])).
% 0.92/1.14 tff(1203,assumption,(c2_1(a9)), introduced(assumption)).
% 0.92/1.14 tff(1204,assumption,(c1_1(a9)), introduced(assumption)).
% 0.92/1.14 tff(1205,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1206,plain,
% 0.92/1.14 ((hskp6 | (~ndr1_0) | (~c2_1(a9)) | (~c1_1(a9)) | (~c3_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30))) <=> (hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1207,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a9)) | (~c1_1(a9)) | (~c3_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1206])).
% 0.92/1.14 tff(1208,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a9)) | (~c1_1(a9)) | (~c3_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1207, 1205])).
% 0.92/1.14 tff(1209,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a9)) | (~c1_1(a9)) | (~c3_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1210,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 0.92/1.14 tff(1211,plain,
% 0.92/1.14 (hskp6 | (~c3_1(a9))),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1210, 160, 1204, 1203, 585, 1005, 1202, 1043])).
% 0.92/1.14 tff(1212,plain,
% 0.92/1.14 (~c3_1(a9)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1211, 1174])).
% 0.92/1.14 tff(1213,assumption,(c0_1(a9)), introduced(assumption)).
% 0.92/1.14 tff(1214,plain,
% 0.92/1.14 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1215,plain,
% 0.92/1.14 ((hskp26 | hskp20 | (~ndr1_0) | c3_1(a9) | (~c2_1(a9)) | (~c0_1(a9))) <=> (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1216,plain,
% 0.92/1.14 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a9) | (~c2_1(a9)) | (~c0_1(a9)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9)))),
% 0.99/1.14 inference(monotonicity,[status(thm)],[1215])).
% 0.99/1.14 tff(1217,plain,
% 0.99/1.14 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a9) | (~c2_1(a9)) | (~c0_1(a9)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9))),
% 0.99/1.14 inference(transitivity,[status(thm)],[1216, 1214])).
% 0.99/1.14 tff(1218,plain,
% 0.99/1.14 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a9) | (~c2_1(a9)) | (~c0_1(a9)))),
% 0.99/1.14 inference(quant_inst,[status(thm)],[])).
% 0.99/1.14 tff(1219,plain,
% 0.99/1.14 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9)),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 0.99/1.14 tff(1220,plain,
% 0.99/1.14 (hskp20 | c3_1(a9)),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1219, 160, 84, 1213, 1203, 1134])).
% 0.99/1.14 tff(1221,plain,
% 0.99/1.14 (hskp20),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1220, 1212])).
% 0.99/1.14 tff(1222,plain,
% 0.99/1.14 (~c3_1(a37)),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1146, 1221])).
% 0.99/1.14 tff(1223,plain,
% 0.99/1.14 (~c0_1(a37)),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1152, 1221])).
% 0.99/1.14 tff(1224,plain,
% 0.99/1.14 (c1_1(a37)),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1160, 1221])).
% 0.99/1.14 tff(1225,plain,
% 0.99/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37)))),
% 0.99/1.14 inference(rewrite,[status(thm)],[])).
% 0.99/1.14 tff(1226,plain,
% 0.99/1.14 (((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37)))),
% 0.99/1.14 inference(rewrite,[status(thm)],[])).
% 0.99/1.14 tff(1227,plain,
% 0.99/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37))))),
% 0.99/1.14 inference(monotonicity,[status(thm)],[1226])).
% 0.99/1.14 tff(1228,plain,
% 0.99/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37)))),
% 0.99/1.14 inference(transitivity,[status(thm)],[1227, 1225])).
% 0.99/1.14 tff(1229,plain,
% 0.99/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 0.99/1.14 inference(quant_inst,[status(thm)],[])).
% 0.99/1.14 tff(1230,plain,
% 0.99/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37))),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 0.99/1.14 tff(1231,plain,
% 0.99/1.14 ($false),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1230, 160, 1224, 972, 1223, 1222, 971, 970, 83, 1192])).
% 0.99/1.14 tff(1232,plain,(hskp6 | (~c2_1(a24)) | c0_1(a24) | c1_1(a24) | hskp26 | (~c0_1(a9)) | (~c2_1(a9)) | (~c1_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.14 tff(1233,plain,
% 0.99/1.14 (hskp6),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1232, 1173, 971, 970, 84, 972, 1172, 1171, 585, 1005, 1013])).
% 0.99/1.14 tff(1234,assumption,(hskp6), introduced(assumption)).
% 0.99/1.14 tff(1235,plain,
% 0.99/1.14 (((~hskp6) | (~c2_1(a8))) <=> ((~hskp6) | (~c2_1(a8)))),
% 0.99/1.14 inference(rewrite,[status(thm)],[])).
% 0.99/1.14 tff(1236,plain,
% 0.99/1.14 (((~c2_1(a8)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a8)))),
% 0.99/1.14 inference(rewrite,[status(thm)],[])).
% 0.99/1.14 tff(1237,axiom,((~c2_1(a8)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.99/1.14 tff(1238,plain,
% 0.99/1.14 ((~hskp6) | (~c2_1(a8))),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 0.99/1.14 tff(1239,plain,
% 0.99/1.14 ((~hskp6) | (~c2_1(a8))),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1238, 1235])).
% 0.99/1.14 tff(1240,plain,
% 0.99/1.14 (~c2_1(a8)),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1239, 1234])).
% 0.99/1.14 tff(1241,plain,
% 0.99/1.14 (((~hskp6) | c1_1(a8)) <=> ((~hskp6) | c1_1(a8))),
% 0.99/1.14 inference(rewrite,[status(thm)],[])).
% 0.99/1.14 tff(1242,axiom,((~hskp6) | c1_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.99/1.14 tff(1243,plain,
% 0.99/1.14 ((~hskp6) | c1_1(a8)),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.99/1.14 tff(1244,plain,
% 0.99/1.14 ((~hskp6) | c1_1(a8)),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1243, 1241])).
% 0.99/1.14 tff(1245,plain,
% 0.99/1.14 ((~hskp6) | c1_1(a8)),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1244, 1241])).
% 0.99/1.14 tff(1246,plain,
% 0.99/1.14 ((~hskp6) | c1_1(a8)),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1245, 1241])).
% 0.99/1.14 tff(1247,plain,
% 0.99/1.14 ((~hskp6) | c1_1(a8)),
% 0.99/1.14 inference(modus_ponens,[status(thm)],[1246, 1241])).
% 0.99/1.14 tff(1248,plain,
% 0.99/1.14 (c1_1(a8)),
% 0.99/1.14 inference(unit_resolution,[status(thm)],[1247, 1234])).
% 0.99/1.14 tff(1249,assumption,(~c3_1(a8)), introduced(assumption)).
% 0.99/1.14 tff(1250,assumption,(~c2_1(a8)), introduced(assumption)).
% 0.99/1.14 tff(1251,assumption,(c1_1(a8)), introduced(assumption)).
% 0.99/1.14 tff(1252,plain,
% 0.99/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24)))),
% 0.99/1.14 inference(rewrite,[status(thm)],[])).
% 0.99/1.14 tff(1253,plain,
% 0.99/1.14 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24)))),
% 0.99/1.14 inference(rewrite,[status(thm)],[])).
% 0.99/1.14 tff(1254,plain,
% 0.99/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24))))),
% 0.99/1.14 inference(monotonicity,[status(thm)],[1253])).
% 0.99/1.14 tff(1255,plain,
% 0.99/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24)))),
% 0.99/1.15 inference(transitivity,[status(thm)],[1254, 1252])).
% 0.99/1.15 tff(1256,plain,
% 0.99/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 0.99/1.15 inference(quant_inst,[status(thm)],[])).
% 0.99/1.15 tff(1257,plain,
% 0.99/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 0.99/1.15 tff(1258,plain,
% 0.99/1.15 ($false),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1257, 160, 972, 668, 1251, 971, 970, 2, 1250, 425, 3, 1249])).
% 0.99/1.15 tff(1259,plain,(c3_1(a8) | (~c2_1(a24)) | (~c0_1(a16)) | (~c1_1(a8)) | c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.15 tff(1260,plain,
% 0.99/1.15 (c3_1(a8)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1259, 1248, 668, 3, 971, 970, 2, 1240, 972])).
% 0.99/1.15 tff(1261,plain,
% 0.99/1.15 (((~hskp6) | c0_1(a8)) <=> ((~hskp6) | c0_1(a8))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1262,axiom,((~hskp6) | c0_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.99/1.15 tff(1263,plain,
% 0.99/1.15 ((~hskp6) | c0_1(a8)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.99/1.15 tff(1264,plain,
% 0.99/1.15 ((~hskp6) | c0_1(a8)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1263, 1261])).
% 0.99/1.15 tff(1265,plain,
% 0.99/1.15 ((~hskp6) | c0_1(a8)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1264, 1261])).
% 0.99/1.15 tff(1266,plain,
% 0.99/1.15 ((~hskp6) | c0_1(a8)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1265, 1261])).
% 0.99/1.15 tff(1267,plain,
% 0.99/1.15 ((~hskp6) | c0_1(a8)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1266, 1261])).
% 0.99/1.15 tff(1268,plain,
% 0.99/1.15 (c0_1(a8)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1267, 1234])).
% 0.99/1.15 tff(1269,plain,
% 0.99/1.15 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1270,plain,
% 0.99/1.15 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8))) <=> (hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1271,plain,
% 0.99/1.15 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8))))),
% 0.99/1.15 inference(monotonicity,[status(thm)],[1270])).
% 0.99/1.15 tff(1272,plain,
% 0.99/1.15 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8)))),
% 0.99/1.15 inference(transitivity,[status(thm)],[1271, 1269])).
% 0.99/1.15 tff(1273,plain,
% 0.99/1.15 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)))),
% 0.99/1.15 inference(quant_inst,[status(thm)],[])).
% 0.99/1.15 tff(1274,plain,
% 0.99/1.15 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.99/1.15 tff(1275,plain,
% 0.99/1.15 ($false),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1274, 160, 674, 595, 1268, 1240, 684, 1260])).
% 0.99/1.15 tff(1276,plain,((~hskp6) | hskp18 | hskp17 | (~c0_1(a16)) | c1_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~c2_1(a24))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.15 tff(1277,plain,
% 0.99/1.15 (hskp18),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1276, 1233, 595, 668, 3, 971, 970, 2, 972])).
% 0.99/1.15 tff(1278,plain,
% 0.99/1.15 (~c1_1(a32)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[882, 1277])).
% 0.99/1.15 tff(1279,plain,
% 0.99/1.15 (((~hskp18) | (~c0_1(a32))) <=> ((~hskp18) | (~c0_1(a32)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1280,plain,
% 0.99/1.15 (((~c0_1(a32)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a32)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1281,axiom,((~c0_1(a32)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.99/1.15 tff(1282,plain,
% 0.99/1.15 ((~hskp18) | (~c0_1(a32))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.99/1.15 tff(1283,plain,
% 0.99/1.15 ((~hskp18) | (~c0_1(a32))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1282, 1279])).
% 0.99/1.15 tff(1284,plain,
% 0.99/1.15 (~c0_1(a32)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1283, 1277])).
% 0.99/1.15 tff(1285,plain,
% 0.99/1.15 (~c3_1(a32)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[888, 1277])).
% 0.99/1.15 tff(1286,assumption,(~c0_1(a32)), introduced(assumption)).
% 0.99/1.15 tff(1287,plain,
% 0.99/1.15 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1288,plain,
% 0.99/1.15 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a32) | (~c2_1(a32)) | c0_1(a32)) <=> (hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1289,plain,
% 0.99/1.15 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a32) | (~c2_1(a32)) | c0_1(a32))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32))))),
% 0.99/1.15 inference(monotonicity,[status(thm)],[1288])).
% 0.99/1.15 tff(1290,plain,
% 0.99/1.15 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a32) | (~c2_1(a32)) | c0_1(a32))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32)))),
% 0.99/1.15 inference(transitivity,[status(thm)],[1289, 1287])).
% 0.99/1.15 tff(1291,plain,
% 0.99/1.15 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a32) | (~c2_1(a32)) | c0_1(a32))),
% 0.99/1.15 inference(quant_inst,[status(thm)],[])).
% 0.99/1.15 tff(1292,plain,
% 0.99/1.15 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.99/1.15 tff(1293,plain,
% 0.99/1.15 (hskp25 | c0_1(a32) | (~c2_1(a32))),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1292, 160, 84, 902, 1023])).
% 0.99/1.15 tff(1294,plain,
% 0.99/1.15 (~c2_1(a32)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1293, 1024, 1286])).
% 0.99/1.15 tff(1295,plain,
% 0.99/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1296,plain,
% 0.99/1.15 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a32) | c0_1(a32) | c3_1(a32)) <=> (c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1297,plain,
% 0.99/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32)))),
% 0.99/1.15 inference(monotonicity,[status(thm)],[1296])).
% 0.99/1.15 tff(1298,plain,
% 0.99/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32))),
% 0.99/1.15 inference(transitivity,[status(thm)],[1297, 1295])).
% 0.99/1.15 tff(1299,plain,
% 0.99/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a32) | c0_1(a32) | c3_1(a32))),
% 0.99/1.15 inference(quant_inst,[status(thm)],[])).
% 0.99/1.15 tff(1300,plain,
% 0.99/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 0.99/1.15 tff(1301,plain,
% 0.99/1.15 (c1_1(a18)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1300, 160, 586, 1083, 1286, 902, 1005, 1067, 13, 1294, 1043])).
% 0.99/1.15 tff(1302,plain,
% 0.99/1.15 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.99/1.15 inference(bind,[status(th)],[])).
% 0.99/1.15 tff(1303,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.99/1.15 inference(quant_intro,[status(thm)],[1302])).
% 0.99/1.15 tff(1304,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1305,plain,
% 0.99/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.99/1.15 inference(bind,[status(th)],[])).
% 0.99/1.15 tff(1306,plain,
% 0.99/1.15 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.99/1.15 inference(quant_intro,[status(thm)],[1305])).
% 0.99/1.15 tff(1307,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.99/1.15 tff(1308,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 0.99/1.15 tff(1309,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1308, 1304])).
% 0.99/1.15 tff(1310,plain,(
% 0.99/1.15 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.99/1.15 inference(skolemize,[status(sab)],[1309])).
% 0.99/1.15 tff(1311,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1310, 1303])).
% 0.99/1.15 tff(1312,assumption,(hskp5), introduced(assumption)).
% 0.99/1.15 tff(1313,plain,
% 0.99/1.15 (((~hskp5) | (~c0_1(a7))) <=> ((~hskp5) | (~c0_1(a7)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1314,plain,
% 0.99/1.15 (((~c0_1(a7)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a7)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1315,axiom,((~c0_1(a7)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.99/1.15 tff(1316,plain,
% 0.99/1.15 ((~hskp5) | (~c0_1(a7))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 0.99/1.15 tff(1317,plain,
% 0.99/1.15 ((~hskp5) | (~c0_1(a7))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1316, 1313])).
% 0.99/1.15 tff(1318,plain,
% 0.99/1.15 (~c0_1(a7)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1317, 1312])).
% 0.99/1.15 tff(1319,plain,
% 0.99/1.15 (((~hskp5) | c1_1(a7)) <=> ((~hskp5) | c1_1(a7))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1320,axiom,((~hskp5) | c1_1(a7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.99/1.15 tff(1321,plain,
% 0.99/1.15 ((~hskp5) | c1_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 0.99/1.15 tff(1322,plain,
% 0.99/1.15 ((~hskp5) | c1_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1321, 1319])).
% 0.99/1.15 tff(1323,plain,
% 0.99/1.15 ((~hskp5) | c1_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1322, 1319])).
% 0.99/1.15 tff(1324,plain,
% 0.99/1.15 ((~hskp5) | c1_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1323, 1319])).
% 0.99/1.15 tff(1325,plain,
% 0.99/1.15 ((~hskp5) | c1_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1324, 1319])).
% 0.99/1.15 tff(1326,plain,
% 0.99/1.15 (c1_1(a7)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1325, 1312])).
% 0.99/1.15 tff(1327,assumption,(c2_1(a7)), introduced(assumption)).
% 0.99/1.15 tff(1328,assumption,(~c0_1(a7)), introduced(assumption)).
% 0.99/1.15 tff(1329,assumption,(c1_1(a7)), introduced(assumption)).
% 0.99/1.15 tff(1330,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1331,plain,
% 0.99/1.15 (((~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1332,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7))))),
% 0.99/1.15 inference(monotonicity,[status(thm)],[1331])).
% 0.99/1.15 tff(1333,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 0.99/1.15 inference(transitivity,[status(thm)],[1332, 1330])).
% 0.99/1.15 tff(1334,plain,
% 0.99/1.15 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.99/1.15 inference(quant_inst,[status(thm)],[])).
% 0.99/1.15 tff(1335,plain,
% 0.99/1.15 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 0.99/1.15 tff(1336,plain,
% 0.99/1.15 ($false),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1335, 160, 1329, 1286, 903, 902, 1328, 45, 1327])).
% 0.99/1.15 tff(1337,plain,((~c2_1(a7)) | (~c1_1(a7)) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.15 tff(1338,plain,
% 0.99/1.15 (~c2_1(a7)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1337, 1326, 1286, 903, 902, 1318])).
% 0.99/1.15 tff(1339,assumption,(~c2_1(a32)), introduced(assumption)).
% 0.99/1.15 tff(1340,plain,
% 0.99/1.15 (((~hskp5) | c3_1(a7)) <=> ((~hskp5) | c3_1(a7))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1341,axiom,((~hskp5) | c3_1(a7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.99/1.15 tff(1342,plain,
% 0.99/1.15 ((~hskp5) | c3_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.99/1.15 tff(1343,plain,
% 0.99/1.15 ((~hskp5) | c3_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1342, 1340])).
% 0.99/1.15 tff(1344,plain,
% 0.99/1.15 ((~hskp5) | c3_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 0.99/1.15 tff(1345,plain,
% 0.99/1.15 ((~hskp5) | c3_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1344, 1340])).
% 0.99/1.15 tff(1346,plain,
% 0.99/1.15 ((~hskp5) | c3_1(a7)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1345, 1340])).
% 0.99/1.15 tff(1347,plain,
% 0.99/1.15 (c3_1(a7)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1346, 1312])).
% 0.99/1.15 tff(1348,plain,
% 0.99/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1349,plain,
% 0.99/1.15 (((~ndr1_0) | c2_1(a7) | c0_1(a7) | (~c3_1(a7)) | c3_1(a32) | c0_1(a32) | c2_1(a32) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1350,plain,
% 0.99/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | c0_1(a7) | (~c3_1(a7)) | c3_1(a32) | c0_1(a32) | c2_1(a32) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32)))),
% 0.99/1.15 inference(monotonicity,[status(thm)],[1349])).
% 0.99/1.15 tff(1351,plain,
% 0.99/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | c0_1(a7) | (~c3_1(a7)) | c3_1(a32) | c0_1(a32) | c2_1(a32) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32))),
% 0.99/1.15 inference(transitivity,[status(thm)],[1350, 1348])).
% 0.99/1.15 tff(1352,plain,
% 0.99/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | c0_1(a7) | (~c3_1(a7)) | c3_1(a32) | c0_1(a32) | c2_1(a32) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.99/1.15 inference(quant_inst,[status(thm)],[])).
% 0.99/1.15 tff(1353,plain,
% 0.99/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32)),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 0.99/1.15 tff(1354,plain,
% 0.99/1.15 ($false),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1353, 160, 1347, 1286, 903, 902, 1318, 55, 1339, 1338])).
% 0.99/1.15 tff(1355,plain,((~hskp5) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c2_1(a32)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.15 tff(1356,plain,
% 0.99/1.15 (~hskp5),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1355, 1294, 902, 903, 1286])).
% 0.99/1.15 tff(1357,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1358,plain,
% 0.99/1.15 ((hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a30) | c2_1(a30) | (~c1_1(a30))) <=> (hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1359,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a30) | c2_1(a30) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30))))),
% 0.99/1.15 inference(monotonicity,[status(thm)],[1358])).
% 0.99/1.15 tff(1360,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a30) | c2_1(a30) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30)))),
% 0.99/1.15 inference(transitivity,[status(thm)],[1359, 1357])).
% 0.99/1.15 tff(1361,plain,
% 0.99/1.15 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a30) | c2_1(a30) | (~c1_1(a30)))),
% 0.99/1.15 inference(quant_inst,[status(thm)],[])).
% 0.99/1.15 tff(1362,plain,
% 0.99/1.15 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 0.99/1.15 tff(1363,plain,
% 0.99/1.15 ($false),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1362, 160, 1356, 586, 1075, 585, 1005, 1067, 1311, 1301])).
% 0.99/1.15 tff(1364,plain,(hskp25 | (~c1_1(a30)) | c0_1(a30) | c2_1(a30) | c0_1(a32) | c3_1(a32) | (~c3_1(a30)) | c1_1(a32) | (~c2_1(a24)) | c1_1(a24) | hskp26 | c0_1(a24)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.15 tff(1365,plain,
% 0.99/1.15 (hskp25),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1364, 1286, 585, 1005, 586, 902, 1043, 903, 972, 970, 84, 971])).
% 0.99/1.15 tff(1366,plain,
% 0.99/1.15 (hskp19),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[813, 1365, 673, 672, 671])).
% 0.99/1.15 tff(1367,plain,
% 0.99/1.15 (~c0_1(a33)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[819, 1366])).
% 0.99/1.15 tff(1368,plain,
% 0.99/1.15 (c2_1(a33)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[827, 1366])).
% 0.99/1.15 tff(1369,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1370,plain,
% 0.99/1.15 (((~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1371,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))))),
% 0.99/1.15 inference(monotonicity,[status(thm)],[1370])).
% 0.99/1.15 tff(1372,plain,
% 0.99/1.15 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 0.99/1.15 inference(transitivity,[status(thm)],[1371, 1369])).
% 0.99/1.15 tff(1373,plain,
% 0.99/1.15 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.99/1.15 inference(quant_inst,[status(thm)],[])).
% 0.99/1.15 tff(1374,plain,
% 0.99/1.15 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 0.99/1.15 tff(1375,plain,
% 0.99/1.15 (~c1_1(a33)),
% 0.99/1.15 inference(unit_resolution,[status(thm)],[1374, 160, 1368, 1367, 1286, 903, 902, 45])).
% 0.99/1.15 tff(1376,plain,
% 0.99/1.15 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.99/1.15 inference(bind,[status(th)],[])).
% 0.99/1.15 tff(1377,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.99/1.15 inference(quant_intro,[status(thm)],[1376])).
% 0.99/1.15 tff(1378,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.99/1.15 inference(rewrite,[status(thm)],[])).
% 0.99/1.15 tff(1379,plain,
% 0.99/1.15 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.99/1.15 inference(bind,[status(th)],[])).
% 0.99/1.15 tff(1380,plain,
% 0.99/1.15 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.99/1.15 inference(quant_intro,[status(thm)],[1379])).
% 0.99/1.15 tff(1381,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.99/1.15 tff(1382,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 0.99/1.15 tff(1383,plain,
% 0.99/1.15 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.99/1.15 inference(modus_ponens,[status(thm)],[1382, 1378])).
% 0.99/1.16 tff(1384,plain,(
% 0.99/1.16 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.99/1.16 inference(skolemize,[status(sab)],[1383])).
% 0.99/1.16 tff(1385,plain,
% 0.99/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1384, 1377])).
% 0.99/1.16 tff(1386,plain,
% 0.99/1.16 (((~hskp19) | c3_1(a33)) <=> ((~hskp19) | c3_1(a33))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1387,axiom,((~hskp19) | c3_1(a33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.99/1.16 tff(1388,plain,
% 0.99/1.16 ((~hskp19) | c3_1(a33)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 0.99/1.16 tff(1389,plain,
% 0.99/1.16 ((~hskp19) | c3_1(a33)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1388, 1386])).
% 0.99/1.16 tff(1390,plain,
% 0.99/1.16 ((~hskp19) | c3_1(a33)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1389, 1386])).
% 0.99/1.16 tff(1391,plain,
% 0.99/1.16 ((~hskp19) | c3_1(a33)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1390, 1386])).
% 0.99/1.16 tff(1392,plain,
% 0.99/1.16 ((~hskp19) | c3_1(a33)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1391, 1386])).
% 0.99/1.16 tff(1393,plain,
% 0.99/1.16 (c3_1(a33)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1392, 1366])).
% 0.99/1.16 tff(1394,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1395,plain,
% 0.99/1.16 ((hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1396,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[1395])).
% 0.99/1.16 tff(1397,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 0.99/1.16 inference(transitivity,[status(thm)],[1396, 1394])).
% 0.99/1.16 tff(1398,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(1399,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.99/1.16 tff(1400,plain,
% 0.99/1.16 (hskp1),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1399, 160, 1368, 1393, 1286, 903, 902, 1385, 1375])).
% 0.99/1.16 tff(1401,plain,
% 0.99/1.16 (((~hskp1) | (~c0_1(a2))) <=> ((~hskp1) | (~c0_1(a2)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1402,plain,
% 0.99/1.16 (((~c0_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a2)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1403,axiom,((~c0_1(a2)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.99/1.16 tff(1404,plain,
% 0.99/1.16 ((~hskp1) | (~c0_1(a2))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 0.99/1.16 tff(1405,plain,
% 0.99/1.16 ((~hskp1) | (~c0_1(a2))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1404, 1401])).
% 0.99/1.16 tff(1406,plain,
% 0.99/1.16 (~c0_1(a2)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1405, 1400])).
% 0.99/1.16 tff(1407,plain,
% 0.99/1.16 (((~hskp1) | c2_1(a2)) <=> ((~hskp1) | c2_1(a2))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1408,axiom,((~hskp1) | c2_1(a2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.99/1.16 tff(1409,plain,
% 0.99/1.16 ((~hskp1) | c2_1(a2)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.99/1.16 tff(1410,plain,
% 0.99/1.16 ((~hskp1) | c2_1(a2)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1409, 1407])).
% 0.99/1.16 tff(1411,plain,
% 0.99/1.16 ((~hskp1) | c2_1(a2)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1410, 1407])).
% 0.99/1.16 tff(1412,plain,
% 0.99/1.16 ((~hskp1) | c2_1(a2)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1411, 1407])).
% 0.99/1.16 tff(1413,plain,
% 0.99/1.16 ((~hskp1) | c2_1(a2)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1412, 1407])).
% 0.99/1.16 tff(1414,plain,
% 0.99/1.16 (c2_1(a2)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1413, 1400])).
% 0.99/1.16 tff(1415,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1416,plain,
% 0.99/1.16 (((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1417,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[1416])).
% 0.99/1.16 tff(1418,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)))),
% 0.99/1.16 inference(transitivity,[status(thm)],[1417, 1415])).
% 0.99/1.16 tff(1419,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(1420,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 0.99/1.16 tff(1421,plain,
% 0.99/1.16 (~c1_1(a2)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1420, 160, 1414, 1286, 903, 902, 1406, 45])).
% 0.99/1.16 tff(1422,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1423,plain,
% 0.99/1.16 ((hskp10 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1424,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[1423])).
% 0.99/1.16 tff(1425,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 0.99/1.16 inference(transitivity,[status(thm)],[1424, 1422])).
% 0.99/1.16 tff(1426,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(1427,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 0.99/1.16 tff(1428,plain,
% 0.99/1.16 (hskp10),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1427, 160, 1368, 1393, 586, 585, 1053, 1043, 1375])).
% 0.99/1.16 tff(1429,plain,
% 0.99/1.16 (~c3_1(a18)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1066, 1428])).
% 0.99/1.16 tff(1430,plain,
% 0.99/1.16 (c2_1(a18)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1074, 1428])).
% 0.99/1.16 tff(1431,plain,
% 0.99/1.16 (c0_1(a18)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1082, 1428])).
% 0.99/1.16 tff(1432,plain,
% 0.99/1.16 (hskp20),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1140, 160, 84, 1431, 1430, 1429, 1134])).
% 0.99/1.16 tff(1433,plain,
% 0.99/1.16 (~c3_1(a37)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1146, 1432])).
% 0.99/1.16 tff(1434,plain,
% 0.99/1.16 (~c0_1(a37)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1152, 1432])).
% 0.99/1.16 tff(1435,plain,
% 0.99/1.16 (c1_1(a37)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1160, 1432])).
% 0.99/1.16 tff(1436,plain,
% 0.99/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1437,plain,
% 0.99/1.16 (((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a2) | c0_1(a2) | (~c2_1(a2))) <=> (c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1438,plain,
% 0.99/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[1437])).
% 0.99/1.16 tff(1439,plain,
% 0.99/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 0.99/1.16 inference(transitivity,[status(thm)],[1438, 1436])).
% 0.99/1.16 tff(1440,plain,
% 0.99/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a2) | c0_1(a2) | (~c2_1(a2)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(1441,plain,
% 0.99/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.99/1.16 tff(1442,plain,
% 0.99/1.16 ($false),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1441, 160, 1435, 1368, 1393, 1414, 1434, 1433, 1406, 83, 1375, 1421])).
% 0.99/1.16 tff(1443,plain,(c0_1(a32) | c1_1(a32) | c3_1(a32) | hskp26 | (~c1_1(a30)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | c2_1(a30) | (~c2_1(a24)) | c1_1(a24) | c0_1(a24)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.16 tff(1444,plain,
% 0.99/1.16 ($false),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1443, 1285, 1284, 1278, 84, 586, 585, 1013, 673, 672, 671, 1005, 972, 970, 971])).
% 0.99/1.16 tff(1445,plain,(c1_1(a16) | hskp26 | (~c1_1(a30)) | c0_1(a30) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | c2_1(a30) | (~c2_1(a24)) | c1_1(a24) | c0_1(a24) | hskp17 | (~c0_1(a16)) | c3_1(a16) | c0_1(a53) | c1_1(a53) | hskp0 | (~c3_1(a53))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.16 tff(1446,plain,
% 0.99/1.16 ($false),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1445, 1004, 1003, 3, 84, 673, 672, 671, 1002, 972, 970, 971, 595, 668, 2, 340, 339, 314, 341])).
% 0.99/1.16 tff(1447,plain,(hskp26 | c1_1(a16) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | (~c2_1(a24)) | c1_1(a24) | c0_1(a24) | hskp17 | (~c0_1(a16)) | c3_1(a16) | c0_1(a53) | c1_1(a53) | hskp0 | (~c3_1(a53)) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.16 tff(1448,plain,
% 0.99/1.16 (hskp26),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1447, 990, 605, 604, 603, 958, 944, 950, 595, 546, 532, 317, 316, 314, 325, 538])).
% 0.99/1.16 tff(1449,plain,
% 0.99/1.16 (c3_1(a10)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[632, 1448])).
% 0.99/1.16 tff(1450,plain,
% 0.99/1.16 (c0_1(a10)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[615, 1448])).
% 0.99/1.16 tff(1451,plain,
% 0.99/1.16 (c2_1(a10)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[624, 1448])).
% 0.99/1.16 tff(1452,assumption,(c0_1(a5)), introduced(assumption)).
% 0.99/1.16 tff(1453,assumption,(~c2_1(a5)), introduced(assumption)).
% 0.99/1.16 tff(1454,assumption,(hskp18), introduced(assumption)).
% 0.99/1.16 tff(1455,plain,
% 0.99/1.16 (~c1_1(a32)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[882, 1454])).
% 0.99/1.16 tff(1456,plain,
% 0.99/1.16 (~c3_1(a32)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[888, 1454])).
% 0.99/1.16 tff(1457,plain,
% 0.99/1.16 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(1458,plain,
% 0.99/1.16 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[1457])).
% 0.99/1.16 tff(1459,plain,
% 0.99/1.16 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1460,plain,
% 0.99/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | 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)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(1461,plain,
% 0.99/1.16 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[1460])).
% 0.99/1.16 tff(1462,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))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.99/1.16 tff(1463,plain,
% 0.99/1.16 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.99/1.16 tff(1464,plain,
% 0.99/1.16 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1463, 1459])).
% 0.99/1.16 tff(1465,plain,(
% 0.99/1.16 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.99/1.16 inference(skolemize,[status(sab)],[1464])).
% 0.99/1.16 tff(1466,plain,
% 0.99/1.16 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1465, 1458])).
% 0.99/1.16 tff(1467,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1468,plain,
% 0.99/1.16 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32))) <=> (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1469,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[1468])).
% 0.99/1.16 tff(1470,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32)))),
% 0.99/1.16 inference(transitivity,[status(thm)],[1469, 1467])).
% 0.99/1.16 tff(1471,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(1472,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.99/1.16 tff(1473,plain,
% 0.99/1.16 (c1_1(a32) | (~c2_1(a32))),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1472, 160, 656, 655, 654, 902, 1466])).
% 0.99/1.16 tff(1474,plain,
% 0.99/1.16 (~c2_1(a32)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1473, 903])).
% 0.99/1.16 tff(1475,plain,
% 0.99/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1476,plain,
% 0.99/1.16 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32) | c0_1(a32) | c3_1(a32)) <=> (c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1477,plain,
% 0.99/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32)))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[1476])).
% 0.99/1.16 tff(1478,plain,
% 0.99/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32))),
% 0.99/1.16 inference(transitivity,[status(thm)],[1477, 1475])).
% 0.99/1.16 tff(1479,plain,
% 0.99/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32) | c0_1(a32) | c3_1(a32))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(1480,plain,
% 0.99/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 0.99/1.16 tff(1481,plain,
% 0.99/1.16 (c0_1(a32)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1480, 160, 668, 673, 672, 902, 2, 671, 13, 3, 1474])).
% 0.99/1.16 tff(1482,plain,
% 0.99/1.16 (~hskp18),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1283, 1481])).
% 0.99/1.16 tff(1483,plain,
% 0.99/1.16 (~c0_1(a6)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[861, 1482])).
% 0.99/1.16 tff(1484,plain,
% 0.99/1.16 (~hskp6),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1276, 1482, 595, 668, 3, 971, 970, 2, 972])).
% 0.99/1.16 tff(1485,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1486,plain,
% 0.99/1.16 ((hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6))) <=> (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(1487,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6)))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[1486])).
% 0.99/1.16 tff(1488,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6))),
% 0.99/1.16 inference(transitivity,[status(thm)],[1487, 1485])).
% 0.99/1.16 tff(1489,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(1490,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 0.99/1.16 tff(1491,plain,
% 0.99/1.16 (~c1_1(a10)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1490, 160, 1484, 655, 654, 672, 671, 1202, 1483])).
% 0.99/1.16 tff(1492,assumption,(~c1_1(a10)), introduced(assumption)).
% 0.99/1.16 tff(1493,plain,
% 0.99/1.16 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(1494,plain,
% 0.99/1.16 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[1493])).
% 0.99/1.16 tff(1495,plain,
% 0.99/1.16 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1496,plain,
% 0.99/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.99/1.17 inference(bind,[status(th)],[])).
% 0.99/1.17 tff(1497,plain,
% 0.99/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.99/1.17 inference(quant_intro,[status(thm)],[1496])).
% 0.99/1.17 tff(1498,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.99/1.17 tff(1499,plain,
% 0.99/1.17 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 0.99/1.17 tff(1500,plain,
% 0.99/1.17 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[1499, 1495])).
% 0.99/1.17 tff(1501,plain,(
% 0.99/1.17 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.99/1.17 inference(skolemize,[status(sab)],[1500])).
% 0.99/1.17 tff(1502,plain,
% 0.99/1.17 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[1501, 1494])).
% 0.99/1.17 tff(1503,assumption,(~hskp13), introduced(assumption)).
% 0.99/1.17 tff(1504,plain,
% 0.99/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1505,plain,
% 0.99/1.17 ((hskp13 | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5))) <=> (hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1506,plain,
% 0.99/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[1505])).
% 0.99/1.17 tff(1507,plain,
% 0.99/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[1506, 1504])).
% 0.99/1.17 tff(1508,plain,
% 0.99/1.17 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(1509,plain,
% 0.99/1.17 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[1508, 1507])).
% 0.99/1.17 tff(1510,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1509, 160, 1503, 656, 654, 969, 1453, 1502, 1452, 1492])).
% 0.99/1.17 tff(1511,plain,(c1_1(a10) | hskp13 | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(1512,plain,
% 0.99/1.17 (hskp13),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1511, 1491, 656, 654, 969, 1453, 1452])).
% 0.99/1.17 tff(1513,plain,
% 0.99/1.17 (~c3_1(a22)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[449, 1512])).
% 0.99/1.17 tff(1514,plain,
% 0.99/1.17 (~c2_1(a22)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[455, 1512])).
% 0.99/1.17 tff(1515,plain,
% 0.99/1.17 (~c0_1(a22)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[461, 1512])).
% 0.99/1.17 tff(1516,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1517,plain,
% 0.99/1.17 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> ((~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1518,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[1517])).
% 0.99/1.17 tff(1519,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[1518, 1516])).
% 0.99/1.17 tff(1520,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(1521,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 0.99/1.17 tff(1522,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1521, 160, 673, 672, 1481, 903, 902, 1515, 1514, 1513, 671, 13])).
% 0.99/1.17 tff(1523,plain,(c1_1(a32) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c2_1(a6) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | (~c2_1(a10)) | hskp17 | (~c0_1(a16)) | c1_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~c2_1(a24))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(1524,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1523, 1456, 1455, 672, 673, 671, 656, 654, 969, 1453, 1452, 655, 595, 668, 3, 971, 970, 2, 972])).
% 0.99/1.17 tff(1525,plain,((~hskp18) | (~c3_1(a6)) | (~c1_1(a6)) | c2_1(a6) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | (~c2_1(a10)) | hskp17 | (~c0_1(a16)) | c1_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~c2_1(a24))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(1526,plain,
% 0.99/1.17 (~hskp18),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1525, 1450, 605, 603, 604, 1449, 967, 991, 999, 1451, 595, 546, 990, 950, 944, 532, 958])).
% 0.99/1.17 tff(1527,plain,
% 0.99/1.17 (hskp18 | (~c0_1(a6))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[860, 160, 595, 604, 603, 684])).
% 0.99/1.17 tff(1528,plain,
% 0.99/1.17 (~c0_1(a6)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1527, 1526])).
% 0.99/1.17 tff(1529,plain,
% 0.99/1.17 (~hskp6),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1276, 1526, 595, 546, 990, 950, 944, 532, 958])).
% 0.99/1.17 tff(1530,plain,
% 0.99/1.17 (~c1_1(a10)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1490, 160, 1529, 1451, 1449, 604, 603, 1202, 1528])).
% 0.99/1.17 tff(1531,plain,
% 0.99/1.17 (hskp13),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1511, 1530, 1450, 1449, 967, 991, 999])).
% 0.99/1.17 tff(1532,plain,
% 0.99/1.17 (~c3_1(a22)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[449, 1531])).
% 0.99/1.17 tff(1533,plain,
% 0.99/1.17 (~c2_1(a22)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[455, 1531])).
% 0.99/1.17 tff(1534,plain,
% 0.99/1.17 (~c0_1(a22)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[461, 1531])).
% 0.99/1.17 tff(1535,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1536,plain,
% 0.99/1.17 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1537,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[1536])).
% 0.99/1.17 tff(1538,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[1537, 1535])).
% 0.99/1.17 tff(1539,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(1540,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 0.99/1.17 tff(1541,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1540, 160, 546, 605, 604, 1534, 1533, 1532, 532, 603, 13, 990])).
% 0.99/1.17 tff(1542,plain,(hskp2 | hskp17 | hskp0 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(1543,plain,
% 0.99/1.17 (hskp2),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1542, 314, 595, 73])).
% 0.99/1.17 tff(1544,plain,
% 0.99/1.17 (~c3_1(a4)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[370, 1543])).
% 0.99/1.17 tff(1545,plain,
% 0.99/1.17 (~c2_1(a4)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[384, 1543])).
% 0.99/1.17 tff(1546,plain,
% 0.99/1.17 (c1_1(a4)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[378, 1543])).
% 0.99/1.17 tff(1547,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1548,plain,
% 0.99/1.17 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1549,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[1548])).
% 0.99/1.17 tff(1550,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[1549, 1547])).
% 0.99/1.17 tff(1551,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(1552,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 0.99/1.17 tff(1553,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1552, 160, 616, 625, 633, 668, 388, 24, 2, 407, 387, 406])).
% 0.99/1.17 tff(1554,plain,((~hskp26) | (~c0_1(a16)) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(1555,plain,
% 0.99/1.17 (~hskp26),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1554, 407, 668, 24, 2, 388, 387])).
% 0.99/1.17 tff(1556,plain,
% 0.99/1.17 (hskp16),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1000, 1555])).
% 0.99/1.17 tff(1557,plain,
% 0.99/1.17 (~c2_1(a30)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[567, 1556])).
% 0.99/1.17 tff(1558,plain,
% 0.99/1.17 (~c0_1(a30)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[573, 1556])).
% 0.99/1.17 tff(1559,plain,
% 0.99/1.17 (c1_1(a16) | c3_1(a30)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1011, 160, 668, 673, 672, 1558, 1557, 2, 671, 13])).
% 0.99/1.17 tff(1560,plain,
% 0.99/1.17 (c3_1(a30)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1559, 3])).
% 0.99/1.17 tff(1561,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1562,plain,
% 0.99/1.17 (((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(1563,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53))))),
% 1.02/1.17 inference(monotonicity,[status(thm)],[1562])).
% 1.02/1.17 tff(1564,plain,
% 1.02/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53)))),
% 1.02/1.17 inference(transitivity,[status(thm)],[1563, 1561])).
% 1.02/1.17 tff(1565,plain,
% 1.02/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.02/1.17 inference(quant_inst,[status(thm)],[])).
% 1.02/1.17 tff(1566,plain,
% 1.02/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53))),
% 1.02/1.17 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 1.02/1.17 tff(1567,plain,
% 1.02/1.17 (c1_1(a16) | (~c2_1(a53))),
% 1.02/1.17 inference(unit_resolution,[status(thm)],[1566, 160, 668, 388, 340, 339, 2, 407, 387, 425])).
% 1.02/1.17 tff(1568,plain,
% 1.02/1.17 (~c2_1(a53)),
% 1.02/1.17 inference(unit_resolution,[status(thm)],[1567, 3])).
% 1.02/1.17 tff(1569,plain,
% 1.02/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.02/1.17 inference(rewrite,[status(thm)],[])).
% 1.02/1.17 tff(1570,plain,
% 1.02/1.17 (((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.02/1.17 inference(rewrite,[status(thm)],[])).
% 1.02/1.17 tff(1571,plain,
% 1.02/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42))))),
% 1.02/1.17 inference(monotonicity,[status(thm)],[1570])).
% 1.02/1.17 tff(1572,plain,
% 1.02/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.02/1.17 inference(transitivity,[status(thm)],[1571, 1569])).
% 1.02/1.17 tff(1573,plain,
% 1.02/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.02/1.17 inference(quant_inst,[status(thm)],[])).
% 1.02/1.17 tff(1574,plain,
% 1.02/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42))),
% 1.02/1.17 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 1.02/1.17 tff(1575,plain,
% 1.02/1.17 (~c0_1(a42)),
% 1.02/1.17 inference(unit_resolution,[status(thm)],[1574, 160, 746, 738, 668, 388, 24, 2, 407, 387, 406])).
% 1.02/1.17 tff(1576,plain,
% 1.02/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42))),
% 1.02/1.17 inference(rewrite,[status(thm)],[])).
% 1.02/1.17 tff(1577,plain,
% 1.02/1.17 (((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42))) <=> (c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42))),
% 1.02/1.17 inference(rewrite,[status(thm)],[])).
% 1.02/1.17 tff(1578,plain,
% 1.02/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42)))),
% 1.02/1.17 inference(monotonicity,[status(thm)],[1577])).
% 1.02/1.17 tff(1579,plain,
% 1.02/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42))),
% 1.02/1.17 inference(transitivity,[status(thm)],[1578, 1576])).
% 1.02/1.17 tff(1580,plain,
% 1.02/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42)))),
% 1.02/1.17 inference(quant_inst,[status(thm)],[])).
% 1.02/1.17 tff(1581,plain,
% 1.02/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42)),
% 1.02/1.17 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 1.02/1.17 tff(1582,plain,
% 1.02/1.17 ($false),
% 1.02/1.17 inference(unit_resolution,[status(thm)],[1581, 160, 746, 668, 388, 759, 2, 407, 387, 425, 3, 1575])).
% 1.02/1.17 tff(1583,plain,((~hskp21) | (~c0_1(a16)) | (~c1_1(a4)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | c1_1(a16) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.17 tff(1584,plain,
% 1.02/1.17 (~hskp21),
% 1.02/1.17 inference(unit_resolution,[status(thm)],[1583, 3, 388, 2, 407, 387, 668, 24])).
% 1.02/1.17 tff(1585,plain,
% 1.02/1.17 (hskp25),
% 1.02/1.17 inference(unit_resolution,[status(thm)],[158, 1584, 595])).
% 1.02/1.18 tff(1586,plain,
% 1.02/1.18 (c2_1(a9)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[787, 1585])).
% 1.02/1.18 tff(1587,plain,
% 1.02/1.18 (c0_1(a9)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[803, 1585])).
% 1.02/1.18 tff(1588,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1589,plain,
% 1.02/1.18 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1590,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[1589])).
% 1.02/1.18 tff(1591,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[1590, 1588])).
% 1.02/1.18 tff(1592,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(1593,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 1.02/1.18 tff(1594,plain,
% 1.02/1.18 (~c3_1(a9)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1593, 160, 1587, 1586, 668, 388, 24, 2, 407, 387, 406])).
% 1.02/1.18 tff(1595,plain,
% 1.02/1.18 (hskp20 | c3_1(a9)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1219, 160, 1555, 1587, 1586, 1134])).
% 1.02/1.18 tff(1596,plain,
% 1.02/1.18 (hskp20),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1595, 1594])).
% 1.02/1.18 tff(1597,plain,
% 1.02/1.18 (~c3_1(a37)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1146, 1596])).
% 1.02/1.18 tff(1598,plain,
% 1.02/1.18 (~c0_1(a37)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1152, 1596])).
% 1.02/1.18 tff(1599,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1600,plain,
% 1.02/1.18 (((~ndr1_0) | c2_1(a30) | c0_1(a30) | (~c3_1(a30)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a53) | c1_1(a53) | c0_1(a53)) <=> (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1601,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a30) | c0_1(a30) | (~c3_1(a30)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a53) | c1_1(a53) | c0_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53)))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[1600])).
% 1.02/1.18 tff(1602,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a30) | c0_1(a30) | (~c3_1(a30)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a53) | c1_1(a53) | c0_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53))),
% 1.02/1.18 inference(transitivity,[status(thm)],[1601, 1599])).
% 1.02/1.18 tff(1603,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a30) | c0_1(a30) | (~c3_1(a30)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a53) | c1_1(a53) | c0_1(a53))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(1604,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53)),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.02/1.18 tff(1605,plain,
% 1.02/1.18 (c2_1(a37)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1604, 160, 340, 339, 1598, 1597, 1558, 1557, 55, 1568, 1560])).
% 1.02/1.18 tff(1606,plain,
% 1.02/1.18 (c1_1(a9)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[795, 1585])).
% 1.02/1.18 tff(1607,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1608,plain,
% 1.02/1.18 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37))) <=> (c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1609,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[1608])).
% 1.02/1.18 tff(1610,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[1609, 1607])).
% 1.02/1.18 tff(1611,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(1612,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 1.02/1.18 tff(1613,plain,
% 1.02/1.18 ($false),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1612, 160, 1587, 1606, 1586, 388, 1598, 1597, 407, 387, 34, 1605])).
% 1.02/1.18 tff(1614,plain,(c1_1(a16) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | c0_1(a53) | c1_1(a53) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | hskp17 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.18 tff(1615,plain,
% 1.02/1.18 (c1_1(a16)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1614, 1546, 1545, 1544, 317, 316, 546, 538, 532, 595, 605, 604, 603])).
% 1.02/1.18 tff(1616,plain,
% 1.02/1.18 (~hskp26),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1554, 1545, 546, 538, 532, 1546, 1544])).
% 1.02/1.18 tff(1617,plain,
% 1.02/1.18 (~hskp27),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[717, 674, 24, 2, 709, 668, 595])).
% 1.02/1.18 tff(1618,assumption,(~c0_1(a6)), introduced(assumption)).
% 1.02/1.18 tff(1619,plain,
% 1.02/1.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1620,plain,
% 1.02/1.18 ((hskp10 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a6) | (~c3_1(a6)) | (~c1_1(a6))) <=> (hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1621,plain,
% 1.02/1.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[1620])).
% 1.02/1.18 tff(1622,plain,
% 1.02/1.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.02/1.18 tff(1623,plain,
% 1.02/1.18 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(1624,plain,
% 1.02/1.18 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.02/1.18 tff(1625,plain,
% 1.02/1.18 (hskp10),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1624, 160, 746, 738, 673, 672, 759, 1053, 1618])).
% 1.02/1.18 tff(1626,plain,
% 1.02/1.18 (~c3_1(a18)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1066, 1625])).
% 1.02/1.18 tff(1627,plain,
% 1.02/1.18 (c2_1(a18)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1074, 1625])).
% 1.02/1.18 tff(1628,plain,
% 1.02/1.18 (c0_1(a18)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1082, 1625])).
% 1.02/1.18 tff(1629,plain,
% 1.02/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1630,plain,
% 1.02/1.18 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a42) | (~c3_1(a42)) | (~c2_1(a42))) <=> (hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1631,plain,
% 1.02/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a42) | (~c3_1(a42)) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42)))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[1630])).
% 1.02/1.18 tff(1632,plain,
% 1.02/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a42) | (~c3_1(a42)) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.02/1.18 inference(transitivity,[status(thm)],[1631, 1629])).
% 1.02/1.18 tff(1633,plain,
% 1.02/1.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a42) | (~c3_1(a42)) | (~c2_1(a42)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(1634,plain,
% 1.02/1.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42)),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 1.02/1.18 tff(1635,plain,
% 1.02/1.18 (hskp11),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1634, 160, 746, 738, 1628, 1627, 1626, 1042, 753])).
% 1.02/1.18 tff(1636,plain,
% 1.02/1.18 (~c1_1(a19)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1116, 1635])).
% 1.02/1.18 tff(1637,plain,
% 1.02/1.18 (hskp20),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1140, 160, 84, 1628, 1627, 1626, 1134])).
% 1.02/1.18 tff(1638,plain,
% 1.02/1.18 (~c3_1(a37)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1146, 1637])).
% 1.02/1.18 tff(1639,plain,
% 1.02/1.18 (~c0_1(a37)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1152, 1637])).
% 1.02/1.18 tff(1640,plain,
% 1.02/1.18 (c2_1(a19)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1103, 1635])).
% 1.02/1.18 tff(1641,plain,
% 1.02/1.18 (c1_1(a37)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1160, 1637])).
% 1.02/1.18 tff(1642,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1643,plain,
% 1.02/1.18 (((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a19) | c0_1(a19) | (~c2_1(a19))) <=> (c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1644,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a19) | c0_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[1643])).
% 1.02/1.18 tff(1645,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a19) | c0_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[1644, 1642])).
% 1.02/1.18 tff(1646,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a19) | c0_1(a19) | (~c2_1(a19)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(1647,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 1.02/1.18 tff(1648,plain,
% 1.02/1.18 (c0_1(a19)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1647, 160, 746, 738, 1641, 1640, 759, 1639, 1638, 1636, 83])).
% 1.02/1.18 tff(1649,plain,
% 1.02/1.18 (^[U: $i] : refl((hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) <=> (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))))),
% 1.02/1.18 inference(bind,[status(th)],[])).
% 1.02/1.18 tff(1650,plain,
% 1.02/1.18 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.02/1.18 inference(quant_intro,[status(thm)],[1649])).
% 1.02/1.18 tff(1651,plain,
% 1.02/1.18 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1652,plain,
% 1.02/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_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)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp12) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) | hskp12))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))))),
% 1.02/1.18 inference(bind,[status(th)],[])).
% 1.02/1.18 tff(1653,plain,
% 1.02/1.18 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp12) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.02/1.18 inference(quant_intro,[status(thm)],[1652])).
% 1.02/1.18 tff(1654,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.02/1.18 tff(1655,plain,
% 1.02/1.18 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 1.02/1.18 tff(1656,plain,
% 1.02/1.18 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1655, 1651])).
% 1.02/1.18 tff(1657,plain,(
% 1.02/1.18 ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.02/1.18 inference(skolemize,[status(sab)],[1656])).
% 1.02/1.18 tff(1658,plain,
% 1.02/1.18 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1657, 1650])).
% 1.02/1.18 tff(1659,plain,
% 1.02/1.18 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1660,plain,
% 1.02/1.18 ((hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42) | (~c3_1(a42))) <=> (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1661,plain,
% 1.02/1.18 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42) | (~c3_1(a42)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42)))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[1660])).
% 1.02/1.18 tff(1662,plain,
% 1.02/1.18 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42) | (~c3_1(a42)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.02/1.18 inference(transitivity,[status(thm)],[1661, 1659])).
% 1.02/1.18 tff(1663,plain,
% 1.02/1.18 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42) | (~c3_1(a42)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(1664,plain,
% 1.02/1.18 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42)),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 1.02/1.18 tff(1665,plain,
% 1.02/1.18 (hskp12),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1664, 829, 160, 746, 738, 1658, 753])).
% 1.02/1.18 tff(1666,plain,
% 1.02/1.18 (((~hskp12) | (~c2_1(a21))) <=> ((~hskp12) | (~c2_1(a21)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(1667,plain,
% 1.02/1.18 (((~c2_1(a21)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a21)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1668,axiom,((~c2_1(a21)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.02/1.19 tff(1669,plain,
% 1.02/1.19 ((~hskp12) | (~c2_1(a21))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 1.02/1.19 tff(1670,plain,
% 1.02/1.19 ((~hskp12) | (~c2_1(a21))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1669, 1666])).
% 1.02/1.19 tff(1671,plain,
% 1.02/1.19 (~c2_1(a21)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1670, 1665])).
% 1.02/1.19 tff(1672,plain,
% 1.02/1.19 (((~hskp12) | (~c1_1(a21))) <=> ((~hskp12) | (~c1_1(a21)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1673,plain,
% 1.02/1.19 (((~c1_1(a21)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a21)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1674,axiom,((~c1_1(a21)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.02/1.19 tff(1675,plain,
% 1.02/1.19 ((~hskp12) | (~c1_1(a21))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 1.02/1.19 tff(1676,plain,
% 1.02/1.19 ((~hskp12) | (~c1_1(a21))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1675, 1672])).
% 1.02/1.19 tff(1677,plain,
% 1.02/1.19 (~c1_1(a21)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1676, 1665])).
% 1.02/1.19 tff(1678,plain,
% 1.02/1.19 (((~hskp12) | (~c0_1(a21))) <=> ((~hskp12) | (~c0_1(a21)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1679,plain,
% 1.02/1.19 (((~c0_1(a21)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a21)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1680,axiom,((~c0_1(a21)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.02/1.19 tff(1681,plain,
% 1.02/1.19 ((~hskp12) | (~c0_1(a21))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 1.02/1.19 tff(1682,plain,
% 1.02/1.19 ((~hskp12) | (~c0_1(a21))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1681, 1678])).
% 1.02/1.19 tff(1683,plain,
% 1.02/1.19 (~c0_1(a21)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1682, 1665])).
% 1.02/1.19 tff(1684,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1685,plain,
% 1.02/1.19 ((hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a21) | c0_1(a21) | c2_1(a21)) <=> (hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1686,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a21) | c0_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1685])).
% 1.02/1.19 tff(1687,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a21) | c0_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1686, 1684])).
% 1.02/1.19 tff(1688,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a21) | c0_1(a21) | c2_1(a21))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1689,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 1.02/1.19 tff(1690,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1689, 160, 314, 1640, 1683, 1677, 1671, 1636, 312, 1648])).
% 1.02/1.19 tff(1691,plain,((~hskp21) | hskp0 | hskp26 | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | hskp27 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(1692,plain,
% 1.02/1.19 (~hskp21),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1691, 862, 84, 673, 672, 314, 1617, 668, 24, 2, 709])).
% 1.02/1.19 tff(1693,plain,
% 1.02/1.19 (hskp25),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[158, 1692, 595])).
% 1.02/1.19 tff(1694,plain,
% 1.02/1.19 (hskp19),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[813, 1693, 673, 672, 671])).
% 1.02/1.19 tff(1695,plain,
% 1.02/1.19 (~c0_1(a33)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[819, 1694])).
% 1.02/1.19 tff(1696,plain,
% 1.02/1.19 (c2_1(a33)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[827, 1694])).
% 1.02/1.19 tff(1697,plain,
% 1.02/1.19 (~c1_1(a33)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[835, 1617, 160, 84, 1696, 1695, 728])).
% 1.02/1.19 tff(1698,plain,
% 1.02/1.19 (c2_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[787, 1693])).
% 1.02/1.19 tff(1699,plain,
% 1.02/1.19 (c0_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[803, 1693])).
% 1.02/1.19 tff(1700,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1701,plain,
% 1.02/1.19 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1702,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1701])).
% 1.02/1.19 tff(1703,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1702, 1700])).
% 1.02/1.19 tff(1704,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1705,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 1.02/1.19 tff(1706,plain,
% 1.02/1.19 (~c3_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1705, 160, 1699, 1698, 668, 24, 2, 406, 709])).
% 1.02/1.19 tff(1707,plain,
% 1.02/1.19 (hskp20 | c3_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1219, 160, 84, 1699, 1698, 1134])).
% 1.02/1.19 tff(1708,plain,
% 1.02/1.19 (hskp20),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1707, 1706])).
% 1.02/1.19 tff(1709,plain,
% 1.02/1.19 (~c3_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1146, 1708])).
% 1.02/1.19 tff(1710,plain,
% 1.02/1.19 (~c0_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1152, 1708])).
% 1.02/1.19 tff(1711,plain,
% 1.02/1.19 (c3_1(a33)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1392, 1694])).
% 1.02/1.19 tff(1712,plain,
% 1.02/1.19 (c1_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1160, 1708])).
% 1.02/1.19 tff(1713,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1714,plain,
% 1.02/1.19 (((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1715,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1714])).
% 1.02/1.19 tff(1716,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1715, 1713])).
% 1.02/1.19 tff(1717,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1718,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.02/1.19 tff(1719,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1718, 160, 1712, 1696, 1711, 1710, 1709, 1695, 83, 1697])).
% 1.02/1.19 tff(1720,plain,(hskp18 | hskp26 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(1721,plain,
% 1.02/1.19 (hskp18),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1720, 1616, 546, 538, 532, 1615, 605, 604, 603, 595, 314])).
% 1.02/1.19 tff(1722,plain,
% 1.02/1.19 (~c3_1(a32)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[888, 1721])).
% 1.02/1.19 tff(1723,plain,
% 1.02/1.19 (~c1_1(a32)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[882, 1721])).
% 1.02/1.19 tff(1724,plain,
% 1.02/1.19 (~c0_1(a32)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1283, 1721])).
% 1.02/1.19 tff(1725,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[909, 160, 73, 546, 1724, 1723, 1722, 532, 901, 1615])).
% 1.02/1.19 tff(1726,plain,(hskp0 | hskp24 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(1727,plain,
% 1.02/1.19 (hskp0),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1726, 595, 73])).
% 1.02/1.19 tff(1728,plain,
% 1.02/1.19 (~c2_1(a1)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[241, 1727])).
% 1.02/1.19 tff(1729,plain,
% 1.02/1.19 (~c0_1(a1)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[262, 1727])).
% 1.02/1.19 tff(1730,plain,
% 1.02/1.19 (c3_1(a1)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[249, 1727])).
% 1.02/1.19 tff(1731,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1732,plain,
% 1.02/1.19 ((hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1733,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1732])).
% 1.02/1.19 tff(1734,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1733, 1731])).
% 1.02/1.19 tff(1735,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1736,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 1.02/1.19 tff(1737,plain,
% 1.02/1.19 (hskp4 | (~c1_1(a1)) | c1_1(a16)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1736, 160, 668, 463, 2, 444, 584])).
% 1.02/1.19 tff(1738,plain,
% 1.02/1.19 (~c1_1(a1)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1737, 193, 3])).
% 1.02/1.19 tff(1739,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[269, 160, 193, 598, 463, 599, 597, 444, 65, 1738])).
% 1.02/1.19 tff(1740,plain,(hskp4 | (~c3_1(a1)) | c0_1(a1) | c1_1(a16) | (~c0_1(a16)) | c3_1(a16) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(1741,plain,
% 1.02/1.19 (hskp4),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1740, 3, 444, 463, 668, 2, 595])).
% 1.02/1.19 tff(1742,plain,
% 1.02/1.19 (~c2_1(a6)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[111, 1741])).
% 1.02/1.19 tff(1743,plain,
% 1.02/1.19 (c3_1(a6)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[119, 1741])).
% 1.02/1.19 tff(1744,plain,
% 1.02/1.19 (c1_1(a6)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[127, 1741])).
% 1.02/1.19 tff(1745,plain,
% 1.02/1.19 (c3_1(a30)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1011, 160, 668, 673, 672, 1004, 1002, 2, 671, 13, 3])).
% 1.02/1.19 tff(1746,assumption,(hskp2), introduced(assumption)).
% 1.02/1.19 tff(1747,plain,
% 1.02/1.19 (~c3_1(a4)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[370, 1746])).
% 1.02/1.19 tff(1748,plain,
% 1.02/1.19 (~c2_1(a4)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[384, 1746])).
% 1.02/1.19 tff(1749,plain,
% 1.02/1.19 (c1_1(a4)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[378, 1746])).
% 1.02/1.19 tff(1750,plain,
% 1.02/1.19 (~hskp21),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1583, 1749, 3, 2, 1748, 1747, 668, 24])).
% 1.02/1.19 tff(1751,plain,
% 1.02/1.19 (hskp25),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[158, 1750, 595])).
% 1.02/1.19 tff(1752,plain,
% 1.02/1.19 (c2_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[787, 1751])).
% 1.02/1.19 tff(1753,plain,
% 1.02/1.19 (c0_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[803, 1751])).
% 1.02/1.19 tff(1754,plain,
% 1.02/1.19 (~c3_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1593, 160, 1753, 1752, 668, 1749, 24, 2, 1748, 1747, 406])).
% 1.02/1.19 tff(1755,plain,
% 1.02/1.19 (hskp20 | c3_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1219, 160, 84, 1753, 1752, 1134])).
% 1.02/1.19 tff(1756,plain,
% 1.02/1.19 (hskp20),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1755, 1754])).
% 1.02/1.19 tff(1757,plain,
% 1.02/1.19 (~c3_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1146, 1756])).
% 1.02/1.19 tff(1758,plain,
% 1.02/1.19 (~c0_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1152, 1756])).
% 1.02/1.19 tff(1759,plain,
% 1.02/1.19 (c1_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[795, 1751])).
% 1.02/1.19 tff(1760,plain,
% 1.02/1.19 (~c2_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1612, 160, 1753, 1759, 1752, 1749, 1758, 1757, 1748, 1747, 34])).
% 1.02/1.19 tff(1761,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1762,plain,
% 1.02/1.19 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1763,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37)))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1762])).
% 1.02/1.19 tff(1764,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1763, 1761])).
% 1.02/1.19 tff(1765,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1766,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 1.02/1.19 tff(1767,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1766, 160, 1003, 668, 1758, 1757, 1002, 2, 13, 1760, 3, 1043])).
% 1.02/1.19 tff(1768,plain,((~hskp2) | (~c0_1(a16)) | c3_1(a16) | c1_1(a16) | (~c3_1(a30)) | hskp26 | c2_1(a16) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(1769,plain,
% 1.02/1.19 (~hskp2),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1768, 1745, 2, 3, 668, 84, 24, 595])).
% 1.02/1.19 tff(1770,plain,
% 1.02/1.19 (hskp14),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[669, 1769, 3])).
% 1.02/1.19 tff(1771,plain,
% 1.02/1.19 (~c0_1(a24)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[949, 1770])).
% 1.02/1.19 tff(1772,assumption,(~c2_1(a24)), introduced(assumption)).
% 1.02/1.19 tff(1773,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1774,plain,
% 1.02/1.19 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a24) | c0_1(a24) | c3_1(a24)) <=> (c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1775,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a24) | c0_1(a24) | c3_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1774])).
% 1.02/1.19 tff(1776,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a24) | c0_1(a24) | c3_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1775, 1773])).
% 1.02/1.19 tff(1777,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a24) | c0_1(a24) | c3_1(a24))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1778,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.02/1.19 tff(1779,plain,
% 1.02/1.19 (c3_1(a24)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1778, 160, 1003, 1772, 668, 1002, 971, 2, 13, 3, 1043])).
% 1.02/1.19 tff(1780,plain,
% 1.02/1.19 (~hskp14),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[957, 1772])).
% 1.02/1.19 tff(1781,plain,
% 1.02/1.19 (hskp2),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[669, 1780, 3])).
% 1.02/1.19 tff(1782,plain,
% 1.02/1.19 (~c3_1(a4)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[370, 1781])).
% 1.02/1.19 tff(1783,plain,
% 1.02/1.19 (~c2_1(a4)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[384, 1781])).
% 1.02/1.19 tff(1784,plain,
% 1.02/1.19 (c1_1(a4)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[378, 1781])).
% 1.02/1.19 tff(1785,plain,
% 1.02/1.19 (~hskp21),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1583, 1784, 3, 2, 1783, 1782, 668, 24])).
% 1.02/1.19 tff(1786,plain,
% 1.02/1.19 (hskp25),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[158, 1785, 595])).
% 1.02/1.19 tff(1787,plain,
% 1.02/1.19 (c2_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[787, 1786])).
% 1.02/1.19 tff(1788,plain,
% 1.02/1.19 (c0_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[803, 1786])).
% 1.02/1.19 tff(1789,plain,
% 1.02/1.19 (~c3_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1593, 160, 1788, 1787, 668, 1784, 24, 2, 1783, 1782, 406])).
% 1.02/1.19 tff(1790,plain,
% 1.02/1.19 (hskp20 | c3_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1219, 160, 84, 1788, 1787, 1134])).
% 1.02/1.19 tff(1791,plain,
% 1.02/1.19 (hskp20),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1790, 1789])).
% 1.02/1.19 tff(1792,plain,
% 1.02/1.19 (~c3_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1146, 1791])).
% 1.02/1.19 tff(1793,plain,
% 1.02/1.19 (~c0_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1152, 1791])).
% 1.02/1.19 tff(1794,plain,
% 1.02/1.19 (c1_1(a9)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[795, 1786])).
% 1.02/1.19 tff(1795,plain,
% 1.02/1.19 (~c2_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1612, 160, 1788, 1794, 1787, 1784, 1793, 1792, 1783, 1782, 34])).
% 1.02/1.19 tff(1796,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1797,plain,
% 1.02/1.19 (((~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a24) | c1_1(a24) | c0_1(a24)) <=> (c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1798,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37)))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1797])).
% 1.02/1.19 tff(1799,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.02/1.19 tff(1800,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a24) | c1_1(a24) | c0_1(a24))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1801,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.02/1.19 tff(1802,plain,
% 1.02/1.19 (c1_1(a24) | c2_1(a37)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1801, 160, 1772, 1793, 1792, 971, 55, 1779])).
% 1.02/1.19 tff(1803,plain,
% 1.02/1.19 (c1_1(a24)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1802, 1795])).
% 1.02/1.20 tff(1804,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1805,plain,
% 1.02/1.20 (((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1806,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37)))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1805])).
% 1.02/1.20 tff(1807,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1806, 1804])).
% 1.02/1.20 tff(1808,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1809,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 1.02/1.20 tff(1810,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1809, 160, 1772, 668, 1793, 1792, 1803, 2, 13, 1795, 3, 1779])).
% 1.02/1.20 tff(1811,plain,(c2_1(a24) | (~c0_1(a16)) | c3_1(a16) | c1_1(a16) | c0_1(a24) | hskp26 | (~c3_1(a30)) | c2_1(a16) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1812,plain,
% 1.02/1.20 (c2_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1811, 971, 2, 3, 668, 84, 1043, 24, 595])).
% 1.02/1.20 tff(1813,plain,
% 1.02/1.20 (~hskp6),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1276, 970, 595, 668, 3, 674, 972, 2, 971])).
% 1.02/1.20 tff(1814,plain,
% 1.02/1.20 (hskp6 | c1_1(a24) | c3_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1190, 160, 84, 972, 1184])).
% 1.02/1.20 tff(1815,plain,
% 1.02/1.20 (c3_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1814, 1813, 970])).
% 1.02/1.20 tff(1816,plain,
% 1.02/1.20 (hskp10),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1059, 160, 586, 972, 585, 970, 1053, 1043, 1815])).
% 1.02/1.20 tff(1817,plain,
% 1.02/1.20 (~c3_1(a18)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1066, 1816])).
% 1.02/1.20 tff(1818,plain,
% 1.02/1.20 (c2_1(a18)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1074, 1816])).
% 1.02/1.20 tff(1819,plain,
% 1.02/1.20 (c0_1(a18)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1082, 1816])).
% 1.02/1.20 tff(1820,plain,
% 1.02/1.20 (hskp11),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1089, 160, 972, 1819, 1818, 971, 1817, 1042, 1815])).
% 1.02/1.20 tff(1821,plain,
% 1.02/1.20 (~c3_1(a19)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1095, 1820])).
% 1.02/1.20 tff(1822,plain,
% 1.02/1.20 (~c1_1(a19)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1116, 1820])).
% 1.02/1.20 tff(1823,plain,
% 1.02/1.20 (c2_1(a19)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1103, 1820])).
% 1.02/1.20 tff(1824,plain,
% 1.02/1.20 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1825,plain,
% 1.02/1.20 ((hskp26 | hskp6 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c2_1(a19))) <=> (hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1826,plain,
% 1.02/1.20 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1825])).
% 1.02/1.20 tff(1827,plain,
% 1.02/1.20 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1826, 1824])).
% 1.02/1.20 tff(1828,plain,
% 1.02/1.20 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1829,plain,
% 1.02/1.20 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.02/1.20 tff(1830,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1829, 160, 84, 1813, 1823, 1822, 1821, 1184])).
% 1.02/1.20 tff(1831,plain,(c1_1(a24) | hskp26 | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a30)) | c0_1(a30) | (~c3_1(a30)) | hskp17 | (~c0_1(a16)) | c1_1(a16) | hskp18 | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1832,plain,
% 1.02/1.20 (c1_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1831, 1812, 84, 971, 1003, 1004, 1043, 595, 668, 3, 674, 2])).
% 1.02/1.20 tff(1833,plain,
% 1.02/1.20 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1834,plain,
% 1.02/1.20 ((hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a24))) <=> (hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1835,plain,
% 1.02/1.20 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a24)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1834])).
% 1.02/1.20 tff(1836,plain,
% 1.02/1.20 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a24)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1835, 1833])).
% 1.02/1.20 tff(1837,plain,
% 1.02/1.20 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a24)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1838,plain,
% 1.02/1.20 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 1.02/1.20 tff(1839,plain,
% 1.02/1.20 (hskp27 | (~c1_1(a24)) | (~c2_1(a24))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1838, 160, 84, 971, 728])).
% 1.02/1.20 tff(1840,plain,
% 1.02/1.20 (hskp27),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1839, 1832, 1812])).
% 1.02/1.20 tff(1841,plain,
% 1.02/1.20 (c3_1(a11)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[692, 1840])).
% 1.02/1.20 tff(1842,plain,
% 1.02/1.20 (c0_1(a11)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[700, 1840])).
% 1.02/1.20 tff(1843,plain,
% 1.02/1.20 (c2_1(a11)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[707, 160, 674, 595, 1842, 1841, 684])).
% 1.02/1.20 tff(1844,plain,
% 1.02/1.20 (~hskp14),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[943, 1832])).
% 1.02/1.20 tff(1845,plain,
% 1.02/1.20 (hskp2),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[669, 1844, 3])).
% 1.02/1.20 tff(1846,plain,
% 1.02/1.20 (~c3_1(a4)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[370, 1845])).
% 1.02/1.20 tff(1847,plain,
% 1.02/1.20 (~c2_1(a4)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[384, 1845])).
% 1.02/1.20 tff(1848,plain,
% 1.02/1.20 (c1_1(a4)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[378, 1845])).
% 1.02/1.20 tff(1849,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1850,plain,
% 1.02/1.20 (((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1851,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1850])).
% 1.02/1.20 tff(1852,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1851, 1849])).
% 1.02/1.20 tff(1853,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1854,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.02/1.20 tff(1855,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1854, 160, 1842, 1841, 668, 1848, 24, 2, 1847, 1846, 406, 1843])).
% 1.02/1.20 tff(1856,plain,(c0_1(a24) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | hskp18 | hskp17 | c1_1(a16) | hskp26 | (~c3_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1857,plain,
% 1.02/1.20 (hskp18),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1856, 1771, 24, 2, 668, 595, 3, 84, 1745])).
% 1.02/1.20 tff(1858,plain,
% 1.02/1.20 (~c1_1(a32)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[882, 1857])).
% 1.02/1.20 tff(1859,plain,
% 1.02/1.20 (~c1_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[943, 1770])).
% 1.02/1.20 tff(1860,plain,
% 1.02/1.20 (c2_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[957, 1770])).
% 1.02/1.20 tff(1861,plain,
% 1.02/1.20 (~c0_1(a32)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1283, 1857])).
% 1.02/1.20 tff(1862,plain,
% 1.02/1.20 (~c3_1(a32)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[888, 1857])).
% 1.02/1.20 tff(1863,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1443, 1862, 1861, 1771, 84, 1003, 1004, 1745, 673, 672, 671, 1002, 1860, 1859, 1858])).
% 1.02/1.20 tff(1864,plain,(hskp26 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)) | hskp17 | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1865,plain,
% 1.02/1.20 (hskp26),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1864, 1744, 1743, 1742, 24, 2, 668, 595, 3])).
% 1.02/1.20 tff(1866,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1554, 1748, 1749, 668, 24, 2, 608, 1747])).
% 1.02/1.20 tff(1867,plain,((~hskp2) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~hskp26)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1868,plain,
% 1.02/1.20 (~hskp2),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1867, 1865, 24, 2, 668])).
% 1.02/1.20 tff(1869,plain,
% 1.02/1.20 (hskp14),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[669, 1868, 3])).
% 1.02/1.20 tff(1870,plain,
% 1.02/1.20 (~c1_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[943, 1869])).
% 1.02/1.20 tff(1871,plain,
% 1.02/1.20 (~c0_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[949, 1869])).
% 1.02/1.20 tff(1872,plain,
% 1.02/1.20 (c2_1(a24)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[957, 1869])).
% 1.02/1.20 tff(1873,plain,
% 1.02/1.20 (hskp3),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[964, 160, 1868, 1872, 1871, 1870, 23])).
% 1.02/1.20 tff(1874,plain,
% 1.02/1.20 (~c3_1(a5)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[867, 1873])).
% 1.02/1.20 tff(1875,plain,
% 1.02/1.20 (~c2_1(a5)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[331, 1873])).
% 1.02/1.20 tff(1876,plain,
% 1.02/1.20 (c0_1(a5)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[997, 160, 668, 1744, 1743, 2, 1742, 1875, 1874, 13, 3])).
% 1.02/1.20 tff(1877,plain,
% 1.02/1.20 (~c1_1(a5)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[337, 1873])).
% 1.02/1.20 tff(1878,plain,
% 1.02/1.20 (c3_1(a10)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[632, 1865])).
% 1.02/1.20 tff(1879,plain,
% 1.02/1.20 (c0_1(a10)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[615, 1865])).
% 1.02/1.20 tff(1880,plain,
% 1.02/1.20 (c2_1(a10)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[624, 1865])).
% 1.02/1.20 tff(1881,plain,
% 1.02/1.20 (~hskp18),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1525, 1876, 1744, 1742, 1879, 1878, 1872, 1875, 1877, 1880, 595, 668, 3, 1871, 1870, 2, 1743])).
% 1.02/1.20 tff(1882,plain,
% 1.02/1.20 (~hskp6),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1276, 1881, 595, 668, 3, 1870, 1872, 2, 1871])).
% 1.02/1.20 tff(1883,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1884,plain,
% 1.02/1.20 ((hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1))) <=> (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1885,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1884])).
% 1.02/1.20 tff(1886,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1885, 1883])).
% 1.02/1.20 tff(1887,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1888,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.02/1.20 tff(1889,plain,
% 1.02/1.20 (hskp6 | (~c1_1(a10))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1888, 160, 1880, 1878, 463, 444, 443, 1202])).
% 1.02/1.20 tff(1890,plain,
% 1.02/1.20 (~c1_1(a10)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1889, 1882])).
% 1.02/1.20 tff(1891,plain,
% 1.02/1.20 (hskp13),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1511, 1890, 1879, 1878, 1877, 1875, 1876])).
% 1.02/1.20 tff(1892,plain,
% 1.02/1.20 (~c3_1(a22)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[449, 1891])).
% 1.02/1.20 tff(1893,plain,
% 1.02/1.20 (~c2_1(a22)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[455, 1891])).
% 1.02/1.20 tff(1894,plain,
% 1.02/1.20 (~c0_1(a22)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[461, 1891])).
% 1.02/1.20 tff(1895,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1540, 160, 668, 1744, 1743, 1894, 1893, 1892, 2, 1742, 13, 3])).
% 1.02/1.20 tff(1896,plain,(c1_1(a16) | (~c0_1(a16)) | c3_1(a16) | (~c3_1(a1)) | c0_1(a1) | c2_1(a1) | hskp17 | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1897,plain,
% 1.02/1.20 (c1_1(a16)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1896, 1730, 532, 546, 1729, 1728, 595, 538])).
% 1.02/1.20 tff(1898,plain,
% 1.02/1.20 (~c0_1(a32)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1283, 1454])).
% 1.02/1.20 tff(1899,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[909, 160, 73, 546, 1898, 1455, 1456, 532, 901, 709])).
% 1.02/1.20 tff(1900,plain,((~hskp18) | hskp24 | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1901,plain,
% 1.02/1.20 (~hskp18),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1900, 1897, 73])).
% 1.02/1.20 tff(1902,assumption,(~c3_1(a15)), introduced(assumption)).
% 1.02/1.20 tff(1903,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1904,plain,
% 1.02/1.20 ((hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1905,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1904])).
% 1.02/1.20 tff(1906,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1905, 1903])).
% 1.02/1.20 tff(1907,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1908,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 1.02/1.20 tff(1909,plain,
% 1.02/1.20 (~c3_1(a30)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1908, 160, 193, 586, 192, 585, 194, 584, 1902])).
% 1.02/1.20 tff(1910,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1911,plain,
% 1.02/1.20 ((hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1912,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1911])).
% 1.02/1.20 tff(1913,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1912, 1910])).
% 1.02/1.20 tff(1914,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1915,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.02/1.20 tff(1916,plain,
% 1.02/1.20 (~c1_1(a1)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1915, 160, 193, 192, 463, 194, 444, 584, 1902])).
% 1.02/1.20 tff(1917,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1918,plain,
% 1.02/1.20 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a30) | c0_1(a30) | c2_1(a30) | c2_1(a1) | c1_1(a1) | c0_1(a1)) <=> (c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1919,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a30) | c0_1(a30) | c2_1(a30) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30)))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1918])).
% 1.02/1.20 tff(1920,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a30) | c0_1(a30) | c2_1(a30) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1919, 1917])).
% 1.02/1.20 tff(1921,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a30) | c0_1(a30) | c2_1(a30) | c2_1(a1) | c1_1(a1) | c0_1(a1))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1922,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 1.02/1.20 tff(1923,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1922, 160, 463, 585, 1005, 444, 443, 55, 1916, 1909])).
% 1.02/1.20 tff(1924,plain,(c3_1(a15) | (~c3_1(a1)) | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | hskp4 | (~c0_1(a15)) | c1_1(a15) | (~c1_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1925,plain,
% 1.02/1.20 (c3_1(a15)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1924, 598, 585, 1005, 444, 443, 586, 193, 599, 463])).
% 1.02/1.20 tff(1926,plain,
% 1.02/1.20 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1927,plain,
% 1.02/1.20 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15))) <=> (hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1928,plain,
% 1.02/1.20 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1927])).
% 1.02/1.20 tff(1929,plain,
% 1.02/1.20 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1928, 1926])).
% 1.02/1.20 tff(1930,plain,
% 1.02/1.20 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1931,plain,
% 1.02/1.20 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 1.02/1.20 tff(1932,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1931, 160, 674, 595, 598, 597, 684, 1925])).
% 1.02/1.20 tff(1933,plain,(hskp4 | hskp18 | hskp17 | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~c1_1(a30)) | (~c3_1(a1))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1934,plain,
% 1.02/1.20 (hskp4),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1933, 1004, 595, 674, 1002, 444, 443, 1003, 463])).
% 1.02/1.20 tff(1935,plain,
% 1.02/1.20 (~c2_1(a6)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[111, 1934])).
% 1.02/1.20 tff(1936,plain,
% 1.02/1.20 (c1_1(a16)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1896, 463, 2, 668, 444, 443, 595, 24])).
% 1.02/1.20 tff(1937,plain,
% 1.02/1.20 (c1_1(a6)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[127, 1934])).
% 1.02/1.20 tff(1938,plain,
% 1.02/1.20 (c3_1(a6)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[119, 1934])).
% 1.02/1.20 tff(1939,plain,
% 1.02/1.20 (hskp19),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[813, 780, 673, 672, 671])).
% 1.02/1.20 tff(1940,plain,
% 1.02/1.20 (~c0_1(a33)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[819, 1939])).
% 1.02/1.20 tff(1941,plain,
% 1.02/1.20 (c2_1(a33)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[827, 1939])).
% 1.02/1.20 tff(1942,plain,
% 1.02/1.20 (~c1_1(a33)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[835, 829, 160, 84, 1941, 1940, 728])).
% 1.02/1.20 tff(1943,plain,
% 1.02/1.20 (~c3_1(a9)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1705, 160, 804, 788, 668, 24, 2, 406, 709])).
% 1.02/1.20 tff(1944,plain,
% 1.02/1.20 (hskp20 | c3_1(a9)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1219, 160, 84, 804, 788, 1134])).
% 1.02/1.20 tff(1945,plain,
% 1.02/1.20 (hskp20),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1944, 1943])).
% 1.02/1.20 tff(1946,plain,
% 1.02/1.20 (~c3_1(a37)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1146, 1945])).
% 1.02/1.20 tff(1947,plain,
% 1.02/1.20 (~c0_1(a37)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1152, 1945])).
% 1.02/1.20 tff(1948,plain,
% 1.02/1.20 (c3_1(a33)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1392, 1939])).
% 1.02/1.20 tff(1949,plain,
% 1.02/1.20 (c1_1(a37)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1160, 1945])).
% 1.02/1.20 tff(1950,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1718, 160, 1949, 1941, 1948, 1947, 1946, 1940, 83, 1942])).
% 1.02/1.20 tff(1951,plain,((~hskp25) | hskp26 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | hskp27 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1952,plain,
% 1.02/1.20 (~hskp25),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1951, 1617, 668, 24, 2, 709, 84, 673, 672, 671])).
% 1.02/1.20 tff(1953,plain,
% 1.02/1.20 (hskp21),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[158, 1952, 595])).
% 1.02/1.20 tff(1954,plain,
% 1.02/1.20 (c3_1(a42)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[737, 1953])).
% 1.02/1.20 tff(1955,plain,
% 1.02/1.20 (c2_1(a42)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[745, 1953])).
% 1.02/1.20 tff(1956,plain,
% 1.02/1.20 (~c0_1(a42)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[752, 160, 1955, 1954, 668, 24, 2, 406, 709])).
% 1.02/1.20 tff(1957,plain,
% 1.02/1.20 (~c1_1(a42)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[758, 1953])).
% 1.02/1.20 tff(1958,plain,
% 1.02/1.20 (hskp10),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1624, 160, 1955, 1954, 673, 672, 1957, 1053, 862])).
% 1.02/1.20 tff(1959,plain,
% 1.02/1.20 (~c3_1(a18)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1066, 1958])).
% 1.02/1.20 tff(1960,plain,
% 1.02/1.20 (c2_1(a18)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1074, 1958])).
% 1.02/1.20 tff(1961,plain,
% 1.02/1.20 (c0_1(a18)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1082, 1958])).
% 1.02/1.20 tff(1962,plain,
% 1.02/1.20 (hskp11),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1634, 160, 1955, 1954, 1961, 1960, 1959, 1042, 1956])).
% 1.02/1.20 tff(1963,plain,
% 1.02/1.20 (~c1_1(a19)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1116, 1962])).
% 1.02/1.21 tff(1964,plain,
% 1.02/1.21 (hskp20),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1140, 160, 84, 1961, 1960, 1959, 1134])).
% 1.02/1.21 tff(1965,plain,
% 1.02/1.21 (~c3_1(a37)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1146, 1964])).
% 1.02/1.21 tff(1966,plain,
% 1.02/1.21 (~c0_1(a37)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1152, 1964])).
% 1.02/1.21 tff(1967,plain,
% 1.02/1.21 (c2_1(a19)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1103, 1962])).
% 1.02/1.21 tff(1968,plain,
% 1.02/1.21 (c1_1(a37)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1160, 1964])).
% 1.02/1.21 tff(1969,plain,
% 1.02/1.21 (c0_1(a19)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1647, 160, 1955, 1954, 1968, 1967, 1957, 1966, 1965, 1963, 83])).
% 1.02/1.21 tff(1970,plain,
% 1.02/1.21 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1971,plain,
% 1.02/1.21 ((hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a37)) | c0_1(a37) | (~c1_1(a37))) <=> (hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1972,plain,
% 1.02/1.21 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a37)) | c0_1(a37) | (~c1_1(a37)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[1971])).
% 1.02/1.21 tff(1973,plain,
% 1.02/1.21 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a37)) | c0_1(a37) | (~c1_1(a37)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[1972, 1970])).
% 1.02/1.21 tff(1974,plain,
% 1.02/1.21 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a37)) | c0_1(a37) | (~c1_1(a37)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(1975,plain,
% 1.02/1.21 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1974, 1973])).
% 1.02/1.21 tff(1976,plain,
% 1.02/1.21 (~c2_1(a37)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1975, 1617, 160, 84, 1968, 1966, 728])).
% 1.02/1.21 tff(1977,plain,
% 1.02/1.21 (~c3_1(a19)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1095, 1962])).
% 1.02/1.21 tff(1978,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1979,plain,
% 1.02/1.21 (((~ndr1_0) | c3_1(a37) | c2_1(a37) | (~c1_1(a37)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42))) <=> (c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1980,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a37) | c2_1(a37) | (~c1_1(a37)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42)))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[1979])).
% 1.02/1.21 tff(1981,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a37) | c2_1(a37) | (~c1_1(a37)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42))),
% 1.02/1.21 inference(transitivity,[status(thm)],[1980, 1978])).
% 1.02/1.21 tff(1982,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a37) | c2_1(a37) | (~c1_1(a37)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(1983,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42)),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 1.02/1.21 tff(1984,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1983, 160, 1955, 1968, 1957, 1965, 1963, 1977, 425, 1976, 1956, 1969])).
% 1.02/1.21 tff(1985,plain,(hskp18 | hskp26 | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | hskp17 | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(1986,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1985, 1938, 1937, 674, 84, 668, 24, 2, 1936, 595, 1935])).
% 1.02/1.21 tff(1987,plain,(hskp26 | hskp18 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | hskp17 | c0_1(a1) | c2_1(a1) | (~c3_1(a1))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(1988,plain,
% 1.02/1.21 (hskp26),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1987, 1901, 546, 538, 532, 595, 1729, 1728, 1730])).
% 1.02/1.21 tff(1989,plain,
% 1.02/1.21 (c3_1(a10)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[632, 1988])).
% 1.02/1.21 tff(1990,plain,
% 1.02/1.21 (c2_1(a10)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[624, 1988])).
% 1.02/1.21 tff(1991,plain,
% 1.02/1.21 (c0_1(a10)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[615, 1988])).
% 1.02/1.21 tff(1992,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[662, 160, 1991, 1990, 1989, 546, 538, 532, 406, 1897])).
% 1.02/1.21 tff(1993,plain,(hskp17 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(1994,plain,
% 1.02/1.21 (hskp17),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1993, 73])).
% 1.02/1.21 tff(1995,plain,
% 1.02/1.21 (c2_1(a31)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[298, 1994])).
% 1.02/1.21 tff(1996,plain,
% 1.02/1.21 (c0_1(a31)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[290, 1994])).
% 1.02/1.21 tff(1997,plain,
% 1.02/1.21 (~c1_1(a31)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[71, 1994])).
% 1.02/1.21 tff(1998,plain,
% 1.02/1.21 (hskp0),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[435, 193, 1997, 1996, 1995, 73])).
% 1.02/1.21 tff(1999,plain,
% 1.02/1.21 (~c2_1(a1)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[241, 1998])).
% 1.02/1.21 tff(2000,plain,
% 1.02/1.21 (~c0_1(a1)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[262, 1998])).
% 1.02/1.21 tff(2001,plain,
% 1.02/1.21 (c3_1(a1)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[249, 1998])).
% 1.02/1.21 tff(2002,plain,
% 1.02/1.21 (c1_1(a1)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1922, 160, 2001, 585, 1005, 2000, 1999, 55, 594])).
% 1.02/1.21 tff(2003,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1736, 160, 193, 546, 2001, 532, 2000, 584, 2002, 3])).
% 1.02/1.21 tff(2004,plain,(hskp4 | c1_1(a16) | c0_1(a30) | c2_1(a30) | (~c1_1(a30)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(2005,plain,
% 1.02/1.21 (hskp4),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2004, 574, 3, 568, 562, 73])).
% 1.02/1.21 tff(2006,plain,
% 1.02/1.21 (~c2_1(a6)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[111, 2005])).
% 1.02/1.21 tff(2007,plain,
% 1.02/1.21 (c3_1(a6)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[119, 2005])).
% 1.02/1.21 tff(2008,plain,
% 1.02/1.21 (c1_1(a6)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[127, 2005])).
% 1.02/1.21 tff(2009,plain,
% 1.02/1.21 (c3_1(a30)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1011, 160, 546, 2008, 2007, 574, 568, 532, 2006, 13, 3])).
% 1.02/1.21 tff(2010,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2011,plain,
% 1.02/1.21 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2012,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[2011])).
% 1.02/1.21 tff(2013,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[2012, 2010])).
% 1.02/1.21 tff(2014,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(2015,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 1.02/1.21 tff(2016,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2015, 160, 586, 668, 1005, 462, 456, 450, 2, 13, 3, 1043])).
% 1.02/1.21 tff(2017,plain,((~hskp13) | (~c1_1(a30)) | (~c0_1(a16)) | c2_1(a30) | c3_1(a16) | c1_1(a16) | (~c3_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(2018,plain,
% 1.02/1.21 (~hskp13),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2017, 2009, 546, 568, 532, 3, 562])).
% 1.02/1.21 tff(2019,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2020,plain,
% 1.02/1.21 ((hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a16) | c2_1(a16) | (~c0_1(a16))) <=> (hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2021,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[2020])).
% 1.02/1.21 tff(2022,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[2021, 2019])).
% 1.02/1.21 tff(2023,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(2024,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 1.02/1.21 tff(2025,plain,
% 1.02/1.21 (hskp13 | (~c3_1(a31))),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2024, 160, 1996, 546, 1997, 538, 1502, 3])).
% 1.02/1.21 tff(2026,plain,
% 1.02/1.21 (~c3_1(a31)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2025, 2018])).
% 1.02/1.21 tff(2027,plain,
% 1.02/1.21 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2028,plain,
% 1.02/1.21 ((hskp26 | hskp20 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31))) <=> (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2029,plain,
% 1.02/1.21 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[2028])).
% 1.02/1.21 tff(2030,plain,
% 1.02/1.21 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[2029, 2027])).
% 1.02/1.21 tff(2031,plain,
% 1.02/1.21 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(2032,plain,
% 1.02/1.21 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.02/1.21 tff(2033,plain,
% 1.02/1.21 (hskp26 | hskp20 | c3_1(a31)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2032, 160, 1996, 1995, 1134])).
% 1.02/1.21 tff(2034,plain,
% 1.02/1.21 (hskp20),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2033, 2026, 84])).
% 1.02/1.21 tff(2035,plain,
% 1.02/1.21 (~c3_1(a37)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1146, 2034])).
% 1.02/1.21 tff(2036,plain,
% 1.02/1.21 (~c0_1(a37)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1152, 2034])).
% 1.02/1.21 tff(2037,assumption,(~c2_1(a37)), introduced(assumption)).
% 1.02/1.21 tff(2038,assumption,(~c3_1(a37)), introduced(assumption)).
% 1.02/1.21 tff(2039,assumption,(~c0_1(a37)), introduced(assumption)).
% 1.02/1.21 tff(2040,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1766, 160, 586, 668, 2039, 2038, 1005, 2, 13, 2037, 3, 1043])).
% 1.02/1.21 tff(2041,plain,(c2_1(a37) | (~c1_1(a30)) | (~c0_1(a16)) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | c1_1(a16) | (~c3_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(2042,plain,
% 1.02/1.21 (c2_1(a37)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2041, 562, 546, 2036, 2035, 568, 532, 3, 2009])).
% 1.02/1.21 tff(2043,plain,
% 1.02/1.21 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2044,plain,
% 1.02/1.21 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a37) | (~c2_1(a37)) | c0_1(a37)) <=> (hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2045,plain,
% 1.02/1.21 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a37) | (~c2_1(a37)) | c0_1(a37))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[2044])).
% 1.02/1.21 tff(2046,plain,
% 1.02/1.21 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a37) | (~c2_1(a37)) | c0_1(a37))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[2045, 2043])).
% 1.02/1.21 tff(2047,plain,
% 1.02/1.21 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a37) | (~c2_1(a37)) | c0_1(a37))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(2048,plain,
% 1.02/1.21 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 1.02/1.21 tff(2049,plain,
% 1.02/1.21 (hskp25 | (~c2_1(a37))),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2048, 160, 84, 2036, 2035, 1023])).
% 1.02/1.21 tff(2050,plain,
% 1.02/1.21 (hskp25),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2049, 2042])).
% 1.02/1.21 tff(2051,plain,
% 1.02/1.21 (c2_1(a9)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[787, 2050])).
% 1.02/1.21 tff(2052,plain,
% 1.02/1.21 (c1_1(a9)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[795, 2050])).
% 1.02/1.21 tff(2053,plain,
% 1.02/1.21 (c0_1(a9)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[803, 2050])).
% 1.02/1.21 tff(2054,assumption,(c2_1(a37)), introduced(assumption)).
% 1.02/1.21 tff(2055,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1612, 160, 1213, 1204, 1203, 1749, 2039, 2038, 1748, 1747, 34, 2054])).
% 1.02/1.21 tff(2056,plain,((~hskp2) | (~c0_1(a9)) | (~c1_1(a9)) | (~c2_1(a9)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(2057,plain,
% 1.02/1.21 (~hskp2),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2056, 2053, 2052, 2051, 2036, 2035, 2042])).
% 1.02/1.21 tff(2058,plain,
% 1.02/1.21 (hskp14),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[890, 2057, 3])).
% 1.02/1.21 tff(2059,plain,
% 1.02/1.21 (~c1_1(a24)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[943, 2058])).
% 1.02/1.21 tff(2060,plain,
% 1.02/1.21 (~c0_1(a24)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[949, 2058])).
% 1.02/1.21 tff(2061,plain,
% 1.02/1.21 (c2_1(a24)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[957, 2058])).
% 1.02/1.21 tff(2062,plain,
% 1.02/1.21 (c1_1(a37)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1160, 2034])).
% 1.02/1.21 tff(2063,plain,
% 1.02/1.21 (~c3_1(a24)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1230, 160, 2062, 2061, 2036, 2035, 2060, 2059, 83])).
% 1.02/1.21 tff(2064,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2065,plain,
% 1.02/1.21 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31))) <=> (c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2066,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[2065])).
% 1.02/1.21 tff(2067,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[2066, 2064])).
% 1.02/1.21 tff(2068,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(2069,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[2068, 2067])).
% 1.02/1.21 tff(2070,plain,
% 1.02/1.21 (~c3_1(a9)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2069, 160, 2053, 2051, 1995, 1997, 1466, 2026])).
% 1.02/1.21 tff(2071,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2072,plain,
% 1.02/1.21 ((hskp24 | (~ndr1_0) | c3_1(a9) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a24) | c1_1(a24) | c0_1(a24)) <=> (hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(2073,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a9) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[2072])).
% 1.02/1.21 tff(2074,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a9) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[2073, 2071])).
% 1.02/1.21 tff(2075,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a9) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a24) | c1_1(a24) | c0_1(a24))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(2076,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.02/1.21 tff(2077,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2076, 160, 73, 2053, 2052, 2060, 2059, 901, 2070, 2063])).
% 1.02/1.21 tff(2078,plain,(hskp26 | hskp24 | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(2079,plain,
% 1.02/1.21 (hskp26),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2078, 3, 73])).
% 1.02/1.21 tff(2080,plain,
% 1.02/1.21 (c0_1(a10)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[615, 2079])).
% 1.02/1.21 tff(2081,plain,
% 1.02/1.22 (c2_1(a10)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[624, 2079])).
% 1.02/1.22 tff(2082,plain,
% 1.02/1.22 (~hskp2),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1867, 2079, 538, 532, 546])).
% 1.02/1.22 tff(2083,plain,
% 1.02/1.22 (c3_1(a10)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[632, 2079])).
% 1.02/1.22 tff(2084,plain,
% 1.02/1.22 (hskp14),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[664, 2083, 526, 2082, 2081, 2080])).
% 1.02/1.22 tff(2085,plain,
% 1.02/1.22 (~c1_1(a24)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[943, 2084])).
% 1.02/1.22 tff(2086,plain,
% 1.02/1.22 (c2_1(a24)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[957, 2084])).
% 1.02/1.22 tff(2087,assumption,(~c3_1(a24)), introduced(assumption)).
% 1.02/1.22 tff(2088,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2089,plain,
% 1.02/1.22 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24))) <=> (c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2090,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24)))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2089])).
% 1.02/1.22 tff(2091,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2090, 2088])).
% 1.02/1.22 tff(2092,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2093,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24)),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 1.02/1.22 tff(2094,plain,
% 1.02/1.22 ($false),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2093, 160, 656, 655, 654, 972, 970, 1466, 2087])).
% 1.02/1.22 tff(2095,plain,(c3_1(a24) | (~c0_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c1_1(a24)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.22 tff(2096,plain,
% 1.02/1.22 (c3_1(a24)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2095, 2080, 2081, 2083, 2086, 2085])).
% 1.02/1.22 tff(2097,plain,
% 1.02/1.22 (~c0_1(a24)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[949, 2084])).
% 1.02/1.22 tff(2098,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2099,plain,
% 1.02/1.22 ((hskp4 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24))) <=> (hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2100,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2099])).
% 1.02/1.22 tff(2101,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.02/1.22 tff(2102,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2103,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.02/1.22 tff(2104,plain,
% 1.02/1.22 (hskp4 | (~c3_1(a24))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2103, 160, 546, 2097, 2085, 538, 65, 3])).
% 1.02/1.22 tff(2105,plain,
% 1.02/1.22 (hskp4),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2104, 2096])).
% 1.02/1.22 tff(2106,plain,
% 1.02/1.22 (~c2_1(a6)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[111, 2105])).
% 1.02/1.22 tff(2107,plain,
% 1.02/1.22 (c3_1(a6)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[119, 2105])).
% 1.02/1.22 tff(2108,plain,
% 1.02/1.22 (c1_1(a6)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[127, 2105])).
% 1.02/1.22 tff(2109,plain,
% 1.02/1.22 ($false),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1540, 160, 668, 673, 672, 462, 456, 450, 2, 671, 13, 3])).
% 1.02/1.22 tff(2110,plain,((~hskp13) | (~c0_1(a16)) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c2_1(a6) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.22 tff(2111,plain,
% 1.02/1.22 (~hskp13),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2110, 2108, 546, 2107, 532, 2106, 3])).
% 1.02/1.22 tff(2112,plain,
% 1.02/1.22 (~c3_1(a31)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2025, 2111])).
% 1.02/1.22 tff(2113,plain,
% 1.02/1.22 (hskp3),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[964, 160, 2082, 2086, 2097, 2085, 23])).
% 1.02/1.22 tff(2114,plain,
% 1.02/1.22 (~c3_1(a5)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[867, 2113])).
% 1.02/1.22 tff(2115,plain,
% 1.02/1.22 (~c2_1(a5)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[331, 2113])).
% 1.02/1.22 tff(2116,plain,
% 1.02/1.22 (c0_1(a5)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[997, 160, 546, 2108, 2107, 532, 2106, 2115, 2114, 13, 3])).
% 1.02/1.22 tff(2117,plain,
% 1.02/1.22 (~c1_1(a5)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[337, 2113])).
% 1.02/1.22 tff(2118,plain,
% 1.02/1.22 (c1_1(a10)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1511, 2111, 2080, 2083, 2117, 2115, 2116])).
% 1.02/1.22 tff(2119,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2120,plain,
% 1.02/1.22 ((hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6))) <=> (hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2121,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2120])).
% 1.02/1.22 tff(2122,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2121, 2119])).
% 1.02/1.22 tff(2123,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2124,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 1.02/1.22 tff(2125,plain,
% 1.02/1.22 (hskp19 | (~c1_1(a10))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2124, 160, 2080, 2081, 2108, 2107, 2106, 779])).
% 1.02/1.22 tff(2126,plain,
% 1.02/1.22 (hskp19),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2125, 2118])).
% 1.02/1.22 tff(2127,plain,
% 1.02/1.22 (~c0_1(a33)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[819, 2126])).
% 1.02/1.22 tff(2128,plain,
% 1.02/1.22 (c3_1(a33)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1392, 2126])).
% 1.02/1.22 tff(2129,plain,
% 1.02/1.22 (c2_1(a33)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[827, 2126])).
% 1.02/1.22 tff(2130,assumption,(hskp11), introduced(assumption)).
% 1.02/1.22 tff(2131,plain,
% 1.02/1.22 (~c3_1(a19)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1095, 2130])).
% 1.02/1.22 tff(2132,plain,
% 1.02/1.22 (~c1_1(a19)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1116, 2130])).
% 1.02/1.22 tff(2133,plain,
% 1.02/1.22 (c2_1(a19)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1103, 2130])).
% 1.02/1.22 tff(2134,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2135,plain,
% 1.02/1.22 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19))) <=> (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2136,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2135])).
% 1.02/1.22 tff(2137,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2136, 2134])).
% 1.02/1.22 tff(2138,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2139,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 1.02/1.22 tff(2140,plain,
% 1.02/1.22 ($false),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2139, 160, 656, 655, 654, 2133, 2132, 2131, 1466])).
% 1.02/1.22 tff(2141,plain,((~hskp11) | (~c0_1(a10)) | (~c2_1(a10)) | (~c3_1(a10))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.22 tff(2142,plain,
% 1.02/1.22 (~hskp11),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2141, 2080, 2081, 2083])).
% 1.02/1.22 tff(2143,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2144,plain,
% 1.02/1.22 ((hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2145,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2144])).
% 1.02/1.22 tff(2146,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2145, 2143])).
% 1.02/1.22 tff(2147,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2148,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.02/1.22 tff(2149,plain,
% 1.02/1.22 ($false),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2148, 160, 2142, 2129, 2128, 1996, 1995, 2127, 1042, 2112])).
% 1.02/1.22 tff(2150,plain,(c1_1(a16) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.02/1.22 tff(2151,plain,
% 1.02/1.22 (c1_1(a16)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2150, 73])).
% 1.02/1.22 tff(2152,plain,
% 1.02/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2153,plain,
% 1.02/1.22 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2154,plain,
% 1.02/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2153])).
% 1.02/1.22 tff(2155,plain,
% 1.02/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2154, 2152])).
% 1.02/1.22 tff(2156,plain,
% 1.02/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2157,plain,
% 1.02/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 1.02/1.22 tff(2158,plain,
% 1.02/1.22 ((~c1_1(a16)) | (~c3_1(a31))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2157, 160, 1996, 1995, 546, 538, 532, 406])).
% 1.02/1.22 tff(2159,plain,
% 1.02/1.22 (~c3_1(a31)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2158, 2151])).
% 1.02/1.22 tff(2160,plain,
% 1.02/1.22 (~hskp2),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1867, 608, 644, 653, 645])).
% 1.02/1.22 tff(2161,plain,
% 1.02/1.22 (hskp14),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[666, 608, 2160, 617])).
% 1.02/1.22 tff(2162,plain,
% 1.02/1.22 (c2_1(a24)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[957, 2161])).
% 1.02/1.22 tff(2163,plain,
% 1.02/1.22 (~c1_1(a24)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[943, 2161])).
% 1.02/1.22 tff(2164,plain,
% 1.02/1.22 (c3_1(a24)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2095, 2163, 625, 633, 2162, 616])).
% 1.02/1.22 tff(2165,assumption,(~c3_1(a31)), introduced(assumption)).
% 1.02/1.22 tff(2166,plain,
% 1.02/1.22 (~c0_1(a24)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[949, 2161])).
% 1.02/1.22 tff(2167,plain,
% 1.02/1.22 (~hskp11),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2141, 616, 625, 633])).
% 1.02/1.22 tff(2168,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2169,plain,
% 1.02/1.22 ((hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24))) <=> (hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2170,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2169])).
% 1.02/1.22 tff(2171,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2170, 2168])).
% 1.02/1.22 tff(2172,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2173,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.02/1.22 tff(2174,plain,
% 1.02/1.22 ($false),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2173, 160, 2167, 301, 302, 2162, 2166, 1042, 2165, 2164])).
% 1.02/1.22 tff(2175,plain,((~hskp26) | (~c0_1(a31)) | (~c2_1(a31)) | c3_1(a31) | (~hskp9)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.22 tff(2176,plain,
% 1.02/1.22 (~hskp26),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2175, 1996, 1995, 2159, 526])).
% 1.02/1.22 tff(2177,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2178,plain,
% 1.02/1.22 ((hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2179,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2178])).
% 1.02/1.22 tff(2180,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2179, 2177])).
% 1.02/1.22 tff(2181,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2182,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.02/1.22 tff(2183,plain,
% 1.02/1.22 (~c3_1(a30)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2182, 160, 193, 301, 1003, 313, 1004, 584, 2165])).
% 1.02/1.22 tff(2184,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2185,plain,
% 1.02/1.22 ((hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(2186,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[2185])).
% 1.02/1.22 tff(2187,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.02/1.22 tff(2188,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(2189,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.02/1.22 tff(2190,plain,
% 1.02/1.22 (~c1_1(a1)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2189, 160, 193, 301, 463, 313, 444, 584, 2165])).
% 1.02/1.22 tff(2191,plain,
% 1.02/1.22 (hskp26 | hskp20 | c3_1(a31)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2032, 160, 301, 302, 1134])).
% 1.02/1.23 tff(2192,plain,
% 1.02/1.23 (hskp20),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[2191, 84, 2165])).
% 1.02/1.23 tff(2193,plain,
% 1.02/1.23 (~c3_1(a37)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[1146, 2192])).
% 1.02/1.23 tff(2194,plain,
% 1.02/1.23 (~c0_1(a37)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[1152, 2192])).
% 1.02/1.23 tff(2195,plain,
% 1.02/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37))),
% 1.02/1.23 inference(rewrite,[status(thm)],[])).
% 1.02/1.23 tff(2196,plain,
% 1.02/1.23 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a1) | c1_1(a1) | c0_1(a1)) <=> (c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37))),
% 1.02/1.23 inference(rewrite,[status(thm)],[])).
% 1.02/1.23 tff(2197,plain,
% 1.02/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37)))),
% 1.02/1.23 inference(monotonicity,[status(thm)],[2196])).
% 1.02/1.23 tff(2198,plain,
% 1.02/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37))),
% 1.02/1.23 inference(transitivity,[status(thm)],[2197, 2195])).
% 1.02/1.23 tff(2199,plain,
% 1.02/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a1) | c1_1(a1) | c0_1(a1))),
% 1.02/1.23 inference(quant_inst,[status(thm)],[])).
% 1.02/1.23 tff(2200,plain,
% 1.02/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37)),
% 1.02/1.23 inference(modus_ponens,[status(thm)],[2199, 2198])).
% 1.02/1.23 tff(2201,plain,
% 1.02/1.23 (c2_1(a37)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[2200, 160, 463, 2194, 2193, 444, 443, 55, 2190])).
% 1.02/1.23 tff(2202,plain,
% 1.02/1.23 (hskp25 | (~c2_1(a37))),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[2048, 160, 84, 2194, 2193, 1023])).
% 1.02/1.23 tff(2203,plain,
% 1.02/1.23 (hskp25),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[2202, 2201])).
% 1.02/1.23 tff(2204,plain,
% 1.02/1.23 (c2_1(a9)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[787, 2203])).
% 1.02/1.23 tff(2205,plain,
% 1.02/1.23 (c1_1(a9)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[795, 2203])).
% 1.02/1.23 tff(2206,plain,
% 1.02/1.23 (c0_1(a9)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[803, 2203])).
% 1.02/1.23 tff(2207,plain,
% 1.02/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.02/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2208,plain,
% 1.07/1.23 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a30) | c2_1(a30) | (~c1_1(a30)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37))) <=> (c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2209,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a30) | c2_1(a30) | (~c1_1(a30)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2208])).
% 1.07/1.23 tff(2210,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a30) | c2_1(a30) | (~c1_1(a30)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2209, 2207])).
% 1.07/1.23 tff(2211,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a30) | c2_1(a30) | (~c1_1(a30)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2212,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 1.07/1.23 tff(2213,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2212, 160, 2206, 2205, 2204, 1003, 2194, 2193, 1002, 34, 2201, 2183])).
% 1.07/1.23 tff(2214,plain,(hskp26 | (~c3_1(a1)) | c0_1(a1) | c2_1(a1) | hskp4 | (~c0_1(a31)) | c1_1(a31) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(2215,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2214, 2000, 2001, 2176, 1999, 193, 1996, 1997, 2159, 1995, 546, 538, 532])).
% 1.07/1.23 tff(2216,plain,(hskp4 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(2217,plain,
% 1.07/1.23 (hskp4),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2216, 73])).
% 1.07/1.23 tff(2218,plain,
% 1.07/1.23 (~c2_1(a6)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[111, 2217])).
% 1.07/1.23 tff(2219,plain,
% 1.07/1.23 (hskp16),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[553, 2176])).
% 1.07/1.23 tff(2220,plain,
% 1.07/1.23 (~c2_1(a30)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[567, 2219])).
% 1.07/1.23 tff(2221,plain,
% 1.07/1.23 (~c0_1(a30)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[573, 2219])).
% 1.07/1.23 tff(2222,plain,
% 1.07/1.23 (c3_1(a6)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[119, 2217])).
% 1.07/1.23 tff(2223,plain,
% 1.07/1.23 (c1_1(a6)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[127, 2217])).
% 1.07/1.23 tff(2224,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2225,plain,
% 1.07/1.23 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30)) <=> (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2226,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2225])).
% 1.07/1.23 tff(2227,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2226, 2224])).
% 1.07/1.23 tff(2228,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2229,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 1.07/1.23 tff(2230,plain,
% 1.07/1.23 (c3_1(a30)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2229, 160, 1996, 2223, 2222, 1997, 2221, 2220, 2218, 13, 2159])).
% 1.07/1.23 tff(2231,plain,
% 1.07/1.23 (hskp20),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2033, 2176, 2159])).
% 1.07/1.23 tff(2232,plain,
% 1.07/1.23 (~c3_1(a37)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1146, 2231])).
% 1.07/1.23 tff(2233,plain,
% 1.07/1.23 (~c0_1(a37)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1152, 2231])).
% 1.07/1.23 tff(2234,plain,
% 1.07/1.23 (hskp25 | (~c2_1(a37))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2048, 160, 84, 2039, 2038, 1023])).
% 1.07/1.23 tff(2235,plain,
% 1.07/1.23 (hskp25),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2234, 2054])).
% 1.07/1.23 tff(2236,plain,
% 1.07/1.23 (c2_1(a9)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[787, 2235])).
% 1.07/1.23 tff(2237,plain,
% 1.07/1.23 (c1_1(a9)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[795, 2235])).
% 1.07/1.23 tff(2238,plain,
% 1.07/1.23 (c0_1(a9)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[803, 2235])).
% 1.07/1.23 tff(2239,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2240,plain,
% 1.07/1.23 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37))) <=> (c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2241,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2240])).
% 1.07/1.23 tff(2242,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2241, 2239])).
% 1.07/1.23 tff(2243,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2244,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2243, 2242])).
% 1.07/1.23 tff(2245,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2244, 160, 2238, 2237, 2236, 2039, 2038, 24, 2, 34, 2054, 709])).
% 1.07/1.23 tff(2246,plain,((~c2_1(a37)) | c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(2247,plain,
% 1.07/1.23 (~c2_1(a37)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2246, 2233, 2232, 538, 532, 2151, 2176])).
% 1.07/1.23 tff(2248,plain,
% 1.07/1.23 (c1_1(a30)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[561, 2219])).
% 1.07/1.23 tff(2249,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2250,plain,
% 1.07/1.23 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2251,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37)))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2250])).
% 1.07/1.23 tff(2252,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2251, 2249])).
% 1.07/1.23 tff(2253,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2254,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 1.07/1.23 tff(2255,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2254, 160, 1996, 2248, 2233, 2232, 1997, 2220, 13, 2159, 2247, 2230])).
% 1.07/1.23 tff(2256,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(2257,plain,
% 1.07/1.23 (((~hskp24) | c2_1(a3)) <=> ((~hskp24) | c2_1(a3))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2258,axiom,((~hskp24) | c2_1(a3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.07/1.23 tff(2259,plain,
% 1.07/1.23 ((~hskp24) | c2_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 1.07/1.23 tff(2260,plain,
% 1.07/1.23 ((~hskp24) | c2_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2259, 2257])).
% 1.07/1.23 tff(2261,plain,
% 1.07/1.23 ((~hskp24) | c2_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2260, 2257])).
% 1.07/1.23 tff(2262,plain,
% 1.07/1.23 ((~hskp24) | c2_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2261, 2257])).
% 1.07/1.23 tff(2263,plain,
% 1.07/1.23 ((~hskp24) | c2_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2262, 2257])).
% 1.07/1.23 tff(2264,plain,
% 1.07/1.23 (c2_1(a3)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2263, 2256])).
% 1.07/1.23 tff(2265,plain,
% 1.07/1.23 (((~hskp24) | c1_1(a3)) <=> ((~hskp24) | c1_1(a3))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2266,axiom,((~hskp24) | c1_1(a3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.07/1.23 tff(2267,plain,
% 1.07/1.23 ((~hskp24) | c1_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 1.07/1.23 tff(2268,plain,
% 1.07/1.23 ((~hskp24) | c1_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2267, 2265])).
% 1.07/1.23 tff(2269,plain,
% 1.07/1.23 ((~hskp24) | c1_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2268, 2265])).
% 1.07/1.23 tff(2270,plain,
% 1.07/1.23 ((~hskp24) | c1_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2269, 2265])).
% 1.07/1.23 tff(2271,plain,
% 1.07/1.23 ((~hskp24) | c1_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2270, 2265])).
% 1.07/1.23 tff(2272,plain,
% 1.07/1.23 (c1_1(a3)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2271, 2256])).
% 1.07/1.23 tff(2273,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2274,plain,
% 1.07/1.23 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a16) | c1_1(a16) | c0_1(a16)) <=> (c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2275,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16)))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2274])).
% 1.07/1.23 tff(2276,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2275, 2273])).
% 1.07/1.23 tff(2277,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a16) | c1_1(a16) | c0_1(a16))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2278,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 1.07/1.23 tff(2279,plain,
% 1.07/1.23 (c0_1(a16) | c0_1(a3) | c1_1(a16)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2278, 160, 2272, 2264, 2, 45])).
% 1.07/1.23 tff(2280,plain,
% 1.07/1.23 (c0_1(a3)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2279, 3, 35])).
% 1.07/1.23 tff(2281,plain,
% 1.07/1.23 (c2_1(a31)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[298, 66])).
% 1.07/1.23 tff(2282,plain,
% 1.07/1.23 (((~hskp24) | c3_1(a3)) <=> ((~hskp24) | c3_1(a3))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2283,axiom,((~hskp24) | c3_1(a3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.07/1.23 tff(2284,plain,
% 1.07/1.23 ((~hskp24) | c3_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 1.07/1.23 tff(2285,plain,
% 1.07/1.23 ((~hskp24) | c3_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2284, 2282])).
% 1.07/1.23 tff(2286,plain,
% 1.07/1.23 ((~hskp24) | c3_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2285, 2282])).
% 1.07/1.23 tff(2287,plain,
% 1.07/1.23 ((~hskp24) | c3_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2286, 2282])).
% 1.07/1.23 tff(2288,plain,
% 1.07/1.23 ((~hskp24) | c3_1(a3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2287, 2282])).
% 1.07/1.23 tff(2289,plain,
% 1.07/1.23 (c3_1(a3)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2288, 2256])).
% 1.07/1.23 tff(2290,assumption,(c0_1(a3)), introduced(assumption)).
% 1.07/1.23 tff(2291,assumption,(c3_1(a3)), introduced(assumption)).
% 1.07/1.23 tff(2292,assumption,(c2_1(a3)), introduced(assumption)).
% 1.07/1.23 tff(2293,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2294,plain,
% 1.07/1.23 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31))) <=> (c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2295,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31)))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2294])).
% 1.07/1.23 tff(2296,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2295, 2293])).
% 1.07/1.23 tff(2297,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2298,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 1.07/1.23 tff(2299,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2298, 160, 2292, 2291, 302, 313, 1466, 2165, 2290])).
% 1.07/1.23 tff(2300,plain,(c3_1(a31) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(2301,plain,
% 1.07/1.23 (c3_1(a31) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a3))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2300, 2289, 2264])).
% 1.07/1.23 tff(2302,plain,
% 1.07/1.23 (c3_1(a31)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2301, 2281, 2280, 72])).
% 1.07/1.23 tff(2303,plain,
% 1.07/1.23 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(2304,plain,
% 1.07/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[2303])).
% 1.07/1.23 tff(2305,plain,
% 1.07/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2306,plain,
% 1.07/1.23 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(2307,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[2306])).
% 1.07/1.24 tff(2308,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.07/1.24 tff(2309,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 1.07/1.24 tff(2310,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2309, 2305])).
% 1.07/1.24 tff(2311,plain,(
% 1.07/1.24 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.24 inference(skolemize,[status(sab)],[2310])).
% 1.07/1.24 tff(2312,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2311, 2304])).
% 1.07/1.24 tff(2313,assumption,(hskp1), introduced(assumption)).
% 1.07/1.24 tff(2314,plain,
% 1.07/1.24 (((~hskp1) | (~c3_1(a2))) <=> ((~hskp1) | (~c3_1(a2)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2315,plain,
% 1.07/1.24 (((~c3_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2316,axiom,((~c3_1(a2)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.07/1.24 tff(2317,plain,
% 1.07/1.24 ((~hskp1) | (~c3_1(a2))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 1.07/1.24 tff(2318,plain,
% 1.07/1.24 ((~hskp1) | (~c3_1(a2))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2317, 2314])).
% 1.07/1.24 tff(2319,plain,
% 1.07/1.24 (~c3_1(a2)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2318, 2313])).
% 1.07/1.24 tff(2320,plain,
% 1.07/1.24 (~c0_1(a2)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[1405, 2313])).
% 1.07/1.24 tff(2321,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2322,plain,
% 1.07/1.24 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c1_1(a16) | (~c2_1(a16))) <=> ((~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2323,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c1_1(a16) | (~c2_1(a16)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2322])).
% 1.07/1.24 tff(2324,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c1_1(a16) | (~c2_1(a16)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2323, 2321])).
% 1.07/1.24 tff(2325,plain,
% 1.07/1.24 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c1_1(a16) | (~c2_1(a16)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2326,plain,
% 1.07/1.24 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 1.07/1.24 tff(2327,plain,
% 1.07/1.24 ((~c2_1(a16)) | (~c0_1(a3)) | c1_1(a16)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2326, 160, 2264, 2289, 2, 1466])).
% 1.07/1.24 tff(2328,plain,
% 1.07/1.24 (~c2_1(a16)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2327, 2280, 3])).
% 1.07/1.24 tff(2329,plain,
% 1.07/1.24 (c2_1(a2)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[1413, 2313])).
% 1.07/1.24 tff(2330,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2331,plain,
% 1.07/1.24 (((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16)) <=> (c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2332,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2331])).
% 1.07/1.24 tff(2333,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2332, 2330])).
% 1.07/1.24 tff(2334,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2335,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 1.07/1.24 tff(2336,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2335, 160, 35, 2329, 2328, 2, 2320, 2319, 2312, 3])).
% 1.07/1.24 tff(2337,plain,((~hskp1) | c0_1(a16) | c3_1(a16) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2338,plain,
% 1.07/1.24 (~hskp1),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2337, 3, 2, 35])).
% 1.07/1.24 tff(2339,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2340,plain,
% 1.07/1.24 ((hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c1_1(a16) | c0_1(a16)) <=> (hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2341,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2340])).
% 1.07/1.24 tff(2342,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2341, 2339])).
% 1.07/1.24 tff(2343,plain,
% 1.07/1.24 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c1_1(a16) | c0_1(a16))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2344,plain,
% 1.07/1.24 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 1.07/1.24 tff(2345,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2344, 160, 2338, 2281, 35, 72, 2, 1385, 2302, 3])).
% 1.07/1.24 tff(2346,plain,((~hskp17) | c0_1(a16) | c3_1(a16) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2347,plain,
% 1.07/1.24 (~hskp17),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2346, 3, 2, 35])).
% 1.07/1.24 tff(2348,plain,
% 1.07/1.24 (hskp8),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[282, 193, 2347])).
% 1.07/1.24 tff(2349,plain,
% 1.07/1.24 (~c2_1(a15)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[175, 2348])).
% 1.07/1.24 tff(2350,plain,
% 1.07/1.24 (~c1_1(a15)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[189, 2348])).
% 1.07/1.24 tff(2351,assumption,(~hskp15), introduced(assumption)).
% 1.07/1.24 tff(2352,plain,
% 1.07/1.24 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2353,plain,
% 1.07/1.24 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15))) <=> (hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2354,plain,
% 1.07/1.24 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2353])).
% 1.07/1.24 tff(2355,plain,
% 1.07/1.24 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2354, 2352])).
% 1.07/1.24 tff(2356,plain,
% 1.07/1.24 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2357,plain,
% 1.07/1.24 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.07/1.24 tff(2358,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2357, 160, 607, 606, 184, 190, 176, 643])).
% 1.07/1.24 tff(2359,plain,((~hskp8) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2360,plain,
% 1.07/1.24 (~hskp8),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2359, 606, 607])).
% 1.07/1.24 tff(2361,plain,
% 1.07/1.24 (hskp17),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[282, 2360, 193])).
% 1.07/1.24 tff(2362,plain,
% 1.07/1.24 (c2_1(a31)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[298, 2361])).
% 1.07/1.24 tff(2363,plain,
% 1.07/1.24 (~c1_1(a31)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[71, 2361])).
% 1.07/1.24 tff(2364,plain,
% 1.07/1.24 (c0_1(a31)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[290, 2361])).
% 1.07/1.24 tff(2365,plain,
% 1.07/1.24 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(2366,plain,
% 1.07/1.24 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[2365])).
% 1.07/1.24 tff(2367,plain,
% 1.07/1.24 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2368,plain,
% 1.07/1.24 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(2369,plain,
% 1.07/1.24 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[2368])).
% 1.07/1.24 tff(2370,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.07/1.24 tff(2371,plain,
% 1.07/1.24 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 1.07/1.24 tff(2372,plain,
% 1.07/1.24 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2371, 2367])).
% 1.07/1.24 tff(2373,plain,(
% 1.07/1.24 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.07/1.24 inference(skolemize,[status(sab)],[2372])).
% 1.07/1.24 tff(2374,plain,
% 1.07/1.24 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2373, 2366])).
% 1.07/1.24 tff(2375,plain,
% 1.07/1.24 (^[U: $i] : refl((hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(2376,plain,
% 1.07/1.24 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[2375])).
% 1.07/1.24 tff(2377,plain,
% 1.07/1.24 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2378,plain,
% 1.07/1.24 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(2379,plain,
% 1.07/1.24 (![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp7) <=> ![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[2378])).
% 1.07/1.24 tff(2380,axiom,(![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.07/1.24 tff(2381,plain,
% 1.07/1.24 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 1.07/1.24 tff(2382,plain,
% 1.07/1.24 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2381, 2377])).
% 1.07/1.24 tff(2383,plain,(
% 1.07/1.24 ![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.07/1.24 inference(skolemize,[status(sab)],[2382])).
% 1.07/1.24 tff(2384,plain,
% 1.07/1.24 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2383, 2376])).
% 1.07/1.24 tff(2385,plain,
% 1.07/1.24 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2386,plain,
% 1.07/1.24 ((hskp7 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31))) <=> (hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2387,plain,
% 1.07/1.24 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2386])).
% 1.07/1.24 tff(2388,plain,
% 1.07/1.24 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2387, 2385])).
% 1.07/1.24 tff(2389,plain,
% 1.07/1.24 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2390,plain,
% 1.07/1.24 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 1.07/1.24 tff(2391,plain,
% 1.07/1.24 (hskp7 | c3_1(a31)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2390, 160, 302, 313, 2384])).
% 1.07/1.24 tff(2392,plain,
% 1.07/1.24 (hskp7),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2391, 2165])).
% 1.07/1.24 tff(2393,plain,
% 1.07/1.24 (~c2_1(a14)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[489, 2392])).
% 1.07/1.24 tff(2394,plain,
% 1.07/1.24 (c3_1(a14)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[497, 2392])).
% 1.07/1.24 tff(2395,plain,
% 1.07/1.24 (c0_1(a14)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[516, 2392])).
% 1.07/1.24 tff(2396,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2397,plain,
% 1.07/1.24 ((hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1))) <=> (hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2398,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2397])).
% 1.07/1.24 tff(2399,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2398, 2396])).
% 1.07/1.24 tff(2400,plain,
% 1.07/1.24 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2401,plain,
% 1.07/1.24 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 1.07/1.24 tff(2402,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2401, 160, 2351, 2395, 2394, 463, 2393, 443, 2374, 2190])).
% 1.07/1.24 tff(2403,plain,(c3_1(a31) | hskp15 | (~c3_1(a1)) | c2_1(a1) | hskp4 | (~c0_1(a31)) | c1_1(a31) | c0_1(a1) | (~c2_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2404,plain,
% 1.07/1.24 (c3_1(a31)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2403, 441, 2351, 438, 193, 2364, 2363, 439, 2362])).
% 1.07/1.24 tff(2405,assumption,(hskp22), introduced(assumption)).
% 1.07/1.24 tff(2406,plain,
% 1.07/1.24 (((~hskp22) | (~c1_1(a45))) <=> ((~hskp22) | (~c1_1(a45)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2407,plain,
% 1.07/1.24 (((~c1_1(a45)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a45)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2408,axiom,((~c1_1(a45)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.07/1.24 tff(2409,plain,
% 1.07/1.24 ((~hskp22) | (~c1_1(a45))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2408, 2407])).
% 1.07/1.24 tff(2410,plain,
% 1.07/1.24 ((~hskp22) | (~c1_1(a45))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2409, 2406])).
% 1.07/1.24 tff(2411,plain,
% 1.07/1.24 (~c1_1(a45)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2410, 2405])).
% 1.07/1.24 tff(2412,plain,
% 1.07/1.24 (((~hskp22) | (~c3_1(a45))) <=> ((~hskp22) | (~c3_1(a45)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2413,plain,
% 1.07/1.24 (((~c3_1(a45)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a45)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2414,axiom,((~c3_1(a45)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.07/1.24 tff(2415,plain,
% 1.07/1.24 ((~hskp22) | (~c3_1(a45))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.07/1.24 tff(2416,plain,
% 1.07/1.24 ((~hskp22) | (~c3_1(a45))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2415, 2412])).
% 1.07/1.24 tff(2417,plain,
% 1.07/1.24 (~c3_1(a45)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2416, 2405])).
% 1.07/1.24 tff(2418,assumption,(~c1_1(a45)), introduced(assumption)).
% 1.07/1.25 tff(2419,assumption,(~c3_1(a45)), introduced(assumption)).
% 1.07/1.25 tff(2420,assumption,(~c2_1(a45)), introduced(assumption)).
% 1.07/1.25 tff(2421,plain,
% 1.07/1.25 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2422,plain,
% 1.07/1.25 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a45) | c2_1(a45) | (~c0_1(a45))) <=> (hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2423,plain,
% 1.07/1.25 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a45) | c2_1(a45) | (~c0_1(a45)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45)))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2422])).
% 1.07/1.25 tff(2424,plain,
% 1.07/1.25 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a45) | c2_1(a45) | (~c0_1(a45)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2423, 2421])).
% 1.07/1.25 tff(2425,plain,
% 1.07/1.25 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a45) | c2_1(a45) | (~c0_1(a45)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2426,plain,
% 1.07/1.25 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 1.07/1.25 tff(2427,plain,
% 1.07/1.25 ((~c0_1(a45)) | c2_1(a45)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2426, 160, 607, 606, 2418, 643])).
% 1.07/1.25 tff(2428,plain,
% 1.07/1.25 (~c0_1(a45)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2427, 2420])).
% 1.07/1.25 tff(2429,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2430,plain,
% 1.07/1.25 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a45) | c1_1(a45) | c0_1(a45)) <=> (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2431,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a45) | c1_1(a45) | c0_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45)))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2430])).
% 1.07/1.25 tff(2432,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a45) | c1_1(a45) | c0_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2431, 2429])).
% 1.07/1.25 tff(2433,plain,
% 1.07/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a45) | c1_1(a45) | c0_1(a45))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2434,plain,
% 1.07/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.07/1.25 tff(2435,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2434, 160, 2428, 463, 2418, 2419, 444, 443, 55, 2420])).
% 1.07/1.25 tff(2436,plain,(c2_1(a45) | (~c3_1(a1)) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2437,plain,
% 1.07/1.25 (c2_1(a45)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2436, 2418, 463, 2419, 444, 443, 607, 606])).
% 1.07/1.25 tff(2438,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2439,plain,
% 1.07/1.25 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45))) <=> (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2440,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2439])).
% 1.07/1.25 tff(2441,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2440, 2438])).
% 1.07/1.25 tff(2442,plain,
% 1.07/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2443,plain,
% 1.07/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 1.07/1.25 tff(2444,plain,
% 1.07/1.25 (c1_1(a45) | (~c3_1(a31)) | (~c2_1(a45))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2443, 160, 2364, 2362, 2419, 1466])).
% 1.07/1.25 tff(2445,plain,
% 1.07/1.25 (~c3_1(a31)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2444, 2437, 2418])).
% 1.07/1.25 tff(2446,plain,
% 1.07/1.25 (~c1_1(a1)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2189, 160, 193, 2364, 463, 2363, 444, 584, 2445])).
% 1.07/1.25 tff(2447,plain,
% 1.07/1.25 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2448,plain,
% 1.07/1.25 ((hskp7 | (~ndr1_0) | c3_1(a45) | c1_1(a45) | (~c2_1(a45))) <=> (hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2449,plain,
% 1.07/1.25 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2448])).
% 1.07/1.25 tff(2450,plain,
% 1.07/1.25 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2449, 2447])).
% 1.07/1.25 tff(2451,plain,
% 1.07/1.25 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2452,plain,
% 1.07/1.25 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 1.07/1.25 tff(2453,plain,
% 1.07/1.25 (hskp7 | c1_1(a45) | (~c2_1(a45))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2452, 160, 2419, 2384])).
% 1.07/1.25 tff(2454,plain,
% 1.07/1.25 (hskp7),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2453, 2437, 2418])).
% 1.07/1.25 tff(2455,plain,
% 1.07/1.25 (~c2_1(a14)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[489, 2454])).
% 1.07/1.25 tff(2456,plain,
% 1.07/1.25 (c3_1(a14)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[497, 2454])).
% 1.07/1.25 tff(2457,plain,
% 1.07/1.25 (c0_1(a14)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[516, 2454])).
% 1.07/1.25 tff(2458,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2401, 160, 2351, 2457, 2456, 463, 2455, 443, 2374, 2446])).
% 1.07/1.25 tff(2459,plain,(c1_1(a45) | hskp15 | (~c3_1(a1)) | c2_1(a1) | hskp4 | c0_1(a1) | c3_1(a45) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2460,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2459, 2417, 2411, 463, 443, 193, 444, 2351, 607, 606])).
% 1.07/1.25 tff(2461,plain,((~hskp22) | (~c3_1(a1)) | c2_1(a1) | hskp4 | c0_1(a1) | hskp15 | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2462,plain,
% 1.07/1.25 (~hskp22),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2461, 441, 438, 193, 439, 2351, 607, 606])).
% 1.07/1.25 tff(2463,plain,
% 1.07/1.25 (~hskp13),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[471, 442, 444, 443, 463])).
% 1.07/1.25 tff(2464,assumption,(~hskp22), introduced(assumption)).
% 1.07/1.25 tff(2465,assumption,(c3_1(a31)), introduced(assumption)).
% 1.07/1.25 tff(2466,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2467,plain,
% 1.07/1.25 ((hskp15 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1))) <=> (hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2468,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2467])).
% 1.07/1.25 tff(2469,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2468, 2466])).
% 1.07/1.25 tff(2470,plain,
% 1.07/1.25 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2471,plain,
% 1.07/1.25 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 1.07/1.25 tff(2472,plain,
% 1.07/1.25 (~c3_1(a8)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2471, 160, 2351, 1268, 463, 1240, 443, 2374, 442])).
% 1.07/1.25 tff(2473,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2474,plain,
% 1.07/1.25 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2475,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2474])).
% 1.07/1.25 tff(2476,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2475, 2473])).
% 1.07/1.25 tff(2477,plain,
% 1.07/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2478,plain,
% 1.07/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.07/1.25 tff(2479,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2478, 160, 301, 302, 1268, 1248, 1240, 406, 2465, 2472])).
% 1.07/1.25 tff(2480,plain,((~hskp6) | (~c0_1(a31)) | (~c2_1(a31)) | (~c3_1(a31)) | hskp15 | (~c3_1(a1)) | c2_1(a1) | c1_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2481,plain,
% 1.07/1.25 (~hskp6),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2480, 442, 302, 2465, 2351, 463, 443, 301])).
% 1.10/1.25 tff(2482,plain,
% 1.10/1.25 ((hskp26 | hskp22 | hskp6) <=> (hskp26 | hskp22 | hskp6)),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2483,plain,
% 1.10/1.25 (((hskp26 | hskp6) | hskp22) <=> (hskp26 | hskp22 | hskp6)),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2484,plain,
% 1.10/1.25 ((hskp6 | hskp26) <=> (hskp26 | hskp6)),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2485,plain,
% 1.10/1.25 (((hskp6 | hskp26) | hskp22) <=> ((hskp26 | hskp6) | hskp22)),
% 1.10/1.25 inference(monotonicity,[status(thm)],[2484])).
% 1.10/1.25 tff(2486,plain,
% 1.10/1.25 (((hskp6 | hskp26) | hskp22) <=> (hskp26 | hskp22 | hskp6)),
% 1.10/1.25 inference(transitivity,[status(thm)],[2485, 2483])).
% 1.10/1.25 tff(2487,axiom,((hskp6 | hskp26) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 1.10/1.25 tff(2488,plain,
% 1.10/1.25 (hskp26 | hskp22 | hskp6),
% 1.10/1.25 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 1.10/1.25 tff(2489,plain,
% 1.10/1.25 (hskp26 | hskp22 | hskp6),
% 1.10/1.25 inference(modus_ponens,[status(thm)],[2488, 2482])).
% 1.10/1.25 tff(2490,plain,
% 1.10/1.25 (hskp26 | hskp22 | hskp6),
% 1.10/1.25 inference(modus_ponens,[status(thm)],[2489, 2482])).
% 1.10/1.25 tff(2491,plain,
% 1.10/1.25 (hskp26 | hskp22 | hskp6),
% 1.10/1.25 inference(modus_ponens,[status(thm)],[2490, 2482])).
% 1.10/1.25 tff(2492,plain,
% 1.10/1.25 (hskp26 | hskp22 | hskp6),
% 1.10/1.25 inference(modus_ponens,[status(thm)],[2491, 2482])).
% 1.10/1.25 tff(2493,plain,
% 1.10/1.25 (hskp26),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[2492, 2481, 2464])).
% 1.10/1.25 tff(2494,plain,
% 1.10/1.25 (c3_1(a10)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[632, 2493])).
% 1.10/1.25 tff(2495,plain,
% 1.10/1.25 (c2_1(a10)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[624, 2493])).
% 1.10/1.25 tff(2496,plain,
% 1.10/1.25 (c0_1(a10)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[615, 2493])).
% 1.10/1.25 tff(2497,plain,
% 1.10/1.25 (~hskp9),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[664, 2496, 2495, 2494, 607, 606])).
% 1.10/1.25 tff(2498,plain,
% 1.10/1.25 (hskp7),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[483, 2497, 2463])).
% 1.10/1.25 tff(2499,plain,
% 1.10/1.25 (~c2_1(a14)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[489, 2498])).
% 1.10/1.25 tff(2500,plain,
% 1.10/1.25 (c3_1(a14)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[497, 2498])).
% 1.10/1.25 tff(2501,plain,
% 1.10/1.25 (c0_1(a14)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[516, 2498])).
% 1.10/1.25 tff(2502,plain,
% 1.10/1.25 ($false),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[2401, 160, 2351, 2501, 2500, 463, 2499, 443, 2374, 442])).
% 1.10/1.25 tff(2503,plain,(c1_1(a1) | hskp15 | (~c3_1(a1)) | c2_1(a1) | hskp14 | hskp2 | c0_1(a1) | hskp22 | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.25 tff(2504,plain,
% 1.10/1.25 (c1_1(a1)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[2503, 2462, 441, 438, 607, 606, 439, 2351, 2362, 2404, 2364])).
% 1.10/1.25 tff(2505,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2506,plain,
% 1.10/1.25 ((hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2507,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.10/1.25 inference(monotonicity,[status(thm)],[2506])).
% 1.10/1.25 tff(2508,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.25 inference(transitivity,[status(thm)],[2507, 2505])).
% 1.10/1.25 tff(2509,plain,
% 1.10/1.25 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.10/1.25 inference(quant_inst,[status(thm)],[])).
% 1.10/1.25 tff(2510,plain,
% 1.10/1.25 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.10/1.25 inference(modus_ponens,[status(thm)],[2509, 2508])).
% 1.10/1.25 tff(2511,plain,
% 1.10/1.25 (hskp10 | (~c1_1(a1)) | (~c3_1(a31))),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[2510, 160, 2362, 441, 2363, 439, 1053])).
% 1.10/1.25 tff(2512,plain,
% 1.10/1.25 (hskp10),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[2511, 2504, 2404])).
% 1.10/1.25 tff(2513,plain,
% 1.10/1.25 (~c3_1(a18)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[1066, 2512])).
% 1.10/1.25 tff(2514,plain,
% 1.10/1.25 (c2_1(a18)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[1074, 2512])).
% 1.10/1.25 tff(2515,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2516,plain,
% 1.10/1.25 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2517,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.10/1.25 inference(monotonicity,[status(thm)],[2516])).
% 1.10/1.25 tff(2518,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.25 inference(transitivity,[status(thm)],[2517, 2515])).
% 1.10/1.25 tff(2519,plain,
% 1.10/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.25 inference(quant_inst,[status(thm)],[])).
% 1.10/1.25 tff(2520,plain,
% 1.10/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.10/1.25 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 1.10/1.25 tff(2521,plain,
% 1.10/1.25 (c1_1(a18)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[2520, 160, 2364, 2362, 2514, 2513, 1466, 2404])).
% 1.10/1.25 tff(2522,plain,
% 1.10/1.25 (c0_1(a18)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[1082, 2512])).
% 1.10/1.25 tff(2523,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2524,plain,
% 1.10/1.25 ((hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2525,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18))))),
% 1.10/1.25 inference(monotonicity,[status(thm)],[2524])).
% 1.10/1.25 tff(2526,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.25 inference(transitivity,[status(thm)],[2525, 2523])).
% 1.10/1.25 tff(2527,plain,
% 1.10/1.25 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.10/1.25 inference(quant_inst,[status(thm)],[])).
% 1.10/1.25 tff(2528,plain,
% 1.10/1.25 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18))),
% 1.10/1.25 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 1.10/1.25 tff(2529,plain,
% 1.10/1.25 (hskp19 | (~c1_1(a18))),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[2528, 160, 2522, 2514, 441, 438, 779, 2504])).
% 1.10/1.25 tff(2530,plain,
% 1.10/1.25 (hskp19),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[2529, 2521])).
% 1.10/1.25 tff(2531,plain,
% 1.10/1.25 (~c0_1(a33)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[819, 2530])).
% 1.10/1.25 tff(2532,plain,
% 1.10/1.25 (c3_1(a33)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[1392, 2530])).
% 1.10/1.25 tff(2533,plain,
% 1.10/1.25 (c2_1(a33)),
% 1.10/1.25 inference(unit_resolution,[status(thm)],[827, 2530])).
% 1.10/1.25 tff(2534,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2535,plain,
% 1.10/1.25 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19))) <=> (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.25 inference(rewrite,[status(thm)],[])).
% 1.10/1.25 tff(2536,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.10/1.25 inference(monotonicity,[status(thm)],[2535])).
% 1.10/1.25 tff(2537,plain,
% 1.10/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[2536, 2534])).
% 1.10/1.26 tff(2538,plain,
% 1.10/1.26 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2539,plain,
% 1.10/1.26 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2538, 2537])).
% 1.10/1.26 tff(2540,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2539, 160, 301, 302, 2133, 2132, 2131, 1466, 2465])).
% 1.10/1.26 tff(2541,plain,((~hskp11) | (~c0_1(a31)) | (~c2_1(a31)) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(2542,plain,
% 1.10/1.26 (~hskp11),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2541, 2404, 2362, 2364])).
% 1.10/1.26 tff(2543,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2544,plain,
% 1.10/1.26 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2545,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[2544])).
% 1.10/1.26 tff(2546,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[2545, 2543])).
% 1.10/1.26 tff(2547,plain,
% 1.10/1.26 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2548,plain,
% 1.10/1.26 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2547, 2546])).
% 1.10/1.26 tff(2549,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2548, 160, 2542, 2533, 2532, 2522, 2514, 2531, 2513, 1042])).
% 1.10/1.26 tff(2550,plain,((~hskp0) | hskp14 | hskp2 | hskp15 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(2551,plain,
% 1.10/1.26 (~hskp0),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2550, 606, 607, 2351, 193])).
% 1.10/1.26 tff(2552,plain,
% 1.10/1.26 (hskp7 | c3_1(a31)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2390, 160, 2362, 2363, 2384])).
% 1.10/1.26 tff(2553,plain,
% 1.10/1.26 (hskp7),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2552, 2165])).
% 1.10/1.26 tff(2554,plain,
% 1.10/1.26 (~c2_1(a14)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[489, 2553])).
% 1.10/1.26 tff(2555,plain,
% 1.10/1.26 (c0_1(a14)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[516, 2553])).
% 1.10/1.26 tff(2556,plain,
% 1.10/1.26 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2557,plain,
% 1.10/1.26 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14))) <=> (hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2558,plain,
% 1.10/1.26 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[2557])).
% 1.10/1.26 tff(2559,plain,
% 1.10/1.26 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[2558, 2556])).
% 1.10/1.26 tff(2560,plain,
% 1.10/1.26 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2561,plain,
% 1.10/1.26 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 1.10/1.26 tff(2562,plain,
% 1.10/1.26 (c1_1(a14)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2561, 160, 607, 606, 2555, 2554, 643])).
% 1.10/1.26 tff(2563,plain,
% 1.10/1.26 (c3_1(a14)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[497, 2553])).
% 1.10/1.26 tff(2564,plain,
% 1.10/1.26 (^[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))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(2565,plain,
% 1.10/1.26 (![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)))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[2564])).
% 1.10/1.26 tff(2566,plain,
% 1.10/1.26 (![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)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2567,plain,
% 1.10/1.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_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)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_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)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(2568,plain,
% 1.10/1.26 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[2567])).
% 1.10/1.26 tff(2569,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.10/1.26 tff(2570,plain,
% 1.10/1.26 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.10/1.26 tff(2571,plain,
% 1.10/1.26 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2570, 2566])).
% 1.10/1.26 tff(2572,plain,(
% 1.10/1.26 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.10/1.26 inference(skolemize,[status(sab)],[2571])).
% 1.10/1.26 tff(2573,plain,
% 1.10/1.26 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2572, 2565])).
% 1.10/1.26 tff(2574,assumption,(c1_1(a14)), introduced(assumption)).
% 1.10/1.26 tff(2575,plain,
% 1.10/1.26 (hskp24 | hskp9),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[504, 160, 2394, 2393, 104, 2574])).
% 1.10/1.26 tff(2576,plain,
% 1.10/1.26 (hskp24),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2575, 105])).
% 1.10/1.26 tff(2577,plain,
% 1.10/1.26 (c2_1(a3)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2263, 2576])).
% 1.10/1.26 tff(2578,plain,
% 1.10/1.26 (c1_1(a3)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2271, 2576])).
% 1.10/1.26 tff(2579,assumption,(~hskp8), introduced(assumption)).
% 1.10/1.26 tff(2580,plain,
% 1.10/1.26 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2581,plain,
% 1.10/1.26 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2582,plain,
% 1.10/1.26 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2581, 2580])).
% 1.10/1.26 tff(2583,plain,
% 1.10/1.26 (c0_1(a3)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2582, 160, 105, 2579, 2578, 2577, 2573])).
% 1.10/1.26 tff(2584,plain,
% 1.10/1.26 (c3_1(a3)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2288, 2576])).
% 1.10/1.26 tff(2585,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2298, 160, 2577, 2584, 302, 313, 1466, 2165, 2583])).
% 1.10/1.26 tff(2586,plain,(hskp9 | (~c2_1(a31)) | c1_1(a31) | c3_1(a31) | hskp8 | (~c1_1(a14))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(2587,plain,
% 1.10/1.26 (hskp9),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2586, 2165, 2363, 2362, 2360, 2562])).
% 1.10/1.26 tff(2588,plain,
% 1.10/1.26 (~c2_1(a16)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[537, 2587])).
% 1.10/1.26 tff(2589,assumption,(hskp16), introduced(assumption)).
% 1.10/1.26 tff(2590,plain,
% 1.10/1.26 (~c0_1(a30)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[573, 2589])).
% 1.10/1.26 tff(2591,plain,
% 1.10/1.26 (c1_1(a30)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[561, 2589])).
% 1.10/1.26 tff(2592,plain,
% 1.10/1.26 (~c3_1(a30)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2182, 160, 193, 301, 2591, 313, 2590, 584, 2165])).
% 1.10/1.26 tff(2593,assumption,(~c2_1(a14)), introduced(assumption)).
% 1.10/1.26 tff(2594,plain,
% 1.10/1.26 (~c2_1(a30)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[567, 2589])).
% 1.10/1.26 tff(2595,assumption,(c3_1(a14)), introduced(assumption)).
% 1.10/1.26 tff(2596,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2597,plain,
% 1.10/1.26 (((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30)) <=> (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2598,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[2597])).
% 1.10/1.26 tff(2599,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[2598, 2596])).
% 1.10/1.26 tff(2600,plain,
% 1.10/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2601,plain,
% 1.10/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 1.10/1.26 tff(2602,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2601, 160, 301, 2595, 313, 2590, 2594, 2593, 13, 2165, 2574, 2592])).
% 1.10/1.26 tff(2603,plain,((~hskp16) | (~c0_1(a31)) | (~c3_1(a14)) | c1_1(a31) | c2_1(a14) | c3_1(a31) | (~c1_1(a14)) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(2604,plain,
% 1.10/1.26 (~hskp16),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2603, 2563, 2364, 2363, 2554, 2165, 2562, 193])).
% 1.10/1.26 tff(2605,plain,
% 1.10/1.26 (~c3_1(a16)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[531, 2587])).
% 1.10/1.26 tff(2606,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2607,plain,
% 1.10/1.26 (((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16)) <=> (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2608,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[2607])).
% 1.10/1.26 tff(2609,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[2608, 2606])).
% 1.10/1.26 tff(2610,plain,
% 1.10/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2611,plain,
% 1.10/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 1.10/1.26 tff(2612,plain,
% 1.10/1.26 (c0_1(a16) | c3_1(a16)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2611, 160, 301, 2595, 313, 24, 2593, 13, 2165, 2574])).
% 1.10/1.26 tff(2613,plain,
% 1.10/1.26 (c0_1(a16)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2612, 2])).
% 1.10/1.26 tff(2614,assumption,(~hskp16), introduced(assumption)).
% 1.10/1.26 tff(2615,plain,
% 1.10/1.26 (c3_1(a16) | (~c0_1(a16))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[552, 160, 84, 2614, 24, 94])).
% 1.10/1.26 tff(2616,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2615, 2613, 2])).
% 1.10/1.26 tff(2617,plain,(c3_1(a16) | hskp26 | hskp16 | c2_1(a16) | (~c0_1(a31)) | (~c3_1(a14)) | c1_1(a31) | c2_1(a14) | c3_1(a31) | (~c1_1(a14))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(2618,plain,
% 1.10/1.26 (hskp26),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2617, 2605, 2604, 2588, 2364, 2563, 2363, 2554, 2165, 2562])).
% 1.10/1.26 tff(2619,plain,
% 1.10/1.26 (c3_1(a10)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[632, 2618])).
% 1.10/1.26 tff(2620,plain,
% 1.10/1.26 (c0_1(a10)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[615, 2618])).
% 1.10/1.26 tff(2621,plain,
% 1.10/1.26 (c2_1(a10)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[624, 2618])).
% 1.10/1.26 tff(2622,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[664, 2621, 2620, 2587, 2619, 607, 606])).
% 1.10/1.26 tff(2623,plain,(c3_1(a31) | hskp14 | hskp2 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(2624,plain,
% 1.10/1.26 (c3_1(a31)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2623, 606, 607, 193])).
% 1.10/1.26 tff(2625,assumption,(~c0_1(a45)), introduced(assumption)).
% 1.10/1.26 tff(2626,plain,
% 1.10/1.26 (c1_1(a45) | (~c2_1(a45))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2443, 160, 301, 302, 2419, 1466, 2465])).
% 1.10/1.26 tff(2627,plain,
% 1.10/1.26 (~c2_1(a45)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2626, 2418])).
% 1.10/1.26 tff(2628,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2629,plain,
% 1.10/1.26 ((hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | c0_1(a45)) <=> (hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2630,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | c0_1(a45))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[2629])).
% 1.10/1.26 tff(2631,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | c0_1(a45))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[2630, 2628])).
% 1.10/1.26 tff(2632,plain,
% 1.10/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | c0_1(a45))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2633,plain,
% 1.10/1.26 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2632, 2631])).
% 1.10/1.26 tff(2634,plain,
% 1.10/1.26 (hskp1 | c0_1(a45) | c1_1(a45)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2633, 160, 302, 2419, 313, 1385, 2465])).
% 1.10/1.26 tff(2635,plain,
% 1.10/1.26 (hskp1),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2634, 2418, 2625])).
% 1.10/1.26 tff(2636,plain,
% 1.10/1.26 (~c3_1(a2)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2318, 2635])).
% 1.10/1.26 tff(2637,plain,
% 1.10/1.26 (~c0_1(a2)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[1405, 2635])).
% 1.10/1.26 tff(2638,plain,
% 1.10/1.26 (c2_1(a2)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[1413, 2635])).
% 1.10/1.26 tff(2639,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2640,plain,
% 1.10/1.26 (((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a45) | c1_1(a45) | c2_1(a45) | c2_1(a45) | c0_1(a45) | c3_1(a45)) <=> (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2641,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a45) | c1_1(a45) | c2_1(a45) | c2_1(a45) | c0_1(a45) | c3_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45)))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[2640])).
% 1.10/1.26 tff(2642,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a45) | c1_1(a45) | c2_1(a45) | c2_1(a45) | c0_1(a45) | c3_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45))),
% 1.10/1.26 inference(transitivity,[status(thm)],[2641, 2639])).
% 1.10/1.26 tff(2643,plain,
% 1.10/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a45) | c1_1(a45) | c2_1(a45) | c2_1(a45) | c0_1(a45) | c3_1(a45))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2644,plain,
% 1.10/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2643, 2642])).
% 1.10/1.26 tff(2645,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2644, 160, 2625, 2638, 2418, 2419, 2637, 2636, 2312, 2627])).
% 1.10/1.26 tff(2646,plain,(c1_1(a45) | c0_1(a45) | c3_1(a45) | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(2647,plain,
% 1.10/1.26 (c1_1(a45)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2646, 2625, 2419, 302, 313, 2465, 301])).
% 1.10/1.26 tff(2648,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2157, 160, 301, 302, 645, 644, 653, 406, 2465, 652])).
% 1.10/1.26 tff(2649,plain,((~hskp9) | (~c0_1(a31)) | (~c2_1(a31)) | (~c3_1(a31)) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(2650,plain,
% 1.10/1.26 (~hskp9),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2649, 301, 302, 2465, 607, 606])).
% 1.10/1.26 tff(2651,assumption,(c1_1(a45)), introduced(assumption)).
% 1.10/1.26 tff(2652,plain,
% 1.10/1.26 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2653,plain,
% 1.10/1.26 ((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a45)) | c0_1(a45) | (~c1_1(a45))) <=> (hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(2654,plain,
% 1.10/1.26 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a45)) | c0_1(a45) | (~c1_1(a45)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[2653])).
% 1.10/1.26 tff(2655,plain,
% 1.10/1.26 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a45)) | c0_1(a45) | (~c1_1(a45)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[2654, 2652])).
% 1.10/1.26 tff(2656,plain,
% 1.10/1.26 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a45)) | c0_1(a45) | (~c1_1(a45)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(2657,plain,
% 1.10/1.26 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[2656, 2655])).
% 1.10/1.26 tff(2658,plain,
% 1.10/1.26 (hskp9 | (~c1_1(a45)) | (~c2_1(a45))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2657, 160, 2579, 2625, 2573])).
% 1.10/1.26 tff(2659,plain,
% 1.10/1.26 (~c2_1(a45)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[2658, 105, 2651])).
% 1.10/1.26 tff(2660,assumption,(c0_1(a8)), introduced(assumption)).
% 1.10/1.26 tff(2661,plain,
% 1.10/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2662,plain,
% 1.10/1.27 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> ((~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2663,plain,
% 1.10/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45)))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2662])).
% 1.10/1.27 tff(2664,plain,
% 1.10/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2663, 2661])).
% 1.10/1.27 tff(2665,plain,
% 1.10/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2666,plain,
% 1.10/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2665, 2664])).
% 1.10/1.27 tff(2667,plain,
% 1.10/1.27 ((~c1_1(a45)) | c3_1(a8) | c2_1(a45)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2666, 160, 301, 302, 2660, 2419, 1250, 406, 2465])).
% 1.10/1.27 tff(2668,plain,
% 1.10/1.27 (c3_1(a8)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2667, 2659, 2651])).
% 1.10/1.27 tff(2669,plain,
% 1.10/1.27 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2670,plain,
% 1.10/1.27 ((hskp24 | hskp9 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8))) <=> (hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2671,plain,
% 1.10/1.27 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2670])).
% 1.10/1.27 tff(2672,plain,
% 1.10/1.27 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2671, 2669])).
% 1.10/1.27 tff(2673,plain,
% 1.10/1.27 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2674,plain,
% 1.10/1.27 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 1.10/1.27 tff(2675,plain,
% 1.10/1.27 (hskp24 | hskp9 | (~c3_1(a8))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2674, 160, 1251, 1250, 104])).
% 1.10/1.27 tff(2676,plain,
% 1.10/1.27 (hskp24),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2675, 2668, 105])).
% 1.10/1.27 tff(2677,plain,
% 1.10/1.27 (c2_1(a3)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2263, 2676])).
% 1.10/1.27 tff(2678,plain,
% 1.10/1.27 (c1_1(a3)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2271, 2676])).
% 1.10/1.27 tff(2679,plain,
% 1.10/1.27 (c0_1(a3)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2582, 160, 105, 2579, 2678, 2677, 2573])).
% 1.10/1.27 tff(2680,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2681,plain,
% 1.10/1.27 ((hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8))) <=> (hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2682,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2681])).
% 1.10/1.27 tff(2683,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.10/1.27 tff(2684,plain,
% 1.10/1.27 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2685,plain,
% 1.10/1.27 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.10/1.27 tff(2686,plain,
% 1.10/1.27 (hskp19),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2685, 160, 2678, 2677, 1251, 1250, 779, 2668, 2679])).
% 1.10/1.27 tff(2687,plain,
% 1.10/1.27 (~c0_1(a33)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[819, 2686])).
% 1.10/1.27 tff(2688,plain,
% 1.10/1.27 (c2_1(a33)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[827, 2686])).
% 1.10/1.27 tff(2689,plain,
% 1.10/1.27 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2690,plain,
% 1.10/1.27 ((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33))) <=> (hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2691,plain,
% 1.10/1.27 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2690])).
% 1.10/1.27 tff(2692,plain,
% 1.10/1.27 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2691, 2689])).
% 1.10/1.27 tff(2693,plain,
% 1.10/1.27 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2694,plain,
% 1.10/1.27 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2693, 2692])).
% 1.10/1.27 tff(2695,plain,
% 1.10/1.27 (~c1_1(a33)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2694, 160, 105, 2579, 2688, 2687, 2573])).
% 1.10/1.27 tff(2696,plain,
% 1.10/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2697,plain,
% 1.10/1.27 (((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2698,plain,
% 1.10/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2697])).
% 1.10/1.27 tff(2699,plain,
% 1.10/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2698, 2696])).
% 1.10/1.27 tff(2700,plain,
% 1.10/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2701,plain,
% 1.10/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2700, 2699])).
% 1.10/1.27 tff(2702,plain,
% 1.10/1.27 ($false),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2701, 160, 2625, 2688, 302, 2651, 2419, 2687, 313, 83, 2465, 2695])).
% 1.10/1.27 tff(2703,plain,(hskp9 | c0_1(a45) | (~c2_1(a31)) | (~c1_1(a45)) | c3_1(a45) | c1_1(a31) | (~c3_1(a31)) | hskp8 | (~c1_1(a8)) | c2_1(a8) | (~c0_1(a31)) | (~c0_1(a8))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.27 tff(2704,plain,
% 1.10/1.27 ($false),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2703, 1240, 1248, 302, 105, 2419, 313, 2465, 2579, 2625, 2647, 301, 1268])).
% 1.10/1.27 tff(2705,plain,((~hskp6) | (~c2_1(a31)) | hskp9 | c3_1(a45) | c1_1(a31) | (~c3_1(a31)) | hskp8 | c0_1(a45) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.27 tff(2706,plain,
% 1.10/1.27 (~hskp6),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2705, 2625, 2650, 2419, 313, 2465, 2360, 302, 301])).
% 1.10/1.27 tff(2707,assumption,(~c3_1(a14)), introduced(assumption)).
% 1.10/1.27 tff(2708,plain,
% 1.10/1.27 ((~c1_1(a45)) | (~c2_1(a45))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2657, 160, 105, 2579, 2625, 2573])).
% 1.10/1.27 tff(2709,plain,
% 1.10/1.27 (~c2_1(a45)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2708, 2647])).
% 1.10/1.27 tff(2710,plain,
% 1.10/1.27 (((~hskp22) | c0_1(a45)) <=> ((~hskp22) | c0_1(a45))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2711,axiom,((~hskp22) | c0_1(a45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.10/1.27 tff(2712,plain,
% 1.10/1.27 ((~hskp22) | c0_1(a45)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 1.10/1.27 tff(2713,plain,
% 1.10/1.27 ((~hskp22) | c0_1(a45)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2712, 2710])).
% 1.10/1.27 tff(2714,plain,
% 1.10/1.27 ((~hskp22) | c0_1(a45)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2713, 2710])).
% 1.10/1.27 tff(2715,plain,
% 1.10/1.27 ((~hskp22) | c0_1(a45)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2714, 2710])).
% 1.10/1.27 tff(2716,plain,
% 1.10/1.27 ((~hskp22) | c0_1(a45)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2715, 2710])).
% 1.10/1.27 tff(2717,plain,
% 1.10/1.27 (~hskp22),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2716, 2625])).
% 1.10/1.27 tff(2718,plain,
% 1.10/1.27 (~hskp6),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2705, 2625, 105, 2419, 313, 2465, 2579, 302, 301])).
% 1.10/1.27 tff(2719,plain,
% 1.10/1.27 (hskp26),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2492, 2718, 2717])).
% 1.10/1.27 tff(2720,plain,
% 1.10/1.27 (c3_1(a10)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[632, 2719])).
% 1.10/1.27 tff(2721,plain,
% 1.10/1.27 (c2_1(a10)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[624, 2719])).
% 1.10/1.27 tff(2722,plain,
% 1.10/1.27 (c0_1(a10)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[615, 2719])).
% 1.10/1.27 tff(2723,plain,
% 1.10/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2724,plain,
% 1.10/1.27 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a14) | c3_1(a14) | (~c0_1(a14))) <=> (c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2725,plain,
% 1.10/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a14) | c3_1(a14) | (~c0_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45)))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2724])).
% 1.10/1.27 tff(2726,plain,
% 1.10/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a14) | c3_1(a14) | (~c0_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2725, 2723])).
% 1.10/1.27 tff(2727,plain,
% 1.10/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a14) | c3_1(a14) | (~c0_1(a14)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2728,plain,
% 1.10/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2727, 2726])).
% 1.10/1.27 tff(2729,plain,
% 1.10/1.27 (c3_1(a14) | (~c0_1(a14))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2728, 160, 2722, 2721, 2720, 2647, 2419, 2593, 406, 2709])).
% 1.10/1.27 tff(2730,plain,
% 1.10/1.27 (~c0_1(a14)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2729, 2707])).
% 1.10/1.27 tff(2731,plain,
% 1.10/1.27 (~hskp7),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[497, 2707])).
% 1.10/1.27 tff(2732,assumption,(hskp24), introduced(assumption)).
% 1.10/1.27 tff(2733,plain,
% 1.10/1.27 (c2_1(a3)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2263, 2732])).
% 1.10/1.27 tff(2734,plain,
% 1.10/1.27 (c1_1(a3)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2271, 2732])).
% 1.10/1.27 tff(2735,plain,
% 1.10/1.27 (c0_1(a3)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2582, 160, 105, 2579, 2734, 2733, 2573])).
% 1.10/1.27 tff(2736,plain,
% 1.10/1.27 (^[U: $i] : refl((hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(2737,plain,
% 1.10/1.27 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[2736])).
% 1.10/1.27 tff(2738,plain,
% 1.10/1.27 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2739,plain,
% 1.10/1.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) | hskp10) <=> ((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp10))), rewrite(((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) | hskp10) <=> (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(2740,plain,
% 1.10/1.27 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) | hskp10) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[2739])).
% 1.10/1.27 tff(2741,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.10/1.27 tff(2742,plain,
% 1.10/1.27 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 1.10/1.27 tff(2743,plain,
% 1.10/1.27 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2742, 2738])).
% 1.10/1.27 tff(2744,plain,(
% 1.10/1.27 ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.10/1.27 inference(skolemize,[status(sab)],[2743])).
% 1.10/1.27 tff(2745,plain,
% 1.10/1.27 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2744, 2737])).
% 1.10/1.27 tff(2746,plain,
% 1.10/1.27 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2747,plain,
% 1.10/1.27 ((hskp10 | hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))) <=> (hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2748,plain,
% 1.10/1.27 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2747])).
% 1.10/1.27 tff(2749,plain,
% 1.10/1.27 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2748, 2746])).
% 1.10/1.27 tff(2750,plain,
% 1.10/1.27 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2751,plain,
% 1.10/1.27 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2750, 2749])).
% 1.10/1.27 tff(2752,plain,
% 1.10/1.27 (hskp10 | (~c0_1(a3))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2751, 160, 1174, 2734, 2733, 2745])).
% 1.10/1.27 tff(2753,plain,
% 1.10/1.27 (hskp10),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2752, 2735])).
% 1.10/1.27 tff(2754,plain,
% 1.10/1.27 (~c3_1(a18)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[1066, 2753])).
% 1.10/1.27 tff(2755,plain,
% 1.10/1.27 (c2_1(a18)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[1074, 2753])).
% 1.10/1.27 tff(2756,assumption,(~hskp7), introduced(assumption)).
% 1.10/1.27 tff(2757,plain,
% 1.10/1.27 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2758,plain,
% 1.10/1.27 ((hskp7 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2759,plain,
% 1.10/1.27 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2758])).
% 1.10/1.27 tff(2760,plain,
% 1.10/1.27 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2759, 2757])).
% 1.10/1.27 tff(2761,plain,
% 1.10/1.27 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2762,plain,
% 1.10/1.27 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 1.10/1.27 tff(2763,plain,
% 1.10/1.27 (c1_1(a18)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2762, 160, 2756, 2755, 2754, 2384])).
% 1.10/1.27 tff(2764,plain,
% 1.10/1.27 (~c2_1(a45)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2708, 2651])).
% 1.10/1.27 tff(2765,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2766,plain,
% 1.10/1.27 ((hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a45) | c2_1(a45) | (~c1_1(a45))) <=> (hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(2767,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a45) | c2_1(a45) | (~c1_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45)))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[2766])).
% 1.10/1.27 tff(2768,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a45) | c2_1(a45) | (~c1_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45))),
% 1.10/1.27 inference(transitivity,[status(thm)],[2767, 2765])).
% 1.10/1.27 tff(2769,plain,
% 1.10/1.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a45) | c2_1(a45) | (~c1_1(a45)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(2770,plain,
% 1.10/1.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 1.10/1.27 tff(2771,plain,
% 1.10/1.27 (hskp5),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[2770, 160, 2625, 2755, 2651, 2754, 1311, 2764, 2763])).
% 1.10/1.27 tff(2772,plain,
% 1.10/1.27 (~c0_1(a7)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[1317, 2771])).
% 1.10/1.27 tff(2773,plain,
% 1.10/1.27 (c1_1(a7)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[1325, 2771])).
% 1.10/1.27 tff(2774,plain,
% 1.10/1.27 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2775,plain,
% 1.10/1.28 ((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7))) <=> (hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2776,plain,
% 1.10/1.28 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2775])).
% 1.10/1.28 tff(2777,plain,
% 1.10/1.28 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[2776, 2774])).
% 1.10/1.28 tff(2778,plain,
% 1.10/1.28 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(2779,plain,
% 1.10/1.28 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 1.10/1.28 tff(2780,plain,
% 1.10/1.28 (~c2_1(a7)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2779, 160, 105, 2579, 2773, 2772, 2573])).
% 1.10/1.28 tff(2781,plain,
% 1.10/1.28 (c3_1(a7)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[1346, 2771])).
% 1.10/1.28 tff(2782,plain,
% 1.10/1.28 (c3_1(a3)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2288, 2732])).
% 1.10/1.28 tff(2783,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2784,plain,
% 1.10/1.28 ((hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a7) | c2_1(a7) | (~c3_1(a7))) <=> (hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2785,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a7) | c2_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7)))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2784])).
% 1.10/1.28 tff(2786,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a7) | c2_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7))),
% 1.10/1.28 inference(transitivity,[status(thm)],[2785, 2783])).
% 1.10/1.28 tff(2787,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a7) | c2_1(a7) | (~c3_1(a7)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(2788,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 1.10/1.28 tff(2789,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2788, 160, 1174, 2734, 2733, 2782, 2781, 2772, 1202, 2780])).
% 1.10/1.28 tff(2790,plain,((~hskp24) | hskp6 | hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(2791,plain,
% 1.10/1.28 (~hskp24),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2790, 2731, 105, 2579, 2625, 2647, 2718])).
% 1.10/1.28 tff(2792,plain,
% 1.10/1.28 (hskp23),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[235, 2791, 314])).
% 1.10/1.28 tff(2793,assumption,(~c0_1(a14)), introduced(assumption)).
% 1.10/1.28 tff(2794,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2795,plain,
% 1.10/1.28 (((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a14) | c0_1(a14) | (~c1_1(a14)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2796,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a14) | c0_1(a14) | (~c1_1(a14)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2795])).
% 1.10/1.28 tff(2797,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a14) | c0_1(a14) | (~c1_1(a14)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[2796, 2794])).
% 1.10/1.28 tff(2798,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a14) | c0_1(a14) | (~c1_1(a14)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(2799,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 1.10/1.28 tff(2800,plain,
% 1.10/1.28 (~c2_1(a53)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2799, 160, 215, 2793, 2707, 207, 201, 83, 2574])).
% 1.10/1.28 tff(2801,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[323, 160, 314, 301, 302, 207, 201, 313, 312, 2800])).
% 1.10/1.28 tff(2802,plain,((~hskp23) | hskp0 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | c0_1(a14) | c3_1(a14) | (~c1_1(a14))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(2803,plain,
% 1.10/1.28 (~c1_1(a14)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2802, 2792, 301, 302, 313, 2730, 2707, 314])).
% 1.10/1.28 tff(2804,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2805,plain,
% 1.10/1.28 ((hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a14) | c1_1(a14) | c0_1(a14)) <=> (hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2806,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a14) | c1_1(a14) | c0_1(a14))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2805])).
% 1.10/1.28 tff(2807,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a14) | c1_1(a14) | c0_1(a14))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[2806, 2804])).
% 1.10/1.28 tff(2808,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a14) | c1_1(a14) | c0_1(a14))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(2809,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 1.10/1.28 tff(2810,plain,
% 1.10/1.28 (hskp1 | c1_1(a14)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2809, 160, 302, 2730, 2707, 313, 1385, 2465])).
% 1.10/1.28 tff(2811,plain,
% 1.10/1.28 (hskp1),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2810, 2803])).
% 1.10/1.28 tff(2812,plain,
% 1.10/1.28 (~c3_1(a2)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2318, 2811])).
% 1.10/1.28 tff(2813,plain,
% 1.10/1.28 (~c0_1(a2)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[1405, 2811])).
% 1.10/1.28 tff(2814,plain,
% 1.10/1.28 (hskp13),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[483, 2731, 105])).
% 1.10/1.28 tff(2815,plain,
% 1.10/1.28 (~c3_1(a22)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[449, 2814])).
% 1.10/1.28 tff(2816,plain,
% 1.10/1.28 (~c2_1(a22)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[455, 2814])).
% 1.10/1.28 tff(2817,plain,
% 1.10/1.28 (~c0_1(a22)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[461, 2814])).
% 1.10/1.28 tff(2818,plain,
% 1.10/1.28 (c2_1(a2)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[1413, 2811])).
% 1.10/1.28 tff(2819,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2820,plain,
% 1.10/1.28 (((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a14) | c1_1(a14) | c2_1(a14) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2821,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a14) | c1_1(a14) | c2_1(a14) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14)))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2820])).
% 1.10/1.28 tff(2822,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a14) | c1_1(a14) | c2_1(a14) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14))),
% 1.10/1.28 inference(transitivity,[status(thm)],[2821, 2819])).
% 1.10/1.28 tff(2823,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a14) | c1_1(a14) | c2_1(a14) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(2824,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[2823, 2822])).
% 1.10/1.28 tff(2825,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2824, 160, 2707, 2818, 2817, 2816, 2815, 2593, 2813, 2812, 2312, 2803])).
% 1.10/1.28 tff(2826,plain,(c3_1(a14) | c2_1(a14) | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | (~c0_1(a31)) | hskp0 | hskp9 | hskp8 | c0_1(a45) | c3_1(a45)), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(2827,plain,
% 1.10/1.28 (c3_1(a14)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2826, 2593, 302, 313, 2465, 301, 314, 2650, 2360, 2625, 2419])).
% 1.10/1.28 tff(2828,plain,
% 1.10/1.28 ((~c1_1(a45)) | (~c2_1(a45))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2657, 160, 2650, 2360, 2625, 2573])).
% 1.10/1.28 tff(2829,plain,
% 1.10/1.28 (~c2_1(a45)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2828, 2647])).
% 1.10/1.28 tff(2830,assumption,(~c1_1(a14)), introduced(assumption)).
% 1.10/1.28 tff(2831,plain,
% 1.10/1.28 (c1_1(a14) | (~c0_1(a14))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2561, 160, 607, 606, 2593, 643])).
% 1.10/1.28 tff(2832,plain,
% 1.10/1.28 (~c0_1(a14)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2831, 2830])).
% 1.10/1.28 tff(2833,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2834,plain,
% 1.10/1.28 (((~ndr1_0) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a14) | c1_1(a14) | c0_1(a14)) <=> (c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2835,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a14) | c1_1(a14) | c0_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45)))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2834])).
% 1.10/1.28 tff(2836,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a14) | c1_1(a14) | c0_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45))),
% 1.10/1.28 inference(transitivity,[status(thm)],[2835, 2833])).
% 1.10/1.28 tff(2837,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a14) | c1_1(a14) | c0_1(a14))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(2838,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 1.10/1.28 tff(2839,plain,
% 1.10/1.28 (c0_1(a14) | c1_1(a14) | (~c3_1(a14))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2838, 160, 2625, 2419, 2593, 55, 2420])).
% 1.10/1.28 tff(2840,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2839, 2832, 2830, 2595])).
% 1.10/1.28 tff(2841,plain,(c1_1(a14) | (~c3_1(a14)) | c0_1(a45) | c3_1(a45) | c2_1(a14) | c2_1(a45) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(2842,plain,
% 1.10/1.28 (c1_1(a14)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2841, 2827, 2625, 2419, 2593, 2829, 607, 606])).
% 1.10/1.28 tff(2843,plain,
% 1.10/1.28 (hskp24 | (~c1_1(a14)) | (~c3_1(a14))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[504, 160, 2650, 2593, 104])).
% 1.10/1.28 tff(2844,plain,
% 1.10/1.28 (hskp24),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2843, 2842, 2827])).
% 1.10/1.28 tff(2845,plain,
% 1.10/1.28 (c2_1(a3)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2263, 2844])).
% 1.10/1.28 tff(2846,plain,
% 1.10/1.28 (c1_1(a3)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2271, 2844])).
% 1.10/1.28 tff(2847,plain,
% 1.10/1.28 (c0_1(a3)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2582, 160, 2650, 2360, 2846, 2845, 2573])).
% 1.10/1.28 tff(2848,plain,
% 1.10/1.28 (hskp10 | (~c0_1(a3))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2751, 160, 2706, 2846, 2845, 2745])).
% 1.10/1.28 tff(2849,plain,
% 1.10/1.28 (hskp10),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2848, 2847])).
% 1.10/1.28 tff(2850,plain,
% 1.10/1.28 (~c3_1(a18)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[1066, 2849])).
% 1.10/1.28 tff(2851,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2852,plain,
% 1.10/1.28 ((hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14))) <=> (hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2853,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2852])).
% 1.10/1.28 tff(2854,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[2853, 2851])).
% 1.10/1.28 tff(2855,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(2856,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[2855, 2854])).
% 1.10/1.28 tff(2857,plain,
% 1.10/1.28 (hskp19),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2856, 160, 2846, 2845, 2827, 2593, 779, 2842, 2847])).
% 1.10/1.28 tff(2858,plain,
% 1.10/1.28 (~c0_1(a33)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[819, 2857])).
% 1.10/1.28 tff(2859,plain,
% 1.10/1.28 (c2_1(a18)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[1074, 2849])).
% 1.10/1.28 tff(2860,plain,
% 1.10/1.28 (c0_1(a18)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[1082, 2849])).
% 1.10/1.28 tff(2861,plain,
% 1.10/1.28 (c3_1(a33)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[1392, 2857])).
% 1.10/1.28 tff(2862,plain,
% 1.10/1.28 (c2_1(a33)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[827, 2857])).
% 1.10/1.28 tff(2863,plain,
% 1.10/1.28 (~hskp11),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2541, 2465, 302, 301])).
% 1.10/1.28 tff(2864,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2548, 160, 2863, 2862, 2861, 2860, 2859, 2858, 2850, 1042])).
% 1.10/1.28 tff(2865,plain,(c2_1(a14) | c0_1(a45) | c3_1(a45) | hskp14 | hskp2 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | (~c0_1(a31)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(2866,plain,
% 1.10/1.28 (c2_1(a14)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2865, 2625, 2419, 607, 606, 302, 313, 2465, 301, 314])).
% 1.10/1.28 tff(2867,plain,
% 1.10/1.28 (~hskp7),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[489, 2866])).
% 1.10/1.28 tff(2868,plain,
% 1.10/1.28 (~hskp24),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2790, 2867, 2650, 2360, 2625, 2647, 2706])).
% 1.10/1.28 tff(2869,plain,
% 1.10/1.28 (hskp23),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[235, 2868, 314])).
% 1.10/1.28 tff(2870,plain,
% 1.10/1.28 (~c1_1(a53)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[200, 2869])).
% 1.10/1.28 tff(2871,plain,
% 1.10/1.28 (~c0_1(a53)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[206, 2869])).
% 1.10/1.28 tff(2872,plain,
% 1.10/1.28 (c3_1(a53)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[214, 2869])).
% 1.10/1.28 tff(2873,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2874,plain,
% 1.10/1.28 (((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2875,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2874])).
% 1.10/1.28 tff(2876,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[2875, 2873])).
% 1.10/1.28 tff(2877,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(2878,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[2877, 2876])).
% 1.10/1.28 tff(2879,plain,
% 1.10/1.28 (~c2_1(a53)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2878, 160, 2872, 2625, 2871, 2870, 2647, 2419, 83])).
% 1.10/1.28 tff(2880,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[323, 160, 314, 301, 302, 2871, 2870, 313, 312, 2879])).
% 1.10/1.28 tff(2881,plain,(c0_1(a45) | hskp0 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | c3_1(a45) | hskp14 | hskp2 | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(2882,plain,
% 1.10/1.28 (c0_1(a45)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2881, 2419, 301, 302, 313, 314, 607, 606, 2465])).
% 1.10/1.28 tff(2883,assumption,(c0_1(a45)), introduced(assumption)).
% 1.10/1.28 tff(2884,plain,
% 1.10/1.28 (c1_1(a45) | c2_1(a45)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2426, 160, 607, 606, 2883, 643])).
% 1.10/1.28 tff(2885,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2884, 2627, 2418])).
% 1.10/1.28 tff(2886,plain,(c1_1(a45) | hskp14 | hskp2 | (~c0_1(a45)) | (~c0_1(a31)) | (~c2_1(a31)) | c3_1(a45) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(2887,plain,
% 1.10/1.28 (c1_1(a45)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[2886, 2882, 606, 607, 301, 302, 2419, 2465])).
% 1.10/1.28 tff(2888,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2889,plain,
% 1.10/1.28 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45))) <=> ((~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(2890,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45)))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[2889])).
% 1.10/1.29 tff(2891,plain,
% 1.10/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2890, 2888])).
% 1.10/1.29 tff(2892,plain,
% 1.10/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2893,plain,
% 1.10/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2892, 2891])).
% 1.10/1.29 tff(2894,plain,
% 1.10/1.29 ($false),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2893, 160, 2883, 301, 302, 2651, 2419, 406, 2465, 2420])).
% 1.10/1.29 tff(2895,plain,(c2_1(a45) | (~c0_1(a45)) | (~c0_1(a31)) | (~c2_1(a31)) | (~c1_1(a45)) | c3_1(a45) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.29 tff(2896,plain,
% 1.10/1.29 (c2_1(a45)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2895, 2882, 301, 302, 2887, 2419, 2465])).
% 1.10/1.29 tff(2897,assumption,(c2_1(a45)), introduced(assumption)).
% 1.10/1.29 tff(2898,assumption,(hskp19), introduced(assumption)).
% 1.10/1.29 tff(2899,plain,
% 1.10/1.29 (~c0_1(a33)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[819, 2898])).
% 1.10/1.29 tff(2900,plain,
% 1.10/1.29 (c3_1(a33)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1392, 2898])).
% 1.10/1.29 tff(2901,plain,
% 1.10/1.29 (c2_1(a33)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[827, 2898])).
% 1.10/1.29 tff(2902,assumption,(~hskp11), introduced(assumption)).
% 1.10/1.29 tff(2903,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2904,plain,
% 1.10/1.29 ((hskp11 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c0_1(a45)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2905,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c0_1(a45)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2904])).
% 1.10/1.29 tff(2906,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c0_1(a45)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2905, 2903])).
% 1.10/1.29 tff(2907,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c0_1(a45)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2908,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2907, 2906])).
% 1.10/1.29 tff(2909,plain,
% 1.10/1.29 ($false),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2908, 160, 2902, 2883, 2901, 2900, 2419, 2899, 1042, 2897])).
% 1.10/1.29 tff(2910,plain,((~hskp19) | hskp11 | (~c0_1(a45)) | c3_1(a45) | (~c2_1(a45))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.29 tff(2911,plain,
% 1.10/1.29 (~hskp19),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2910, 2882, 2863, 2419, 2896])).
% 1.10/1.29 tff(2912,plain,
% 1.10/1.29 (hskp13),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[483, 2756, 105])).
% 1.10/1.29 tff(2913,plain,
% 1.10/1.29 (~c3_1(a22)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[449, 2912])).
% 1.10/1.29 tff(2914,plain,
% 1.10/1.29 (~c0_1(a22)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[461, 2912])).
% 1.10/1.29 tff(2915,assumption,(~c1_1(a22)), introduced(assumption)).
% 1.10/1.29 tff(2916,assumption,(~c3_1(a22)), introduced(assumption)).
% 1.10/1.29 tff(2917,assumption,(~c0_1(a22)), introduced(assumption)).
% 1.10/1.29 tff(2918,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2919,plain,
% 1.10/1.29 ((hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c1_1(a22) | c0_1(a22)) <=> (hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2920,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2919])).
% 1.10/1.29 tff(2921,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2920, 2918])).
% 1.10/1.29 tff(2922,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2923,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2922, 2921])).
% 1.10/1.29 tff(2924,plain,
% 1.10/1.29 (hskp1 | c1_1(a22)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2923, 160, 302, 313, 2917, 2916, 1385, 2465])).
% 1.10/1.29 tff(2925,plain,
% 1.10/1.29 (hskp1),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2924, 2915])).
% 1.10/1.29 tff(2926,plain,
% 1.10/1.29 (~c0_1(a2)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1405, 2925])).
% 1.10/1.29 tff(2927,plain,
% 1.10/1.29 (c2_1(a2)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1413, 2925])).
% 1.10/1.29 tff(2928,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2929,plain,
% 1.10/1.29 (((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a22) | c1_1(a22) | c0_1(a22)) <=> (c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2930,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22)))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2929])).
% 1.10/1.29 tff(2931,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2930, 2928])).
% 1.10/1.29 tff(2932,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2933,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 1.10/1.29 tff(2934,plain,
% 1.10/1.29 (~c1_1(a2)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2933, 160, 2927, 2917, 2916, 2926, 45, 2915])).
% 1.10/1.29 tff(2935,plain,
% 1.10/1.29 (~c3_1(a2)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2318, 2925])).
% 1.10/1.29 tff(2936,plain,
% 1.10/1.29 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2937,plain,
% 1.10/1.29 ((hskp7 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c2_1(a2))) <=> (hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2938,plain,
% 1.10/1.29 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2937])).
% 1.10/1.29 tff(2939,plain,
% 1.10/1.29 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2938, 2936])).
% 1.10/1.29 tff(2940,plain,
% 1.10/1.29 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c2_1(a2)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2941,plain,
% 1.10/1.29 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2940, 2939])).
% 1.10/1.29 tff(2942,plain,
% 1.10/1.29 ($false),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2941, 160, 2756, 2927, 2935, 2384, 2934])).
% 1.10/1.29 tff(2943,plain,(c1_1(a22) | hskp7 | c0_1(a22) | c3_1(a22) | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.29 tff(2944,plain,
% 1.10/1.29 (c1_1(a22)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2943, 2756, 2914, 2913, 302, 313, 2465])).
% 1.10/1.29 tff(2945,plain,
% 1.10/1.29 (~c2_1(a22)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[455, 2912])).
% 1.10/1.29 tff(2946,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2947,plain,
% 1.10/1.29 ((hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22))) <=> (hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2948,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2947])).
% 1.10/1.29 tff(2949,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2948, 2946])).
% 1.10/1.29 tff(2950,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2951,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2950, 2949])).
% 1.10/1.29 tff(2952,plain,
% 1.10/1.29 (hskp5 | (~c1_1(a22))),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2951, 160, 2651, 2419, 2914, 2945, 1311, 2897])).
% 1.10/1.29 tff(2953,plain,
% 1.10/1.29 (hskp5),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2952, 2944])).
% 1.10/1.29 tff(2954,plain,
% 1.10/1.29 (~c0_1(a7)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1317, 2953])).
% 1.10/1.29 tff(2955,plain,
% 1.10/1.29 (c1_1(a7)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1325, 2953])).
% 1.10/1.29 tff(2956,plain,
% 1.10/1.29 (~c2_1(a7)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2779, 160, 105, 2579, 2955, 2954, 2573])).
% 1.10/1.29 tff(2957,plain,
% 1.10/1.29 (c3_1(a7)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1346, 2953])).
% 1.10/1.29 tff(2958,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2959,plain,
% 1.10/1.29 ((hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a7) | (~c3_1(a7)) | (~c1_1(a7))) <=> (hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2960,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2959])).
% 1.10/1.29 tff(2961,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2960, 2958])).
% 1.10/1.29 tff(2962,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2963,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2962, 2961])).
% 1.10/1.29 tff(2964,plain,
% 1.10/1.29 (hskp10),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2963, 160, 302, 2955, 2957, 313, 2954, 1053, 2465])).
% 1.10/1.29 tff(2965,plain,
% 1.10/1.29 (~c3_1(a18)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1066, 2964])).
% 1.10/1.29 tff(2966,plain,
% 1.10/1.29 (c0_1(a18)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1082, 2964])).
% 1.10/1.29 tff(2967,plain,
% 1.10/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2968,plain,
% 1.10/1.29 (((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2969,plain,
% 1.10/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2968])).
% 1.10/1.29 tff(2970,plain,
% 1.10/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2969, 2967])).
% 1.10/1.29 tff(2971,plain,
% 1.10/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2972,plain,
% 1.10/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2971, 2970])).
% 1.10/1.29 tff(2973,plain,
% 1.10/1.29 (c1_1(a18)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2972, 160, 2966, 2955, 2957, 2914, 2945, 2913, 2965, 13, 2956])).
% 1.10/1.29 tff(2974,plain,
% 1.10/1.29 (c2_1(a18)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[1074, 2964])).
% 1.10/1.29 tff(2975,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2976,plain,
% 1.10/1.29 ((hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7))) <=> (hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2977,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2976])).
% 1.10/1.29 tff(2978,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2977, 2975])).
% 1.10/1.29 tff(2979,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(2980,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 1.10/1.29 tff(2981,plain,
% 1.10/1.29 ($false),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2980, 160, 805, 2966, 2974, 2955, 2957, 779, 2956, 2973])).
% 1.10/1.29 tff(2982,plain,(hskp7 | hskp19 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | hskp9 | hskp8 | (~c1_1(a45)) | c3_1(a45) | (~c2_1(a45))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.29 tff(2983,plain,
% 1.10/1.29 (hskp7),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2982, 2911, 302, 313, 2465, 2650, 2360, 2887, 2419, 2896])).
% 1.10/1.29 tff(2984,plain,
% 1.10/1.29 (~c2_1(a14)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[489, 2983])).
% 1.10/1.29 tff(2985,plain,
% 1.10/1.29 (c0_1(a14)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[516, 2983])).
% 1.10/1.29 tff(2986,plain,
% 1.10/1.29 (c1_1(a14)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2561, 160, 607, 606, 2985, 2984, 643])).
% 1.10/1.29 tff(2987,plain,
% 1.10/1.29 (c3_1(a14)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[497, 2983])).
% 1.10/1.29 tff(2988,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2989,plain,
% 1.10/1.29 ((hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14))) <=> (hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(2990,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[2989])).
% 1.10/1.29 tff(2991,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[2990, 2988])).
% 1.10/1.29 tff(2992,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(2993,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[2992, 2991])).
% 1.10/1.30 tff(2994,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2993, 160, 2911, 2882, 2987, 2887, 2984, 779, 2896, 2986])).
% 1.10/1.30 tff(2995,plain,(c3_1(a45) | hskp14 | hskp2 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | (~c0_1(a31)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(2996,plain,
% 1.10/1.30 (c3_1(a45)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2995, 606, 607, 2362, 2363, 2624, 2364, 2551])).
% 1.10/1.30 tff(2997,plain,
% 1.10/1.30 (~hskp22),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2416, 2996])).
% 1.10/1.30 tff(2998,plain,
% 1.10/1.30 (~hskp9),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2649, 2364, 2362, 2624, 607, 606])).
% 1.10/1.30 tff(2999,plain,
% 1.10/1.30 (~c0_1(a5)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[853, 160, 607, 606, 338, 332, 643])).
% 1.10/1.30 tff(3000,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[354, 160, 314, 301, 302, 313, 338, 332, 312, 2999])).
% 1.10/1.30 tff(3001,plain,((~hskp3) | hskp0 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3002,plain,
% 1.10/1.30 (~hskp3),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3001, 2551, 2364, 2362, 2363, 607, 606])).
% 1.10/1.30 tff(3003,plain,
% 1.10/1.30 (~c1_1(a33)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2694, 160, 105, 2579, 2901, 2899, 2573])).
% 1.10/1.30 tff(3004,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[842, 160, 729, 606, 2901, 2899, 23, 3003])).
% 1.10/1.30 tff(3005,plain,((~hskp19) | hskp3 | hskp2 | hskp9 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3006,plain,
% 1.10/1.30 (~hskp19),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3005, 3002, 606, 2998, 2360])).
% 1.10/1.30 tff(3007,plain,
% 1.10/1.30 (c0_1(a3)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2582, 160, 105, 2360, 2734, 2733, 2573])).
% 1.10/1.30 tff(3008,plain,
% 1.10/1.30 (c1_1(a22)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2943, 2913, 2914, 2756, 302, 313, 2465])).
% 1.10/1.30 tff(3009,assumption,(c1_1(a22)), introduced(assumption)).
% 1.10/1.30 tff(3010,assumption,(~c2_1(a22)), introduced(assumption)).
% 1.10/1.30 tff(3011,assumption,(c1_1(a3)), introduced(assumption)).
% 1.10/1.30 tff(3012,plain,
% 1.10/1.30 (c0_1(a3)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2582, 160, 105, 2579, 3011, 2292, 2573])).
% 1.10/1.30 tff(3013,plain,
% 1.10/1.30 (hskp10 | hskp6 | (~c0_1(a3))),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2751, 160, 3011, 2292, 2745])).
% 1.10/1.30 tff(3014,plain,
% 1.10/1.30 (hskp10),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3013, 1174, 3012])).
% 1.10/1.30 tff(3015,plain,
% 1.10/1.30 (~c3_1(a18)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[1066, 3014])).
% 1.10/1.30 tff(3016,plain,
% 1.10/1.30 (c2_1(a18)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[1074, 3014])).
% 1.10/1.30 tff(3017,plain,
% 1.10/1.30 (hskp26),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2492, 1174, 2464])).
% 1.10/1.30 tff(3018,plain,
% 1.10/1.30 (c3_1(a10)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[632, 3017])).
% 1.10/1.30 tff(3019,plain,
% 1.10/1.30 (c2_1(a10)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[624, 3017])).
% 1.10/1.30 tff(3020,plain,
% 1.10/1.30 (c0_1(a10)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[615, 3017])).
% 1.10/1.30 tff(3021,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3022,plain,
% 1.10/1.30 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3023,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[3022])).
% 1.10/1.30 tff(3024,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[3023, 3021])).
% 1.10/1.30 tff(3025,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(3026,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[3025, 3024])).
% 1.10/1.30 tff(3027,plain,
% 1.10/1.30 (c1_1(a18)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3026, 160, 3020, 3019, 3018, 3016, 3015, 1466])).
% 1.10/1.30 tff(3028,plain,
% 1.10/1.30 (~c2_1(a7)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2779, 160, 105, 2579, 1326, 1318, 2573])).
% 1.10/1.30 tff(3029,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2788, 160, 1174, 3011, 2292, 2291, 1347, 1318, 1202, 3028])).
% 1.10/1.30 tff(3030,plain,((~hskp5) | hskp6 | (~c1_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | hskp9 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3031,plain,
% 1.10/1.30 (~hskp5),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3030, 1174, 3011, 2292, 2291, 105, 2579])).
% 1.10/1.30 tff(3032,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3033,plain,
% 1.10/1.30 ((hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22))) <=> (hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3034,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[3033])).
% 1.10/1.30 tff(3035,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[3034, 3032])).
% 1.10/1.30 tff(3036,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(3037,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 1.10/1.30 tff(3038,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3037, 160, 3031, 3016, 2917, 3010, 3015, 1311, 3009, 3027])).
% 1.10/1.30 tff(3039,plain,(hskp6 | c0_1(a22) | c2_1(a22) | (~c1_1(a22)) | (~c1_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | hskp9 | hskp8 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3040,plain,
% 1.10/1.30 (hskp6),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3039, 2734, 3010, 3009, 2917, 2733, 2782, 105, 2579, 2464])).
% 1.10/1.30 tff(3041,plain,
% 1.10/1.30 (~c2_1(a8)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[1239, 3040])).
% 1.10/1.30 tff(3042,plain,
% 1.10/1.30 (c0_1(a8)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[1267, 3040])).
% 1.10/1.30 tff(3043,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3044,plain,
% 1.10/1.30 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a22) | c2_1(a22) | (~c1_1(a22)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3045,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a22) | c2_1(a22) | (~c1_1(a22)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[3044])).
% 1.10/1.30 tff(3046,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a22) | c2_1(a22) | (~c1_1(a22)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[3045, 3043])).
% 1.10/1.30 tff(3047,plain,
% 1.10/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a22) | c2_1(a22) | (~c1_1(a22)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(3048,plain,
% 1.10/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[3047, 3046])).
% 1.10/1.30 tff(3049,plain,
% 1.10/1.30 (c3_1(a8)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3048, 160, 2733, 2782, 3042, 3010, 2916, 3041, 406, 3009, 2735])).
% 1.10/1.30 tff(3050,plain,
% 1.10/1.30 (c1_1(a8)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[1247, 3040])).
% 1.10/1.30 tff(3051,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2685, 160, 805, 2734, 2733, 3050, 3041, 779, 2735, 3049])).
% 1.10/1.30 tff(3052,plain,((~hskp24) | hskp19 | c2_1(a22) | c3_1(a22) | (~c1_1(a22)) | c0_1(a22) | hskp9 | hskp8 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3053,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3052, 3008, 2913, 805, 2732, 2945, 2914, 105, 2579, 2464])).
% 1.10/1.30 tff(3054,plain,(hskp7 | hskp19 | (~hskp24) | hskp9 | hskp8 | hskp22 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3055,plain,
% 1.10/1.30 (hskp7),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3054, 2732, 805, 105, 2360, 2464, 302, 313, 2465])).
% 1.10/1.30 tff(3056,plain,
% 1.10/1.30 (~c2_1(a14)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[489, 3055])).
% 1.10/1.30 tff(3057,plain,
% 1.10/1.30 (c0_1(a14)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[516, 3055])).
% 1.10/1.30 tff(3058,plain,
% 1.10/1.30 (c1_1(a14)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2561, 160, 607, 606, 3057, 3056, 643])).
% 1.10/1.30 tff(3059,plain,
% 1.10/1.30 (c3_1(a14)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[497, 3055])).
% 1.10/1.30 tff(3060,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2856, 160, 805, 2734, 2733, 3059, 3056, 779, 3058, 3007])).
% 1.10/1.30 tff(3061,plain,((~hskp24) | hskp19 | hskp14 | hskp2 | hskp9 | hskp22 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3062,plain,
% 1.10/1.30 (~hskp24),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3061, 3006, 607, 606, 2998, 2997, 2362, 2363, 2624])).
% 1.10/1.30 tff(3063,plain,
% 1.10/1.30 (hskp23),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[235, 3062, 2551])).
% 1.10/1.30 tff(3064,plain,
% 1.10/1.30 (~c1_1(a53)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[200, 3063])).
% 1.10/1.30 tff(3065,plain,
% 1.10/1.30 (~c0_1(a53)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[206, 3063])).
% 1.10/1.30 tff(3066,plain,
% 1.10/1.30 (~c2_1(a53)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[363, 160, 3002, 606, 3065, 3064, 23])).
% 1.10/1.30 tff(3067,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[323, 160, 2551, 2364, 2362, 3065, 3064, 2363, 312, 3066])).
% 1.10/1.30 tff(3068,plain,(hskp2 | hskp14 | hskp4 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3069,plain,
% 1.10/1.30 (hskp2),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3068, 2351, 193, 607])).
% 1.10/1.30 tff(3070,plain,
% 1.10/1.30 (c1_1(a4)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[378, 3069])).
% 1.10/1.30 tff(3071,plain,
% 1.10/1.30 (~c3_1(a4)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[370, 3069])).
% 1.10/1.30 tff(3072,plain,
% 1.10/1.30 (~c2_1(a4)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[384, 3069])).
% 1.10/1.30 tff(3073,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3074,plain,
% 1.10/1.30 ((hskp15 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c3_1(a15))) <=> (hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3075,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[3074])).
% 1.10/1.30 tff(3076,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[3075, 3073])).
% 1.10/1.30 tff(3077,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(3078,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[3077, 3076])).
% 1.10/1.30 tff(3079,plain,
% 1.10/1.30 (~c3_1(a15)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3078, 160, 2351, 184, 190, 176, 2374])).
% 1.10/1.30 tff(3080,plain,
% 1.10/1.30 (~hskp23),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[223, 184, 193, 190, 176])).
% 1.10/1.30 tff(3081,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3082,plain,
% 1.10/1.30 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15))) <=> (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3083,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[3082])).
% 1.10/1.30 tff(3084,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[3083, 3081])).
% 1.10/1.30 tff(3085,plain,
% 1.10/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(3086,plain,
% 1.10/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 1.10/1.30 tff(3087,plain,
% 1.10/1.30 (~c0_1(a3)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3086, 160, 2733, 2782, 192, 388, 191, 407, 387, 406, 1902])).
% 1.10/1.30 tff(3088,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3089,plain,
% 1.10/1.30 ((hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3090,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[3089])).
% 1.10/1.30 tff(3091,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[3090, 3088])).
% 1.10/1.30 tff(3092,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(3093,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 1.10/1.30 tff(3094,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3093, 160, 193, 2734, 2782, 192, 194, 584, 1902, 3087])).
% 1.10/1.30 tff(3095,plain,((~hskp24) | hskp4 | (~c0_1(a15)) | c1_1(a15) | c3_1(a15) | (~c1_1(a4)) | c2_1(a15) | c2_1(a4) | c3_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3096,plain,
% 1.10/1.30 (~hskp24),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3095, 184, 193, 190, 3079, 388, 176, 407, 387])).
% 1.10/1.30 tff(3097,plain,
% 1.10/1.30 (hskp0),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[235, 3096, 3080])).
% 1.10/1.30 tff(3098,plain,
% 1.10/1.30 (~c0_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[262, 3097])).
% 1.10/1.30 tff(3099,plain,
% 1.10/1.30 (c3_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[249, 3097])).
% 1.10/1.30 tff(3100,plain,
% 1.10/1.30 (~c1_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[1915, 160, 193, 184, 3099, 190, 3098, 584, 3079])).
% 1.10/1.30 tff(3101,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[269, 160, 193, 184, 3099, 190, 176, 3098, 65, 3100])).
% 1.10/1.30 tff(3102,plain,((~hskp8) | hskp4 | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3103,plain,
% 1.10/1.30 (~hskp8),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3102, 388, 193, 407, 387, 2351])).
% 1.10/1.30 tff(3104,plain,
% 1.10/1.30 (hskp17),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[282, 3103, 193])).
% 1.10/1.30 tff(3105,plain,
% 1.10/1.30 (c2_1(a31)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[298, 3104])).
% 1.10/1.30 tff(3106,plain,
% 1.10/1.30 (~c1_1(a31)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[71, 3104])).
% 1.10/1.30 tff(3107,plain,
% 1.10/1.30 (c0_1(a31)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[290, 3104])).
% 1.10/1.30 tff(3108,plain,
% 1.10/1.30 (~c2_1(a53)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[433, 207, 388, 3107, 201, 3106, 407, 387, 3105, 215])).
% 1.10/1.30 tff(3109,plain,
% 1.10/1.30 (hskp0 | c2_1(a53)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[323, 160, 3107, 3105, 207, 201, 3106, 312])).
% 1.10/1.30 tff(3110,plain,
% 1.10/1.30 (hskp0),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3109, 3108])).
% 1.10/1.30 tff(3111,plain,
% 1.10/1.30 (~c0_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[262, 3110])).
% 1.10/1.30 tff(3112,plain,
% 1.10/1.30 (c3_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[249, 3110])).
% 1.10/1.30 tff(3113,plain,
% 1.10/1.30 (~c2_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[241, 3110])).
% 1.10/1.30 tff(3114,plain,
% 1.10/1.30 (c3_1(a31)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2403, 3113, 3105, 3112, 193, 3107, 3106, 3111, 2351])).
% 1.10/1.30 tff(3115,plain,
% 1.10/1.30 ((~c0_1(a4)) | (~c3_1(a31))),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[413, 160, 3107, 3105, 388, 407, 387, 406])).
% 1.10/1.30 tff(3116,plain,
% 1.10/1.30 (~c0_1(a4)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3115, 3114])).
% 1.10/1.30 tff(3117,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3118,plain,
% 1.10/1.30 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a4) | c0_1(a4) | c2_1(a4) | c2_1(a53) | c1_1(a53) | c0_1(a53)) <=> (c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(3119,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a4) | c0_1(a4) | c2_1(a4) | c2_1(a53) | c1_1(a53) | c0_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53)))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[3118])).
% 1.10/1.30 tff(3120,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a4) | c0_1(a4) | c2_1(a4) | c2_1(a53) | c1_1(a53) | c0_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53))),
% 1.10/1.30 inference(transitivity,[status(thm)],[3119, 3117])).
% 1.10/1.30 tff(3121,plain,
% 1.10/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a4) | c0_1(a4) | c2_1(a4) | c2_1(a53) | c1_1(a53) | c0_1(a53))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(3122,plain,
% 1.10/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[3121, 3120])).
% 1.10/1.30 tff(3123,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3122, 160, 3112, 207, 201, 407, 387, 3111, 3113, 55, 3116, 3108])).
% 1.10/1.30 tff(3124,plain,((~hskp23) | c2_1(a4) | c3_1(a4) | (~c1_1(a4)) | hskp4 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3125,plain,
% 1.10/1.30 (~hskp23),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3124, 3072, 3071, 3070, 193, 2351])).
% 1.10/1.30 tff(3126,plain,
% 1.10/1.30 (~hskp8),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3102, 3070, 193, 3072, 3071, 2351])).
% 1.10/1.30 tff(3127,plain,
% 1.10/1.30 (hskp17),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[282, 3126, 193])).
% 1.10/1.30 tff(3128,plain,
% 1.10/1.30 (~c1_1(a31)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[71, 3127])).
% 1.10/1.30 tff(3129,plain,
% 1.10/1.30 (c0_1(a31)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[290, 3127])).
% 1.10/1.30 tff(3130,plain,
% 1.10/1.30 (c2_1(a31)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[298, 3127])).
% 1.10/1.30 tff(3131,assumption,(~hskp23), introduced(assumption)).
% 1.10/1.30 tff(3132,plain,
% 1.10/1.30 (hskp0),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[235, 73, 3131])).
% 1.10/1.30 tff(3133,plain,
% 1.10/1.30 (~c2_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[241, 3132])).
% 1.10/1.30 tff(3134,plain,
% 1.10/1.30 (c3_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[249, 3132])).
% 1.10/1.30 tff(3135,plain,
% 1.10/1.30 (~c1_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[256, 160, 73, 105, 3134, 3133, 104])).
% 1.10/1.30 tff(3136,plain,
% 1.10/1.30 (~c0_1(a1)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[262, 3132])).
% 1.10/1.30 tff(3137,plain,
% 1.10/1.30 (~hskp13),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[471, 3135, 3136, 3133, 3134])).
% 1.10/1.30 tff(3138,plain,
% 1.10/1.30 (hskp7),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[483, 3137, 105])).
% 1.10/1.30 tff(3139,plain,
% 1.10/1.30 (~c2_1(a14)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[489, 3138])).
% 1.10/1.30 tff(3140,plain,
% 1.10/1.30 (c3_1(a14)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[497, 3138])).
% 1.10/1.30 tff(3141,plain,
% 1.10/1.30 (c0_1(a14)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[516, 3138])).
% 1.10/1.30 tff(3142,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2401, 160, 2351, 3141, 3140, 3134, 3139, 3133, 2374, 3135])).
% 1.10/1.30 tff(3143,plain,(hskp24 | hskp15 | hskp9 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(3144,plain,
% 1.10/1.30 (hskp24),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[3143, 105, 2351, 3131])).
% 1.10/1.30 tff(3145,plain,
% 1.10/1.30 (c1_1(a3)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2271, 3144])).
% 1.10/1.30 tff(3146,plain,
% 1.10/1.30 (c3_1(a3)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2288, 3144])).
% 1.10/1.30 tff(3147,plain,
% 1.10/1.30 (c2_1(a3)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[2263, 3144])).
% 1.10/1.30 tff(3148,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3149,plain,
% 1.10/1.31 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4))) <=> (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3150,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3149])).
% 1.10/1.31 tff(3151,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[3150, 3148])).
% 1.10/1.31 tff(3152,plain,
% 1.10/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(3153,plain,
% 1.10/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[3152, 3151])).
% 1.10/1.31 tff(3154,plain,
% 1.10/1.31 (~c0_1(a4)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3153, 160, 2292, 2291, 388, 407, 387, 406, 3012])).
% 1.10/1.31 tff(3155,plain,
% 1.10/1.31 (c3_1(a31)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2300, 2292, 2291, 302, 313, 3012])).
% 1.10/1.31 tff(3156,plain,
% 1.10/1.31 (~hskp6),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2705, 2625, 301, 105, 313, 3155, 2579, 2419, 302])).
% 1.10/1.31 tff(3157,plain,
% 1.10/1.31 (hskp10),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3013, 3156, 3012])).
% 1.10/1.31 tff(3158,plain,
% 1.10/1.31 (~c3_1(a18)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1066, 3157])).
% 1.10/1.31 tff(3159,plain,
% 1.10/1.31 (c2_1(a18)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1074, 3157])).
% 1.10/1.31 tff(3160,plain,
% 1.10/1.31 (hskp26),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2492, 3156, 2717])).
% 1.10/1.31 tff(3161,plain,
% 1.10/1.31 (c3_1(a10)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[632, 3160])).
% 1.10/1.31 tff(3162,plain,
% 1.10/1.31 (c2_1(a10)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[624, 3160])).
% 1.10/1.31 tff(3163,plain,
% 1.10/1.31 (c0_1(a10)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[615, 3160])).
% 1.10/1.31 tff(3164,plain,
% 1.10/1.31 (c1_1(a18)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3026, 160, 3163, 3162, 3161, 3159, 3158, 1466])).
% 1.10/1.31 tff(3165,assumption,(~c0_1(a4)), introduced(assumption)).
% 1.10/1.31 tff(3166,plain,
% 1.10/1.31 (~hskp5),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3030, 3156, 3011, 2292, 2291, 105, 2579])).
% 1.10/1.31 tff(3167,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3168,plain,
% 1.10/1.31 ((hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4))) <=> (hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3169,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3168])).
% 1.10/1.31 tff(3170,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[3169, 3167])).
% 1.10/1.31 tff(3171,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(3172,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[3171, 3170])).
% 1.10/1.31 tff(3173,plain,
% 1.10/1.31 ($false),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3172, 160, 3166, 3159, 388, 3158, 407, 1311, 3165, 3164])).
% 1.10/1.31 tff(3174,plain,(c0_1(a45) | (~c1_1(a4)) | c2_1(a4) | c0_1(a4) | (~c1_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | hskp9 | hskp8 | (~c0_1(a31)) | c1_1(a31) | c3_1(a45) | (~c2_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.31 tff(3175,plain,
% 1.10/1.31 (c0_1(a45)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3174, 2419, 407, 3154, 3011, 2292, 2291, 105, 2579, 301, 313, 388, 302])).
% 1.10/1.31 tff(3176,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3177,plain,
% 1.10/1.31 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45))) <=> (c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3178,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45)))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3177])).
% 1.10/1.31 tff(3179,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45))),
% 1.10/1.31 inference(transitivity,[status(thm)],[3178, 3176])).
% 1.10/1.31 tff(3180,plain,
% 1.10/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(3181,plain,
% 1.10/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[3180, 3179])).
% 1.10/1.31 tff(3182,plain,
% 1.10/1.31 ($false),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3181, 160, 2292, 2291, 2883, 388, 2419, 407, 387, 406, 2420, 2290])).
% 1.10/1.31 tff(3183,plain,(c2_1(a45) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | (~c1_1(a4)) | c3_1(a45) | c2_1(a4) | c3_1(a4) | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.31 tff(3184,plain,
% 1.10/1.31 (c2_1(a45)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3183, 3175, 2291, 2292, 388, 2419, 407, 387, 3012])).
% 1.10/1.31 tff(3185,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3186,plain,
% 1.10/1.31 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45))) <=> (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3187,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3186])).
% 1.10/1.31 tff(3188,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[3187, 3185])).
% 1.10/1.31 tff(3189,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(3190,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 1.10/1.31 tff(3191,plain,
% 1.10/1.31 (c1_1(a45) | (~c2_1(a45))),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3190, 160, 2292, 2291, 2419, 1466, 3012])).
% 1.10/1.31 tff(3192,plain,
% 1.10/1.31 (c1_1(a45)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3191, 3184])).
% 1.10/1.31 tff(3193,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3194,plain,
% 1.10/1.31 ((hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4))) <=> (hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3195,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3194])).
% 1.10/1.31 tff(3196,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[3195, 3193])).
% 1.10/1.31 tff(3197,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(3198,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[3197, 3196])).
% 1.10/1.31 tff(3199,plain,
% 1.10/1.31 (hskp5 | (~c1_1(a45)) | (~c2_1(a45))),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3198, 160, 388, 2419, 407, 1311, 3154])).
% 1.10/1.31 tff(3200,plain,
% 1.10/1.31 (hskp5),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3199, 3184, 3192])).
% 1.10/1.31 tff(3201,plain,
% 1.10/1.31 (hskp6),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3030, 3200, 3011, 2292, 2291, 105, 2579])).
% 1.10/1.31 tff(3202,plain,
% 1.10/1.31 (~c2_1(a8)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1239, 3201])).
% 1.10/1.31 tff(3203,plain,
% 1.10/1.31 (c1_1(a8)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1247, 3201])).
% 1.10/1.31 tff(3204,plain,
% 1.10/1.31 (~hskp11),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2541, 3155, 302, 301])).
% 1.10/1.31 tff(3205,plain,
% 1.10/1.31 (~hskp19),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2910, 3184, 3175, 2419, 3204])).
% 1.10/1.31 tff(3206,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3207,plain,
% 1.10/1.31 ((hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8))) <=> (hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3208,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3207])).
% 1.10/1.31 tff(3209,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[3208, 3206])).
% 1.10/1.31 tff(3210,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(3211,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 1.10/1.31 tff(3212,plain,
% 1.10/1.31 (~c3_1(a8)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3211, 160, 3205, 3175, 3203, 3192, 3202, 779, 3184])).
% 1.10/1.31 tff(3213,plain,
% 1.10/1.31 (c0_1(a8)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1267, 3201])).
% 1.10/1.31 tff(3214,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3215,plain,
% 1.10/1.31 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3216,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3215])).
% 1.10/1.31 tff(3217,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[3216, 3214])).
% 1.10/1.31 tff(3218,plain,
% 1.10/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(3219,plain,
% 1.10/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[3218, 3217])).
% 1.10/1.31 tff(3220,plain,
% 1.10/1.31 ($false),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3219, 160, 2292, 2291, 3213, 388, 3202, 407, 387, 406, 3012, 3212])).
% 1.10/1.31 tff(3221,plain,(c3_1(a45) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c1_1(a3)) | hskp9 | hskp8 | (~c0_1(a31)) | c1_1(a31) | (~c2_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.31 tff(3222,plain,
% 1.10/1.31 (c3_1(a45)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3221, 3147, 3146, 388, 407, 387, 3145, 105, 2579, 301, 313, 302])).
% 1.10/1.31 tff(3223,plain,
% 1.10/1.31 (~hskp22),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2416, 3222])).
% 1.10/1.31 tff(3224,plain,
% 1.10/1.31 (c3_1(a31)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2300, 2733, 2782, 302, 313, 2735])).
% 1.10/1.31 tff(3225,plain,
% 1.10/1.31 (hskp7),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3054, 805, 2732, 105, 2579, 3224, 302, 313, 2464])).
% 1.10/1.31 tff(3226,plain,
% 1.10/1.31 (~c2_1(a14)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[489, 3225])).
% 1.10/1.31 tff(3227,plain,
% 1.10/1.31 (c3_1(a14)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[497, 3225])).
% 1.10/1.31 tff(3228,plain,
% 1.10/1.31 (~c1_1(a14)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2856, 160, 805, 2734, 2733, 3227, 3226, 779, 2735])).
% 1.10/1.31 tff(3229,plain,
% 1.10/1.31 (c0_1(a14)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[516, 3225])).
% 1.10/1.31 tff(3230,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3231,plain,
% 1.10/1.31 ((hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a14) | c2_1(a14) | (~c3_1(a14))) <=> (hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3232,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a14) | c2_1(a14) | (~c3_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3231])).
% 1.10/1.31 tff(3233,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a14) | c2_1(a14) | (~c3_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[3232, 3230])).
% 1.10/1.31 tff(3234,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a14) | c2_1(a14) | (~c3_1(a14)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(3235,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[3234, 3233])).
% 1.10/1.31 tff(3236,plain,
% 1.10/1.31 ($false),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3235, 160, 2351, 3229, 3227, 3226, 2374, 3228])).
% 1.10/1.31 tff(3237,plain,(hskp19 | hskp15 | (~hskp24) | hskp9 | hskp8 | (~c2_1(a31)) | c1_1(a31) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.10/1.31 tff(3238,plain,
% 1.10/1.31 (hskp19),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3237, 3144, 2351, 105, 2579, 302, 313, 3223])).
% 1.10/1.31 tff(3239,plain,
% 1.10/1.31 (~c0_1(a33)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[819, 3238])).
% 1.10/1.31 tff(3240,plain,
% 1.10/1.31 (c2_1(a33)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[827, 3238])).
% 1.10/1.31 tff(3241,plain,
% 1.10/1.31 (~c1_1(a33)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2694, 160, 105, 2579, 3240, 3239, 2573])).
% 1.10/1.31 tff(3242,plain,
% 1.10/1.31 (c0_1(a3)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2582, 160, 105, 2579, 3145, 3147, 2573])).
% 1.10/1.31 tff(3243,plain,
% 1.10/1.31 (~c0_1(a4)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[3153, 160, 3147, 3146, 388, 407, 387, 406, 3242])).
% 1.10/1.31 tff(3244,plain,
% 1.10/1.31 (c3_1(a31)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[2300, 3147, 3146, 302, 313, 3242])).
% 1.10/1.31 tff(3245,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3246,plain,
% 1.10/1.31 (((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(3247,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[3246])).
% 1.10/1.31 tff(3248,plain,
% 1.10/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.10/1.32 inference(transitivity,[status(thm)],[3247, 3245])).
% 1.10/1.32 tff(3249,plain,
% 1.10/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(3250,plain,
% 1.10/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 1.10/1.32 tff(3251,plain,
% 1.10/1.32 ($false),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3250, 160, 3240, 302, 388, 3239, 313, 387, 83, 3244, 3243, 3241])).
% 1.10/1.32 tff(3252,plain,(hskp9 | (~c2_1(a31)) | (~c1_1(a4)) | c1_1(a31) | c3_1(a4) | hskp8 | hskp15 | c2_1(a4) | (~c0_1(a31)) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.10/1.32 tff(3253,plain,
% 1.10/1.32 (hskp9),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3252, 3130, 3070, 3128, 3071, 3126, 2351, 3072, 3129, 3125])).
% 1.10/1.32 tff(3254,plain,
% 1.10/1.32 (~c3_1(a16)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[531, 3253])).
% 1.10/1.32 tff(3255,plain,
% 1.10/1.32 (~c2_1(a16)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[537, 3253])).
% 1.10/1.32 tff(3256,plain,
% 1.10/1.32 (c0_1(a16)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[545, 3253])).
% 1.10/1.32 tff(3257,plain,
% 1.10/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(3258,plain,
% 1.10/1.32 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(3259,plain,
% 1.10/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.10/1.32 inference(monotonicity,[status(thm)],[3258])).
% 1.10/1.32 tff(3260,plain,
% 1.10/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.10/1.32 inference(transitivity,[status(thm)],[3259, 3257])).
% 1.10/1.32 tff(3261,plain,
% 1.10/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(3262,plain,
% 1.10/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3261, 3260])).
% 1.10/1.32 tff(3263,plain,
% 1.10/1.32 (~c3_1(a31)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3262, 160, 3129, 3130, 3256, 3070, 3255, 3254, 3072, 3071, 406])).
% 1.10/1.32 tff(3264,plain,
% 1.10/1.32 ($false),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[2403, 438, 441, 302, 2165, 193, 301, 313, 439, 2351])).
% 1.10/1.32 tff(3265,plain,((~hskp0) | (~c2_1(a31)) | c3_1(a31) | hskp4 | (~c0_1(a31)) | c1_1(a31) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.10/1.32 tff(3266,plain,
% 1.10/1.32 (~hskp0),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3265, 3130, 3263, 193, 3129, 3128, 2351])).
% 1.10/1.32 tff(3267,plain,
% 1.10/1.32 (hskp24),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[235, 3266, 3125])).
% 1.10/1.32 tff(3268,plain,
% 1.10/1.32 (c2_1(a3)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[2263, 3267])).
% 1.10/1.32 tff(3269,plain,
% 1.10/1.32 (c3_1(a3)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[2288, 3267])).
% 1.10/1.32 tff(3270,plain,
% 1.10/1.32 (~c0_1(a3)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[2300, 3269, 3263, 3130, 3128, 3268])).
% 1.10/1.32 tff(3271,plain,
% 1.10/1.32 (c1_1(a3)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[2271, 3267])).
% 1.10/1.32 tff(3272,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(3273,plain,
% 1.10/1.32 ((hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(3274,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31))))),
% 1.10/1.32 inference(monotonicity,[status(thm)],[3273])).
% 1.10/1.32 tff(3275,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31)))),
% 1.10/1.32 inference(transitivity,[status(thm)],[3274, 3272])).
% 1.10/1.32 tff(3276,plain,
% 1.10/1.32 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(3277,plain,
% 1.10/1.32 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3276, 3275])).
% 1.10/1.32 tff(3278,plain,
% 1.10/1.32 ($false),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3277, 160, 193, 3271, 3269, 3129, 3128, 584, 3263, 3270])).
% 1.10/1.32 tff(3279,plain,(hskp15 | hskp4 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.10/1.32 tff(3280,plain,
% 1.10/1.32 (hskp15),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3279, 193, 607])).
% 1.10/1.32 tff(3281,plain,
% 1.10/1.32 (((~hskp15) | (~c3_1(a25))) <=> ((~hskp15) | (~c3_1(a25)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(3282,plain,
% 1.10/1.32 (((~c3_1(a25)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a25)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(3283,axiom,((~c3_1(a25)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.10/1.32 tff(3284,plain,
% 1.10/1.32 ((~hskp15) | (~c3_1(a25))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3283, 3282])).
% 1.10/1.32 tff(3285,plain,
% 1.10/1.32 ((~hskp15) | (~c3_1(a25))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3284, 3281])).
% 1.10/1.32 tff(3286,plain,
% 1.10/1.32 (~c3_1(a25)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3285, 3280])).
% 1.10/1.32 tff(3287,plain,
% 1.10/1.32 (hskp8),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[282, 595, 193])).
% 1.10/1.32 tff(3288,plain,
% 1.10/1.32 (hskp2),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[2359, 3287, 607])).
% 1.10/1.32 tff(3289,plain,
% 1.10/1.32 (~c3_1(a4)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[370, 3288])).
% 1.10/1.32 tff(3290,plain,
% 1.10/1.32 (~c2_1(a4)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[384, 3288])).
% 1.10/1.32 tff(3291,plain,
% 1.10/1.32 (~c2_1(a15)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[175, 3287])).
% 1.10/1.32 tff(3292,plain,
% 1.10/1.32 (~c1_1(a15)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[189, 3287])).
% 1.10/1.32 tff(3293,plain,
% 1.10/1.32 (c0_1(a15)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[183, 3287])).
% 1.10/1.32 tff(3294,plain,
% 1.10/1.32 (((~hskp15) | c0_1(a25)) <=> ((~hskp15) | c0_1(a25))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(3295,axiom,((~hskp15) | c0_1(a25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.10/1.32 tff(3296,plain,
% 1.10/1.32 ((~hskp15) | c0_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3295, 3294])).
% 1.10/1.32 tff(3297,plain,
% 1.10/1.32 ((~hskp15) | c0_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3296, 3294])).
% 1.10/1.32 tff(3298,plain,
% 1.10/1.32 ((~hskp15) | c0_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3297, 3294])).
% 1.10/1.32 tff(3299,plain,
% 1.10/1.32 ((~hskp15) | c0_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3298, 3294])).
% 1.10/1.32 tff(3300,plain,
% 1.10/1.32 ((~hskp15) | c0_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3299, 3294])).
% 1.10/1.32 tff(3301,plain,
% 1.10/1.32 (c0_1(a25)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3300, 3280])).
% 1.10/1.32 tff(3302,plain,
% 1.10/1.32 (((~hskp15) | c1_1(a25)) <=> ((~hskp15) | c1_1(a25))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(3303,axiom,((~hskp15) | c1_1(a25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.10/1.32 tff(3304,plain,
% 1.10/1.32 ((~hskp15) | c1_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 1.10/1.32 tff(3305,plain,
% 1.10/1.32 ((~hskp15) | c1_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3304, 3302])).
% 1.10/1.32 tff(3306,plain,
% 1.10/1.32 ((~hskp15) | c1_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3305, 3302])).
% 1.10/1.32 tff(3307,plain,
% 1.10/1.32 ((~hskp15) | c1_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3306, 3302])).
% 1.10/1.32 tff(3308,plain,
% 1.10/1.32 ((~hskp15) | c1_1(a25)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[3307, 3302])).
% 1.10/1.32 tff(3309,plain,
% 1.10/1.32 (c1_1(a25)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[3308, 3280])).
% 1.17/1.32 tff(3310,plain,
% 1.17/1.32 (c1_1(a4)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[378, 3288])).
% 1.17/1.32 tff(3311,plain,
% 1.17/1.32 (c3_1(a15)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3095, 2732, 3293, 3292, 387, 388, 3291, 407, 193])).
% 1.17/1.32 tff(3312,plain,
% 1.17/1.32 (hskp18 | (~c3_1(a15))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[1931, 160, 595, 3293, 3291, 684])).
% 1.17/1.32 tff(3313,plain,
% 1.17/1.32 (hskp18),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3312, 3311])).
% 1.17/1.32 tff(3314,plain,
% 1.17/1.32 (~c3_1(a32)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[888, 3313])).
% 1.17/1.32 tff(3315,plain,
% 1.17/1.32 (~c1_1(a32)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[882, 3313])).
% 1.17/1.32 tff(3316,plain,
% 1.17/1.32 (~c0_1(a32)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[1283, 3313])).
% 1.17/1.32 tff(3317,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3318,plain,
% 1.17/1.32 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3319,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))))),
% 1.17/1.32 inference(monotonicity,[status(thm)],[3318])).
% 1.17/1.32 tff(3320,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.17/1.32 inference(transitivity,[status(thm)],[3319, 3317])).
% 1.17/1.32 tff(3321,plain,
% 1.17/1.32 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.17/1.32 inference(quant_inst,[status(thm)],[])).
% 1.17/1.32 tff(3322,plain,
% 1.17/1.32 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.17/1.32 inference(modus_ponens,[status(thm)],[3321, 3320])).
% 1.17/1.32 tff(3323,plain,
% 1.17/1.32 (c0_1(a3)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3322, 160, 2734, 2733, 3316, 3315, 3314, 45])).
% 1.17/1.32 tff(3324,plain,
% 1.17/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3325,plain,
% 1.17/1.32 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a32) | c3_1(a32) | (~c2_1(a32))) <=> (c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3326,plain,
% 1.17/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a32) | c3_1(a32) | (~c2_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32))))),
% 1.17/1.32 inference(monotonicity,[status(thm)],[3325])).
% 1.17/1.32 tff(3327,plain,
% 1.17/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a32) | c3_1(a32) | (~c2_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32)))),
% 1.17/1.32 inference(transitivity,[status(thm)],[3326, 3324])).
% 1.17/1.32 tff(3328,plain,
% 1.17/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a32) | c3_1(a32) | (~c2_1(a32)))),
% 1.17/1.32 inference(quant_inst,[status(thm)],[])).
% 1.17/1.32 tff(3329,plain,
% 1.17/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32))),
% 1.17/1.32 inference(modus_ponens,[status(thm)],[3328, 3327])).
% 1.17/1.32 tff(3330,plain,
% 1.17/1.32 ((~c0_1(a3)) | (~c2_1(a32))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3329, 160, 2734, 2733, 388, 3316, 3314, 407, 387, 34])).
% 1.17/1.32 tff(3331,plain,
% 1.17/1.32 (~c2_1(a32)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3330, 3323])).
% 1.17/1.32 tff(3332,plain,
% 1.17/1.32 (~hskp5),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[1355, 3316, 3315, 3314, 3331])).
% 1.17/1.32 tff(3333,plain,
% 1.17/1.32 ((~c0_1(a4)) | (~c0_1(a3))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3153, 160, 2733, 2782, 388, 407, 387, 406])).
% 1.17/1.32 tff(3334,plain,
% 1.17/1.32 (~c0_1(a4)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3333, 3323])).
% 1.17/1.32 tff(3335,assumption,(~c3_1(a25)), introduced(assumption)).
% 1.17/1.32 tff(3336,assumption,(c1_1(a25)), introduced(assumption)).
% 1.17/1.32 tff(3337,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3338,plain,
% 1.17/1.32 ((hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4))) <=> (hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3339,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25))))),
% 1.17/1.32 inference(monotonicity,[status(thm)],[3338])).
% 1.17/1.32 tff(3340,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.17/1.32 inference(transitivity,[status(thm)],[3339, 3337])).
% 1.17/1.32 tff(3341,plain,
% 1.17/1.32 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))),
% 1.17/1.32 inference(quant_inst,[status(thm)],[])).
% 1.17/1.32 tff(3342,plain,
% 1.17/1.32 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25))),
% 1.17/1.32 inference(modus_ponens,[status(thm)],[3341, 3340])).
% 1.17/1.32 tff(3343,plain,
% 1.17/1.32 (hskp5 | (~c2_1(a25))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3342, 160, 3336, 388, 3335, 407, 1311, 3334])).
% 1.17/1.32 tff(3344,plain,
% 1.17/1.32 (~c2_1(a25)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3343, 3332])).
% 1.17/1.32 tff(3345,assumption,(c0_1(a25)), introduced(assumption)).
% 1.17/1.32 tff(3346,plain,
% 1.17/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3347,plain,
% 1.17/1.32 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25))) <=> (c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3348,plain,
% 1.17/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25)))),
% 1.17/1.32 inference(monotonicity,[status(thm)],[3347])).
% 1.17/1.32 tff(3349,plain,
% 1.17/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.17/1.32 inference(transitivity,[status(thm)],[3348, 3346])).
% 1.17/1.32 tff(3350,plain,
% 1.17/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))),
% 1.17/1.32 inference(quant_inst,[status(thm)],[])).
% 1.17/1.32 tff(3351,plain,
% 1.17/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25)),
% 1.17/1.32 inference(modus_ponens,[status(thm)],[3350, 3349])).
% 1.17/1.32 tff(3352,plain,
% 1.17/1.32 ($false),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3351, 160, 2733, 2782, 3345, 3336, 3335, 406, 3323, 3344])).
% 1.17/1.32 tff(3353,plain,((~hskp24) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a25) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | hskp17 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.17/1.32 tff(3354,plain,
% 1.17/1.32 (~hskp24),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3353, 3310, 3309, 3286, 3301, 3290, 3289, 595, 193])).
% 1.17/1.32 tff(3355,plain,
% 1.17/1.32 (hskp9),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[271, 3354, 3293, 3292, 3291, 193])).
% 1.17/1.32 tff(3356,plain,
% 1.17/1.32 (~c3_1(a16)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[531, 3355])).
% 1.17/1.32 tff(3357,plain,
% 1.17/1.32 (~c2_1(a16)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[537, 3355])).
% 1.17/1.32 tff(3358,plain,
% 1.17/1.32 (c0_1(a16)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[545, 3355])).
% 1.17/1.32 tff(3359,plain,
% 1.17/1.32 (~hskp26),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[1554, 3358, 3310, 3357, 3356, 3290, 3289])).
% 1.17/1.32 tff(3360,plain,
% 1.17/1.32 (hskp26 | hskp16),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[552, 160, 3358, 3357, 3356, 94])).
% 1.17/1.32 tff(3361,plain,
% 1.17/1.32 (hskp16),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3360, 3359])).
% 1.17/1.32 tff(3362,plain,
% 1.17/1.32 (c1_1(a30)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[561, 3361])).
% 1.17/1.32 tff(3363,plain,
% 1.17/1.32 (~hskp23),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[223, 3292, 193, 3293, 3291])).
% 1.17/1.32 tff(3364,plain,
% 1.17/1.32 (hskp0),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[235, 3354, 3363])).
% 1.17/1.32 tff(3365,plain,
% 1.17/1.32 (~c2_1(a1)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[241, 3364])).
% 1.17/1.32 tff(3366,plain,
% 1.17/1.32 (~c0_1(a1)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[262, 3364])).
% 1.17/1.32 tff(3367,plain,
% 1.17/1.32 (~c2_1(a30)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[567, 3361])).
% 1.17/1.32 tff(3368,plain,
% 1.17/1.32 (~c0_1(a30)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[573, 3361])).
% 1.17/1.32 tff(3369,plain,
% 1.17/1.32 (c3_1(a1)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[249, 3364])).
% 1.17/1.32 tff(3370,plain,
% 1.17/1.32 (c3_1(a15)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[1924, 3369, 3368, 3367, 3366, 3365, 193, 3293, 3292, 3362])).
% 1.17/1.32 tff(3371,plain,
% 1.17/1.32 (hskp18),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3312, 3370])).
% 1.17/1.32 tff(3372,plain,
% 1.17/1.32 (~c3_1(a32)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[888, 3371])).
% 1.17/1.32 tff(3373,plain,
% 1.17/1.32 (~c1_1(a32)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[882, 3371])).
% 1.17/1.32 tff(3374,plain,
% 1.17/1.32 (~c0_1(a32)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[1283, 3371])).
% 1.17/1.32 tff(3375,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3376,plain,
% 1.17/1.32 ((hskp24 | (~ndr1_0) | c3_1(a25) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3377,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25))))),
% 1.17/1.32 inference(monotonicity,[status(thm)],[3376])).
% 1.17/1.32 tff(3378,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.17/1.32 inference(transitivity,[status(thm)],[3377, 3375])).
% 1.17/1.32 tff(3379,plain,
% 1.17/1.32 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.17/1.32 inference(quant_inst,[status(thm)],[])).
% 1.17/1.32 tff(3380,plain,
% 1.17/1.32 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25))),
% 1.17/1.32 inference(modus_ponens,[status(thm)],[3379, 3378])).
% 1.17/1.32 tff(3381,plain,
% 1.17/1.32 ($false),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3380, 160, 3354, 3301, 3309, 3374, 3373, 3372, 3286, 901])).
% 1.17/1.32 tff(3382,plain,(hskp17 | hskp4 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.17/1.32 tff(3383,plain,
% 1.17/1.32 (hskp14),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[3382, 193, 2347])).
% 1.17/1.32 tff(3384,plain,
% 1.17/1.32 (~c1_1(a24)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[943, 3383])).
% 1.17/1.32 tff(3385,plain,
% 1.17/1.32 (~c0_1(a24)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[949, 3383])).
% 1.17/1.32 tff(3386,plain,
% 1.17/1.32 (c0_1(a15)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[183, 2348])).
% 1.17/1.32 tff(3387,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3388,plain,
% 1.17/1.32 ((hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24))) <=> (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24)))),
% 1.17/1.32 inference(rewrite,[status(thm)],[])).
% 1.17/1.32 tff(3389,plain,
% 1.17/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[3388])).
% 1.17/1.33 tff(3390,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[3389, 3387])).
% 1.17/1.33 tff(3391,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(3392,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[3391, 3390])).
% 1.17/1.33 tff(3393,plain,
% 1.17/1.33 (~c3_1(a24)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3392, 160, 193, 3386, 3385, 3384, 2350, 2349, 65])).
% 1.17/1.33 tff(3394,plain,
% 1.17/1.33 (c2_1(a24)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[957, 3383])).
% 1.17/1.33 tff(3395,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3396,plain,
% 1.17/1.33 (((~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16)) <=> (c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3397,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24)))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[3396])).
% 1.17/1.33 tff(3398,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.33 inference(transitivity,[status(thm)],[3397, 3395])).
% 1.17/1.33 tff(3399,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(3400,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[3399, 3398])).
% 1.17/1.33 tff(3401,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3400, 160, 3394, 35, 3385, 2328, 2, 2312, 3, 3393])).
% 1.17/1.33 tff(3402,plain,(hskp4 | c0_1(a16) | c3_1(a16) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(3403,plain,
% 1.17/1.33 (hskp4),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3402, 3, 2, 35])).
% 1.17/1.33 tff(3404,plain,
% 1.17/1.33 (~c2_1(a6)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[111, 3403])).
% 1.17/1.33 tff(3405,plain,
% 1.17/1.33 (c3_1(a6)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[119, 3403])).
% 1.17/1.33 tff(3406,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3407,plain,
% 1.17/1.33 (((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a16) | c0_1(a16) | c2_1(a16) | c2_1(a16) | c1_1(a16) | c0_1(a16)) <=> (c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3408,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a16) | c0_1(a16) | c2_1(a16) | c2_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16)))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[3407])).
% 1.17/1.33 tff(3409,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a16) | c0_1(a16) | c2_1(a16) | c2_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16))),
% 1.17/1.33 inference(transitivity,[status(thm)],[3408, 3406])).
% 1.17/1.33 tff(3410,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a16) | c0_1(a16) | c2_1(a16) | c2_1(a16) | c1_1(a16) | c0_1(a16))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(3411,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[3410, 3409])).
% 1.17/1.33 tff(3412,plain,
% 1.17/1.33 (c0_1(a6)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3411, 160, 35, 3405, 2328, 2, 3404, 55, 3])).
% 1.17/1.33 tff(3413,plain,
% 1.17/1.33 (hskp18 | (~c0_1(a6))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[860, 160, 2347, 3405, 3404, 684])).
% 1.17/1.33 tff(3414,plain,
% 1.17/1.33 (hskp18),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3413, 3412])).
% 1.17/1.33 tff(3415,plain,
% 1.17/1.33 (~c3_1(a32)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[888, 3414])).
% 1.17/1.33 tff(3416,plain,
% 1.17/1.33 (~c1_1(a32)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[882, 3414])).
% 1.17/1.33 tff(3417,plain,
% 1.17/1.33 (~c0_1(a32)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1283, 3414])).
% 1.17/1.33 tff(3418,plain,
% 1.17/1.33 (c1_1(a6)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[127, 3403])).
% 1.17/1.33 tff(3419,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3420,plain,
% 1.17/1.33 ((hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6))) <=> (hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3421,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[3420])).
% 1.17/1.33 tff(3422,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[3421, 3419])).
% 1.17/1.33 tff(3423,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(3424,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[3423, 3422])).
% 1.17/1.33 tff(3425,plain,
% 1.17/1.33 (hskp19),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3424, 160, 2272, 2264, 3418, 3405, 3404, 779, 2280])).
% 1.17/1.33 tff(3426,plain,
% 1.17/1.33 (~c0_1(a33)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[819, 3425])).
% 1.17/1.33 tff(3427,plain,
% 1.17/1.33 (c2_1(a33)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[827, 3425])).
% 1.17/1.33 tff(3428,plain,
% 1.17/1.33 (~c1_1(a33)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1374, 160, 3427, 3426, 3417, 3416, 3415, 45])).
% 1.17/1.33 tff(3429,plain,
% 1.17/1.33 (c3_1(a33)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1392, 3425])).
% 1.17/1.33 tff(3430,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1399, 160, 2338, 3427, 3429, 3417, 3416, 3415, 1385, 3428])).
% 1.17/1.33 tff(3431,plain,(c1_1(a16) | c0_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(3432,plain,
% 1.17/1.33 (c1_1(a16)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3431, 35, 2])).
% 1.17/1.33 tff(3433,assumption,(hskp14), introduced(assumption)).
% 1.17/1.33 tff(3434,plain,
% 1.17/1.33 (~c1_1(a24)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[943, 3433])).
% 1.17/1.33 tff(3435,plain,
% 1.17/1.33 (~c0_1(a24)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[949, 3433])).
% 1.17/1.33 tff(3436,plain,
% 1.17/1.33 (c2_1(a24)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[957, 3433])).
% 1.17/1.33 tff(3437,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3438,plain,
% 1.17/1.33 (((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3439,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[3438])).
% 1.17/1.33 tff(3440,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[3439, 3437])).
% 1.17/1.33 tff(3441,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(3442,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[3441, 3440])).
% 1.17/1.33 tff(3443,plain,
% 1.17/1.33 (~c3_1(a24)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3442, 160, 3436, 35, 3435, 3434, 2, 83, 3432])).
% 1.17/1.33 tff(3444,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3445,plain,
% 1.17/1.33 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a24) | c3_1(a24) | (~c2_1(a24))) <=> (c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3446,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a24) | c3_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24)))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[3445])).
% 1.17/1.33 tff(3447,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a24) | c3_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.33 inference(transitivity,[status(thm)],[3446, 3444])).
% 1.17/1.33 tff(3448,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a24) | c3_1(a24) | (~c2_1(a24)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(3449,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[3448, 3447])).
% 1.17/1.33 tff(3450,plain,
% 1.17/1.33 ((~c0_1(a3)) | c3_1(a24)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3449, 160, 2272, 2264, 3436, 3435, 24, 2, 34, 3432])).
% 1.17/1.33 tff(3451,plain,
% 1.17/1.33 (~c0_1(a3)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3450, 3443])).
% 1.17/1.33 tff(3452,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3453,plain,
% 1.17/1.33 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24) | c1_1(a24) | c0_1(a24)) <=> (c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3454,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24)))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[3453])).
% 1.17/1.33 tff(3455,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24))),
% 1.17/1.33 inference(transitivity,[status(thm)],[3454, 3452])).
% 1.17/1.33 tff(3456,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24) | c1_1(a24) | c0_1(a24))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(3457,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[3456, 3455])).
% 1.17/1.33 tff(3458,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3457, 160, 2272, 2264, 3435, 3434, 45, 3451, 3443])).
% 1.17/1.33 tff(3459,plain,((~hskp14) | c2_1(a16) | c3_1(a16) | c0_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(3460,plain,
% 1.17/1.33 (~hskp14),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3459, 24, 2, 35])).
% 1.17/1.33 tff(3461,plain,
% 1.17/1.33 (c0_1(a31)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[290, 66])).
% 1.17/1.33 tff(3462,plain,
% 1.17/1.33 (~c0_1(a3)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[2301, 2165, 302, 313])).
% 1.17/1.33 tff(3463,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3277, 160, 193, 2272, 2289, 301, 313, 584, 2165, 3462])).
% 1.17/1.33 tff(3464,plain,(c3_1(a31) | hskp4 | (~c0_1(a31)) | c1_1(a31) | (~c2_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(3465,plain,
% 1.17/1.33 (c3_1(a31)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3464, 193, 301, 313, 302])).
% 1.17/1.33 tff(3466,plain,
% 1.17/1.33 (~hskp11),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[2541, 3465, 302, 301])).
% 1.17/1.33 tff(3467,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3468,plain,
% 1.17/1.33 ((hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3469,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[3468])).
% 1.17/1.33 tff(3470,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[3469, 3467])).
% 1.17/1.33 tff(3471,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(3472,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[3471, 3470])).
% 1.17/1.33 tff(3473,plain,
% 1.17/1.33 (hskp10),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[3472, 160, 2272, 2289, 302, 313, 1053, 2465, 1])).
% 1.17/1.33 tff(3474,plain,
% 1.17/1.33 (~c3_1(a18)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1066, 3473])).
% 1.17/1.33 tff(3475,plain,
% 1.17/1.33 (c2_1(a18)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1074, 3473])).
% 1.17/1.33 tff(3476,plain,
% 1.17/1.33 (c0_1(a18)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1082, 3473])).
% 1.17/1.33 tff(3477,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3478,plain,
% 1.17/1.33 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3))) <=> (hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(3479,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[3478])).
% 1.17/1.34 tff(3480,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[3479, 3477])).
% 1.17/1.34 tff(3481,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(3482,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 1.17/1.34 tff(3483,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3482, 160, 2902, 2264, 2289, 3476, 3475, 3474, 1042, 1])).
% 1.17/1.34 tff(3484,plain,(c0_1(a3) | hskp11 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(3485,plain,
% 1.17/1.34 (c0_1(a3)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3484, 3466, 302, 313, 3465])).
% 1.17/1.34 tff(3486,assumption,(c2_1(a25)), introduced(assumption)).
% 1.17/1.34 tff(3487,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3488,plain,
% 1.17/1.34 ((hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16))) <=> (hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3489,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[3488])).
% 1.17/1.34 tff(3490,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[3489, 3487])).
% 1.17/1.34 tff(3491,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(3492,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[3491, 3490])).
% 1.17/1.34 tff(3493,plain,
% 1.17/1.34 (hskp5 | (~c2_1(a25))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3492, 160, 3336, 35, 3335, 24, 1311, 709])).
% 1.17/1.34 tff(3494,plain,
% 1.17/1.34 (hskp5),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3493, 3486])).
% 1.17/1.34 tff(3495,plain,
% 1.17/1.34 (~c0_1(a7)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1317, 3494])).
% 1.17/1.34 tff(3496,plain,
% 1.17/1.34 (c3_1(a7)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1346, 3494])).
% 1.17/1.34 tff(3497,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3498,plain,
% 1.17/1.34 ((hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7))) <=> (hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3499,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[3498])).
% 1.17/1.34 tff(3500,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[3499, 3497])).
% 1.17/1.34 tff(3501,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(3502,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[3501, 3500])).
% 1.17/1.34 tff(3503,plain,
% 1.17/1.34 (~c2_1(a7)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3502, 160, 2902, 3345, 3496, 3335, 3495, 1042, 3486])).
% 1.17/1.34 tff(3504,plain,
% 1.17/1.34 (c1_1(a7)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1325, 3494])).
% 1.17/1.34 tff(3505,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3506,plain,
% 1.17/1.34 ((hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7))) <=> (hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3507,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7)))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[3506])).
% 1.17/1.34 tff(3508,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7))),
% 1.17/1.34 inference(transitivity,[status(thm)],[3507, 3505])).
% 1.17/1.34 tff(3509,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(3510,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 1.17/1.34 tff(3511,plain,
% 1.17/1.34 (hskp19),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3510, 160, 2272, 2264, 3504, 3496, 779, 2290, 3503])).
% 1.17/1.34 tff(3512,plain,
% 1.17/1.34 (~c0_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[819, 3511])).
% 1.17/1.34 tff(3513,plain,
% 1.17/1.34 (c3_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1392, 3511])).
% 1.17/1.34 tff(3514,plain,
% 1.17/1.34 (c2_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[827, 3511])).
% 1.17/1.34 tff(3515,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3516,plain,
% 1.17/1.34 ((hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3517,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[3516])).
% 1.17/1.34 tff(3518,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[3517, 3515])).
% 1.17/1.34 tff(3519,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(3520,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[3519, 3518])).
% 1.17/1.34 tff(3521,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3520, 160, 2902, 3514, 3513, 3345, 3512, 3335, 1042, 3486])).
% 1.17/1.34 tff(3522,plain,((~c2_1(a25)) | hskp11 | (~c0_1(a25)) | c3_1(a25) | (~c0_1(a3)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(3523,plain,
% 1.17/1.34 (~c2_1(a25)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3522, 3466, 3301, 3286, 3485, 3309, 35, 24, 709])).
% 1.17/1.34 tff(3524,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3351, 160, 2264, 2289, 3301, 3309, 3286, 406, 3485, 3523])).
% 1.17/1.34 tff(3525,plain,(hskp4 | c0_1(a16) | c2_1(a16) | (~c1_1(a16)) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a31)) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(3526,plain,
% 1.17/1.34 (hskp4),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3525, 2281, 24, 3432, 35, 72, 3461, 3460])).
% 1.17/1.34 tff(3527,plain,
% 1.17/1.34 (~c2_1(a6)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[111, 3526])).
% 1.17/1.34 tff(3528,plain,
% 1.17/1.34 (c3_1(a6)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[119, 3526])).
% 1.17/1.34 tff(3529,plain,
% 1.17/1.34 (c1_1(a6)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[127, 3526])).
% 1.17/1.34 tff(3530,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3531,plain,
% 1.17/1.34 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16)) <=> (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3532,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[3531])).
% 1.17/1.34 tff(3533,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[3532, 3530])).
% 1.17/1.34 tff(3534,plain,
% 1.17/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(3535,plain,
% 1.17/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 1.17/1.34 tff(3536,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3535, 160, 301, 35, 673, 672, 313, 24, 2, 671, 13, 2165])).
% 1.17/1.34 tff(3537,plain,(c3_1(a31) | (~c0_1(a31)) | c0_1(a16) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(3538,plain,
% 1.17/1.34 (c3_1(a31)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3537, 3461, 35, 3529, 3528, 72, 24, 2, 3527])).
% 1.17/1.34 tff(3539,plain,
% 1.17/1.34 (~hskp11),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[2541, 3538, 2281, 3461])).
% 1.17/1.34 tff(3540,plain,
% 1.17/1.34 (c0_1(a3)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3484, 3539, 2281, 72, 3538])).
% 1.17/1.34 tff(3541,plain,
% 1.17/1.34 (hskp19 | (~c0_1(a3))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3424, 160, 2272, 2264, 3529, 3528, 3527, 779])).
% 1.17/1.34 tff(3542,plain,
% 1.17/1.34 (hskp19),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3541, 3540])).
% 1.17/1.34 tff(3543,plain,
% 1.17/1.34 (~c0_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[819, 3542])).
% 1.17/1.34 tff(3544,plain,
% 1.17/1.34 (c2_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[827, 3542])).
% 1.17/1.34 tff(3545,assumption,(~c1_1(a33)), introduced(assumption)).
% 1.17/1.34 tff(3546,assumption,(~c0_1(a33)), introduced(assumption)).
% 1.17/1.34 tff(3547,assumption,(c2_1(a33)), introduced(assumption)).
% 1.17/1.34 tff(3548,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3549,plain,
% 1.17/1.34 (((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3550,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[3549])).
% 1.17/1.34 tff(3551,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.17/1.34 inference(transitivity,[status(thm)],[3550, 3548])).
% 1.17/1.34 tff(3552,plain,
% 1.17/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(3553,plain,
% 1.17/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 1.17/1.34 tff(3554,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3553, 160, 3547, 302, 35, 3546, 313, 2, 83, 2465, 3432, 3545])).
% 1.17/1.34 tff(3555,plain,(c1_1(a33) | (~c2_1(a33)) | (~c2_1(a31)) | c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(3556,plain,
% 1.17/1.34 (c1_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3555, 3544, 2281, 35, 3543, 72, 2, 3538])).
% 1.17/1.34 tff(3557,plain,
% 1.17/1.34 (c3_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1392, 3542])).
% 1.17/1.34 tff(3558,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3559,plain,
% 1.17/1.34 ((hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c1_1(a33))) <=> (hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(3560,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[3559])).
% 1.17/1.34 tff(3561,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[3560, 3558])).
% 1.17/1.34 tff(3562,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c1_1(a33)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(3563,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[3562, 3561])).
% 1.17/1.34 tff(3564,plain,
% 1.17/1.34 (hskp10 | (~c1_1(a33))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3563, 160, 3557, 2281, 3543, 72, 1053, 3538])).
% 1.17/1.34 tff(3565,plain,
% 1.17/1.34 (hskp10),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3564, 3556])).
% 1.17/1.34 tff(3566,plain,
% 1.17/1.34 (~c3_1(a18)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1066, 3565])).
% 1.17/1.34 tff(3567,plain,
% 1.17/1.34 (c2_1(a18)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1074, 3565])).
% 1.17/1.34 tff(3568,plain,
% 1.17/1.34 (c0_1(a18)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1082, 3565])).
% 1.17/1.34 tff(3569,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[2548, 160, 3539, 3544, 3557, 3568, 3567, 3543, 3566, 1042])).
% 1.17/1.34 tff(3570,plain,((~hskp17) | c0_1(a16) | c3_1(a16) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(3571,plain,
% 1.17/1.34 (~hskp17),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3570, 24, 2, 35])).
% 1.17/1.34 tff(3572,plain,
% 1.17/1.34 (hskp4),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3382, 3571, 3460])).
% 1.17/1.34 tff(3573,plain,
% 1.17/1.34 (~c2_1(a6)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[111, 3572])).
% 1.17/1.34 tff(3574,plain,
% 1.17/1.34 (c3_1(a6)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[119, 3572])).
% 1.17/1.34 tff(3575,plain,
% 1.17/1.34 (c1_1(a6)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[127, 3572])).
% 1.17/1.34 tff(3576,plain,
% 1.17/1.34 (c0_1(a3)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3322, 160, 2272, 2264, 1898, 1455, 1456, 45])).
% 1.17/1.34 tff(3577,plain,
% 1.17/1.34 (hskp19 | (~c0_1(a3))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3424, 160, 2272, 2264, 673, 672, 671, 779])).
% 1.17/1.34 tff(3578,plain,
% 1.17/1.34 (hskp19),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[3577, 3576])).
% 1.17/1.34 tff(3579,plain,
% 1.17/1.34 (~c0_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[819, 3578])).
% 1.17/1.34 tff(3580,plain,
% 1.17/1.34 (c2_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[827, 3578])).
% 1.17/1.34 tff(3581,plain,
% 1.17/1.34 (~c1_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1374, 160, 3580, 3579, 1898, 1455, 1456, 45])).
% 1.17/1.34 tff(3582,plain,
% 1.17/1.34 (c3_1(a33)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1392, 3578])).
% 1.17/1.34 tff(3583,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3584,plain,
% 1.17/1.35 (((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3585,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[3584])).
% 1.17/1.35 tff(3586,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.17/1.35 inference(transitivity,[status(thm)],[3585, 3583])).
% 1.17/1.35 tff(3587,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3588,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3587, 3586])).
% 1.17/1.35 tff(3589,plain,
% 1.17/1.35 ($false),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3588, 160, 3580, 3582, 35, 3579, 2, 83, 3432, 3581])).
% 1.17/1.35 tff(3590,plain,((~hskp18) | c0_1(a16) | c3_1(a16) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.35 tff(3591,plain,
% 1.17/1.35 (~hskp18),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3590, 3575, 2, 35, 3574, 3573])).
% 1.17/1.35 tff(3592,plain,
% 1.17/1.35 (~c0_1(a6)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[860, 160, 3591, 3571, 3574, 3573, 684])).
% 1.17/1.35 tff(3593,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3594,plain,
% 1.17/1.35 ((hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6))) <=> (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3595,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6)))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[3594])).
% 1.17/1.35 tff(3596,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6))),
% 1.17/1.35 inference(transitivity,[status(thm)],[3595, 3593])).
% 1.17/1.35 tff(3597,plain,
% 1.17/1.35 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3598,plain,
% 1.17/1.35 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3597, 3596])).
% 1.17/1.35 tff(3599,plain,
% 1.17/1.35 (hskp6),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3598, 160, 2272, 2264, 2289, 3574, 3573, 1202, 3592])).
% 1.17/1.35 tff(3600,plain,
% 1.17/1.35 (~c2_1(a8)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1239, 3599])).
% 1.17/1.35 tff(3601,plain,
% 1.17/1.35 (c0_1(a8)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1267, 3599])).
% 1.17/1.35 tff(3602,plain,
% 1.17/1.35 (~c3_1(a8)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1274, 160, 3591, 3571, 3601, 3600, 684])).
% 1.17/1.35 tff(3603,plain,
% 1.17/1.35 (hskp4),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3382, 595, 3460])).
% 1.17/1.35 tff(3604,plain,
% 1.17/1.35 (~c2_1(a6)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[111, 3603])).
% 1.17/1.35 tff(3605,plain,
% 1.17/1.35 (c3_1(a6)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[119, 3603])).
% 1.17/1.35 tff(3606,plain,
% 1.17/1.35 (c1_1(a6)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[127, 3603])).
% 1.17/1.35 tff(3607,plain,
% 1.17/1.35 (~hskp18),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3590, 3606, 2, 35, 3605, 3604])).
% 1.17/1.35 tff(3608,plain,
% 1.17/1.35 (hskp18 | (~c0_1(a6))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[860, 160, 595, 3605, 3604, 684])).
% 1.17/1.35 tff(3609,plain,
% 1.17/1.35 (~c0_1(a6)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3608, 3607])).
% 1.17/1.35 tff(3610,plain,
% 1.17/1.35 (hskp6),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3598, 160, 2272, 2264, 2289, 3605, 3604, 1202, 3609])).
% 1.17/1.35 tff(3611,plain,
% 1.17/1.35 (~c2_1(a8)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1239, 3610])).
% 1.17/1.35 tff(3612,plain,
% 1.17/1.35 (c0_1(a8)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1267, 3610])).
% 1.17/1.35 tff(3613,plain,
% 1.17/1.35 (~c3_1(a8)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1274, 160, 3607, 595, 3612, 3611, 684])).
% 1.17/1.35 tff(3614,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3615,plain,
% 1.17/1.35 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3616,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[3615])).
% 1.17/1.35 tff(3617,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[3616, 3614])).
% 1.17/1.35 tff(3618,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3619,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3618, 3617])).
% 1.17/1.35 tff(3620,plain,
% 1.17/1.35 (~c0_1(a3)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3619, 160, 2264, 2289, 3612, 24, 2, 3611, 406, 3432, 3613])).
% 1.17/1.35 tff(3621,plain,
% 1.17/1.35 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3622,plain,
% 1.17/1.35 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3623,plain,
% 1.17/1.35 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3622, 3621])).
% 1.17/1.35 tff(3624,plain,
% 1.17/1.35 (hskp27 | hskp26 | c0_1(a3)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3623, 160, 2272, 2264, 728])).
% 1.17/1.35 tff(3625,plain,
% 1.17/1.35 (hskp27),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3624, 3620, 84])).
% 1.17/1.35 tff(3626,plain,
% 1.17/1.35 (c3_1(a11)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[692, 3625])).
% 1.17/1.35 tff(3627,plain,
% 1.17/1.35 (c0_1(a11)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[700, 3625])).
% 1.17/1.35 tff(3628,plain,
% 1.17/1.35 (c2_1(a11)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[707, 160, 3607, 595, 3627, 3626, 684])).
% 1.17/1.35 tff(3629,plain,
% 1.17/1.35 (~hskp9),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[545, 35])).
% 1.17/1.35 tff(3630,plain,
% 1.17/1.35 (hskp9 | hskp8 | c0_1(a3)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[2582, 160, 2272, 2264, 2573])).
% 1.17/1.35 tff(3631,plain,
% 1.17/1.35 (hskp8),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3630, 3620, 3629])).
% 1.17/1.35 tff(3632,plain,
% 1.17/1.35 (~c2_1(a15)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[175, 3631])).
% 1.17/1.35 tff(3633,plain,
% 1.17/1.35 (c0_1(a15)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[183, 3631])).
% 1.17/1.35 tff(3634,plain,
% 1.17/1.35 (~c3_1(a15)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1931, 160, 3607, 595, 3633, 3632, 684])).
% 1.17/1.35 tff(3635,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3636,plain,
% 1.17/1.35 (((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3637,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[3636])).
% 1.17/1.35 tff(3638,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[3637, 3635])).
% 1.17/1.35 tff(3639,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3640,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3639, 3638])).
% 1.17/1.35 tff(3641,plain,
% 1.17/1.35 ($false),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3640, 160, 3627, 3626, 3633, 24, 2, 3632, 406, 3432, 3634, 3628])).
% 1.17/1.35 tff(3642,plain,(hskp17 | c2_1(a16) | c3_1(a16) | hskp26 | c0_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.35 tff(3643,plain,
% 1.17/1.35 (hskp26),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3642, 3571, 2, 24, 35])).
% 1.17/1.35 tff(3644,plain,
% 1.17/1.35 (c3_1(a10)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[632, 3643])).
% 1.17/1.35 tff(3645,plain,
% 1.17/1.35 (c2_1(a10)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[624, 3643])).
% 1.17/1.35 tff(3646,plain,
% 1.17/1.35 (c0_1(a10)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[615, 3643])).
% 1.17/1.35 tff(3647,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3648,plain,
% 1.17/1.35 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3649,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[3648])).
% 1.17/1.35 tff(3650,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[3649, 3647])).
% 1.17/1.35 tff(3651,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3652,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 1.17/1.35 tff(3653,plain,
% 1.17/1.35 ($false),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3652, 160, 3646, 3645, 3644, 3601, 24, 2, 3600, 406, 3432, 3602])).
% 1.17/1.35 tff(3654,plain,(c2_1(a16) | c3_1(a16) | c0_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.35 tff(3655,plain,
% 1.17/1.35 (c2_1(a16)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3654, 35, 2])).
% 1.17/1.35 tff(3656,plain,
% 1.17/1.35 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3657,plain,
% 1.17/1.35 ((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a16)) | c0_1(a16) | (~c1_1(a16))) <=> (hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3658,plain,
% 1.17/1.35 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a16)) | c0_1(a16) | (~c1_1(a16)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[3657])).
% 1.17/1.35 tff(3659,plain,
% 1.17/1.35 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a16)) | c0_1(a16) | (~c1_1(a16)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[3658, 3656])).
% 1.17/1.35 tff(3660,plain,
% 1.17/1.35 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a16)) | c0_1(a16) | (~c1_1(a16)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3661,plain,
% 1.17/1.35 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 1.17/1.35 tff(3662,plain,
% 1.17/1.35 (hskp8 | (~c2_1(a16)) | (~c1_1(a16))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3661, 160, 3629, 35, 2573])).
% 1.17/1.35 tff(3663,plain,
% 1.17/1.35 (hskp8),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3662, 3655, 3432])).
% 1.17/1.35 tff(3664,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3665,plain,
% 1.17/1.35 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24))) <=> (c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3666,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24)))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[3665])).
% 1.17/1.35 tff(3667,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24))),
% 1.17/1.35 inference(transitivity,[status(thm)],[3666, 3664])).
% 1.17/1.35 tff(3668,plain,
% 1.17/1.35 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3669,plain,
% 1.17/1.35 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3668, 3667])).
% 1.17/1.35 tff(3670,plain,
% 1.17/1.35 (~c0_1(a3)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3669, 160, 2264, 2289, 3436, 3434, 1466, 3443])).
% 1.17/1.35 tff(3671,plain,
% 1.17/1.35 ($false),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3457, 160, 2272, 2264, 3435, 3434, 45, 3670, 3443])).
% 1.17/1.35 tff(3672,plain,((~hskp14) | c0_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.35 tff(3673,plain,
% 1.17/1.35 (~hskp14),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3672, 35, 2])).
% 1.17/1.35 tff(3674,plain,
% 1.17/1.35 (hskp2),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[2359, 3673, 3663])).
% 1.17/1.35 tff(3675,plain,
% 1.17/1.35 (~c3_1(a4)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[370, 3674])).
% 1.17/1.35 tff(3676,plain,
% 1.17/1.35 (~c2_1(a4)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[384, 3674])).
% 1.17/1.35 tff(3677,plain,
% 1.17/1.35 (c1_1(a4)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[378, 3674])).
% 1.17/1.35 tff(3678,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3679,plain,
% 1.17/1.35 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16))) <=> (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(3680,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[3679])).
% 1.17/1.35 tff(3681,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[3680, 3678])).
% 1.17/1.35 tff(3682,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(3683,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[3682, 3681])).
% 1.17/1.35 tff(3684,plain,
% 1.17/1.35 (~c0_1(a3)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[3683, 160, 2272, 2264, 35, 3677, 3655, 2, 3676, 3675, 34])).
% 1.17/1.35 tff(3685,plain,
% 1.17/1.35 (~c2_1(a15)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[175, 3663])).
% 1.17/1.35 tff(3686,plain,
% 1.17/1.35 (c0_1(a15)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[183, 3663])).
% 1.17/1.35 tff(3687,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3688,plain,
% 1.17/1.36 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16))) <=> (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3689,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[3688])).
% 1.17/1.36 tff(3690,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[3689, 3687])).
% 1.17/1.36 tff(3691,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(3692,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[3691, 3690])).
% 1.17/1.36 tff(3693,plain,
% 1.17/1.36 ($false),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3692, 160, 804, 796, 788, 35, 3677, 3655, 2, 3676, 3675, 34])).
% 1.17/1.36 tff(3694,plain,((~hskp25) | c0_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.36 tff(3695,plain,
% 1.17/1.36 (~hskp25),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3694, 35, 2])).
% 1.17/1.36 tff(3696,plain,
% 1.17/1.36 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3697,plain,
% 1.17/1.36 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | c0_1(a16)) <=> (hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3698,plain,
% 1.17/1.36 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | c0_1(a16))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0)))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[3697])).
% 1.17/1.36 tff(3699,plain,
% 1.17/1.36 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | c0_1(a16))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0))),
% 1.17/1.36 inference(transitivity,[status(thm)],[3698, 3696])).
% 1.17/1.36 tff(3700,plain,
% 1.17/1.36 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | c0_1(a16))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(3701,plain,
% 1.17/1.36 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[3700, 3699])).
% 1.17/1.36 tff(3702,plain,
% 1.17/1.36 (hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16))),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3701, 160, 2, 1023])).
% 1.17/1.36 tff(3703,plain,
% 1.17/1.36 (hskp26),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3702, 3695, 35, 3655])).
% 1.17/1.36 tff(3704,plain,
% 1.17/1.36 (c3_1(a10)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[632, 3703])).
% 1.17/1.36 tff(3705,plain,
% 1.17/1.36 (c2_1(a10)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[624, 3703])).
% 1.17/1.36 tff(3706,plain,
% 1.17/1.36 (c0_1(a10)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[615, 3703])).
% 1.17/1.36 tff(3707,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3708,plain,
% 1.17/1.36 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15))) <=> (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3709,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[3708])).
% 1.17/1.36 tff(3710,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[3709, 3707])).
% 1.17/1.36 tff(3711,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(3712,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[3711, 3710])).
% 1.17/1.36 tff(3713,plain,
% 1.17/1.36 (c3_1(a15)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3712, 160, 3706, 3705, 3704, 3686, 3677, 3685, 3676, 3675, 406])).
% 1.17/1.36 tff(3714,plain,
% 1.17/1.36 (~c1_1(a15)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[189, 3663])).
% 1.17/1.36 tff(3715,plain,
% 1.17/1.36 (hskp15 | (~c3_1(a15))),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3078, 160, 3686, 3714, 3685, 2374])).
% 1.17/1.36 tff(3716,plain,
% 1.17/1.36 (hskp15),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3715, 3713])).
% 1.17/1.36 tff(3717,plain,
% 1.17/1.36 (~c3_1(a25)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3285, 3716])).
% 1.17/1.36 tff(3718,plain,
% 1.17/1.36 (c0_1(a25)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3300, 3716])).
% 1.17/1.36 tff(3719,plain,
% 1.17/1.36 (~hskp11),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2141, 3706, 3705, 3704])).
% 1.17/1.36 tff(3720,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3721,plain,
% 1.17/1.36 ((hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3))) <=> (hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3722,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[3721])).
% 1.17/1.36 tff(3723,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[3722, 3720])).
% 1.17/1.36 tff(3724,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(3725,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[3724, 3723])).
% 1.17/1.36 tff(3726,plain,
% 1.17/1.36 (~c2_1(a25)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3725, 160, 3719, 2264, 2289, 3718, 3717, 1042, 3684])).
% 1.17/1.36 tff(3727,plain,
% 1.17/1.36 (c1_1(a25)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3308, 3716])).
% 1.17/1.36 tff(3728,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3729,plain,
% 1.17/1.36 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25))) <=> (c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3730,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25)))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[3729])).
% 1.17/1.36 tff(3731,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.17/1.36 inference(transitivity,[status(thm)],[3730, 3728])).
% 1.17/1.36 tff(3732,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(3733,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 1.17/1.36 tff(3734,plain,
% 1.17/1.36 ($false),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3733, 160, 3706, 3705, 3704, 3718, 3727, 3717, 406, 3726])).
% 1.17/1.36 tff(3735,plain,(c0_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.36 tff(3736,plain,
% 1.17/1.36 (c0_1(a16)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3735, 2])).
% 1.17/1.36 tff(3737,plain,
% 1.17/1.36 (~hskp26),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1867, 1746, 3736, 2, 24])).
% 1.17/1.36 tff(3738,plain,
% 1.17/1.36 (hskp26 | hskp16 | c2_1(a16) | (~c0_1(a16))),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[552, 160, 2, 94])).
% 1.17/1.36 tff(3739,plain,
% 1.17/1.36 (hskp16),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3738, 3737, 3736, 24])).
% 1.17/1.36 tff(3740,plain,
% 1.17/1.36 (c1_1(a30)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[561, 3739])).
% 1.17/1.36 tff(3741,plain,
% 1.17/1.36 (~c2_1(a30)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[567, 3739])).
% 1.17/1.36 tff(3742,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3743,plain,
% 1.17/1.36 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3744,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[3743])).
% 1.17/1.36 tff(3745,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[3744, 3742])).
% 1.17/1.36 tff(3746,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(3747,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[3746, 3745])).
% 1.17/1.36 tff(3748,plain,
% 1.17/1.36 (~c0_1(a3)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3747, 160, 2264, 2289, 3736, 1749, 24, 2, 1748, 1747, 406])).
% 1.17/1.36 tff(3749,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3750,plain,
% 1.17/1.36 ((hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3751,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[3750])).
% 1.17/1.36 tff(3752,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[3751, 3749])).
% 1.17/1.36 tff(3753,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(3754,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[3753, 3752])).
% 1.17/1.36 tff(3755,plain,
% 1.17/1.36 (hskp4),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3754, 160, 2272, 2289, 3736, 2, 584, 3, 3748])).
% 1.17/1.36 tff(3756,plain,
% 1.17/1.36 (c1_1(a6)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[127, 3755])).
% 1.17/1.36 tff(3757,plain,
% 1.17/1.36 (c3_1(a6)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[119, 3755])).
% 1.17/1.36 tff(3758,plain,
% 1.17/1.36 (~c2_1(a6)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[111, 3755])).
% 1.17/1.36 tff(3759,plain,
% 1.17/1.36 (hskp17),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1864, 3758, 3736, 3, 24, 2, 3737, 3757, 3756])).
% 1.17/1.36 tff(3760,plain,
% 1.17/1.36 (~c1_1(a31)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[71, 3759])).
% 1.17/1.36 tff(3761,plain,
% 1.17/1.36 (c0_1(a31)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[290, 3759])).
% 1.17/1.36 tff(3762,plain,
% 1.17/1.36 (~hskp13),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2110, 3757, 3736, 3, 2, 3758, 3756])).
% 1.17/1.36 tff(3763,plain,
% 1.17/1.36 (~c3_1(a31)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2024, 160, 3762, 3761, 3736, 3760, 24, 1502, 3])).
% 1.17/1.36 tff(3764,plain,
% 1.17/1.36 (c2_1(a31)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[298, 3759])).
% 1.17/1.36 tff(3765,plain,
% 1.17/1.36 (hskp20),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2032, 160, 3737, 3761, 3764, 1134, 3763])).
% 1.17/1.36 tff(3766,plain,
% 1.17/1.36 (~c3_1(a37)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1146, 3765])).
% 1.17/1.36 tff(3767,plain,
% 1.17/1.36 (~c0_1(a37)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1152, 3765])).
% 1.17/1.36 tff(3768,plain,
% 1.17/1.36 (~c0_1(a30)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[573, 3739])).
% 1.17/1.36 tff(3769,plain,
% 1.17/1.36 (c3_1(a30)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1011, 160, 3736, 3756, 3757, 3768, 3741, 2, 3758, 13, 3])).
% 1.17/1.36 tff(3770,plain,
% 1.17/1.36 (c2_1(a37)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2041, 3769, 3736, 3767, 3766, 3741, 2, 3, 3740])).
% 1.17/1.36 tff(3771,plain,
% 1.17/1.36 (hskp25),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2048, 160, 3737, 3767, 3766, 1023, 3770])).
% 1.17/1.36 tff(3772,plain,
% 1.17/1.36 (c2_1(a9)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[787, 3771])).
% 1.17/1.36 tff(3773,plain,
% 1.17/1.36 (c0_1(a9)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[803, 3771])).
% 1.17/1.36 tff(3774,plain,
% 1.17/1.36 (c1_1(a9)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[795, 3771])).
% 1.17/1.36 tff(3775,plain,
% 1.17/1.36 ($false),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2056, 3774, 3773, 1746, 3767, 3766, 3772, 3770])).
% 1.17/1.36 tff(3776,plain,((~hskp2) | c3_1(a16) | c1_1(a16) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.36 tff(3777,plain,
% 1.17/1.36 (~hskp2),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3776, 24, 3, 2])).
% 1.17/1.36 tff(3778,plain,
% 1.17/1.36 (hskp14 | hskp2 | c2_1(a16) | c1_1(a16)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[651, 160, 3736, 643])).
% 1.17/1.36 tff(3779,plain,
% 1.17/1.36 (hskp14),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3778, 3777, 24, 3])).
% 1.17/1.36 tff(3780,plain,
% 1.17/1.36 (~c1_1(a24)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[943, 3779])).
% 1.17/1.36 tff(3781,plain,
% 1.17/1.36 (~c0_1(a24)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[949, 3779])).
% 1.17/1.36 tff(3782,plain,
% 1.17/1.36 (c2_1(a24)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[957, 3779])).
% 1.17/1.36 tff(3783,plain,
% 1.17/1.36 (hskp3),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[964, 160, 3777, 3782, 3781, 3780, 23])).
% 1.17/1.36 tff(3784,plain,
% 1.17/1.36 (~c3_1(a5)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[867, 3783])).
% 1.17/1.36 tff(3785,plain,
% 1.17/1.36 (~c2_1(a5)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[331, 3783])).
% 1.17/1.36 tff(3786,plain,
% 1.17/1.36 (~c1_1(a5)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[337, 3783])).
% 1.17/1.36 tff(3787,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3788,plain,
% 1.17/1.36 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a5) | c1_1(a5) | c0_1(a5)) <=> (c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(3789,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[3788])).
% 1.17/1.36 tff(3790,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[3789, 3787])).
% 1.17/1.36 tff(3791,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a5) | c1_1(a5) | c0_1(a5))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(3792,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[3791, 3790])).
% 1.17/1.36 tff(3793,plain,
% 1.17/1.36 (c0_1(a5) | c0_1(a3)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3792, 160, 2272, 2264, 3786, 3784, 45])).
% 1.17/1.36 tff(3794,plain,
% 1.17/1.36 (c0_1(a5)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3793, 1])).
% 1.17/1.36 tff(3795,plain,
% 1.17/1.36 (hskp4),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3754, 160, 2272, 2289, 3736, 2, 584, 3, 1])).
% 1.17/1.36 tff(3796,plain,
% 1.17/1.36 (c1_1(a6)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[127, 3795])).
% 1.17/1.36 tff(3797,plain,
% 1.17/1.36 (~c2_1(a6)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[111, 3795])).
% 1.17/1.36 tff(3798,plain,
% 1.17/1.36 (c3_1(a6)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[119, 3795])).
% 1.17/1.36 tff(3799,plain,
% 1.17/1.36 (~hskp13),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2110, 672, 3736, 3, 2, 671, 673])).
% 1.17/1.36 tff(3800,plain,
% 1.17/1.36 (hskp26),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1864, 595, 3736, 3, 24, 2, 671, 672, 673])).
% 1.17/1.36 tff(3801,plain,
% 1.17/1.36 (c0_1(a10)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[615, 3800])).
% 1.17/1.36 tff(3802,plain,
% 1.17/1.36 (c3_1(a10)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[632, 3800])).
% 1.17/1.36 tff(3803,plain,
% 1.17/1.36 (c1_1(a10)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1511, 3802, 3786, 1452, 3801, 3785, 3799])).
% 1.17/1.36 tff(3804,plain,
% 1.17/1.36 (c2_1(a10)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[624, 3800])).
% 1.17/1.36 tff(3805,plain,
% 1.17/1.36 (~hskp18),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1525, 3801, 3782, 671, 673, 3802, 3786, 3785, 1452, 3804, 595, 3736, 3, 3781, 3780, 2, 672])).
% 1.17/1.36 tff(3806,plain,
% 1.17/1.36 (hskp18 | hskp17 | (~c0_1(a6))),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[860, 160, 672, 671, 684])).
% 1.17/1.36 tff(3807,plain,
% 1.17/1.36 (~c0_1(a6)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3806, 3805, 595])).
% 1.17/1.36 tff(3808,plain,
% 1.17/1.36 (~hskp6),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1276, 3805, 3736, 3, 595, 3780, 3782, 2, 3781])).
% 1.17/1.36 tff(3809,plain,
% 1.17/1.36 ($false),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1490, 160, 3808, 3804, 3802, 672, 671, 1202, 3807, 3803])).
% 1.17/1.36 tff(3810,plain,(hskp17 | (~c3_1(a6)) | c2_1(a6) | c1_1(a16) | c3_1(a16) | (~c0_1(a5)) | (~c1_1(a6)) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.36 tff(3811,plain,
% 1.17/1.36 (hskp17),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[3810, 3798, 3797, 3, 2, 3794, 3796, 24])).
% 1.17/1.36 tff(3812,plain,
% 1.17/1.36 (~c1_1(a31)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[71, 3811])).
% 1.17/1.36 tff(3813,plain,
% 1.17/1.36 (c0_1(a31)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[290, 3811])).
% 1.17/1.36 tff(3814,plain,
% 1.17/1.36 (~hskp13),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[2110, 3798, 3736, 3, 2, 3797, 3796])).
% 1.17/1.36 tff(3815,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3816,plain,
% 1.21/1.37 ((hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5))) <=> (hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3817,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3816])).
% 1.21/1.37 tff(3818,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3817, 3815])).
% 1.21/1.37 tff(3819,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3820,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3819, 3818])).
% 1.21/1.37 tff(3821,plain,
% 1.21/1.37 (~c3_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3820, 160, 3814, 3813, 3812, 3786, 3785, 1502, 3794])).
% 1.21/1.37 tff(3822,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3457, 160, 2272, 2264, 971, 970, 45, 1, 2087])).
% 1.21/1.37 tff(3823,plain,(c3_1(a24) | c0_1(a24) | c1_1(a24) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(3824,plain,
% 1.21/1.37 (c3_1(a24)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3823, 1, 3780, 3781])).
% 1.21/1.37 tff(3825,assumption,(c3_1(a24)), introduced(assumption)).
% 1.21/1.37 tff(3826,assumption,(hskp20), introduced(assumption)).
% 1.21/1.37 tff(3827,plain,
% 1.21/1.37 (~c3_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1146, 3826])).
% 1.21/1.37 tff(3828,plain,
% 1.21/1.37 (~c0_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1152, 3826])).
% 1.21/1.37 tff(3829,plain,
% 1.21/1.37 (c1_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1160, 3826])).
% 1.21/1.37 tff(3830,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1230, 160, 3829, 972, 3828, 3827, 971, 970, 83, 3825])).
% 1.21/1.37 tff(3831,plain,((~hskp20) | (~c2_1(a24)) | c0_1(a24) | c1_1(a24) | (~c3_1(a24))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(3832,plain,
% 1.21/1.37 (~hskp20),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3831, 3824, 3781, 3780, 3782])).
% 1.21/1.37 tff(3833,plain,
% 1.21/1.37 (c2_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[298, 3811])).
% 1.21/1.37 tff(3834,plain,
% 1.21/1.37 (hskp26 | hskp20 | c3_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2032, 160, 3813, 3833, 1134])).
% 1.21/1.37 tff(3835,plain,
% 1.21/1.37 (hskp26),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3834, 3832, 3821])).
% 1.21/1.37 tff(3836,plain,
% 1.21/1.37 (c3_1(a10)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[632, 3835])).
% 1.21/1.37 tff(3837,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3838,plain,
% 1.21/1.37 ((hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3))) <=> (hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3839,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3838])).
% 1.21/1.37 tff(3840,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3839, 3837])).
% 1.21/1.37 tff(3841,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3842,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3841, 3840])).
% 1.21/1.37 tff(3843,plain,
% 1.21/1.37 (hskp11),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3842, 160, 2264, 2289, 3813, 3833, 1042, 3821, 1])).
% 1.21/1.37 tff(3844,plain,
% 1.21/1.37 (c0_1(a10)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[615, 3835])).
% 1.21/1.37 tff(3845,plain,
% 1.21/1.37 (c2_1(a10)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[624, 3835])).
% 1.21/1.37 tff(3846,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2141, 3845, 3844, 3843, 3836])).
% 1.21/1.37 tff(3847,plain,(c0_1(a3) | c1_1(a16) | c3_1(a16) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(3848,plain,
% 1.21/1.37 (c0_1(a3)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3847, 24, 2, 3])).
% 1.21/1.37 tff(3849,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3669, 160, 2264, 2289, 972, 970, 1466, 2290, 2087])).
% 1.21/1.37 tff(3850,plain,(c3_1(a24) | (~c2_1(a24)) | c1_1(a24) | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(3851,plain,
% 1.21/1.37 (c3_1(a24)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3850, 3782, 3780, 3848])).
% 1.21/1.37 tff(3852,plain,
% 1.21/1.37 (hskp4 | (~c3_1(a24))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2103, 160, 3736, 3781, 3780, 24, 65, 3])).
% 1.21/1.37 tff(3853,plain,
% 1.21/1.37 (hskp4),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3852, 3851])).
% 1.21/1.37 tff(3854,plain,
% 1.21/1.37 (~c2_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[111, 3853])).
% 1.21/1.37 tff(3855,plain,
% 1.21/1.37 (c3_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[119, 3853])).
% 1.21/1.37 tff(3856,plain,
% 1.21/1.37 (c1_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[127, 3853])).
% 1.21/1.37 tff(3857,plain,
% 1.21/1.37 (c0_1(a5)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[997, 160, 3736, 3856, 3855, 2, 3854, 3785, 3784, 13, 3])).
% 1.21/1.37 tff(3858,plain,
% 1.21/1.37 (hskp17),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3810, 3857, 3854, 3, 2, 3855, 3856, 24])).
% 1.21/1.37 tff(3859,plain,
% 1.21/1.37 (~c1_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[71, 3858])).
% 1.21/1.37 tff(3860,plain,
% 1.21/1.37 (c2_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[298, 3858])).
% 1.21/1.37 tff(3861,plain,
% 1.21/1.37 (c3_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2301, 3860, 3848, 3859])).
% 1.21/1.37 tff(3862,plain,
% 1.21/1.37 (c0_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[290, 3858])).
% 1.21/1.37 tff(3863,plain,
% 1.21/1.37 (~hskp13),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2110, 3855, 3736, 3, 2, 3854, 3856])).
% 1.21/1.37 tff(3864,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3820, 160, 3863, 3862, 3859, 3786, 3785, 1502, 3861, 3857])).
% 1.21/1.37 tff(3865,plain,(c2_1(a16) | c1_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(3866,plain,
% 1.21/1.37 (c2_1(a16)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3865, 3, 2])).
% 1.21/1.37 tff(3867,plain,
% 1.21/1.37 (~c0_1(a3)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2327, 3866, 3])).
% 1.21/1.37 tff(3868,plain,
% 1.21/1.37 (~hskp9),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[537, 3866])).
% 1.21/1.37 tff(3869,plain,
% 1.21/1.37 (hskp8),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3630, 3868, 3867])).
% 1.21/1.37 tff(3870,plain,
% 1.21/1.37 (hskp4),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3754, 160, 2272, 2289, 3736, 2, 584, 3, 3867])).
% 1.21/1.37 tff(3871,plain,
% 1.21/1.37 (c1_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[127, 3870])).
% 1.21/1.37 tff(3872,plain,
% 1.21/1.37 (~c2_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[111, 3870])).
% 1.21/1.37 tff(3873,plain,
% 1.21/1.37 (c3_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[119, 3870])).
% 1.21/1.37 tff(3874,plain,
% 1.21/1.37 (~hskp13),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2110, 3873, 3736, 3, 2, 3872, 3871])).
% 1.21/1.37 tff(3875,plain,
% 1.21/1.37 (~c2_1(a15)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[175, 3869])).
% 1.21/1.37 tff(3876,plain,
% 1.21/1.37 (~c1_1(a15)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[189, 3869])).
% 1.21/1.37 tff(3877,plain,
% 1.21/1.37 (c0_1(a15)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[183, 3869])).
% 1.21/1.37 tff(3878,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3879,plain,
% 1.21/1.37 ((hskp13 | (~ndr1_0) | c1_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15))) <=> (hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3880,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3879])).
% 1.21/1.37 tff(3881,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3880, 3878])).
% 1.21/1.37 tff(3882,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3883,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3882, 3881])).
% 1.21/1.37 tff(3884,plain,
% 1.21/1.37 (hskp13 | (~c3_1(a15))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3883, 160, 3877, 3876, 3875, 1502])).
% 1.21/1.37 tff(3885,plain,
% 1.21/1.37 (~c3_1(a15)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3884, 3874])).
% 1.21/1.37 tff(3886,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3887,plain,
% 1.21/1.37 ((hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3))) <=> (hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3888,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3887])).
% 1.21/1.37 tff(3889,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3888, 3886])).
% 1.21/1.37 tff(3890,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3891,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3890, 3889])).
% 1.21/1.37 tff(3892,plain,
% 1.21/1.37 (hskp11),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3891, 160, 2264, 2289, 3736, 3866, 2, 1042, 3867])).
% 1.21/1.37 tff(3893,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2141, 625, 616, 2130, 633])).
% 1.21/1.37 tff(3894,plain,((~hskp26) | (~hskp11)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(3895,plain,
% 1.21/1.37 (~hskp26),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3894, 3892])).
% 1.21/1.37 tff(3896,plain,
% 1.21/1.37 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3897,plain,
% 1.21/1.37 ((hskp26 | hskp16 | (~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c0_1(a15))) <=> (hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3898,plain,
% 1.21/1.37 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3897])).
% 1.21/1.37 tff(3899,plain,
% 1.21/1.37 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3898, 3896])).
% 1.21/1.37 tff(3900,plain,
% 1.21/1.37 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c0_1(a15)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3901,plain,
% 1.21/1.37 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3900, 3899])).
% 1.21/1.37 tff(3902,plain,
% 1.21/1.37 (hskp26 | hskp16 | c3_1(a15)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3901, 160, 3877, 3875, 94])).
% 1.21/1.37 tff(3903,plain,
% 1.21/1.37 (hskp16),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3902, 3895, 3885])).
% 1.21/1.37 tff(3904,plain,
% 1.21/1.37 (c1_1(a30)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[561, 3903])).
% 1.21/1.37 tff(3905,plain,
% 1.21/1.37 (~c2_1(a30)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[567, 3903])).
% 1.21/1.37 tff(3906,plain,
% 1.21/1.37 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3907,plain,
% 1.21/1.37 ((hskp26 | hskp20 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16))) <=> (hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3908,plain,
% 1.21/1.37 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3907])).
% 1.21/1.37 tff(3909,plain,
% 1.21/1.37 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3908, 3906])).
% 1.21/1.37 tff(3910,plain,
% 1.21/1.37 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3911,plain,
% 1.21/1.37 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3910, 3909])).
% 1.21/1.37 tff(3912,plain,
% 1.21/1.37 (hskp26 | hskp20 | (~c2_1(a16)) | (~c0_1(a16))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3911, 160, 2, 1134])).
% 1.21/1.37 tff(3913,plain,
% 1.21/1.37 (hskp20),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3912, 3895, 3736, 3866])).
% 1.21/1.37 tff(3914,plain,
% 1.21/1.37 (~c3_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1146, 3913])).
% 1.21/1.37 tff(3915,plain,
% 1.21/1.37 (~c0_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1152, 3913])).
% 1.21/1.37 tff(3916,plain,
% 1.21/1.37 (~c3_1(a19)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1095, 3892])).
% 1.21/1.37 tff(3917,plain,
% 1.21/1.37 (~c1_1(a19)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1116, 3892])).
% 1.21/1.37 tff(3918,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3919,plain,
% 1.21/1.37 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a19) | c1_1(a19) | c0_1(a19)) <=> (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3920,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a19) | c1_1(a19) | c0_1(a19))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19)))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3919])).
% 1.21/1.37 tff(3921,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a19) | c1_1(a19) | c0_1(a19))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3920, 3918])).
% 1.21/1.37 tff(3922,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a19) | c1_1(a19) | c0_1(a19))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3923,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 1.21/1.37 tff(3924,plain,
% 1.21/1.37 (c0_1(a19)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3923, 160, 2272, 2264, 3917, 3916, 45, 3867])).
% 1.21/1.37 tff(3925,plain,
% 1.21/1.37 (~c0_1(a30)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[573, 3903])).
% 1.21/1.37 tff(3926,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3927,plain,
% 1.21/1.37 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a30) | c0_1(a30) | c3_1(a30)) <=> (c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3928,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30)))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3927])).
% 1.21/1.37 tff(3929,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3928, 3926])).
% 1.21/1.37 tff(3930,plain,
% 1.21/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a30) | c0_1(a30) | c3_1(a30))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3931,plain,
% 1.21/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 1.21/1.37 tff(3932,plain,
% 1.21/1.37 (c3_1(a30)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3931, 160, 3871, 3873, 3925, 3905, 3917, 3916, 3872, 13, 3924])).
% 1.21/1.37 tff(3933,plain,
% 1.21/1.37 (c2_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2041, 3932, 3736, 3915, 3914, 3905, 2, 3, 3904])).
% 1.21/1.37 tff(3934,plain,
% 1.21/1.37 (hskp25 | (~c2_1(a37))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2048, 160, 3895, 3915, 3914, 1023])).
% 1.21/1.37 tff(3935,plain,
% 1.21/1.37 (hskp25),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3934, 3933])).
% 1.21/1.37 tff(3936,plain,
% 1.21/1.37 (c2_1(a9)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[787, 3935])).
% 1.21/1.37 tff(3937,plain,
% 1.21/1.37 (c0_1(a9)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[803, 3935])).
% 1.21/1.37 tff(3938,plain,
% 1.21/1.37 (c1_1(a9)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[795, 3935])).
% 1.21/1.37 tff(3939,plain,
% 1.21/1.37 (~hskp2),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2056, 3938, 3937, 3915, 3914, 3936, 3933])).
% 1.21/1.37 tff(3940,plain,
% 1.21/1.37 (hskp14),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2359, 3939, 3869])).
% 1.21/1.37 tff(3941,plain,
% 1.21/1.37 (c2_1(a24)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[957, 3940])).
% 1.21/1.37 tff(3942,plain,
% 1.21/1.37 (~c1_1(a24)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[943, 3940])).
% 1.21/1.37 tff(3943,plain,
% 1.21/1.37 (~c0_1(a24)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[949, 3940])).
% 1.21/1.37 tff(3944,plain,
% 1.21/1.37 (c3_1(a24)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3823, 3943, 3867, 3942])).
% 1.21/1.37 tff(3945,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3831, 3944, 3943, 3913, 3942, 3941])).
% 1.21/1.37 tff(3946,plain,(c1_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(3947,plain,
% 1.21/1.37 (c1_1(a16)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3946, 2])).
% 1.21/1.37 tff(3948,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3949,plain,
% 1.21/1.37 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3950,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[3949])).
% 1.21/1.37 tff(3951,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[3950, 3948])).
% 1.21/1.37 tff(3952,plain,
% 1.21/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(3953,plain,
% 1.21/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[3952, 3951])).
% 1.21/1.37 tff(3954,plain,
% 1.21/1.37 (~c0_1(a3)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3953, 160, 2264, 2289, 3736, 24, 2, 406, 3947])).
% 1.21/1.37 tff(3955,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3322, 160, 2272, 2264, 1898, 1455, 1456, 45, 1])).
% 1.21/1.37 tff(3956,plain,((~hskp18) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(3957,plain,
% 1.21/1.37 (~hskp18),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3956, 3954])).
% 1.21/1.37 tff(3958,plain,
% 1.21/1.37 (hskp27),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3624, 84, 3954])).
% 1.21/1.37 tff(3959,plain,
% 1.21/1.37 (hskp17),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[717, 3958, 3736, 2, 3947, 24, 3957])).
% 1.21/1.37 tff(3960,plain,
% 1.21/1.37 (c2_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[298, 3959])).
% 1.21/1.37 tff(3961,plain,
% 1.21/1.37 (c0_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[290, 3959])).
% 1.21/1.37 tff(3962,plain,
% 1.21/1.37 (~c3_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2157, 160, 3961, 3960, 3736, 24, 2, 406, 3947])).
% 1.21/1.37 tff(3963,plain,
% 1.21/1.37 (~c1_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[71, 3959])).
% 1.21/1.37 tff(3964,plain,
% 1.21/1.37 (hskp4),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3464, 3962, 3961, 3963, 3960])).
% 1.21/1.37 tff(3965,plain,
% 1.21/1.37 (~c2_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[111, 3964])).
% 1.21/1.37 tff(3966,plain,
% 1.21/1.37 (hskp16),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3738, 84, 3736, 24])).
% 1.21/1.37 tff(3967,plain,
% 1.21/1.37 (~c2_1(a30)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[567, 3966])).
% 1.21/1.37 tff(3968,plain,
% 1.21/1.37 (~c0_1(a30)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[573, 3966])).
% 1.21/1.37 tff(3969,plain,
% 1.21/1.37 (c3_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[119, 3964])).
% 1.21/1.37 tff(3970,plain,
% 1.21/1.37 (c1_1(a6)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[127, 3964])).
% 1.21/1.37 tff(3971,plain,
% 1.21/1.37 (c3_1(a30)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2229, 160, 3961, 3970, 3969, 3963, 3968, 3967, 3965, 13, 3962])).
% 1.21/1.37 tff(3972,plain,
% 1.21/1.37 (hskp20 | c3_1(a31)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2032, 160, 84, 3961, 3960, 1134])).
% 1.21/1.37 tff(3973,plain,
% 1.21/1.37 (hskp20),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3972, 3962])).
% 1.21/1.37 tff(3974,plain,
% 1.21/1.37 (~c0_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1152, 3973])).
% 1.21/1.37 tff(3975,plain,
% 1.21/1.37 (~c3_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1146, 3973])).
% 1.21/1.37 tff(3976,plain,
% 1.21/1.37 (~c2_1(a37)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2246, 3975, 3947, 24, 2, 3974, 84])).
% 1.21/1.37 tff(3977,plain,
% 1.21/1.37 (hskp11),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[3842, 160, 2264, 2289, 3961, 3960, 1042, 3962, 3954])).
% 1.21/1.37 tff(3978,plain,
% 1.21/1.37 (~c3_1(a19)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1095, 3977])).
% 1.21/1.37 tff(3979,plain,
% 1.21/1.37 (~c1_1(a19)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1116, 3977])).
% 1.21/1.37 tff(3980,plain,
% 1.21/1.37 (c1_1(a30)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[561, 3966])).
% 1.21/1.37 tff(3981,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3982,plain,
% 1.21/1.37 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3983,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37)))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3982])).
% 1.21/1.38 tff(3984,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3983, 3981])).
% 1.21/1.38 tff(3985,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3986,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3985, 3984])).
% 1.21/1.38 tff(3987,plain,
% 1.21/1.38 (~c0_1(a19)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3986, 160, 3980, 3974, 3975, 3967, 3979, 3978, 13, 3976, 3971])).
% 1.21/1.38 tff(3988,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3923, 160, 2272, 2264, 3979, 3978, 45, 3954, 3987])).
% 1.21/1.38 tff(3989,plain,(hskp26 | c2_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(3990,plain,
% 1.21/1.38 (hskp26),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3989, 24, 2])).
% 1.21/1.38 tff(3991,plain,
% 1.21/1.38 (c3_1(a10)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[632, 3990])).
% 1.21/1.38 tff(3992,plain,
% 1.21/1.38 (c2_1(a10)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[624, 3990])).
% 1.21/1.38 tff(3993,plain,
% 1.21/1.38 (c0_1(a10)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[615, 3990])).
% 1.21/1.38 tff(3994,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[662, 160, 3993, 3992, 3991, 3736, 24, 2, 406, 3947])).
% 1.21/1.38 tff(3995,plain,(c2_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(3996,plain,
% 1.21/1.38 (c2_1(a16)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3995, 2])).
% 1.21/1.38 tff(3997,plain,
% 1.21/1.38 (~hskp9),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[537, 3996])).
% 1.21/1.38 tff(3998,plain,
% 1.21/1.38 (hskp8),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3630, 1, 3997])).
% 1.21/1.38 tff(3999,plain,
% 1.21/1.38 (hskp11),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3891, 160, 2264, 2289, 3736, 3996, 2, 1042, 1])).
% 1.21/1.38 tff(4000,plain,
% 1.21/1.38 (~c3_1(a19)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1095, 3999])).
% 1.21/1.38 tff(4001,plain,
% 1.21/1.38 (~c1_1(a19)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1116, 3999])).
% 1.21/1.38 tff(4002,plain,
% 1.21/1.38 (c0_1(a19)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3923, 160, 2272, 2264, 4001, 4000, 45, 1])).
% 1.21/1.38 tff(4003,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4004,plain,
% 1.21/1.38 ((hskp4 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4005,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[4004])).
% 1.21/1.38 tff(4006,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[4005, 4003])).
% 1.21/1.38 tff(4007,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(4008,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[4007, 4006])).
% 1.21/1.38 tff(4009,plain,
% 1.21/1.38 (hskp4 | (~c0_1(a19))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4008, 160, 2272, 2289, 4001, 4000, 584, 1])).
% 1.21/1.38 tff(4010,plain,
% 1.21/1.38 (hskp4),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4009, 4002])).
% 1.21/1.38 tff(4011,plain,
% 1.21/1.38 (~c2_1(a6)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[111, 4010])).
% 1.21/1.38 tff(4012,plain,
% 1.21/1.38 (~hskp26),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3894, 3999])).
% 1.21/1.38 tff(4013,plain,
% 1.21/1.38 (hskp20),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3912, 4012, 3736, 3996])).
% 1.21/1.38 tff(4014,plain,
% 1.21/1.38 (~c3_1(a37)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1146, 4013])).
% 1.21/1.38 tff(4015,plain,
% 1.21/1.38 (~c0_1(a37)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1152, 4013])).
% 1.21/1.38 tff(4016,plain,
% 1.21/1.38 (c3_1(a6)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[119, 4010])).
% 1.21/1.38 tff(4017,plain,
% 1.21/1.38 (c1_1(a6)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[127, 4010])).
% 1.21/1.38 tff(4018,assumption,(c0_1(a19)), introduced(assumption)).
% 1.21/1.38 tff(4019,assumption,(~c3_1(a19)), introduced(assumption)).
% 1.21/1.38 tff(4020,assumption,(~c1_1(a19)), introduced(assumption)).
% 1.21/1.38 tff(4021,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4022,plain,
% 1.21/1.38 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4023,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37)))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[4022])).
% 1.21/1.38 tff(4024,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37))),
% 1.21/1.38 inference(transitivity,[status(thm)],[4023, 4021])).
% 1.21/1.38 tff(4025,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(4026,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[4025, 4024])).
% 1.21/1.38 tff(4027,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4026, 160, 673, 672, 2039, 2038, 4020, 4019, 671, 13, 2037, 4018])).
% 1.21/1.38 tff(4028,plain,(c2_1(a37) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~c0_1(a19))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4029,plain,
% 1.21/1.38 (c2_1(a37)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4028, 4017, 4016, 4015, 4014, 4001, 4000, 4011, 4002])).
% 1.21/1.38 tff(4030,plain,
% 1.21/1.38 (hskp25 | (~c2_1(a37))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2048, 160, 4012, 4015, 4014, 1023])).
% 1.21/1.38 tff(4031,plain,
% 1.21/1.38 (hskp25),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4030, 4029])).
% 1.21/1.38 tff(4032,plain,
% 1.21/1.38 (c2_1(a9)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[787, 4031])).
% 1.21/1.38 tff(4033,plain,
% 1.21/1.38 (c0_1(a9)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[803, 4031])).
% 1.21/1.38 tff(4034,plain,
% 1.21/1.38 (c1_1(a9)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[795, 4031])).
% 1.21/1.38 tff(4035,plain,
% 1.21/1.38 (~hskp2),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2056, 4034, 4033, 4015, 4014, 4032, 4029])).
% 1.21/1.38 tff(4036,plain,
% 1.21/1.38 (hskp14),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2359, 4035, 3998])).
% 1.21/1.38 tff(4037,plain,
% 1.21/1.38 (c2_1(a24)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[957, 4036])).
% 1.21/1.38 tff(4038,plain,
% 1.21/1.38 (~c1_1(a24)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[943, 4036])).
% 1.21/1.38 tff(4039,plain,
% 1.21/1.38 (~c0_1(a24)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[949, 4036])).
% 1.21/1.38 tff(4040,plain,
% 1.21/1.38 (c3_1(a24)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3823, 4039, 1, 4038])).
% 1.21/1.38 tff(4041,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3831, 4040, 4039, 4013, 4038, 4037])).
% 1.21/1.38 tff(4042,plain,(c0_1(a3) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4043,plain,
% 1.21/1.38 (c0_1(a3)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4042, 2])).
% 1.21/1.38 tff(4044,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4045,plain,
% 1.21/1.38 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19))) <=> (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4046,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[4045])).
% 1.21/1.38 tff(4047,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[4046, 4044])).
% 1.21/1.38 tff(4048,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(4049,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[4048, 4047])).
% 1.21/1.38 tff(4050,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4049, 160, 2264, 2289, 2133, 2132, 2131, 1466, 2290])).
% 1.21/1.38 tff(4051,plain,((~hskp11) | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4052,plain,
% 1.21/1.38 (~hskp11),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4051, 4043])).
% 1.21/1.38 tff(4053,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4054,plain,
% 1.21/1.38 ((hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4055,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[4054])).
% 1.21/1.38 tff(4056,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[4055, 4053])).
% 1.21/1.38 tff(4057,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(4058,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[4057, 4056])).
% 1.21/1.38 tff(4059,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4058, 160, 4052, 2901, 2900, 3736, 2899, 3996, 2, 1042])).
% 1.21/1.38 tff(4060,plain,((~hskp19) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4061,plain,
% 1.21/1.38 (~hskp19),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4060, 2])).
% 1.21/1.38 tff(4062,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3424, 160, 805, 2272, 2264, 128, 120, 112, 779, 2290])).
% 1.21/1.38 tff(4063,plain,((~hskp4) | hskp19 | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4064,plain,
% 1.21/1.38 (~hskp4),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4063, 4061, 4043])).
% 1.21/1.38 tff(4065,plain,
% 1.21/1.38 (hskp17),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3382, 607, 4064])).
% 1.21/1.38 tff(4066,plain,
% 1.21/1.38 (c2_1(a31)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[298, 4065])).
% 1.21/1.38 tff(4067,plain,
% 1.21/1.38 (~c1_1(a31)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[71, 4065])).
% 1.21/1.38 tff(4068,plain,
% 1.21/1.38 (c0_1(a31)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[290, 4065])).
% 1.21/1.38 tff(4069,plain,
% 1.21/1.38 (c3_1(a31)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3464, 4068, 4064, 4067, 4066])).
% 1.21/1.38 tff(4070,plain,
% 1.21/1.38 (hskp17),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3382, 193, 607])).
% 1.21/1.38 tff(4071,plain,
% 1.21/1.38 (c0_1(a31)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[290, 4070])).
% 1.21/1.38 tff(4072,plain,
% 1.21/1.38 (~c1_1(a31)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[71, 4070])).
% 1.21/1.38 tff(4073,plain,
% 1.21/1.38 (c2_1(a31)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[298, 4070])).
% 1.21/1.38 tff(4074,plain,
% 1.21/1.38 (~hskp9),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2649, 606, 302, 2465, 607, 301])).
% 1.21/1.38 tff(4075,assumption,(hskp7), introduced(assumption)).
% 1.21/1.38 tff(4076,plain,
% 1.21/1.38 (~c2_1(a14)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[489, 4075])).
% 1.21/1.38 tff(4077,plain,
% 1.21/1.38 (c0_1(a14)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[516, 4075])).
% 1.21/1.38 tff(4078,plain,
% 1.21/1.38 (c1_1(a14)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2561, 160, 607, 606, 4077, 4076, 643])).
% 1.21/1.38 tff(4079,plain,
% 1.21/1.38 (c3_1(a14)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[497, 4075])).
% 1.21/1.38 tff(4080,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[504, 160, 73, 105, 4079, 4076, 104, 4078])).
% 1.21/1.38 tff(4081,plain,((~hskp7) | hskp24 | hskp9 | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4082,plain,
% 1.21/1.38 (~hskp7),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4081, 73, 105, 607, 606])).
% 1.21/1.38 tff(4083,plain,
% 1.21/1.38 (hskp13),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[483, 4082, 105])).
% 1.21/1.38 tff(4084,plain,
% 1.21/1.38 (~hskp0),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[474, 73, 105, 4083])).
% 1.21/1.38 tff(4085,plain,
% 1.21/1.38 (hskp23),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[235, 4084, 73])).
% 1.21/1.38 tff(4086,plain,
% 1.21/1.38 (~c1_1(a53)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[200, 4085])).
% 1.21/1.38 tff(4087,plain,
% 1.21/1.38 (~c0_1(a53)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[206, 4085])).
% 1.21/1.38 tff(4088,plain,
% 1.21/1.38 (~hskp3),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3001, 4084, 301, 302, 313, 607, 606])).
% 1.21/1.38 tff(4089,plain,
% 1.21/1.38 (~c2_1(a53)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[363, 160, 4088, 606, 4087, 4086, 23])).
% 1.21/1.38 tff(4090,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[323, 160, 4084, 301, 302, 4087, 4086, 313, 312, 4089])).
% 1.21/1.38 tff(4091,plain,(hskp24 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | hskp2 | hskp14 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4092,plain,
% 1.21/1.38 (hskp24),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4091, 606, 302, 313, 301, 607, 4074])).
% 1.21/1.38 tff(4093,plain,
% 1.21/1.38 (c3_1(a45)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2995, 314, 606, 302, 313, 2465, 301, 607])).
% 1.21/1.38 tff(4094,plain,
% 1.21/1.38 (~hskp22),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2416, 4093])).
% 1.21/1.38 tff(4095,plain,
% 1.21/1.38 (~hskp3),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3001, 314, 301, 302, 313, 607, 606])).
% 1.21/1.38 tff(4096,plain,
% 1.21/1.38 (~hskp19),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3005, 4095, 606, 4074, 2360])).
% 1.21/1.38 tff(4097,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3061, 4096, 4094, 607, 606, 4074, 2465, 302, 313, 4092])).
% 1.21/1.38 tff(4098,plain,(hskp0 | hskp14 | hskp2 | (~c3_1(a31)) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4099,plain,
% 1.21/1.38 (hskp0),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4098, 606, 607, 2624, 4073, 4072, 4071])).
% 1.21/1.38 tff(4100,plain,
% 1.21/1.38 (~c2_1(a1)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[241, 4099])).
% 1.21/1.38 tff(4101,plain,
% 1.21/1.38 (~c0_1(a1)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[262, 4099])).
% 1.21/1.38 tff(4102,plain,
% 1.21/1.38 (~hskp9),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2649, 606, 4073, 2624, 607, 4071])).
% 1.21/1.38 tff(4103,plain,
% 1.21/1.38 (hskp24),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4091, 606, 4073, 4072, 4071, 607, 4102])).
% 1.21/1.38 tff(4104,plain,
% 1.21/1.38 (hskp0),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4098, 606, 607, 2465, 302, 313, 301])).
% 1.21/1.38 tff(4105,plain,
% 1.21/1.38 (~c2_1(a1)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[241, 4104])).
% 1.21/1.38 tff(4106,plain,
% 1.21/1.38 (~c0_1(a1)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[262, 4104])).
% 1.21/1.38 tff(4107,plain,
% 1.21/1.38 (c3_1(a1)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[249, 4104])).
% 1.21/1.38 tff(4108,plain,
% 1.21/1.38 (c3_1(a3)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2288, 4092])).
% 1.21/1.38 tff(4109,plain,
% 1.21/1.38 (c2_1(a3)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2263, 4092])).
% 1.21/1.38 tff(4110,plain,
% 1.21/1.38 (c1_1(a3)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2271, 4092])).
% 1.21/1.38 tff(4111,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4112,plain,
% 1.21/1.38 ((hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1))) <=> (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4113,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[4112])).
% 1.21/1.38 tff(4114,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[4113, 4111])).
% 1.21/1.38 tff(4115,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(4116,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[4115, 4114])).
% 1.21/1.38 tff(4117,plain,
% 1.21/1.38 (hskp6),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4116, 160, 4110, 4109, 4108, 4107, 4106, 4105, 1202])).
% 1.21/1.38 tff(4118,plain,
% 1.21/1.38 (c0_1(a45)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2705, 2419, 301, 4074, 313, 2465, 2360, 4117, 302])).
% 1.21/1.38 tff(4119,plain,
% 1.21/1.38 (c1_1(a45)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2886, 2419, 606, 2465, 301, 302, 4118, 607])).
% 1.21/1.38 tff(4120,plain,
% 1.21/1.38 (c2_1(a45)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2895, 4119, 301, 302, 2465, 2419, 4118])).
% 1.21/1.38 tff(4121,plain,
% 1.21/1.38 (~hskp22),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2410, 4119])).
% 1.21/1.38 tff(4122,plain,
% 1.21/1.38 (hskp19),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3061, 4121, 607, 606, 4074, 2465, 302, 313, 4092])).
% 1.21/1.38 tff(4123,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2910, 4122, 4120, 2863, 2419, 4118])).
% 1.21/1.38 tff(4124,plain,(c3_1(a45) | hskp14 | hskp2 | (~c3_1(a31)) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4125,plain,
% 1.21/1.38 (c3_1(a45)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4124, 606, 607, 2624, 4073, 4072, 4071])).
% 1.21/1.38 tff(4126,plain,
% 1.21/1.38 (~hskp22),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2416, 4125])).
% 1.21/1.38 tff(4127,plain,
% 1.21/1.38 (hskp19),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3061, 4126, 607, 606, 4102, 2624, 4073, 4072, 4103])).
% 1.21/1.38 tff(4128,plain,
% 1.21/1.38 (hskp3),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3005, 4127, 606, 4102, 2360])).
% 1.21/1.38 tff(4129,plain,
% 1.21/1.38 (~c3_1(a5)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[867, 4128])).
% 1.21/1.38 tff(4130,plain,
% 1.21/1.38 (~c2_1(a5)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[331, 4128])).
% 1.21/1.38 tff(4131,plain,
% 1.21/1.38 (~c1_1(a5)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[337, 4128])).
% 1.21/1.38 tff(4132,plain,
% 1.21/1.38 (c3_1(a1)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[249, 4099])).
% 1.21/1.38 tff(4133,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4134,plain,
% 1.21/1.38 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5)) <=> (c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4135,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5)))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[4134])).
% 1.21/1.38 tff(4136,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5))),
% 1.21/1.38 inference(transitivity,[status(thm)],[4135, 4133])).
% 1.21/1.38 tff(4137,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(4138,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[4137, 4136])).
% 1.21/1.38 tff(4139,plain,
% 1.21/1.38 (c0_1(a5)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4138, 160, 4132, 4131, 4130, 4129, 4101, 4100, 55])).
% 1.21/1.38 tff(4140,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[853, 160, 607, 606, 4131, 4130, 643, 4139])).
% 1.21/1.38 tff(4141,plain,(hskp2 | hskp14 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4142,plain,
% 1.21/1.38 (hskp2),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4141, 607, 4064])).
% 1.21/1.38 tff(4143,plain,
% 1.21/1.38 (~c3_1(a4)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[370, 4142])).
% 1.21/1.38 tff(4144,plain,
% 1.21/1.38 (~c2_1(a4)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[384, 4142])).
% 1.21/1.38 tff(4145,plain,
% 1.21/1.38 (c1_1(a4)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[378, 4142])).
% 1.21/1.38 tff(4146,plain,
% 1.21/1.38 (~c0_1(a4)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[413, 160, 4068, 4066, 4145, 4144, 4143, 406, 4069])).
% 1.21/1.38 tff(4147,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4148,plain,
% 1.21/1.38 ((hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7))) <=> (hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(4149,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[4148])).
% 1.21/1.38 tff(4150,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[4149, 4147])).
% 1.21/1.38 tff(4151,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(4152,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 1.21/1.38 tff(4153,plain,
% 1.21/1.38 (~c2_1(a7)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4152, 160, 4052, 3736, 1347, 3996, 2, 1318, 1042])).
% 1.21/1.38 tff(4154,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3510, 160, 4061, 2272, 2264, 1326, 1347, 779, 4043, 4153])).
% 1.21/1.38 tff(4155,plain,((~hskp5) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(4156,plain,
% 1.21/1.38 (~hskp5),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[4155, 2])).
% 1.21/1.38 tff(4157,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4158,plain,
% 1.21/1.39 ((hskp5 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4))) <=> (hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4159,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[4158])).
% 1.21/1.39 tff(4160,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[4159, 4157])).
% 1.21/1.39 tff(4161,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(4162,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 1.21/1.39 tff(4163,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4162, 160, 4156, 4145, 3996, 2, 4144, 1311, 3947, 4146])).
% 1.21/1.39 tff(4164,plain,(hskp14 | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4165,plain,
% 1.21/1.39 (hskp14),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4164, 2])).
% 1.21/1.39 tff(4166,plain,
% 1.21/1.39 (~c1_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[943, 4165])).
% 1.21/1.39 tff(4167,plain,
% 1.21/1.39 (c2_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[957, 4165])).
% 1.21/1.39 tff(4168,plain,
% 1.21/1.39 (c3_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3850, 4167, 4043, 4166])).
% 1.21/1.39 tff(4169,plain,
% 1.21/1.39 (~c0_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[949, 4165])).
% 1.21/1.39 tff(4170,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4171,plain,
% 1.21/1.39 ((hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24))) <=> (hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4172,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[4171])).
% 1.21/1.39 tff(4173,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[4172, 4170])).
% 1.21/1.39 tff(4174,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(4175,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4174, 4173])).
% 1.21/1.39 tff(4176,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4175, 160, 4052, 4167, 3736, 4169, 3996, 2, 1042, 4168])).
% 1.21/1.39 tff(4177,plain,(c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4178,plain,
% 1.21/1.39 (~hskp9),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[531, 4177])).
% 1.21/1.39 tff(4179,plain,
% 1.21/1.39 (hskp8 | c0_1(a3)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3630, 4178])).
% 1.21/1.39 tff(4180,plain,
% 1.21/1.39 (hskp8),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4179, 1])).
% 1.21/1.39 tff(4181,plain,
% 1.21/1.39 (~c3_1(a31)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3484, 2281, 1, 2902, 72])).
% 1.21/1.39 tff(4182,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3842, 160, 2902, 2264, 2289, 3461, 2281, 1042, 4181, 1])).
% 1.21/1.39 tff(4183,plain,((~hskp17) | hskp11 | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4184,plain,
% 1.21/1.39 (hskp11),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4183, 66, 1])).
% 1.21/1.39 tff(4185,plain,
% 1.21/1.39 (~c3_1(a31)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2541, 4184, 2281, 3461])).
% 1.21/1.39 tff(4186,plain,
% 1.21/1.39 (hskp8),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3630, 1, 4178])).
% 1.21/1.39 tff(4187,plain,
% 1.21/1.39 (~hskp18),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3956, 1])).
% 1.21/1.39 tff(4188,plain,
% 1.21/1.39 (hskp18 | hskp17 | (~c3_1(a8))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1274, 160, 2660, 1250, 684])).
% 1.21/1.39 tff(4189,plain,
% 1.21/1.39 (~c3_1(a8)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4188, 595, 4187])).
% 1.21/1.39 tff(4190,plain,
% 1.21/1.39 (~c2_1(a15)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[175, 4186])).
% 1.21/1.39 tff(4191,plain,
% 1.21/1.39 (c0_1(a15)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[183, 4186])).
% 1.21/1.39 tff(4192,plain,
% 1.21/1.39 (hskp17 | (~c3_1(a15))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1931, 160, 4187, 4191, 4190, 684])).
% 1.21/1.39 tff(4193,plain,
% 1.21/1.39 (~c3_1(a15)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4192, 595])).
% 1.21/1.39 tff(4194,plain,
% 1.21/1.39 (~c1_1(a15)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[189, 4186])).
% 1.21/1.39 tff(4195,plain,
% 1.21/1.39 (hskp17 | (~c3_1(a15))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1931, 160, 674, 192, 191, 684])).
% 1.21/1.39 tff(4196,plain,
% 1.21/1.39 (~c3_1(a15)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4195, 595])).
% 1.21/1.39 tff(4197,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4198,plain,
% 1.21/1.39 (((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15))) <=> (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4199,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[4198])).
% 1.21/1.39 tff(4200,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[4199, 4197])).
% 1.21/1.39 tff(4201,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(4202,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4201, 4200])).
% 1.21/1.39 tff(4203,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4202, 160, 701, 693, 192, 388, 191, 407, 387, 406, 4196, 708])).
% 1.21/1.39 tff(4204,plain,((~hskp27) | (~c0_1(a15)) | (~c1_1(a4)) | c2_1(a15) | c2_1(a4) | c3_1(a4) | hskp18 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4205,plain,
% 1.21/1.39 (~hskp27),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4204, 595, 388, 4190, 407, 387, 4187, 4191])).
% 1.21/1.39 tff(4206,plain,
% 1.21/1.39 (^[U: $i] : refl((hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(4207,plain,
% 1.21/1.39 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[4206])).
% 1.21/1.39 tff(4208,plain,
% 1.21/1.39 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4209,plain,
% 1.21/1.39 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp7) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp7) <=> (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp7) <=> (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(4210,plain,
% 1.21/1.39 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp7) <=> ![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[4209])).
% 1.21/1.39 tff(4211,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.21/1.39 tff(4212,plain,
% 1.21/1.39 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4211, 4210])).
% 1.21/1.39 tff(4213,plain,
% 1.21/1.39 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4212, 4208])).
% 1.21/1.39 tff(4214,plain,(
% 1.21/1.39 ![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.39 inference(skolemize,[status(sab)],[4213])).
% 1.21/1.39 tff(4215,plain,
% 1.21/1.39 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4214, 4207])).
% 1.21/1.39 tff(4216,plain,
% 1.21/1.39 (((~![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp7 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4217,plain,
% 1.21/1.39 ((~![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(4218,plain,
% 1.21/1.39 ((~![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp7 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4217, 4216])).
% 1.21/1.39 tff(4219,plain,
% 1.21/1.39 (hskp27 | hskp7 | c0_1(a3)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4218, 160, 2272, 2264, 4215])).
% 1.21/1.39 tff(4220,plain,
% 1.21/1.39 (hskp7),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4219, 4205, 1])).
% 1.21/1.39 tff(4221,plain,
% 1.21/1.39 (~c2_1(a14)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[489, 4220])).
% 1.21/1.39 tff(4222,plain,
% 1.21/1.39 (c3_1(a14)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[497, 4220])).
% 1.21/1.39 tff(4223,plain,
% 1.21/1.39 (c0_1(a14)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[516, 4220])).
% 1.21/1.39 tff(4224,plain,
% 1.21/1.39 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4225,plain,
% 1.21/1.39 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14))) <=> (hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4226,plain,
% 1.21/1.39 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[4225])).
% 1.21/1.39 tff(4227,plain,
% 1.21/1.39 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[4226, 4224])).
% 1.21/1.39 tff(4228,plain,
% 1.21/1.39 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(4229,plain,
% 1.21/1.39 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4228, 4227])).
% 1.21/1.39 tff(4230,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4229, 160, 4187, 595, 4223, 4222, 4221, 684])).
% 1.21/1.39 tff(4231,plain,(hskp17 | c0_1(a3) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4232,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4231, 1748, 1749, 1, 595, 1747])).
% 1.21/1.39 tff(4233,plain,((~hskp2) | c0_1(a3) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4234,plain,
% 1.21/1.39 (~hskp2),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4233, 595, 1])).
% 1.21/1.39 tff(4235,plain,
% 1.21/1.39 (hskp14),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2359, 4234, 4186])).
% 1.21/1.39 tff(4236,plain,
% 1.21/1.39 (~c1_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[943, 4235])).
% 1.21/1.39 tff(4237,plain,
% 1.21/1.39 (~c0_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[949, 4235])).
% 1.21/1.39 tff(4238,plain,
% 1.21/1.39 (c2_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[957, 4235])).
% 1.21/1.39 tff(4239,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4240,plain,
% 1.21/1.39 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4241,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[4240])).
% 1.21/1.39 tff(4242,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[4241, 4239])).
% 1.21/1.39 tff(4243,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(4244,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4243, 4242])).
% 1.21/1.39 tff(4245,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4244, 160, 4238, 4191, 1251, 4237, 4236, 4194, 1250, 425, 4193, 4189])).
% 1.21/1.39 tff(4246,plain,(hskp17 | (~c1_1(a8)) | c2_1(a8) | c0_1(a3) | (~c0_1(a8))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4247,plain,
% 1.21/1.39 (hskp17),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4246, 1, 1250, 1251, 2660])).
% 1.21/1.39 tff(4248,plain,
% 1.21/1.39 (c2_1(a31)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[298, 4247])).
% 1.21/1.39 tff(4249,plain,
% 1.21/1.39 (~c1_1(a31)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[71, 4247])).
% 1.21/1.39 tff(4250,plain,
% 1.21/1.39 (c0_1(a31)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[290, 4247])).
% 1.21/1.39 tff(4251,plain,
% 1.21/1.39 (hskp11),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4183, 4247, 1])).
% 1.21/1.39 tff(4252,plain,
% 1.21/1.39 (~c3_1(a31)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2541, 4251, 4248, 4250])).
% 1.21/1.39 tff(4253,plain,
% 1.21/1.39 (hskp4),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3464, 4252, 4250, 4249, 4248])).
% 1.21/1.39 tff(4254,plain,
% 1.21/1.39 (c1_1(a6)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[127, 4253])).
% 1.21/1.39 tff(4255,plain,
% 1.21/1.39 (~c2_1(a6)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[111, 4253])).
% 1.21/1.39 tff(4256,plain,
% 1.21/1.39 (~c3_1(a19)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1095, 4251])).
% 1.21/1.39 tff(4257,plain,
% 1.21/1.39 (~c1_1(a19)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1116, 4251])).
% 1.21/1.39 tff(4258,plain,
% 1.21/1.39 (~hskp26),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3894, 4251])).
% 1.21/1.39 tff(4259,plain,
% 1.21/1.39 (hskp20),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2032, 160, 4258, 4250, 4248, 1134, 4252])).
% 1.21/1.39 tff(4260,plain,
% 1.21/1.39 (~c3_1(a37)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1146, 4259])).
% 1.21/1.39 tff(4261,plain,
% 1.21/1.39 (~c0_1(a37)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1152, 4259])).
% 1.21/1.39 tff(4262,plain,
% 1.21/1.39 (c3_1(a6)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[119, 4253])).
% 1.21/1.39 tff(4263,plain,
% 1.21/1.39 (c0_1(a19)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3923, 160, 2272, 2264, 4257, 4256, 45, 1])).
% 1.21/1.39 tff(4264,plain,
% 1.21/1.39 (c2_1(a37)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4028, 4263, 4262, 4261, 4260, 4257, 4256, 4255, 4254])).
% 1.21/1.39 tff(4265,plain,
% 1.21/1.39 (hskp25),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2048, 160, 4258, 4261, 4260, 1023, 4264])).
% 1.21/1.39 tff(4266,plain,
% 1.21/1.39 (c2_1(a9)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[787, 4265])).
% 1.21/1.39 tff(4267,plain,
% 1.21/1.39 (c0_1(a9)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[803, 4265])).
% 1.21/1.39 tff(4268,plain,
% 1.21/1.39 (c1_1(a9)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[795, 4265])).
% 1.21/1.39 tff(4269,plain,
% 1.21/1.39 (~hskp2),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2056, 4268, 4267, 4261, 4260, 4266, 4264])).
% 1.21/1.39 tff(4270,plain,
% 1.21/1.39 (hskp14),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2359, 4269, 4186])).
% 1.21/1.39 tff(4271,plain,
% 1.21/1.39 (c2_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[957, 4270])).
% 1.21/1.39 tff(4272,plain,
% 1.21/1.39 (~c1_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[943, 4270])).
% 1.21/1.39 tff(4273,plain,
% 1.21/1.39 (~c0_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[949, 4270])).
% 1.21/1.39 tff(4274,plain,
% 1.21/1.39 (c3_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3823, 4273, 1, 4272])).
% 1.21/1.39 tff(4275,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3831, 4274, 4273, 4259, 4272, 4271])).
% 1.21/1.39 tff(4276,plain,(c0_1(a3) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4277,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4276, 1240, 1248, 1, 1268])).
% 1.21/1.39 tff(4278,plain,((~hskp6) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4279,plain,
% 1.21/1.39 (~hskp6),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4278, 1])).
% 1.21/1.39 tff(4280,plain,
% 1.21/1.39 (~hskp26),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3894, 4184])).
% 1.21/1.39 tff(4281,plain,
% 1.21/1.39 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4282,plain,
% 1.21/1.39 ((hskp26 | hskp6 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31))) <=> (hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4283,plain,
% 1.21/1.39 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[4282])).
% 1.21/1.39 tff(4284,plain,
% 1.21/1.39 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.21/1.39 inference(transitivity,[status(thm)],[4283, 4281])).
% 1.21/1.39 tff(4285,plain,
% 1.21/1.39 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(4286,plain,
% 1.21/1.39 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[4285, 4284])).
% 1.21/1.39 tff(4287,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4286, 160, 4280, 4279, 2281, 72, 1184, 4185])).
% 1.21/1.39 tff(4288,plain,((~hskp17) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(4289,plain,
% 1.21/1.39 (~hskp17),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4288, 1])).
% 1.21/1.39 tff(4290,plain,
% 1.21/1.39 (~hskp2),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[4233, 4289, 1])).
% 1.21/1.39 tff(4291,plain,
% 1.21/1.39 (hskp14),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2359, 4290, 4180])).
% 1.21/1.39 tff(4292,plain,
% 1.21/1.39 (~c1_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[943, 4291])).
% 1.21/1.39 tff(4293,plain,
% 1.21/1.39 (~c0_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[949, 4291])).
% 1.21/1.39 tff(4294,plain,
% 1.21/1.39 (c3_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3823, 4293, 1, 4292])).
% 1.21/1.39 tff(4295,plain,
% 1.21/1.39 (c2_1(a24)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[957, 4291])).
% 1.21/1.39 tff(4296,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4297,plain,
% 1.21/1.39 ((hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(4298,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[4297])).
% 1.21/1.39 tff(4299,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[4298, 4296])).
% 1.21/1.39 tff(4300,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(4301,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 1.21/1.40 tff(4302,plain,
% 1.21/1.40 (hskp10),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4301, 160, 2272, 2289, 4295, 4292, 1053, 1, 4294])).
% 1.21/1.40 tff(4303,plain,
% 1.21/1.40 (~c3_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1066, 4302])).
% 1.21/1.40 tff(4304,plain,
% 1.21/1.40 (c2_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1074, 4302])).
% 1.21/1.40 tff(4305,plain,
% 1.21/1.40 (c0_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1082, 4302])).
% 1.21/1.40 tff(4306,plain,
% 1.21/1.40 (hskp11),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1089, 160, 4295, 4305, 4304, 4293, 4303, 1042, 4294])).
% 1.21/1.40 tff(4307,plain,
% 1.21/1.40 (~hskp20),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3831, 4294, 4293, 4292, 4295])).
% 1.21/1.40 tff(4308,plain,
% 1.21/1.40 (hskp26),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1140, 160, 4307, 4305, 4304, 4303, 1134])).
% 1.21/1.40 tff(4309,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3894, 4308, 4306])).
% 1.21/1.40 tff(4310,plain,(c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4311,plain,
% 1.21/1.40 (~hskp11),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4051, 2290])).
% 1.21/1.40 tff(4312,assumption,(hskp10), introduced(assumption)).
% 1.21/1.40 tff(4313,plain,
% 1.21/1.40 (~c3_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1066, 4312])).
% 1.21/1.40 tff(4314,plain,
% 1.21/1.40 (c2_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1074, 4312])).
% 1.21/1.40 tff(4315,plain,
% 1.21/1.40 (c0_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1082, 4312])).
% 1.21/1.40 tff(4316,assumption,(c3_1(a33)), introduced(assumption)).
% 1.21/1.40 tff(4317,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2548, 160, 2902, 3547, 4316, 4315, 4314, 3546, 4313, 1042])).
% 1.21/1.40 tff(4318,plain,((~hskp10) | hskp11 | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a33)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4319,plain,
% 1.21/1.40 (~hskp10),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4318, 2901, 4311, 2900, 2899])).
% 1.21/1.40 tff(4320,plain,
% 1.21/1.40 (hskp10 | hskp6 | (~c0_1(a3))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2751, 160, 2272, 2264, 2745])).
% 1.21/1.40 tff(4321,plain,
% 1.21/1.40 (hskp6),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4320, 4319, 2290])).
% 1.21/1.40 tff(4322,plain,
% 1.21/1.40 (~c2_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1239, 4321])).
% 1.21/1.40 tff(4323,plain,
% 1.21/1.40 (c1_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1247, 4321])).
% 1.21/1.40 tff(4324,plain,
% 1.21/1.40 (c0_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1267, 4321])).
% 1.21/1.40 tff(4325,plain,
% 1.21/1.40 (c0_1(a3)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4276, 1250, 1251, 2660])).
% 1.21/1.40 tff(4326,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4327,plain,
% 1.21/1.40 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4328,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[4327])).
% 1.21/1.40 tff(4329,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[4328, 4326])).
% 1.21/1.40 tff(4330,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(4331,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[4330, 4329])).
% 1.21/1.40 tff(4332,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4331, 160, 2264, 2289, 2660, 1251, 1250, 406, 4325, 1249])).
% 1.21/1.40 tff(4333,plain,(c3_1(a8) | (~c0_1(a8)) | (~c1_1(a8)) | c2_1(a8)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4334,plain,
% 1.21/1.40 (c3_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4333, 4324, 4323, 4322])).
% 1.21/1.40 tff(4335,plain,
% 1.21/1.40 (hskp18),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1274, 160, 595, 4324, 4322, 684, 4334])).
% 1.21/1.40 tff(4336,plain,
% 1.21/1.40 (~c3_1(a32)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[888, 4335])).
% 1.21/1.40 tff(4337,plain,
% 1.21/1.40 (~c1_1(a32)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[882, 4335])).
% 1.21/1.40 tff(4338,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4339,plain,
% 1.21/1.40 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32))) <=> (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4340,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[4339])).
% 1.21/1.40 tff(4341,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[4340, 4338])).
% 1.21/1.40 tff(4342,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(4343,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[4342, 4341])).
% 1.21/1.40 tff(4344,plain,
% 1.21/1.40 (~c2_1(a32)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4343, 160, 2264, 2289, 4337, 4336, 1466, 2290])).
% 1.21/1.40 tff(4345,plain,
% 1.21/1.40 (~c0_1(a32)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1283, 4335])).
% 1.21/1.40 tff(4346,plain,
% 1.21/1.40 (~c1_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1374, 160, 2901, 2899, 4345, 4337, 4336, 45])).
% 1.21/1.40 tff(4347,plain,
% 1.21/1.40 (hskp1),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1399, 160, 2901, 2900, 4345, 4337, 4336, 1385, 4346])).
% 1.21/1.40 tff(4348,plain,
% 1.21/1.40 (~c3_1(a2)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2318, 4347])).
% 1.21/1.40 tff(4349,plain,
% 1.21/1.40 (~c0_1(a2)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1405, 4347])).
% 1.21/1.40 tff(4350,plain,
% 1.21/1.40 (c2_1(a2)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1413, 4347])).
% 1.21/1.40 tff(4351,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4352,plain,
% 1.21/1.40 (((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a32) | c1_1(a32) | c2_1(a32) | c2_1(a32) | c0_1(a32) | c3_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4353,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a32) | c1_1(a32) | c2_1(a32) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[4352])).
% 1.21/1.40 tff(4354,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a32) | c1_1(a32) | c2_1(a32) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32))),
% 1.21/1.40 inference(transitivity,[status(thm)],[4353, 4351])).
% 1.21/1.40 tff(4355,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a32) | c1_1(a32) | c2_1(a32) | c2_1(a32) | c0_1(a32) | c3_1(a32))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(4356,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32)),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[4355, 4354])).
% 1.21/1.40 tff(4357,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4356, 160, 4350, 4345, 4337, 4336, 4349, 4348, 2312, 4344])).
% 1.21/1.40 tff(4358,plain,((~hskp19) | (~c0_1(a3)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4359,plain,
% 1.21/1.40 (~hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4358, 595, 2290])).
% 1.21/1.40 tff(4360,plain,
% 1.21/1.40 (~hskp4),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4063, 4359, 2290])).
% 1.21/1.40 tff(4361,plain,
% 1.21/1.40 (hskp14),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3382, 4360, 595])).
% 1.21/1.40 tff(4362,plain,
% 1.21/1.40 (~c1_1(a24)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[943, 4361])).
% 1.21/1.40 tff(4363,plain,
% 1.21/1.40 (c2_1(a24)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[957, 4361])).
% 1.21/1.40 tff(4364,plain,
% 1.21/1.40 (c3_1(a24)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3850, 4363, 2290, 4362])).
% 1.21/1.40 tff(4365,plain,
% 1.21/1.40 (hskp8),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[282, 4360, 595])).
% 1.21/1.40 tff(4366,plain,
% 1.21/1.40 (~c2_1(a15)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[175, 4365])).
% 1.21/1.40 tff(4367,plain,
% 1.21/1.40 (~c1_1(a15)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[189, 4365])).
% 1.21/1.40 tff(4368,plain,
% 1.21/1.40 (~c0_1(a24)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[949, 4361])).
% 1.21/1.40 tff(4369,plain,
% 1.21/1.40 (c0_1(a15)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[183, 4365])).
% 1.21/1.40 tff(4370,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3392, 160, 4360, 4369, 4368, 4362, 4367, 4366, 65, 4364])).
% 1.21/1.40 tff(4371,plain,(hskp17 | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4372,plain,
% 1.21/1.40 (hskp17),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4371, 4310])).
% 1.21/1.40 tff(4373,plain,
% 1.21/1.40 (c2_1(a31)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[298, 4372])).
% 1.21/1.40 tff(4374,plain,
% 1.21/1.40 (~c1_1(a31)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[71, 4372])).
% 1.21/1.40 tff(4375,plain,
% 1.21/1.40 (c3_1(a31)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2301, 4374, 4310, 4373])).
% 1.21/1.40 tff(4376,plain,
% 1.21/1.40 (hskp10),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4320, 1174, 4310])).
% 1.21/1.40 tff(4377,plain,
% 1.21/1.40 (~c3_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1066, 4376])).
% 1.21/1.40 tff(4378,plain,
% 1.21/1.40 (c2_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1074, 4376])).
% 1.21/1.40 tff(4379,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4380,plain,
% 1.21/1.40 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4381,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[4380])).
% 1.21/1.40 tff(4382,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[4381, 4379])).
% 1.21/1.40 tff(4383,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(4384,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[4383, 4382])).
% 1.21/1.40 tff(4385,plain,
% 1.21/1.40 (c1_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4384, 160, 2264, 2289, 4378, 4377, 1466, 4310])).
% 1.21/1.40 tff(4386,plain,
% 1.21/1.40 (~hskp8),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2359, 607, 606])).
% 1.21/1.40 tff(4387,plain,
% 1.21/1.40 (hskp4),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4141, 607, 606])).
% 1.21/1.40 tff(4388,plain,
% 1.21/1.40 (hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4063, 4387, 4310])).
% 1.21/1.40 tff(4389,plain,
% 1.21/1.40 ((~hskp19) | hskp3 | hskp2 | hskp8),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3005, 4178])).
% 1.21/1.40 tff(4390,plain,
% 1.21/1.40 (hskp3),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4389, 4388, 606, 4386])).
% 1.21/1.40 tff(4391,plain,
% 1.21/1.40 (~c1_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[337, 4390])).
% 1.21/1.40 tff(4392,plain,
% 1.21/1.40 (~c3_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[867, 4390])).
% 1.21/1.40 tff(4393,plain,
% 1.21/1.40 (c0_1(a31)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[290, 4372])).
% 1.21/1.40 tff(4394,plain,
% 1.21/1.40 (~c2_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[331, 4390])).
% 1.21/1.40 tff(4395,assumption,(~c0_1(a5)), introduced(assumption)).
% 1.21/1.40 tff(4396,plain,
% 1.21/1.40 (hskp0 | c0_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[354, 160, 301, 302, 313, 969, 1453, 312])).
% 1.21/1.40 tff(4397,plain,
% 1.21/1.40 (hskp0),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4396, 4395])).
% 1.21/1.40 tff(4398,plain,
% 1.21/1.40 (~c2_1(a1)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[241, 4397])).
% 1.21/1.40 tff(4399,plain,
% 1.21/1.40 (~c0_1(a1)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[262, 4397])).
% 1.21/1.40 tff(4400,plain,
% 1.21/1.40 (c3_1(a1)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[249, 4397])).
% 1.21/1.40 tff(4401,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4138, 160, 4400, 969, 1453, 968, 4399, 4398, 55, 4395])).
% 1.21/1.40 tff(4402,plain,(c0_1(a5) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4403,plain,
% 1.21/1.40 (c0_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4402, 4394, 4393, 4392, 4391, 4373, 4374])).
% 1.21/1.40 tff(4404,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[853, 160, 607, 606, 4391, 4394, 643, 4403])).
% 1.21/1.40 tff(4405,plain,(hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4406,plain,
% 1.21/1.40 (hskp14),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4405, 606])).
% 1.21/1.40 tff(4407,plain,
% 1.21/1.40 (~c1_1(a24)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[943, 4406])).
% 1.21/1.40 tff(4408,plain,
% 1.21/1.40 (~c0_1(a24)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[949, 4406])).
% 1.21/1.40 tff(4409,plain,
% 1.21/1.40 (c2_1(a24)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[957, 4406])).
% 1.21/1.40 tff(4410,plain,
% 1.21/1.40 (hskp3),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[964, 160, 606, 4409, 4408, 4407, 23])).
% 1.21/1.40 tff(4411,plain,
% 1.21/1.40 (~c1_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[337, 4410])).
% 1.21/1.40 tff(4412,plain,
% 1.21/1.40 (~c3_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[867, 4410])).
% 1.21/1.40 tff(4413,plain,
% 1.21/1.40 (~c2_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[331, 4410])).
% 1.21/1.40 tff(4414,plain,
% 1.21/1.40 (c0_1(a5)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4402, 4413, 4393, 4412, 4411, 4373, 4374])).
% 1.21/1.40 tff(4415,plain,
% 1.21/1.40 (c3_1(a24)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3850, 4409, 4310, 4407])).
% 1.21/1.40 tff(4416,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4417,plain,
% 1.21/1.40 ((hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24))) <=> (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4418,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[4417])).
% 1.21/1.40 tff(4419,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[4418, 4416])).
% 1.21/1.40 tff(4420,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(4421,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[4420, 4419])).
% 1.21/1.40 tff(4422,plain,
% 1.21/1.40 (hskp4),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4421, 160, 4408, 4407, 4411, 4413, 65, 4414, 4415])).
% 1.21/1.40 tff(4423,plain,
% 1.21/1.40 (hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4063, 4422, 4310])).
% 1.21/1.40 tff(4424,plain,
% 1.21/1.40 (~c0_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[819, 4423])).
% 1.21/1.40 tff(4425,plain,
% 1.21/1.40 (c2_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[827, 4423])).
% 1.21/1.40 tff(4426,plain,
% 1.21/1.40 (~hskp11),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4051, 4310])).
% 1.21/1.40 tff(4427,plain,
% 1.21/1.40 (c3_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1392, 4423])).
% 1.21/1.40 tff(4428,plain,
% 1.21/1.40 (~hskp10),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4318, 4427, 4426, 4425, 4424])).
% 1.21/1.40 tff(4429,plain,
% 1.21/1.40 (hskp6),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4320, 4428, 4310])).
% 1.21/1.40 tff(4430,plain,
% 1.21/1.40 (~c2_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1239, 4429])).
% 1.21/1.40 tff(4431,plain,
% 1.21/1.40 (c1_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1247, 4429])).
% 1.21/1.40 tff(4432,plain,
% 1.21/1.40 (c0_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1267, 4429])).
% 1.21/1.40 tff(4433,plain,
% 1.21/1.40 (c3_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4333, 4432, 4431, 4430])).
% 1.21/1.40 tff(4434,plain,
% 1.21/1.40 (hskp13),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3820, 160, 4393, 4374, 4411, 4413, 1502, 4375, 4414])).
% 1.21/1.40 tff(4435,plain,
% 1.21/1.40 (~c3_1(a22)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[449, 4434])).
% 1.21/1.40 tff(4436,plain,
% 1.21/1.40 (~c2_1(a22)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[455, 4434])).
% 1.21/1.40 tff(4437,plain,
% 1.21/1.40 (~c0_1(a22)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[461, 4434])).
% 1.21/1.40 tff(4438,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4439,plain,
% 1.21/1.40 (((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4440,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[4439])).
% 1.21/1.40 tff(4441,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[4440, 4438])).
% 1.21/1.40 tff(4442,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(4443,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[4442, 4441])).
% 1.21/1.40 tff(4444,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4443, 160, 4431, 4437, 4436, 4435, 4430, 4411, 4412, 13, 4433, 4414])).
% 1.21/1.40 tff(4445,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4446,plain,
% 1.21/1.40 (~c3_1(a4)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[370, 4445])).
% 1.21/1.40 tff(4447,plain,
% 1.21/1.40 (~c2_1(a4)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[384, 4445])).
% 1.21/1.40 tff(4448,plain,
% 1.21/1.40 (c1_1(a4)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[378, 4445])).
% 1.21/1.40 tff(4449,plain,
% 1.21/1.40 (~c0_1(a4)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3153, 160, 2264, 2289, 4448, 4447, 4446, 406, 4310])).
% 1.21/1.40 tff(4450,plain,
% 1.21/1.40 (hskp5),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3172, 160, 4378, 4448, 4377, 4447, 1311, 4449, 4385])).
% 1.21/1.40 tff(4451,plain,
% 1.21/1.40 (~c0_1(a7)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1317, 4450])).
% 1.21/1.40 tff(4452,plain,
% 1.21/1.40 (c3_1(a7)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1346, 4450])).
% 1.21/1.40 tff(4453,plain,
% 1.21/1.40 (c0_1(a18)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1082, 4376])).
% 1.21/1.40 tff(4454,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4455,plain,
% 1.21/1.40 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7))) <=> (hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4456,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[4455])).
% 1.21/1.40 tff(4457,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[4456, 4454])).
% 1.21/1.40 tff(4458,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(4459,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[4458, 4457])).
% 1.21/1.40 tff(4460,plain,
% 1.21/1.40 (~c2_1(a7)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4459, 160, 4426, 4453, 4378, 4452, 4377, 4451, 1042])).
% 1.21/1.40 tff(4461,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2788, 160, 1174, 2272, 2264, 2289, 4452, 4451, 1202, 4460])).
% 1.21/1.40 tff(4462,plain,(hskp6), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4463,plain,
% 1.21/1.40 (c3_1(a8)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4333, 1268, 1248, 1240])).
% 1.21/1.40 tff(4464,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2685, 160, 805, 2272, 2264, 1248, 1240, 779, 4310, 4463])).
% 1.21/1.40 tff(4465,plain,((~hskp6) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4466,plain,
% 1.21/1.40 (hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4465, 4462])).
% 1.21/1.40 tff(4467,plain,
% 1.21/1.40 (~c0_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[819, 4466])).
% 1.21/1.40 tff(4468,plain,
% 1.21/1.40 (c3_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1392, 4466])).
% 1.21/1.40 tff(4469,plain,
% 1.21/1.40 (c2_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[827, 4466])).
% 1.21/1.40 tff(4470,plain,
% 1.21/1.40 (~hskp10),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4318, 4468, 4426, 4469, 4467])).
% 1.21/1.40 tff(4471,plain,
% 1.21/1.40 (~c1_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3563, 160, 4470, 4468, 4373, 4467, 4374, 1053, 4375])).
% 1.21/1.40 tff(4472,plain,
% 1.21/1.40 (~c1_1(a33)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2694, 160, 4178, 2579, 2901, 2899, 2573])).
% 1.21/1.40 tff(4473,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3250, 160, 2901, 4373, 388, 2899, 4374, 387, 83, 4375, 3165, 4472])).
% 1.21/1.40 tff(4474,plain,((~hskp19) | (~c1_1(a4)) | c3_1(a4) | c0_1(a4) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(4475,plain,
% 1.21/1.40 (hskp8),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[4474, 4466, 4446, 4449, 4448])).
% 1.21/1.40 tff(4476,plain,
% 1.21/1.40 (~c2_1(a15)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[175, 4475])).
% 1.21/1.40 tff(4477,plain,
% 1.21/1.40 (~c1_1(a15)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[189, 4475])).
% 1.21/1.40 tff(4478,plain,
% 1.21/1.40 (c0_1(a15)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[183, 4475])).
% 1.21/1.40 tff(4479,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4480,plain,
% 1.21/1.40 ((hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15))) <=> (hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(4481,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[4480])).
% 1.21/1.41 tff(4482,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[4481, 4479])).
% 1.21/1.41 tff(4483,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(4484,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[4483, 4482])).
% 1.21/1.41 tff(4485,plain,
% 1.21/1.41 (hskp13),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[4484, 160, 4393, 4478, 4374, 4477, 4476, 1502, 4375])).
% 1.21/1.41 tff(4486,plain,
% 1.21/1.41 (~c3_1(a22)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[449, 4485])).
% 1.21/1.41 tff(4487,plain,
% 1.21/1.41 (~c0_1(a22)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[461, 4485])).
% 1.21/1.41 tff(4488,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(4489,plain,
% 1.21/1.41 (((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c0_1(a22) | (~c1_1(a22)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(4490,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c0_1(a22) | (~c1_1(a22)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[4489])).
% 1.21/1.41 tff(4491,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c0_1(a22) | (~c1_1(a22)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.21/1.41 inference(transitivity,[status(thm)],[4490, 4488])).
% 1.21/1.41 tff(4492,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c0_1(a22) | (~c1_1(a22)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(4493,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[4492, 4491])).
% 1.21/1.41 tff(4494,plain,
% 1.21/1.41 (~c1_1(a22)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[4493, 160, 4469, 4373, 4467, 4374, 4487, 4486, 83, 4375, 4471])).
% 1.21/1.41 tff(4495,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(4496,plain,
% 1.21/1.41 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a2) | c3_1(a2) | (~c2_1(a2))) <=> (c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(4497,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a2) | c3_1(a2) | (~c2_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[4496])).
% 1.21/1.41 tff(4498,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a2) | c3_1(a2) | (~c2_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[4497, 4495])).
% 1.21/1.41 tff(4499,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a2) | c3_1(a2) | (~c2_1(a2)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(4500,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[4499, 4498])).
% 1.21/1.41 tff(4501,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[4500, 160, 2272, 2264, 388, 2329, 407, 387, 2320, 2319, 34, 4310])).
% 1.21/1.41 tff(4502,plain,((~hskp1) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(4503,plain,
% 1.21/1.41 (~hskp1),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[4502, 4448, 4447, 4446])).
% 1.21/1.41 tff(4504,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2923, 160, 4503, 4373, 4374, 4487, 4486, 1385, 4375, 4494])).
% 1.21/1.41 % SZS output end Proof
% 1.21/1.41 % E exiting
%------------------------------------------------------------------------------