%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN447-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:08 AM UTC 2025
% Result : Unsatisfiable 1.23s 1.43s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN447-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:35:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 1.23/1.43 % SZS status Unsatisfiable
% 1.23/1.43 % SZS output start Proof
% 1.23/1.43 tff(c2_1_type, type, (
% 1.23/1.43 c2_1: $i > $o)).
% 1.23/1.43 tff(c0_1_type, type, (
% 1.23/1.43 c0_1: $i > $o)).
% 1.23/1.43 tff(c3_1_type, type, (
% 1.23/1.43 c3_1: $i > $o)).
% 1.23/1.43 tff(c1_1_type, type, (
% 1.23/1.43 c1_1: $i > $o)).
% 1.23/1.43 tff(ndr1_0_type, type, (
% 1.23/1.43 ndr1_0: $o)).
% 1.23/1.43 tff(a1073_type, type, (
% 1.23/1.43 a1073: $i)).
% 1.23/1.43 tff(hskp53_type, type, (
% 1.23/1.43 hskp53: $o)).
% 1.23/1.43 tff(a1031_type, type, (
% 1.23/1.43 a1031: $i)).
% 1.23/1.43 tff(hskp33_type, type, (
% 1.23/1.43 hskp33: $o)).
% 1.23/1.43 tff(a1043_type, type, (
% 1.23/1.43 a1043: $i)).
% 1.23/1.43 tff(a1059_type, type, (
% 1.23/1.43 a1059: $i)).
% 1.23/1.43 tff(hskp15_type, type, (
% 1.23/1.43 hskp15: $o)).
% 1.23/1.43 tff(a1083_type, type, (
% 1.23/1.43 a1083: $i)).
% 1.23/1.43 tff(hskp22_type, type, (
% 1.23/1.43 hskp22: $o)).
% 1.23/1.43 tff(hskp56_type, type, (
% 1.23/1.43 hskp56: $o)).
% 1.23/1.43 tff(a1088_type, type, (
% 1.23/1.43 a1088: $i)).
% 1.23/1.43 tff(hskp23_type, type, (
% 1.23/1.43 hskp23: $o)).
% 1.23/1.43 tff(a1062_type, type, (
% 1.23/1.43 a1062: $i)).
% 1.23/1.43 tff(hskp48_type, type, (
% 1.23/1.43 hskp48: $o)).
% 1.23/1.43 tff(a1039_type, type, (
% 1.23/1.43 a1039: $i)).
% 1.23/1.43 tff(hskp10_type, type, (
% 1.23/1.43 hskp10: $o)).
% 1.23/1.43 tff(a1049_type, type, (
% 1.23/1.43 a1049: $i)).
% 1.23/1.43 tff(hskp43_type, type, (
% 1.23/1.43 hskp43: $o)).
% 1.23/1.43 tff(a1095_type, type, (
% 1.23/1.43 a1095: $i)).
% 1.23/1.43 tff(hskp59_type, type, (
% 1.23/1.43 hskp59: $o)).
% 1.23/1.43 tff(a1080_type, type, (
% 1.23/1.43 a1080: $i)).
% 1.23/1.43 tff(hskp20_type, type, (
% 1.23/1.43 hskp20: $o)).
% 1.23/1.43 tff(hskp19_type, type, (
% 1.23/1.43 hskp19: $o)).
% 1.23/1.43 tff(a1079_type, type, (
% 1.23/1.43 a1079: $i)).
% 1.23/1.43 tff(hskp63_type, type, (
% 1.23/1.43 hskp63: $o)).
% 1.23/1.43 tff(hskp62_type, type, (
% 1.23/1.43 hskp62: $o)).
% 1.23/1.43 tff(a1085_type, type, (
% 1.23/1.43 a1085: $i)).
% 1.23/1.43 tff(hskp57_type, type, (
% 1.23/1.43 hskp57: $o)).
% 1.23/1.43 tff(a1046_type, type, (
% 1.23/1.43 a1046: $i)).
% 1.23/1.43 tff(a1033_type, type, (
% 1.23/1.43 a1033: $i)).
% 1.23/1.43 tff(hskp35_type, type, (
% 1.23/1.43 hskp35: $o)).
% 1.23/1.43 tff(a1091_type, type, (
% 1.23/1.43 a1091: $i)).
% 1.23/1.43 tff(a1023_type, type, (
% 1.23/1.43 a1023: $i)).
% 1.23/1.43 tff(hskp1_type, type, (
% 1.23/1.43 hskp1: $o)).
% 1.23/1.43 tff(a1084_type, type, (
% 1.23/1.43 a1084: $i)).
% 1.23/1.43 tff(hskp25_type, type, (
% 1.23/1.43 hskp25: $o)).
% 1.23/1.43 tff(a1032_type, type, (
% 1.23/1.43 a1032: $i)).
% 1.23/1.43 tff(hskp34_type, type, (
% 1.23/1.43 hskp34: $o)).
% 1.23/1.43 tff(a1056_type, type, (
% 1.23/1.43 a1056: $i)).
% 1.23/1.43 tff(hskp47_type, type, (
% 1.23/1.43 hskp47: $o)).
% 1.23/1.43 tff(a1034_type, type, (
% 1.23/1.43 a1034: $i)).
% 1.23/1.43 tff(hskp36_type, type, (
% 1.23/1.43 hskp36: $o)).
% 1.23/1.43 tff(hskp42_type, type, (
% 1.23/1.43 hskp42: $o)).
% 1.23/1.43 tff(a1035_type, type, (
% 1.23/1.43 a1035: $i)).
% 1.23/1.43 tff(hskp12_type, type, (
% 1.23/1.43 hskp12: $o)).
% 1.23/1.43 tff(hskp7_type, type, (
% 1.23/1.43 hskp7: $o)).
% 1.23/1.43 tff(a1055_type, type, (
% 1.23/1.43 a1055: $i)).
% 1.23/1.43 tff(hskp14_type, type, (
% 1.23/1.43 hskp14: $o)).
% 1.23/1.43 tff(hskp38_type, type, (
% 1.23/1.43 hskp38: $o)).
% 1.23/1.43 tff(a1040_type, type, (
% 1.23/1.43 a1040: $i)).
% 1.23/1.43 tff(hskp46_type, type, (
% 1.23/1.43 hskp46: $o)).
% 1.23/1.43 tff(a1053_type, type, (
% 1.23/1.43 a1053: $i)).
% 1.23/1.43 tff(a1105_type, type, (
% 1.23/1.43 a1105: $i)).
% 1.23/1.43 tff(a1103_type, type, (
% 1.23/1.43 a1103: $i)).
% 1.23/1.43 tff(1,plain,
% 1.23/1.43 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(2,plain,
% 1.23/1.43 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[1])).
% 1.23/1.43 tff(3,plain,
% 1.23/1.43 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(4,plain,
% 1.23/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) | (~c2_1(U))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c2_1(U))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) | (~c2_1(U))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(5,plain,
% 1.23/1.43 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) | (~c2_1(U))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[4])).
% 1.23/1.43 tff(6,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) | (~c2_1(U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause311')).
% 1.23/1.43 tff(7,plain,
% 1.23/1.43 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.23/1.43 tff(8,plain,
% 1.23/1.43 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.23/1.43 tff(9,plain,(
% 1.23/1.43 ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(skolemize,[status(sab)],[8])).
% 1.23/1.43 tff(10,plain,
% 1.23/1.43 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.23/1.43 tff(11,plain,
% 1.23/1.43 (^[V: $i, U: $i] : refl((hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(12,plain,
% 1.23/1.43 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[11])).
% 1.23/1.43 tff(13,plain,
% 1.23/1.43 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(14,plain,
% 1.23/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp53) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp53))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(15,plain,
% 1.23/1.43 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp53) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[14])).
% 1.23/1.43 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause309')).
% 1.23/1.43 tff(17,plain,
% 1.23/1.43 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.23/1.43 tff(18,plain,
% 1.23/1.43 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.23/1.43 tff(19,plain,(
% 1.23/1.43 ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(skolemize,[status(sab)],[18])).
% 1.23/1.43 tff(20,plain,
% 1.23/1.43 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.23/1.43 tff(21,assumption,(~hskp33), introduced(assumption)).
% 1.23/1.43 tff(22,plain,
% 1.23/1.43 (^[U: $i] : refl((hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(23,plain,
% 1.23/1.43 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[22])).
% 1.23/1.43 tff(24,plain,
% 1.23/1.43 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(25,plain,
% 1.23/1.43 (^[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)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp56) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp56))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp56) <=> (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp56) <=> (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(26,plain,
% 1.23/1.43 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp56) <=> ![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[25])).
% 1.23/1.43 tff(27,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause281')).
% 1.23/1.43 tff(28,plain,
% 1.23/1.43 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.23/1.43 tff(29,plain,
% 1.23/1.43 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.23/1.43 tff(30,plain,(
% 1.23/1.43 ![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.23/1.43 inference(skolemize,[status(sab)],[29])).
% 1.23/1.43 tff(31,plain,
% 1.23/1.43 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.23/1.43 tff(32,plain,
% 1.23/1.43 (^[U: $i] : refl((hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(33,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[32])).
% 1.23/1.43 tff(34,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(35,plain,
% 1.23/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp33))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp33) <=> (hskp33 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) <=> (hskp33 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) | hskp23) <=> ((hskp33 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp23))), rewrite(((hskp33 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp23) <=> (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) | hskp23) <=> (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(36,plain,
% 1.23/1.43 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) | hskp23) <=> ![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[35])).
% 1.23/1.43 tff(37,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause284')).
% 1.23/1.43 tff(38,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.23/1.43 tff(39,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.23/1.43 tff(40,plain,(
% 1.23/1.43 ![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(skolemize,[status(sab)],[39])).
% 1.23/1.43 tff(41,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.23/1.43 tff(42,assumption,(~hskp15), introduced(assumption)).
% 1.23/1.43 tff(43,plain,
% 1.23/1.43 (^[U: $i] : refl((hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(44,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[43])).
% 1.23/1.43 tff(45,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(46,plain,
% 1.23/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) | hskp33) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp33))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp33) <=> (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) | hskp33) <=> (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(47,plain,
% 1.23/1.43 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) | hskp33) <=> ![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[46])).
% 1.23/1.43 tff(48,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) | hskp33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause266')).
% 1.23/1.43 tff(49,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.23/1.43 tff(50,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[49, 45])).
% 1.23/1.43 tff(51,plain,(
% 1.23/1.43 ![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.23/1.43 inference(skolemize,[status(sab)],[50])).
% 1.23/1.43 tff(52,plain,
% 1.23/1.43 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[51, 44])).
% 1.23/1.43 tff(53,assumption,(~hskp10), introduced(assumption)).
% 1.23/1.43 tff(54,plain,
% 1.23/1.43 (^[U: $i] : refl((hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(55,plain,
% 1.23/1.43 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[54])).
% 1.23/1.43 tff(56,plain,
% 1.23/1.43 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(57,plain,
% 1.23/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp43) <=> ((hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp43))), rewrite(((hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp43) <=> (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp43) <=> (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.43 tff(58,plain,
% 1.23/1.43 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp43) <=> ![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(quant_intro,[status(thm)],[57])).
% 1.23/1.43 tff(59,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause277')).
% 1.23/1.43 tff(60,plain,
% 1.23/1.43 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.23/1.43 tff(61,plain,
% 1.23/1.43 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.23/1.43 tff(62,plain,(
% 1.23/1.43 ![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(skolemize,[status(sab)],[61])).
% 1.23/1.43 tff(63,plain,
% 1.23/1.43 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.23/1.43 tff(64,plain,
% 1.23/1.43 (^[U: $i] : refl((hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)))),
% 1.23/1.43 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(65,plain,
% 1.23/1.44 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[64])).
% 1.23/1.44 tff(66,plain,
% 1.23/1.44 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(67,plain,
% 1.23/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U)))), (((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U)) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))), (((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)))), ((((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))), ((((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(68,plain,
% 1.23/1.44 (![U: $i] : (((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) | hskp10) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[67])).
% 1.23/1.44 tff(69,axiom,(![U: $i] : (((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause262')).
% 1.23/1.44 tff(70,plain,
% 1.23/1.44 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.23/1.44 tff(71,plain,
% 1.23/1.44 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.23/1.44 tff(72,plain,(
% 1.23/1.44 ![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 1.23/1.44 inference(skolemize,[status(sab)],[71])).
% 1.23/1.44 tff(73,plain,
% 1.23/1.44 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[72, 65])).
% 1.23/1.44 tff(74,assumption,(hskp19), introduced(assumption)).
% 1.23/1.44 tff(75,plain,
% 1.23/1.44 (((~hskp19) | (~c2_1(a1079))) <=> ((~hskp19) | (~c2_1(a1079)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(76,plain,
% 1.23/1.44 (((~c2_1(a1079)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1079)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(77,axiom,((~c2_1(a1079)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause227')).
% 1.23/1.44 tff(78,plain,
% 1.23/1.44 ((~hskp19) | (~c2_1(a1079))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.23/1.44 tff(79,plain,
% 1.23/1.44 ((~hskp19) | (~c2_1(a1079))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[78, 75])).
% 1.23/1.44 tff(80,plain,
% 1.23/1.44 (~c2_1(a1079)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[79, 74])).
% 1.23/1.44 tff(81,plain,
% 1.23/1.44 (((~hskp19) | (~c0_1(a1079))) <=> ((~hskp19) | (~c0_1(a1079)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(82,plain,
% 1.23/1.44 (((~c0_1(a1079)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a1079)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(83,axiom,((~c0_1(a1079)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause226')).
% 1.23/1.44 tff(84,plain,
% 1.23/1.44 ((~hskp19) | (~c0_1(a1079))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.23/1.44 tff(85,plain,
% 1.23/1.44 ((~hskp19) | (~c0_1(a1079))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[84, 81])).
% 1.23/1.44 tff(86,plain,
% 1.23/1.44 (~c0_1(a1079)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[85, 74])).
% 1.23/1.44 tff(87,assumption,(~ndr1_0), introduced(assumption)).
% 1.23/1.44 tff(88,plain,
% 1.23/1.44 ((ndr1_0 | (~hskp56)) <=> (ndr1_0 | (~hskp56))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(89,plain,
% 1.23/1.44 (((~hskp56) | ndr1_0) <=> (ndr1_0 | (~hskp56))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(90,axiom,((~hskp56) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause8')).
% 1.23/1.44 tff(91,plain,
% 1.23/1.44 (ndr1_0 | (~hskp56)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.23/1.44 tff(92,plain,
% 1.23/1.44 (ndr1_0 | (~hskp56)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[91, 88])).
% 1.23/1.44 tff(93,plain,
% 1.23/1.44 (~hskp56),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[92, 87])).
% 1.23/1.44 tff(94,plain,
% 1.23/1.44 (((~hskp63) | ndr1_0) <=> ((~hskp63) | ndr1_0)),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(95,axiom,((~hskp63) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.23/1.44 tff(96,plain,
% 1.23/1.44 ((~hskp63) | ndr1_0),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.23/1.44 tff(97,plain,
% 1.23/1.44 ((~hskp63) | ndr1_0),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[96, 94])).
% 1.23/1.44 tff(98,plain,
% 1.23/1.44 ((~hskp63) | ndr1_0),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[97, 94])).
% 1.23/1.44 tff(99,plain,
% 1.23/1.44 ((~hskp63) | ndr1_0),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.23/1.44 tff(100,plain,
% 1.23/1.44 ((~hskp63) | ndr1_0),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[99, 94])).
% 1.23/1.44 tff(101,plain,
% 1.23/1.44 (~hskp63),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[100, 87])).
% 1.23/1.44 tff(102,plain,
% 1.23/1.44 ((ndr1_0 | (~hskp62)) <=> (ndr1_0 | (~hskp62))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(103,plain,
% 1.23/1.44 (((~hskp62) | ndr1_0) <=> (ndr1_0 | (~hskp62))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(104,axiom,((~hskp62) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.23/1.44 tff(105,plain,
% 1.23/1.44 (ndr1_0 | (~hskp62)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.23/1.44 tff(106,plain,
% 1.23/1.44 (ndr1_0 | (~hskp62)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[105, 102])).
% 1.23/1.44 tff(107,plain,
% 1.23/1.44 (~hskp62),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[106, 87])).
% 1.23/1.44 tff(108,plain,
% 1.23/1.44 ((hskp63 | hskp62 | hskp56) <=> (hskp63 | hskp62 | hskp56)),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(109,plain,
% 1.23/1.44 (((hskp62 | hskp56) | hskp63) <=> (hskp63 | hskp62 | hskp56)),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(110,plain,
% 1.23/1.44 ((hskp62 | hskp56) <=> (hskp62 | hskp56)),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(111,plain,
% 1.23/1.44 (((hskp62 | hskp56) | hskp63) <=> ((hskp62 | hskp56) | hskp63)),
% 1.23/1.44 inference(monotonicity,[status(thm)],[110])).
% 1.23/1.44 tff(112,plain,
% 1.23/1.44 (((hskp62 | hskp56) | hskp63) <=> (hskp63 | hskp62 | hskp56)),
% 1.23/1.44 inference(transitivity,[status(thm)],[111, 109])).
% 1.23/1.44 tff(113,axiom,((hskp62 | hskp56) | hskp63), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.23/1.44 tff(114,plain,
% 1.23/1.44 (hskp63 | hskp62 | hskp56),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.23/1.44 tff(115,plain,
% 1.23/1.44 (hskp63 | hskp62 | hskp56),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[114, 108])).
% 1.23/1.44 tff(116,plain,
% 1.23/1.44 (hskp63 | hskp62 | hskp56),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[115, 108])).
% 1.23/1.44 tff(117,plain,
% 1.23/1.44 (hskp63 | hskp62 | hskp56),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[116, 108])).
% 1.23/1.44 tff(118,plain,
% 1.23/1.44 (hskp63 | hskp62 | hskp56),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[117, 108])).
% 1.23/1.44 tff(119,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[118, 107, 101, 93])).
% 1.23/1.44 tff(120,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(121,plain,
% 1.23/1.44 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(122,plain,
% 1.23/1.44 ((hskp10 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | c3_1(a1079)) <=> (hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(123,plain,
% 1.23/1.44 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | c3_1(a1079))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[122])).
% 1.23/1.44 tff(124,plain,
% 1.23/1.44 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | c3_1(a1079))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079))),
% 1.23/1.44 inference(transitivity,[status(thm)],[123, 121])).
% 1.23/1.44 tff(125,plain,
% 1.23/1.44 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | c3_1(a1079))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(126,plain,
% 1.23/1.44 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.23/1.44 tff(127,plain,
% 1.23/1.44 (c3_1(a1079)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[126, 120, 53, 86, 80, 73])).
% 1.23/1.44 tff(128,plain,
% 1.23/1.44 (^[V: $i, U: $i] : refl((hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(129,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[128])).
% 1.23/1.44 tff(130,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(131,plain,
% 1.23/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) | hskp59) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp59))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp59) <=> (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) | hskp59) <=> (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(132,plain,
% 1.23/1.44 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) | hskp59) <=> ![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[131])).
% 1.23/1.44 tff(133,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) | hskp59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause297')).
% 1.23/1.44 tff(134,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.23/1.44 tff(135,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[134, 130])).
% 1.23/1.44 tff(136,plain,(
% 1.23/1.44 ![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.23/1.44 inference(skolemize,[status(sab)],[135])).
% 1.23/1.44 tff(137,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[136, 129])).
% 1.23/1.44 tff(138,plain,
% 1.23/1.44 (((~hskp19) | c1_1(a1079)) <=> ((~hskp19) | c1_1(a1079))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(139,axiom,((~hskp19) | c1_1(a1079)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.23/1.44 tff(140,plain,
% 1.23/1.44 ((~hskp19) | c1_1(a1079)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.23/1.44 tff(141,plain,
% 1.23/1.44 ((~hskp19) | c1_1(a1079)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[140, 138])).
% 1.23/1.44 tff(142,plain,
% 1.23/1.44 ((~hskp19) | c1_1(a1079)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[141, 138])).
% 1.23/1.44 tff(143,plain,
% 1.23/1.44 ((~hskp19) | c1_1(a1079)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[142, 138])).
% 1.23/1.44 tff(144,plain,
% 1.23/1.44 ((~hskp19) | c1_1(a1079)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[143, 138])).
% 1.23/1.44 tff(145,plain,
% 1.23/1.44 (c1_1(a1079)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[144, 74])).
% 1.23/1.44 tff(146,plain,
% 1.23/1.44 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(147,plain,
% 1.23/1.44 ((hskp59 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079))) <=> (hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(148,plain,
% 1.23/1.44 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[147])).
% 1.23/1.44 tff(149,plain,
% 1.23/1.44 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 1.23/1.44 inference(transitivity,[status(thm)],[148, 146])).
% 1.23/1.44 tff(150,plain,
% 1.23/1.44 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(151,plain,
% 1.23/1.44 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.23/1.44 tff(152,plain,
% 1.23/1.44 (hskp59 | (~c3_1(a1079))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[151, 120, 145, 86, 80, 137])).
% 1.23/1.44 tff(153,plain,
% 1.23/1.44 (hskp59),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[152, 127])).
% 1.23/1.44 tff(154,plain,
% 1.23/1.44 (((~hskp59) | (~c3_1(a1095))) <=> ((~hskp59) | (~c3_1(a1095)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(155,plain,
% 1.23/1.44 (((~c3_1(a1095)) | (~hskp59)) <=> ((~hskp59) | (~c3_1(a1095)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(156,axiom,((~c3_1(a1095)) | (~hskp59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.23/1.44 tff(157,plain,
% 1.23/1.44 ((~hskp59) | (~c3_1(a1095))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.23/1.44 tff(158,plain,
% 1.23/1.44 ((~hskp59) | (~c3_1(a1095))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[157, 154])).
% 1.23/1.44 tff(159,plain,
% 1.23/1.44 (~c3_1(a1095)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[158, 153])).
% 1.23/1.44 tff(160,plain,
% 1.23/1.44 (((~hskp59) | (~c0_1(a1095))) <=> ((~hskp59) | (~c0_1(a1095)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(161,plain,
% 1.23/1.44 (((~c0_1(a1095)) | (~hskp59)) <=> ((~hskp59) | (~c0_1(a1095)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(162,axiom,((~c0_1(a1095)) | (~hskp59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.23/1.44 tff(163,plain,
% 1.23/1.44 ((~hskp59) | (~c0_1(a1095))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.23/1.44 tff(164,plain,
% 1.23/1.44 ((~hskp59) | (~c0_1(a1095))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[163, 160])).
% 1.23/1.44 tff(165,plain,
% 1.23/1.44 (~c0_1(a1095)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[164, 153])).
% 1.23/1.44 tff(166,plain,
% 1.23/1.44 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(167,plain,
% 1.23/1.44 ((hskp10 | (~ndr1_0) | c0_1(a1095) | c2_1(a1095) | c3_1(a1095)) <=> (hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(168,plain,
% 1.23/1.44 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1095) | c2_1(a1095) | c3_1(a1095))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[167])).
% 1.23/1.44 tff(169,plain,
% 1.23/1.44 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1095) | c2_1(a1095) | c3_1(a1095))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095))),
% 1.23/1.44 inference(transitivity,[status(thm)],[168, 166])).
% 1.23/1.44 tff(170,plain,
% 1.23/1.44 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1095) | c2_1(a1095) | c3_1(a1095))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(171,plain,
% 1.23/1.44 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.23/1.44 tff(172,plain,
% 1.23/1.44 (c2_1(a1095)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[171, 120, 53, 165, 159, 73])).
% 1.23/1.44 tff(173,plain,
% 1.23/1.44 (((~hskp59) | c1_1(a1095)) <=> ((~hskp59) | c1_1(a1095))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(174,axiom,((~hskp59) | c1_1(a1095)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.23/1.44 tff(175,plain,
% 1.23/1.44 ((~hskp59) | c1_1(a1095)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[174, 173])).
% 1.23/1.44 tff(176,plain,
% 1.23/1.44 ((~hskp59) | c1_1(a1095)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[175, 173])).
% 1.23/1.44 tff(177,plain,
% 1.23/1.44 ((~hskp59) | c1_1(a1095)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[176, 173])).
% 1.23/1.44 tff(178,plain,
% 1.23/1.44 ((~hskp59) | c1_1(a1095)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[177, 173])).
% 1.23/1.44 tff(179,plain,
% 1.23/1.44 ((~hskp59) | c1_1(a1095)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[178, 173])).
% 1.23/1.44 tff(180,plain,
% 1.23/1.44 (c1_1(a1095)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[179, 153])).
% 1.23/1.44 tff(181,plain,
% 1.23/1.44 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(182,plain,
% 1.23/1.44 ((hskp43 | hskp10 | (~ndr1_0) | c0_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095))) <=> (hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(183,plain,
% 1.23/1.44 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[182])).
% 1.23/1.44 tff(184,plain,
% 1.23/1.44 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 1.23/1.44 inference(transitivity,[status(thm)],[183, 181])).
% 1.23/1.44 tff(185,plain,
% 1.23/1.44 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(186,plain,
% 1.23/1.44 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.23/1.44 tff(187,plain,
% 1.23/1.44 (hskp43),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[186, 120, 53, 180, 165, 63, 172])).
% 1.23/1.44 tff(188,plain,
% 1.23/1.44 (((~hskp43) | c1_1(a1049)) <=> ((~hskp43) | c1_1(a1049))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(189,axiom,((~hskp43) | c1_1(a1049)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.23/1.44 tff(190,plain,
% 1.23/1.44 ((~hskp43) | c1_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[189, 188])).
% 1.23/1.44 tff(191,plain,
% 1.23/1.44 ((~hskp43) | c1_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[190, 188])).
% 1.23/1.44 tff(192,plain,
% 1.23/1.44 ((~hskp43) | c1_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[191, 188])).
% 1.23/1.44 tff(193,plain,
% 1.23/1.44 ((~hskp43) | c1_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[192, 188])).
% 1.23/1.44 tff(194,plain,
% 1.23/1.44 ((~hskp43) | c1_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[193, 188])).
% 1.23/1.44 tff(195,plain,
% 1.23/1.44 (c1_1(a1049)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[194, 187])).
% 1.23/1.44 tff(196,plain,
% 1.23/1.44 (((~hskp43) | c2_1(a1049)) <=> ((~hskp43) | c2_1(a1049))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(197,axiom,((~hskp43) | c2_1(a1049)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.23/1.44 tff(198,plain,
% 1.23/1.44 ((~hskp43) | c2_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.23/1.44 tff(199,plain,
% 1.23/1.44 ((~hskp43) | c2_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[198, 196])).
% 1.23/1.44 tff(200,plain,
% 1.23/1.44 ((~hskp43) | c2_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[199, 196])).
% 1.23/1.44 tff(201,plain,
% 1.23/1.44 ((~hskp43) | c2_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[200, 196])).
% 1.23/1.44 tff(202,plain,
% 1.23/1.44 ((~hskp43) | c2_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[201, 196])).
% 1.23/1.44 tff(203,plain,
% 1.23/1.44 (c2_1(a1049)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[202, 187])).
% 1.23/1.44 tff(204,plain,
% 1.23/1.44 (((~hskp43) | c0_1(a1049)) <=> ((~hskp43) | c0_1(a1049))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(205,axiom,((~hskp43) | c0_1(a1049)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.23/1.44 tff(206,plain,
% 1.23/1.44 ((~hskp43) | c0_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.23/1.44 tff(207,plain,
% 1.23/1.44 ((~hskp43) | c0_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[206, 204])).
% 1.23/1.44 tff(208,plain,
% 1.23/1.44 ((~hskp43) | c0_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[207, 204])).
% 1.23/1.44 tff(209,plain,
% 1.23/1.44 ((~hskp43) | c0_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.23/1.44 tff(210,plain,
% 1.23/1.44 ((~hskp43) | c0_1(a1049)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[209, 204])).
% 1.23/1.44 tff(211,plain,
% 1.23/1.44 (c0_1(a1049)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[210, 187])).
% 1.23/1.44 tff(212,plain,
% 1.23/1.44 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(213,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[212])).
% 1.23/1.44 tff(214,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(215,plain,
% 1.23/1.44 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), (((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W))), (((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W)))), ((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W))), ((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W)))), (((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(216,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[215])).
% 1.23/1.44 tff(217,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause313')).
% 1.23/1.44 tff(218,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.23/1.44 tff(219,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[218, 214])).
% 1.23/1.44 tff(220,plain,(
% 1.23/1.44 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.23/1.44 inference(skolemize,[status(sab)],[219])).
% 1.23/1.44 tff(221,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[220, 213])).
% 1.23/1.44 tff(222,assumption,(hskp56), introduced(assumption)).
% 1.23/1.44 tff(223,plain,
% 1.23/1.44 (((~hskp56) | (~c1_1(a1084))) <=> ((~hskp56) | (~c1_1(a1084)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(224,plain,
% 1.23/1.44 (((~c1_1(a1084)) | (~hskp56)) <=> ((~hskp56) | (~c1_1(a1084)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(225,axiom,((~c1_1(a1084)) | (~hskp56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.23/1.44 tff(226,plain,
% 1.23/1.44 ((~hskp56) | (~c1_1(a1084))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.23/1.44 tff(227,plain,
% 1.23/1.44 ((~hskp56) | (~c1_1(a1084))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[226, 223])).
% 1.23/1.44 tff(228,plain,
% 1.23/1.44 (~c1_1(a1084)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[227, 222])).
% 1.23/1.44 tff(229,plain,
% 1.23/1.44 (((~hskp56) | (~c3_1(a1084))) <=> ((~hskp56) | (~c3_1(a1084)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(230,plain,
% 1.23/1.44 (((~c3_1(a1084)) | (~hskp56)) <=> ((~hskp56) | (~c3_1(a1084)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(231,axiom,((~c3_1(a1084)) | (~hskp56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.23/1.44 tff(232,plain,
% 1.23/1.44 ((~hskp56) | (~c3_1(a1084))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.23/1.44 tff(233,plain,
% 1.23/1.44 ((~hskp56) | (~c3_1(a1084))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[232, 229])).
% 1.23/1.44 tff(234,plain,
% 1.23/1.44 (~c3_1(a1084)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[233, 222])).
% 1.23/1.44 tff(235,plain,
% 1.23/1.44 (((~hskp56) | c0_1(a1084)) <=> ((~hskp56) | c0_1(a1084))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(236,axiom,((~hskp56) | c0_1(a1084)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.23/1.44 tff(237,plain,
% 1.23/1.44 ((~hskp56) | c0_1(a1084)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.23/1.44 tff(238,plain,
% 1.23/1.44 ((~hskp56) | c0_1(a1084)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[237, 235])).
% 1.23/1.44 tff(239,plain,
% 1.23/1.44 ((~hskp56) | c0_1(a1084)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[238, 235])).
% 1.23/1.44 tff(240,plain,
% 1.23/1.44 ((~hskp56) | c0_1(a1084)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[239, 235])).
% 1.23/1.44 tff(241,plain,
% 1.23/1.44 ((~hskp56) | c0_1(a1084)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[240, 235])).
% 1.23/1.44 tff(242,plain,
% 1.23/1.44 (c0_1(a1084)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[241, 222])).
% 1.23/1.44 tff(243,plain,
% 1.23/1.44 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(244,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[243])).
% 1.23/1.44 tff(245,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(246,plain,
% 1.23/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> (((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp25) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp25))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(247,plain,
% 1.23/1.45 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[246])).
% 1.23/1.45 tff(248,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause305')).
% 1.23/1.45 tff(249,plain,
% 1.23/1.45 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.23/1.45 tff(250,plain,
% 1.23/1.45 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[249, 245])).
% 1.23/1.45 tff(251,plain,(
% 1.23/1.45 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.45 inference(skolemize,[status(sab)],[250])).
% 1.23/1.45 tff(252,plain,
% 1.23/1.45 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[251, 244])).
% 1.23/1.45 tff(253,assumption,(c0_1(a1084)), introduced(assumption)).
% 1.23/1.45 tff(254,assumption,(~c3_1(a1084)), introduced(assumption)).
% 1.23/1.45 tff(255,assumption,(~c1_1(a1084)), introduced(assumption)).
% 1.23/1.45 tff(256,assumption,(~hskp1), introduced(assumption)).
% 1.23/1.45 tff(257,assumption,(~c2_1(a1084)), introduced(assumption)).
% 1.23/1.45 tff(258,assumption,(hskp33), introduced(assumption)).
% 1.23/1.45 tff(259,plain,
% 1.23/1.45 (((~hskp33) | (~c1_1(a1031))) <=> ((~hskp33) | (~c1_1(a1031)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(260,plain,
% 1.23/1.45 (((~c1_1(a1031)) | (~hskp33)) <=> ((~hskp33) | (~c1_1(a1031)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(261,axiom,((~c1_1(a1031)) | (~hskp33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 1.23/1.45 tff(262,plain,
% 1.23/1.45 ((~hskp33) | (~c1_1(a1031))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[261, 260])).
% 1.23/1.45 tff(263,plain,
% 1.23/1.45 ((~hskp33) | (~c1_1(a1031))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[262, 259])).
% 1.23/1.45 tff(264,plain,
% 1.23/1.45 (~c1_1(a1031)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[263, 258])).
% 1.23/1.45 tff(265,plain,
% 1.23/1.45 (((~hskp33) | c2_1(a1031)) <=> ((~hskp33) | c2_1(a1031))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(266,axiom,((~hskp33) | c2_1(a1031)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.23/1.45 tff(267,plain,
% 1.23/1.45 ((~hskp33) | c2_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.23/1.45 tff(268,plain,
% 1.23/1.45 ((~hskp33) | c2_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[267, 265])).
% 1.23/1.45 tff(269,plain,
% 1.23/1.45 ((~hskp33) | c2_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[268, 265])).
% 1.23/1.45 tff(270,plain,
% 1.23/1.45 ((~hskp33) | c2_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[269, 265])).
% 1.23/1.45 tff(271,plain,
% 1.23/1.45 ((~hskp33) | c2_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[270, 265])).
% 1.23/1.45 tff(272,plain,
% 1.23/1.45 (c2_1(a1031)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[271, 258])).
% 1.23/1.45 tff(273,assumption,(~c0_1(a1031)), introduced(assumption)).
% 1.23/1.45 tff(274,assumption,(~c1_1(a1031)), introduced(assumption)).
% 1.23/1.45 tff(275,assumption,(c2_1(a1031)), introduced(assumption)).
% 1.23/1.45 tff(276,plain,
% 1.23/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(277,plain,
% 1.23/1.45 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084)) <=> (c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(278,plain,
% 1.23/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[277])).
% 1.23/1.45 tff(279,plain,
% 1.23/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[278, 276])).
% 1.23/1.45 tff(280,plain,
% 1.23/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(281,plain,
% 1.23/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.23/1.45 tff(282,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[281, 120, 253, 275, 254, 255, 274, 221, 257, 273])).
% 1.23/1.45 tff(283,plain,(c0_1(a1031) | (~c0_1(a1084)) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | c2_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(284,plain,
% 1.23/1.45 (c0_1(a1031)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[283, 272, 253, 254, 255, 264, 257])).
% 1.23/1.45 tff(285,plain,
% 1.23/1.45 (((~hskp33) | c3_1(a1031)) <=> ((~hskp33) | c3_1(a1031))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(286,axiom,((~hskp33) | c3_1(a1031)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.23/1.45 tff(287,plain,
% 1.23/1.45 ((~hskp33) | c3_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.23/1.45 tff(288,plain,
% 1.23/1.45 ((~hskp33) | c3_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[287, 285])).
% 1.23/1.45 tff(289,plain,
% 1.23/1.45 ((~hskp33) | c3_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[288, 285])).
% 1.23/1.45 tff(290,plain,
% 1.23/1.45 ((~hskp33) | c3_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[289, 285])).
% 1.23/1.45 tff(291,plain,
% 1.23/1.45 ((~hskp33) | c3_1(a1031)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[290, 285])).
% 1.23/1.45 tff(292,plain,
% 1.23/1.45 (c3_1(a1031)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[291, 258])).
% 1.23/1.45 tff(293,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(294,plain,
% 1.23/1.45 ((hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031))) <=> (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(295,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[294])).
% 1.23/1.45 tff(296,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[295, 293])).
% 1.23/1.45 tff(297,plain,
% 1.23/1.45 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(298,plain,
% 1.23/1.45 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[297, 296])).
% 1.23/1.45 tff(299,plain,
% 1.23/1.45 (hskp53 | (~c0_1(a1031))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[298, 120, 292, 272, 264, 20])).
% 1.23/1.45 tff(300,plain,
% 1.23/1.45 (hskp53),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[299, 284])).
% 1.23/1.45 tff(301,plain,
% 1.23/1.45 (((~hskp53) | c0_1(a1073)) <=> ((~hskp53) | c0_1(a1073))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(302,axiom,((~hskp53) | c0_1(a1073)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.23/1.45 tff(303,plain,
% 1.23/1.45 ((~hskp53) | c0_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[302, 301])).
% 1.23/1.45 tff(304,plain,
% 1.23/1.45 ((~hskp53) | c0_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[303, 301])).
% 1.23/1.45 tff(305,plain,
% 1.23/1.45 ((~hskp53) | c0_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[304, 301])).
% 1.23/1.45 tff(306,plain,
% 1.23/1.45 ((~hskp53) | c0_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[305, 301])).
% 1.23/1.45 tff(307,plain,
% 1.23/1.45 ((~hskp53) | c0_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[306, 301])).
% 1.23/1.45 tff(308,plain,
% 1.23/1.45 (c0_1(a1073)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[307, 300])).
% 1.23/1.45 tff(309,plain,
% 1.23/1.45 (((~hskp53) | c2_1(a1073)) <=> ((~hskp53) | c2_1(a1073))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(310,axiom,((~hskp53) | c2_1(a1073)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.23/1.45 tff(311,plain,
% 1.23/1.45 ((~hskp53) | c2_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[310, 309])).
% 1.23/1.45 tff(312,plain,
% 1.23/1.45 ((~hskp53) | c2_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[311, 309])).
% 1.23/1.45 tff(313,plain,
% 1.23/1.45 ((~hskp53) | c2_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[312, 309])).
% 1.23/1.45 tff(314,plain,
% 1.23/1.45 ((~hskp53) | c2_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[313, 309])).
% 1.23/1.45 tff(315,plain,
% 1.23/1.45 ((~hskp53) | c2_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[314, 309])).
% 1.23/1.45 tff(316,plain,
% 1.23/1.45 (c2_1(a1073)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[315, 300])).
% 1.23/1.45 tff(317,plain,
% 1.23/1.45 (((~hskp53) | c1_1(a1073)) <=> ((~hskp53) | c1_1(a1073))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(318,axiom,((~hskp53) | c1_1(a1073)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.23/1.45 tff(319,plain,
% 1.23/1.45 ((~hskp53) | c1_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.23/1.45 tff(320,plain,
% 1.23/1.45 ((~hskp53) | c1_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[319, 317])).
% 1.23/1.45 tff(321,plain,
% 1.23/1.45 ((~hskp53) | c1_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[320, 317])).
% 1.23/1.45 tff(322,plain,
% 1.23/1.45 ((~hskp53) | c1_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[321, 317])).
% 1.23/1.45 tff(323,plain,
% 1.23/1.45 ((~hskp53) | c1_1(a1073)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[322, 317])).
% 1.23/1.45 tff(324,plain,
% 1.23/1.45 (c1_1(a1073)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[323, 300])).
% 1.23/1.45 tff(325,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(326,plain,
% 1.23/1.45 (((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031))) <=> ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(327,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[326])).
% 1.23/1.45 tff(328,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[327, 325])).
% 1.23/1.45 tff(329,plain,
% 1.23/1.45 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(330,plain,
% 1.23/1.45 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[329, 328])).
% 1.23/1.45 tff(331,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[330, 120, 324, 316, 308, 292, 272, 10, 284])).
% 1.23/1.45 tff(332,plain,((~hskp33) | (~c0_1(a1084)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(333,plain,
% 1.23/1.45 (~hskp33),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[332, 257, 254, 255, 253])).
% 1.23/1.45 tff(334,assumption,(hskp15), introduced(assumption)).
% 1.23/1.45 tff(335,plain,
% 1.23/1.45 (((~hskp15) | (~c1_1(a1059))) <=> ((~hskp15) | (~c1_1(a1059)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(336,plain,
% 1.23/1.45 (((~c1_1(a1059)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a1059)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(337,axiom,((~c1_1(a1059)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause232')).
% 1.23/1.45 tff(338,plain,
% 1.23/1.45 ((~hskp15) | (~c1_1(a1059))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.23/1.45 tff(339,plain,
% 1.23/1.45 ((~hskp15) | (~c1_1(a1059))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[338, 335])).
% 1.23/1.45 tff(340,plain,
% 1.23/1.45 (~c1_1(a1059)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[339, 334])).
% 1.23/1.45 tff(341,plain,
% 1.23/1.45 (((~hskp15) | c2_1(a1059)) <=> ((~hskp15) | c2_1(a1059))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(342,axiom,((~hskp15) | c2_1(a1059)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 1.23/1.45 tff(343,plain,
% 1.23/1.45 ((~hskp15) | c2_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.23/1.45 tff(344,plain,
% 1.23/1.45 ((~hskp15) | c2_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[343, 341])).
% 1.23/1.45 tff(345,plain,
% 1.23/1.45 ((~hskp15) | c2_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[344, 341])).
% 1.23/1.45 tff(346,plain,
% 1.23/1.45 ((~hskp15) | c2_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[345, 341])).
% 1.23/1.45 tff(347,plain,
% 1.23/1.45 ((~hskp15) | c2_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[346, 341])).
% 1.23/1.45 tff(348,plain,
% 1.23/1.45 (c2_1(a1059)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[347, 334])).
% 1.23/1.45 tff(349,assumption,(~c0_1(a1059)), introduced(assumption)).
% 1.23/1.45 tff(350,assumption,(~c1_1(a1059)), introduced(assumption)).
% 1.23/1.45 tff(351,assumption,(c2_1(a1059)), introduced(assumption)).
% 1.23/1.45 tff(352,plain,
% 1.23/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(353,plain,
% 1.23/1.45 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084)) <=> (c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(354,plain,
% 1.23/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[353])).
% 1.23/1.45 tff(355,plain,
% 1.23/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[354, 352])).
% 1.23/1.45 tff(356,plain,
% 1.23/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(357,plain,
% 1.23/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[356, 355])).
% 1.23/1.45 tff(358,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[357, 120, 253, 351, 254, 255, 350, 221, 257, 349])).
% 1.23/1.45 tff(359,plain,(c0_1(a1059) | (~c0_1(a1084)) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | c2_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(360,plain,
% 1.23/1.45 (c0_1(a1059)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[359, 348, 257, 254, 255, 340, 253])).
% 1.23/1.45 tff(361,plain,
% 1.23/1.45 (((~hskp15) | c3_1(a1059)) <=> ((~hskp15) | c3_1(a1059))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(362,axiom,((~hskp15) | c3_1(a1059)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.23/1.45 tff(363,plain,
% 1.23/1.45 ((~hskp15) | c3_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.23/1.45 tff(364,plain,
% 1.23/1.45 ((~hskp15) | c3_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[363, 361])).
% 1.23/1.45 tff(365,plain,
% 1.23/1.45 ((~hskp15) | c3_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[364, 361])).
% 1.23/1.45 tff(366,plain,
% 1.23/1.45 ((~hskp15) | c3_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[365, 361])).
% 1.23/1.45 tff(367,plain,
% 1.23/1.45 ((~hskp15) | c3_1(a1059)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[366, 361])).
% 1.23/1.45 tff(368,plain,
% 1.23/1.45 (c3_1(a1059)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[367, 334])).
% 1.23/1.45 tff(369,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(370,plain,
% 1.23/1.45 ((hskp53 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059))) <=> (hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(371,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[370])).
% 1.23/1.45 tff(372,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[371, 369])).
% 1.23/1.45 tff(373,plain,
% 1.23/1.45 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(374,plain,
% 1.23/1.45 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[373, 372])).
% 1.23/1.45 tff(375,plain,
% 1.23/1.45 (hskp53),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[374, 120, 368, 348, 340, 20, 360])).
% 1.23/1.45 tff(376,plain,
% 1.23/1.45 (c0_1(a1073)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[307, 375])).
% 1.23/1.45 tff(377,plain,
% 1.23/1.45 (c2_1(a1073)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[315, 375])).
% 1.23/1.45 tff(378,plain,
% 1.23/1.45 (c1_1(a1073)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[323, 375])).
% 1.23/1.45 tff(379,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(380,plain,
% 1.23/1.45 (((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059))) <=> ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(381,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[380])).
% 1.23/1.45 tff(382,plain,
% 1.23/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[381, 379])).
% 1.23/1.45 tff(383,plain,
% 1.23/1.45 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(384,plain,
% 1.23/1.45 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.23/1.45 tff(385,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[384, 120, 378, 377, 376, 368, 348, 10, 360])).
% 1.23/1.45 tff(386,plain,((~hskp15) | c2_1(a1084) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(387,plain,
% 1.23/1.45 (~hskp15),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[386, 257, 254, 255, 253])).
% 1.23/1.45 tff(388,assumption,(hskp10), introduced(assumption)).
% 1.23/1.45 tff(389,plain,
% 1.23/1.45 (((~hskp10) | (~c2_1(a1039))) <=> ((~hskp10) | (~c2_1(a1039)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(390,plain,
% 1.23/1.45 (((~c2_1(a1039)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a1039)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(391,axiom,((~c2_1(a1039)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause241')).
% 1.23/1.45 tff(392,plain,
% 1.23/1.45 ((~hskp10) | (~c2_1(a1039))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.23/1.45 tff(393,plain,
% 1.23/1.45 ((~hskp10) | (~c2_1(a1039))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[392, 389])).
% 1.23/1.45 tff(394,plain,
% 1.23/1.45 (~c2_1(a1039)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[393, 388])).
% 1.23/1.45 tff(395,plain,
% 1.23/1.45 (((~hskp10) | c1_1(a1039)) <=> ((~hskp10) | c1_1(a1039))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(396,axiom,((~hskp10) | c1_1(a1039)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.23/1.46 tff(397,plain,
% 1.23/1.46 ((~hskp10) | c1_1(a1039)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.23/1.46 tff(398,plain,
% 1.23/1.46 ((~hskp10) | c1_1(a1039)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[397, 395])).
% 1.23/1.46 tff(399,plain,
% 1.23/1.46 ((~hskp10) | c1_1(a1039)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[398, 395])).
% 1.23/1.46 tff(400,plain,
% 1.23/1.46 ((~hskp10) | c1_1(a1039)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[399, 395])).
% 1.23/1.46 tff(401,plain,
% 1.23/1.46 ((~hskp10) | c1_1(a1039)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[400, 395])).
% 1.23/1.46 tff(402,plain,
% 1.23/1.46 (c1_1(a1039)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[401, 388])).
% 1.23/1.46 tff(403,plain,
% 1.23/1.46 (((~hskp10) | (~c0_1(a1039))) <=> ((~hskp10) | (~c0_1(a1039)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(404,plain,
% 1.23/1.46 (((~c0_1(a1039)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a1039)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(405,axiom,((~c0_1(a1039)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause242')).
% 1.23/1.46 tff(406,plain,
% 1.23/1.46 ((~hskp10) | (~c0_1(a1039))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[405, 404])).
% 1.23/1.46 tff(407,plain,
% 1.23/1.46 ((~hskp10) | (~c0_1(a1039))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[406, 403])).
% 1.23/1.46 tff(408,plain,
% 1.23/1.46 (~c0_1(a1039)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[407, 388])).
% 1.23/1.46 tff(409,assumption,(~c0_1(a1039)), introduced(assumption)).
% 1.23/1.46 tff(410,assumption,(~c2_1(a1039)), introduced(assumption)).
% 1.23/1.46 tff(411,assumption,(c1_1(a1039)), introduced(assumption)).
% 1.23/1.46 tff(412,assumption,(c2_1(a1084)), introduced(assumption)).
% 1.23/1.46 tff(413,plain,
% 1.23/1.46 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.23/1.46 inference(bind,[status(th)],[])).
% 1.23/1.46 tff(414,plain,
% 1.23/1.46 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.23/1.46 inference(quant_intro,[status(thm)],[413])).
% 1.23/1.46 tff(415,plain,
% 1.23/1.46 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(416,plain,
% 1.23/1.46 (^[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) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.31/1.46 inference(bind,[status(th)],[])).
% 1.31/1.46 tff(417,plain,
% 1.31/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.46 inference(quant_intro,[status(thm)],[416])).
% 1.31/1.46 tff(418,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause292')).
% 1.31/1.46 tff(419,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.31/1.46 tff(420,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[419, 415])).
% 1.31/1.46 tff(421,plain,(
% 1.31/1.46 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.46 inference(skolemize,[status(sab)],[420])).
% 1.31/1.46 tff(422,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[421, 414])).
% 1.31/1.46 tff(423,plain,
% 1.31/1.46 (^[V: $i, U: $i] : refl((hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.31/1.46 inference(bind,[status(th)],[])).
% 1.31/1.46 tff(424,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.46 inference(quant_intro,[status(thm)],[423])).
% 1.31/1.46 tff(425,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(426,plain,
% 1.31/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~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(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp47) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp47))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp47) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp47) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.31/1.46 inference(bind,[status(th)],[])).
% 1.31/1.46 tff(427,plain,
% 1.31/1.46 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp47) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.46 inference(quant_intro,[status(thm)],[426])).
% 1.31/1.46 tff(428,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause303')).
% 1.31/1.46 tff(429,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[428, 427])).
% 1.31/1.46 tff(430,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[429, 425])).
% 1.31/1.46 tff(431,plain,(
% 1.31/1.46 ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.46 inference(skolemize,[status(sab)],[430])).
% 1.31/1.46 tff(432,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[431, 424])).
% 1.31/1.46 tff(433,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(434,plain,
% 1.31/1.46 ((hskp47 | (~ndr1_0) | c3_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084))) <=> (hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(435,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084))))),
% 1.31/1.46 inference(monotonicity,[status(thm)],[434])).
% 1.31/1.46 tff(436,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.31/1.46 inference(transitivity,[status(thm)],[435, 433])).
% 1.31/1.46 tff(437,plain,
% 1.31/1.46 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 1.31/1.46 inference(quant_inst,[status(thm)],[])).
% 1.31/1.46 tff(438,plain,
% 1.31/1.46 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.31/1.46 tff(439,plain,
% 1.31/1.46 (hskp47 | (~c2_1(a1084))),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[438, 120, 253, 254, 255, 432])).
% 1.31/1.46 tff(440,plain,
% 1.31/1.46 (hskp47),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[439, 412])).
% 1.31/1.46 tff(441,plain,
% 1.31/1.46 (((~hskp47) | c3_1(a1056)) <=> ((~hskp47) | c3_1(a1056))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(442,axiom,((~hskp47) | c3_1(a1056)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.31/1.46 tff(443,plain,
% 1.31/1.46 ((~hskp47) | c3_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[442, 441])).
% 1.31/1.46 tff(444,plain,
% 1.31/1.46 ((~hskp47) | c3_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[443, 441])).
% 1.31/1.46 tff(445,plain,
% 1.31/1.46 ((~hskp47) | c3_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[444, 441])).
% 1.31/1.46 tff(446,plain,
% 1.31/1.46 ((~hskp47) | c3_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[445, 441])).
% 1.31/1.46 tff(447,plain,
% 1.31/1.46 ((~hskp47) | c3_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[446, 441])).
% 1.31/1.46 tff(448,plain,
% 1.31/1.46 (c3_1(a1056)),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[447, 440])).
% 1.31/1.46 tff(449,plain,
% 1.31/1.46 (((~hskp47) | c1_1(a1056)) <=> ((~hskp47) | c1_1(a1056))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(450,axiom,((~hskp47) | c1_1(a1056)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.31/1.46 tff(451,plain,
% 1.31/1.46 ((~hskp47) | c1_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.31/1.46 tff(452,plain,
% 1.31/1.46 ((~hskp47) | c1_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[451, 449])).
% 1.31/1.46 tff(453,plain,
% 1.31/1.46 ((~hskp47) | c1_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[452, 449])).
% 1.31/1.46 tff(454,plain,
% 1.31/1.46 ((~hskp47) | c1_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[453, 449])).
% 1.31/1.46 tff(455,plain,
% 1.31/1.46 ((~hskp47) | c1_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[454, 449])).
% 1.31/1.46 tff(456,plain,
% 1.31/1.46 (c1_1(a1056)),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[455, 440])).
% 1.31/1.46 tff(457,plain,
% 1.31/1.46 (((~hskp47) | c2_1(a1056)) <=> ((~hskp47) | c2_1(a1056))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(458,axiom,((~hskp47) | c2_1(a1056)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.31/1.46 tff(459,plain,
% 1.31/1.46 ((~hskp47) | c2_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.31/1.46 tff(460,plain,
% 1.31/1.46 ((~hskp47) | c2_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[459, 457])).
% 1.31/1.46 tff(461,plain,
% 1.31/1.46 ((~hskp47) | c2_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[460, 457])).
% 1.31/1.46 tff(462,plain,
% 1.31/1.46 ((~hskp47) | c2_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[461, 457])).
% 1.31/1.46 tff(463,plain,
% 1.31/1.46 ((~hskp47) | c2_1(a1056)),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[462, 457])).
% 1.31/1.46 tff(464,plain,
% 1.31/1.46 (c2_1(a1056)),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[463, 440])).
% 1.31/1.46 tff(465,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(466,plain,
% 1.31/1.46 (((~ndr1_0) | (~c1_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)) | (~c3_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056))) <=> ((~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(467,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)) | (~c3_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056))))),
% 1.31/1.46 inference(monotonicity,[status(thm)],[466])).
% 1.31/1.46 tff(468,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)) | (~c3_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056)))),
% 1.31/1.46 inference(transitivity,[status(thm)],[467, 465])).
% 1.31/1.46 tff(469,plain,
% 1.31/1.46 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)) | (~c3_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)))),
% 1.31/1.46 inference(quant_inst,[status(thm)],[])).
% 1.31/1.46 tff(470,plain,
% 1.31/1.46 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[469, 468])).
% 1.31/1.46 tff(471,plain,
% 1.31/1.46 (~c0_1(a1056)),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[470, 120, 464, 456, 448, 10])).
% 1.31/1.46 tff(472,plain,
% 1.31/1.46 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)))),
% 1.31/1.46 inference(bind,[status(th)],[])).
% 1.31/1.46 tff(473,plain,
% 1.31/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 1.31/1.46 inference(quant_intro,[status(thm)],[472])).
% 1.31/1.46 tff(474,plain,
% 1.31/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(475,plain,
% 1.31/1.46 (^[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))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), (((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), ((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W))), (((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))))),
% 1.31/1.46 inference(bind,[status(th)],[])).
% 1.31/1.46 tff(476,plain,
% 1.31/1.46 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 1.31/1.46 inference(quant_intro,[status(thm)],[475])).
% 1.31/1.46 tff(477,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause315')).
% 1.31/1.46 tff(478,plain,
% 1.31/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[477, 476])).
% 1.31/1.46 tff(479,plain,
% 1.31/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[478, 474])).
% 1.31/1.46 tff(480,plain,(
% 1.31/1.46 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 1.31/1.46 inference(skolemize,[status(sab)],[479])).
% 1.31/1.46 tff(481,plain,
% 1.31/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[480, 473])).
% 1.31/1.46 tff(482,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(483,plain,
% 1.31/1.46 ((hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039))) <=> (hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(484,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056))))),
% 1.31/1.46 inference(monotonicity,[status(thm)],[483])).
% 1.31/1.46 tff(485,plain,
% 1.31/1.46 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)))),
% 1.31/1.46 inference(transitivity,[status(thm)],[484, 482])).
% 1.31/1.46 tff(486,plain,
% 1.31/1.46 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))),
% 1.31/1.46 inference(quant_inst,[status(thm)],[])).
% 1.31/1.46 tff(487,plain,
% 1.31/1.46 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[486, 485])).
% 1.31/1.46 tff(488,plain,
% 1.31/1.46 (hskp25),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[487, 120, 464, 456, 448, 411, 410, 409, 252])).
% 1.31/1.46 tff(489,plain,
% 1.31/1.46 (((~hskp25) | (~c2_1(a1091))) <=> ((~hskp25) | (~c2_1(a1091)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(490,plain,
% 1.31/1.46 (((~c2_1(a1091)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a1091)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(491,axiom,((~c2_1(a1091)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause215')).
% 1.31/1.46 tff(492,plain,
% 1.31/1.46 ((~hskp25) | (~c2_1(a1091))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.31/1.46 tff(493,plain,
% 1.31/1.46 ((~hskp25) | (~c2_1(a1091))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[492, 489])).
% 1.31/1.46 tff(494,plain,
% 1.31/1.46 (~c2_1(a1091)),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[493, 488])).
% 1.31/1.46 tff(495,plain,
% 1.31/1.46 (((~hskp25) | (~c0_1(a1091))) <=> ((~hskp25) | (~c0_1(a1091)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(496,plain,
% 1.31/1.46 (((~c0_1(a1091)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1091)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(497,axiom,((~c0_1(a1091)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause214')).
% 1.31/1.46 tff(498,plain,
% 1.31/1.46 ((~hskp25) | (~c0_1(a1091))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[497, 496])).
% 1.31/1.46 tff(499,plain,
% 1.31/1.46 ((~hskp25) | (~c0_1(a1091))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[498, 495])).
% 1.31/1.46 tff(500,plain,
% 1.31/1.46 (~c0_1(a1091)),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[499, 488])).
% 1.31/1.46 tff(501,plain,
% 1.31/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(502,plain,
% 1.31/1.46 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1056) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1091) | c1_1(a1091) | c2_1(a1091)) <=> (c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(503,plain,
% 1.31/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1056) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1091) | c1_1(a1091) | c2_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084))))),
% 1.31/1.46 inference(monotonicity,[status(thm)],[502])).
% 1.31/1.46 tff(504,plain,
% 1.31/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1056) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1091) | c1_1(a1091) | c2_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084)))),
% 1.31/1.46 inference(transitivity,[status(thm)],[503, 501])).
% 1.31/1.46 tff(505,plain,
% 1.31/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1056) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1091) | c1_1(a1091) | c2_1(a1091))),
% 1.31/1.46 inference(quant_inst,[status(thm)],[])).
% 1.31/1.46 tff(506,plain,
% 1.31/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[505, 504])).
% 1.31/1.46 tff(507,plain,
% 1.31/1.46 (c1_1(a1091)),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[506, 120, 464, 448, 254, 255, 500, 494, 481, 412, 471])).
% 1.31/1.46 tff(508,plain,
% 1.31/1.46 (^[V: $i, U: $i] : refl((hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.31/1.46 inference(bind,[status(th)],[])).
% 1.31/1.46 tff(509,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.31/1.46 inference(quant_intro,[status(thm)],[508])).
% 1.31/1.46 tff(510,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.31/1.46 inference(rewrite,[status(thm)],[])).
% 1.31/1.46 tff(511,plain,
% 1.31/1.46 (^[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(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp34) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp34))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp34) <=> (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp34) <=> (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.31/1.46 inference(bind,[status(th)],[])).
% 1.31/1.46 tff(512,plain,
% 1.31/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp34) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.31/1.46 inference(quant_intro,[status(thm)],[511])).
% 1.31/1.46 tff(513,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause289')).
% 1.31/1.46 tff(514,plain,
% 1.31/1.46 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.31/1.46 inference(modus_ponens,[status(thm)],[513, 512])).
% 1.31/1.47 tff(515,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[514, 510])).
% 1.31/1.47 tff(516,plain,(
% 1.31/1.47 ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.31/1.47 inference(skolemize,[status(sab)],[515])).
% 1.31/1.47 tff(517,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[516, 509])).
% 1.31/1.47 tff(518,plain,
% 1.31/1.47 (((~hskp25) | (~c3_1(a1091))) <=> ((~hskp25) | (~c3_1(a1091)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(519,plain,
% 1.31/1.47 (((~c3_1(a1091)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a1091)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(520,axiom,((~c3_1(a1091)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause213')).
% 1.31/1.47 tff(521,plain,
% 1.31/1.47 ((~hskp25) | (~c3_1(a1091))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.31/1.47 tff(522,plain,
% 1.31/1.47 ((~hskp25) | (~c3_1(a1091))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[521, 518])).
% 1.31/1.47 tff(523,plain,
% 1.31/1.47 (~c3_1(a1091)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[522, 488])).
% 1.31/1.47 tff(524,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(525,plain,
% 1.31/1.47 ((hskp34 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c3_1(a1091) | c2_1(a1091) | (~c1_1(a1091))) <=> (hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(526,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c3_1(a1091) | c2_1(a1091) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[525])).
% 1.31/1.47 tff(527,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c3_1(a1091) | c2_1(a1091) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[526, 524])).
% 1.31/1.47 tff(528,plain,
% 1.31/1.47 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c3_1(a1091) | c2_1(a1091) | (~c1_1(a1091)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(529,plain,
% 1.31/1.47 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.31/1.47 tff(530,plain,
% 1.31/1.47 (hskp34),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[529, 120, 253, 254, 255, 523, 494, 517, 507])).
% 1.31/1.47 tff(531,plain,
% 1.31/1.47 (((~hskp34) | (~c1_1(a1032))) <=> ((~hskp34) | (~c1_1(a1032)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(532,plain,
% 1.31/1.47 (((~c1_1(a1032)) | (~hskp34)) <=> ((~hskp34) | (~c1_1(a1032)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(533,axiom,((~c1_1(a1032)) | (~hskp34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 1.31/1.47 tff(534,plain,
% 1.31/1.47 ((~hskp34) | (~c1_1(a1032))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.31/1.47 tff(535,plain,
% 1.31/1.47 ((~hskp34) | (~c1_1(a1032))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[534, 531])).
% 1.31/1.47 tff(536,plain,
% 1.31/1.47 (~c1_1(a1032)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[535, 530])).
% 1.31/1.47 tff(537,plain,
% 1.31/1.47 (((~hskp34) | (~c2_1(a1032))) <=> ((~hskp34) | (~c2_1(a1032)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(538,plain,
% 1.31/1.47 (((~c2_1(a1032)) | (~hskp34)) <=> ((~hskp34) | (~c2_1(a1032)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(539,axiom,((~c2_1(a1032)) | (~hskp34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.31/1.47 tff(540,plain,
% 1.31/1.47 ((~hskp34) | (~c2_1(a1032))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[539, 538])).
% 1.31/1.47 tff(541,plain,
% 1.31/1.47 ((~hskp34) | (~c2_1(a1032))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[540, 537])).
% 1.31/1.47 tff(542,plain,
% 1.31/1.47 (~c2_1(a1032)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[541, 530])).
% 1.31/1.47 tff(543,plain,
% 1.31/1.47 (((~hskp34) | c3_1(a1032)) <=> ((~hskp34) | c3_1(a1032))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(544,axiom,((~hskp34) | c3_1(a1032)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.31/1.47 tff(545,plain,
% 1.31/1.47 ((~hskp34) | c3_1(a1032)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[544, 543])).
% 1.31/1.47 tff(546,plain,
% 1.31/1.47 ((~hskp34) | c3_1(a1032)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[545, 543])).
% 1.31/1.47 tff(547,plain,
% 1.31/1.47 ((~hskp34) | c3_1(a1032)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[546, 543])).
% 1.31/1.47 tff(548,plain,
% 1.31/1.47 ((~hskp34) | c3_1(a1032)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[547, 543])).
% 1.31/1.47 tff(549,plain,
% 1.31/1.47 ((~hskp34) | c3_1(a1032)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[548, 543])).
% 1.31/1.47 tff(550,plain,
% 1.31/1.47 (c3_1(a1032)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[549, 530])).
% 1.31/1.47 tff(551,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(552,plain,
% 1.31/1.47 ((hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1032) | c1_1(a1032) | (~c3_1(a1032))) <=> (hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(553,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1032) | c1_1(a1032) | (~c3_1(a1032)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[552])).
% 1.31/1.47 tff(554,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1032) | c1_1(a1032) | (~c3_1(a1032)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[553, 551])).
% 1.31/1.47 tff(555,plain,
% 1.31/1.47 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1032) | c1_1(a1032) | (~c3_1(a1032)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(556,plain,
% 1.31/1.47 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.31/1.47 tff(557,plain,
% 1.31/1.47 ($false),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[556, 120, 256, 253, 550, 255, 542, 536, 422, 412])).
% 1.31/1.47 tff(558,plain,((~c2_1(a1084)) | hskp1 | (~c0_1(a1084)) | c1_1(a1084) | c3_1(a1084) | (~c1_1(a1039)) | c2_1(a1039) | c0_1(a1039)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.47 tff(559,plain,
% 1.31/1.47 (~c2_1(a1084)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[558, 256, 253, 255, 254, 411, 410, 409])).
% 1.31/1.47 tff(560,plain,
% 1.31/1.47 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(561,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[560])).
% 1.31/1.47 tff(562,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(563,plain,
% 1.31/1.47 (^[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(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))))),
% 1.32/1.47 inference(bind,[status(th)],[])).
% 1.32/1.47 tff(564,plain,
% 1.32/1.47 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.32/1.47 inference(quant_intro,[status(thm)],[563])).
% 1.32/1.47 tff(565,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause288')).
% 1.32/1.47 tff(566,plain,
% 1.32/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[565, 564])).
% 1.32/1.47 tff(567,plain,
% 1.32/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[566, 562])).
% 1.32/1.47 tff(568,plain,(
% 1.32/1.47 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.32/1.47 inference(skolemize,[status(sab)],[567])).
% 1.32/1.47 tff(569,plain,
% 1.32/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[568, 561])).
% 1.32/1.47 tff(570,plain,
% 1.32/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(571,plain,
% 1.32/1.47 ((hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039)) <=> (hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(572,plain,
% 1.32/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084))))),
% 1.32/1.47 inference(monotonicity,[status(thm)],[571])).
% 1.32/1.47 tff(573,plain,
% 1.32/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.47 inference(transitivity,[status(thm)],[572, 570])).
% 1.32/1.47 tff(574,plain,
% 1.32/1.47 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))),
% 1.32/1.47 inference(quant_inst,[status(thm)],[])).
% 1.32/1.47 tff(575,plain,
% 1.32/1.47 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.32/1.47 tff(576,plain,
% 1.32/1.47 (c3_1(a1039)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[575, 120, 256, 253, 255, 410, 409, 569, 559])).
% 1.32/1.47 tff(577,plain,
% 1.32/1.47 (~hskp33),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[332, 559, 254, 255, 253])).
% 1.32/1.47 tff(578,plain,
% 1.32/1.47 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(579,plain,
% 1.32/1.47 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039))) <=> (hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(580,plain,
% 1.32/1.47 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039))))),
% 1.32/1.47 inference(monotonicity,[status(thm)],[579])).
% 1.32/1.47 tff(581,plain,
% 1.32/1.47 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)))),
% 1.32/1.47 inference(transitivity,[status(thm)],[580, 578])).
% 1.32/1.47 tff(582,plain,
% 1.32/1.47 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)))),
% 1.32/1.47 inference(quant_inst,[status(thm)],[])).
% 1.32/1.47 tff(583,plain,
% 1.32/1.47 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[582, 581])).
% 1.32/1.47 tff(584,plain,
% 1.32/1.47 (hskp33 | hskp15 | c2_1(a1039) | (~c3_1(a1039))),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[583, 120, 409, 52])).
% 1.32/1.47 tff(585,plain,
% 1.32/1.47 (hskp15),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[584, 577, 410, 576])).
% 1.32/1.47 tff(586,plain,
% 1.32/1.47 (~c1_1(a1059)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[339, 585])).
% 1.32/1.47 tff(587,plain,
% 1.32/1.47 (c2_1(a1059)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[347, 585])).
% 1.32/1.47 tff(588,plain,
% 1.32/1.47 (c0_1(a1059)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[359, 587, 253, 254, 255, 586, 559])).
% 1.32/1.47 tff(589,plain,
% 1.32/1.47 (c3_1(a1059)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[367, 585])).
% 1.32/1.47 tff(590,plain,
% 1.32/1.47 (hskp53 | (~c0_1(a1059))),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[374, 120, 589, 587, 586, 20])).
% 1.32/1.47 tff(591,plain,
% 1.32/1.47 (hskp53),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[590, 588])).
% 1.32/1.47 tff(592,plain,
% 1.32/1.47 (c0_1(a1073)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[307, 591])).
% 1.32/1.47 tff(593,plain,
% 1.32/1.47 (c2_1(a1073)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[315, 591])).
% 1.32/1.47 tff(594,plain,
% 1.32/1.47 (c1_1(a1073)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[323, 591])).
% 1.32/1.47 tff(595,plain,
% 1.32/1.47 ($false),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[384, 120, 594, 593, 592, 589, 587, 10, 588])).
% 1.32/1.47 tff(596,plain,(hskp1 | (~c0_1(a1084)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~c1_1(a1039))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.47 tff(597,plain,
% 1.32/1.47 ($false),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[596, 408, 402, 254, 255, 253, 256, 394])).
% 1.32/1.47 tff(598,plain,((~hskp10) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.32/1.47 tff(599,plain,
% 1.32/1.47 (~hskp10),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[598, 256, 255, 253, 254])).
% 1.32/1.47 tff(600,assumption,(~c0_1(a1079)), introduced(assumption)).
% 1.32/1.47 tff(601,assumption,(~c2_1(a1079)), introduced(assumption)).
% 1.32/1.47 tff(602,plain,
% 1.32/1.47 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(603,plain,
% 1.32/1.47 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079))) <=> (hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(604,plain,
% 1.32/1.47 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079))))),
% 1.32/1.47 inference(monotonicity,[status(thm)],[603])).
% 1.32/1.47 tff(605,plain,
% 1.32/1.47 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079)))),
% 1.32/1.47 inference(transitivity,[status(thm)],[604, 602])).
% 1.32/1.47 tff(606,plain,
% 1.32/1.47 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)))),
% 1.32/1.47 inference(quant_inst,[status(thm)],[])).
% 1.32/1.47 tff(607,plain,
% 1.32/1.47 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.32/1.47 tff(608,plain,
% 1.32/1.47 (c0_1(a1079) | (~c3_1(a1079))),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[607, 120, 21, 42, 601, 52])).
% 1.32/1.47 tff(609,plain,
% 1.32/1.47 (~c3_1(a1079)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[608, 600])).
% 1.32/1.47 tff(610,plain,
% 1.32/1.47 (c0_1(a1079) | c3_1(a1079)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[126, 120, 53, 601, 73])).
% 1.32/1.47 tff(611,plain,
% 1.32/1.47 ($false),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[610, 609, 600])).
% 1.32/1.47 tff(612,plain,(c0_1(a1079) | hskp10 | c2_1(a1079) | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.32/1.47 tff(613,plain,
% 1.32/1.47 ($false),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[612, 80, 86, 53, 21, 42])).
% 1.32/1.47 tff(614,plain,((~hskp19) | hskp10 | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.32/1.47 tff(615,plain,
% 1.32/1.47 (~hskp19),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[614, 21, 599, 42])).
% 1.32/1.47 tff(616,plain,
% 1.32/1.47 (^[U: $i] : refl((hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.32/1.47 inference(bind,[status(th)],[])).
% 1.32/1.47 tff(617,plain,
% 1.32/1.47 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.32/1.47 inference(quant_intro,[status(thm)],[616])).
% 1.32/1.47 tff(618,plain,
% 1.32/1.47 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(619,plain,
% 1.32/1.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp20))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.32/1.47 inference(bind,[status(th)],[])).
% 1.32/1.47 tff(620,plain,
% 1.32/1.47 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.32/1.47 inference(quant_intro,[status(thm)],[619])).
% 1.32/1.47 tff(621,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause269')).
% 1.32/1.47 tff(622,plain,
% 1.32/1.47 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[621, 620])).
% 1.32/1.47 tff(623,plain,
% 1.32/1.47 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[622, 618])).
% 1.32/1.47 tff(624,plain,(
% 1.32/1.47 ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.32/1.47 inference(skolemize,[status(sab)],[623])).
% 1.32/1.47 tff(625,plain,
% 1.32/1.47 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[624, 617])).
% 1.32/1.47 tff(626,plain,
% 1.32/1.47 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(627,plain,
% 1.32/1.47 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084))) <=> (hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(628,plain,
% 1.32/1.47 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084))))),
% 1.32/1.47 inference(monotonicity,[status(thm)],[627])).
% 1.32/1.47 tff(629,plain,
% 1.32/1.47 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)))),
% 1.32/1.47 inference(transitivity,[status(thm)],[628, 626])).
% 1.32/1.47 tff(630,plain,
% 1.32/1.47 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.47 inference(quant_inst,[status(thm)],[])).
% 1.32/1.47 tff(631,plain,
% 1.32/1.47 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[630, 629])).
% 1.32/1.47 tff(632,plain,
% 1.32/1.47 (hskp20 | hskp19),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[631, 120, 253, 254, 255, 625])).
% 1.32/1.47 tff(633,plain,
% 1.32/1.47 (hskp20),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[632, 615])).
% 1.32/1.47 tff(634,assumption,(hskp20), introduced(assumption)).
% 1.32/1.47 tff(635,plain,
% 1.32/1.47 (((~hskp20) | (~c2_1(a1080))) <=> ((~hskp20) | (~c2_1(a1080)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(636,plain,
% 1.32/1.47 (((~c2_1(a1080)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a1080)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(637,axiom,((~c2_1(a1080)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause224')).
% 1.32/1.47 tff(638,plain,
% 1.32/1.47 ((~hskp20) | (~c2_1(a1080))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[637, 636])).
% 1.32/1.47 tff(639,plain,
% 1.32/1.47 ((~hskp20) | (~c2_1(a1080))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[638, 635])).
% 1.32/1.47 tff(640,plain,
% 1.32/1.47 (~c2_1(a1080)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[639, 634])).
% 1.32/1.47 tff(641,plain,
% 1.32/1.47 (((~hskp20) | (~c0_1(a1080))) <=> ((~hskp20) | (~c0_1(a1080)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(642,plain,
% 1.32/1.47 (((~c0_1(a1080)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a1080)))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(643,axiom,((~c0_1(a1080)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause223')).
% 1.32/1.48 tff(644,plain,
% 1.32/1.48 ((~hskp20) | (~c0_1(a1080))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.32/1.48 tff(645,plain,
% 1.32/1.48 ((~hskp20) | (~c0_1(a1080))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[644, 641])).
% 1.32/1.48 tff(646,plain,
% 1.32/1.48 (~c0_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[645, 634])).
% 1.32/1.48 tff(647,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(648,plain,
% 1.32/1.48 ((hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1080) | c3_1(a1080) | c2_1(a1080)) <=> (hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(649,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1080) | c3_1(a1080) | c2_1(a1080))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[648])).
% 1.32/1.48 tff(650,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1080) | c3_1(a1080) | c2_1(a1080))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.48 inference(transitivity,[status(thm)],[649, 647])).
% 1.32/1.48 tff(651,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1080) | c3_1(a1080) | c2_1(a1080))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(652,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[651, 650])).
% 1.32/1.48 tff(653,plain,
% 1.32/1.48 (c3_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[652, 120, 256, 253, 255, 646, 640, 569, 257])).
% 1.32/1.48 tff(654,plain,
% 1.32/1.48 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(655,plain,
% 1.32/1.48 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080))) <=> (hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(656,plain,
% 1.32/1.48 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[655])).
% 1.32/1.48 tff(657,plain,
% 1.32/1.48 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)))),
% 1.32/1.48 inference(transitivity,[status(thm)],[656, 654])).
% 1.32/1.48 tff(658,plain,
% 1.32/1.48 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(659,plain,
% 1.32/1.48 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[658, 657])).
% 1.32/1.48 tff(660,plain,
% 1.32/1.48 ($false),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[659, 120, 21, 42, 646, 640, 52, 653])).
% 1.32/1.48 tff(661,plain,((~hskp20) | hskp33 | hskp15 | hskp1 | (~c0_1(a1084)) | c1_1(a1084) | c2_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.48 tff(662,plain,
% 1.32/1.48 (c2_1(a1084)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[661, 633, 42, 256, 253, 255, 21])).
% 1.32/1.48 tff(663,plain,
% 1.32/1.48 (((~hskp20) | (~c1_1(a1080))) <=> ((~hskp20) | (~c1_1(a1080)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(664,plain,
% 1.32/1.48 (((~c1_1(a1080)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a1080)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(665,axiom,((~c1_1(a1080)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause225')).
% 1.32/1.48 tff(666,plain,
% 1.32/1.48 ((~hskp20) | (~c1_1(a1080))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[665, 664])).
% 1.32/1.48 tff(667,plain,
% 1.32/1.48 ((~hskp20) | (~c1_1(a1080))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[666, 663])).
% 1.32/1.48 tff(668,plain,
% 1.32/1.48 (~c1_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[667, 633])).
% 1.32/1.48 tff(669,plain,
% 1.32/1.48 (~c2_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[639, 633])).
% 1.32/1.48 tff(670,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(671,plain,
% 1.32/1.48 ((hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080))) <=> (hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(672,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[671])).
% 1.32/1.48 tff(673,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 1.32/1.48 inference(transitivity,[status(thm)],[672, 670])).
% 1.32/1.48 tff(674,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(675,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[674, 673])).
% 1.32/1.48 tff(676,plain,
% 1.32/1.48 (~c3_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[675, 120, 256, 253, 255, 669, 668, 422, 662])).
% 1.32/1.48 tff(677,plain,
% 1.32/1.48 (~c0_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[645, 633])).
% 1.32/1.48 tff(678,plain,
% 1.32/1.48 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(679,plain,
% 1.32/1.48 ((hskp10 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | c3_1(a1080)) <=> (hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(680,plain,
% 1.32/1.48 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | c3_1(a1080))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080)))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[679])).
% 1.32/1.48 tff(681,plain,
% 1.32/1.48 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | c3_1(a1080))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080))),
% 1.32/1.48 inference(transitivity,[status(thm)],[680, 678])).
% 1.32/1.48 tff(682,plain,
% 1.32/1.48 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | c3_1(a1080))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(683,plain,
% 1.32/1.48 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[682, 681])).
% 1.32/1.48 tff(684,plain,
% 1.32/1.48 ($false),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[683, 120, 599, 677, 669, 73, 676])).
% 1.32/1.48 tff(685,plain,(hskp33 | hskp1 | (~c0_1(a1084)) | c1_1(a1084) | hskp15 | c3_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.48 tff(686,plain,
% 1.32/1.48 ($false),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[685, 387, 333, 253, 255, 256, 254])).
% 1.32/1.48 tff(687,plain,(c2_1(a1084) | (~c0_1(a1084)) | c1_1(a1084) | hskp1 | c3_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.48 tff(688,plain,
% 1.32/1.48 (c2_1(a1084)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[687, 256, 255, 253, 254])).
% 1.32/1.48 tff(689,plain,
% 1.32/1.48 (^[V: $i, U: $i] : refl((hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(690,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[689])).
% 1.32/1.48 tff(691,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(692,plain,
% 1.32/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp33) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp33))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp33) <=> (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp33) <=> (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(693,plain,
% 1.32/1.48 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp33) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[692])).
% 1.32/1.48 tff(694,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause300')).
% 1.32/1.48 tff(695,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[694, 693])).
% 1.32/1.48 tff(696,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[695, 691])).
% 1.32/1.48 tff(697,plain,(
% 1.32/1.48 ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.32/1.48 inference(skolemize,[status(sab)],[696])).
% 1.32/1.48 tff(698,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[697, 690])).
% 1.32/1.48 tff(699,plain,
% 1.32/1.48 (^[V: $i, U: $i] : refl((hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(700,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[699])).
% 1.32/1.48 tff(701,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(702,plain,
% 1.32/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) | hskp36) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) | hskp36))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(703,plain,
% 1.32/1.48 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) | hskp36) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[702])).
% 1.32/1.48 tff(704,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) | hskp36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause310')).
% 1.32/1.48 tff(705,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[704, 703])).
% 1.32/1.48 tff(706,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[705, 701])).
% 1.32/1.48 tff(707,plain,(
% 1.32/1.48 ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.48 inference(skolemize,[status(sab)],[706])).
% 1.32/1.48 tff(708,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[707, 700])).
% 1.32/1.48 tff(709,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(710,plain,
% 1.32/1.48 ((hskp36 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056))) <=> (hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(711,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[710])).
% 1.32/1.48 tff(712,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 1.32/1.48 inference(transitivity,[status(thm)],[711, 709])).
% 1.32/1.48 tff(713,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(714,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[713, 712])).
% 1.32/1.48 tff(715,plain,
% 1.32/1.48 (hskp36),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[714, 120, 464, 456, 448, 708, 471])).
% 1.32/1.48 tff(716,plain,
% 1.32/1.48 (((~hskp36) | (~c0_1(a1034))) <=> ((~hskp36) | (~c0_1(a1034)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(717,plain,
% 1.32/1.48 (((~c0_1(a1034)) | (~hskp36)) <=> ((~hskp36) | (~c0_1(a1034)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(718,axiom,((~c0_1(a1034)) | (~hskp36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.32/1.48 tff(719,plain,
% 1.32/1.48 ((~hskp36) | (~c0_1(a1034))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[718, 717])).
% 1.32/1.48 tff(720,plain,
% 1.32/1.48 ((~hskp36) | (~c0_1(a1034))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[719, 716])).
% 1.32/1.48 tff(721,plain,
% 1.32/1.48 (~c0_1(a1034)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[720, 715])).
% 1.32/1.48 tff(722,plain,
% 1.32/1.48 (((~hskp36) | c1_1(a1034)) <=> ((~hskp36) | c1_1(a1034))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(723,axiom,((~hskp36) | c1_1(a1034)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.32/1.48 tff(724,plain,
% 1.32/1.48 ((~hskp36) | c1_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[723, 722])).
% 1.32/1.48 tff(725,plain,
% 1.32/1.48 ((~hskp36) | c1_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[724, 722])).
% 1.32/1.48 tff(726,plain,
% 1.32/1.48 ((~hskp36) | c1_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[725, 722])).
% 1.32/1.48 tff(727,plain,
% 1.32/1.48 ((~hskp36) | c1_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[726, 722])).
% 1.32/1.48 tff(728,plain,
% 1.32/1.48 ((~hskp36) | c1_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[727, 722])).
% 1.32/1.48 tff(729,plain,
% 1.32/1.48 (c1_1(a1034)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[728, 715])).
% 1.32/1.48 tff(730,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(731,plain,
% 1.32/1.48 ((hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1034) | c2_1(a1034) | (~c1_1(a1034))) <=> (hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(732,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1034) | c2_1(a1034) | (~c1_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[731])).
% 1.32/1.48 tff(733,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1034) | c2_1(a1034) | (~c1_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034)))),
% 1.32/1.48 inference(transitivity,[status(thm)],[732, 730])).
% 1.32/1.48 tff(734,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1034) | c2_1(a1034) | (~c1_1(a1034)))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(735,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.32/1.48 tff(736,plain,
% 1.32/1.48 (hskp33 | c2_1(a1034)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[735, 120, 464, 456, 448, 729, 721, 698])).
% 1.32/1.48 tff(737,plain,
% 1.32/1.48 (c2_1(a1034)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[736, 21])).
% 1.32/1.48 tff(738,assumption,(c3_1(a1056)), introduced(assumption)).
% 1.32/1.48 tff(739,assumption,(c1_1(a1056)), introduced(assumption)).
% 1.32/1.48 tff(740,assumption,(c2_1(a1056)), introduced(assumption)).
% 1.32/1.48 tff(741,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(742,plain,
% 1.32/1.48 ((hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079))) <=> (hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(743,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[742])).
% 1.32/1.48 tff(744,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 1.32/1.48 inference(transitivity,[status(thm)],[743, 741])).
% 1.32/1.48 tff(745,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(746,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[745, 744])).
% 1.32/1.48 tff(747,plain,
% 1.32/1.48 ($false),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[746, 120, 21, 740, 739, 738, 145, 86, 80, 698])).
% 1.32/1.48 tff(748,plain,((~hskp19) | hskp33 | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.48 tff(749,plain,
% 1.32/1.48 (~hskp19),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[748, 21, 464, 456, 448])).
% 1.32/1.48 tff(750,plain,
% 1.32/1.48 (hskp20),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[632, 749])).
% 1.32/1.48 tff(751,plain,
% 1.32/1.48 (~c1_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[667, 750])).
% 1.32/1.48 tff(752,plain,
% 1.32/1.48 (~c2_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[639, 750])).
% 1.32/1.48 tff(753,plain,
% 1.32/1.48 (~c0_1(a1080)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[645, 750])).
% 1.32/1.48 tff(754,plain,
% 1.32/1.48 (((~hskp36) | c3_1(a1034)) <=> ((~hskp36) | c3_1(a1034))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(755,axiom,((~hskp36) | c3_1(a1034)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.32/1.48 tff(756,plain,
% 1.32/1.48 ((~hskp36) | c3_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.32/1.48 tff(757,plain,
% 1.32/1.48 ((~hskp36) | c3_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[756, 754])).
% 1.32/1.48 tff(758,plain,
% 1.32/1.48 ((~hskp36) | c3_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[757, 754])).
% 1.32/1.48 tff(759,plain,
% 1.32/1.48 ((~hskp36) | c3_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[758, 754])).
% 1.32/1.48 tff(760,plain,
% 1.32/1.48 ((~hskp36) | c3_1(a1034)),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[759, 754])).
% 1.32/1.48 tff(761,plain,
% 1.32/1.48 (c3_1(a1034)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[760, 715])).
% 1.32/1.48 tff(762,plain,
% 1.32/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(763,plain,
% 1.32/1.48 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080)) <=> (c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(764,plain,
% 1.32/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[763])).
% 1.32/1.49 tff(765,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[764, 762])).
% 1.32/1.49 tff(766,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(767,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[766, 765])).
% 1.32/1.49 tff(768,plain,
% 1.32/1.49 ($false),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[767, 120, 761, 254, 255, 721, 753, 752, 751, 481, 412, 737])).
% 1.32/1.49 tff(769,plain,(hskp33 | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.49 tff(770,plain,
% 1.32/1.49 (hskp33),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[769, 688, 255, 254, 253])).
% 1.32/1.49 tff(771,plain,
% 1.32/1.49 (c2_1(a1031)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[271, 770])).
% 1.32/1.49 tff(772,plain,
% 1.32/1.49 (c3_1(a1031)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[291, 770])).
% 1.32/1.49 tff(773,plain,
% 1.32/1.49 (hskp47),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[439, 688])).
% 1.32/1.49 tff(774,plain,
% 1.32/1.49 (c3_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[447, 773])).
% 1.32/1.49 tff(775,plain,
% 1.32/1.49 (c1_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[455, 773])).
% 1.32/1.49 tff(776,plain,
% 1.32/1.49 (c2_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[463, 773])).
% 1.32/1.49 tff(777,plain,
% 1.32/1.49 (~c0_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[470, 120, 776, 775, 774, 10])).
% 1.32/1.49 tff(778,plain,
% 1.32/1.49 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(779,plain,
% 1.32/1.49 ((hskp43 | hskp10 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c2_1(a1056))) <=> (hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(780,plain,
% 1.32/1.49 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c2_1(a1056)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[779])).
% 1.32/1.49 tff(781,plain,
% 1.32/1.49 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c2_1(a1056)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[780, 778])).
% 1.32/1.49 tff(782,plain,
% 1.32/1.49 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c2_1(a1056)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(783,plain,
% 1.32/1.49 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[782, 781])).
% 1.32/1.49 tff(784,plain,
% 1.32/1.49 (hskp43 | c0_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[783, 120, 599, 776, 775, 63])).
% 1.32/1.49 tff(785,plain,
% 1.32/1.49 (hskp43),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[784, 777])).
% 1.32/1.49 tff(786,plain,
% 1.32/1.49 (c1_1(a1049)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[194, 785])).
% 1.32/1.49 tff(787,plain,
% 1.32/1.49 (c2_1(a1049)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[202, 785])).
% 1.32/1.49 tff(788,plain,
% 1.32/1.49 (c0_1(a1049)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[210, 785])).
% 1.32/1.49 tff(789,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(790,plain,
% 1.32/1.49 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(791,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[790])).
% 1.32/1.49 tff(792,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[791, 789])).
% 1.32/1.49 tff(793,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(794,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.32/1.49 tff(795,plain,
% 1.32/1.49 (~c0_1(a1031)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[794, 120, 788, 787, 786, 772, 771, 10])).
% 1.32/1.49 tff(796,plain,
% 1.32/1.49 (~c1_1(a1080)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[667, 634])).
% 1.32/1.49 tff(797,assumption,(c3_1(a1031)), introduced(assumption)).
% 1.32/1.49 tff(798,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(799,plain,
% 1.32/1.49 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080)) <=> (c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(800,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[799])).
% 1.32/1.49 tff(801,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[800, 798])).
% 1.32/1.49 tff(802,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(803,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[802, 801])).
% 1.32/1.49 tff(804,plain,
% 1.32/1.49 ($false),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[803, 120, 797, 275, 254, 255, 646, 640, 796, 481, 412, 273])).
% 1.32/1.49 tff(805,plain,((~hskp20) | (~c3_1(a1031)) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.49 tff(806,plain,
% 1.32/1.49 (~hskp20),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[805, 772, 771, 254, 255, 688, 795])).
% 1.32/1.49 tff(807,plain,
% 1.32/1.49 (hskp19),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[632, 806])).
% 1.32/1.49 tff(808,plain,
% 1.32/1.49 (~c2_1(a1079)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[79, 807])).
% 1.32/1.49 tff(809,plain,
% 1.32/1.49 (~c0_1(a1079)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[85, 807])).
% 1.32/1.49 tff(810,plain,
% 1.32/1.49 (c1_1(a1079)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[144, 807])).
% 1.32/1.49 tff(811,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(812,plain,
% 1.32/1.49 ((hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079))) <=> (hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(813,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[812])).
% 1.32/1.49 tff(814,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[813, 811])).
% 1.32/1.49 tff(815,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(816,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[815, 814])).
% 1.32/1.49 tff(817,plain,
% 1.32/1.49 (hskp25),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[816, 120, 776, 775, 774, 810, 809, 808, 252])).
% 1.32/1.49 tff(818,plain,
% 1.32/1.49 (~c2_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[493, 817])).
% 1.32/1.49 tff(819,plain,
% 1.32/1.49 (~c0_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[499, 817])).
% 1.32/1.49 tff(820,plain,
% 1.32/1.49 (~c3_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[522, 817])).
% 1.32/1.49 tff(821,plain,
% 1.32/1.49 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(822,plain,
% 1.32/1.49 ((hskp10 | (~ndr1_0) | c0_1(a1091) | c2_1(a1091) | c3_1(a1091)) <=> (hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(823,plain,
% 1.32/1.49 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1091) | c2_1(a1091) | c3_1(a1091))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0)))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[822])).
% 1.32/1.49 tff(824,plain,
% 1.32/1.49 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1091) | c2_1(a1091) | c3_1(a1091))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0))),
% 1.32/1.49 inference(transitivity,[status(thm)],[823, 821])).
% 1.32/1.49 tff(825,plain,
% 1.32/1.49 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1091) | c2_1(a1091) | c3_1(a1091))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(826,plain,
% 1.32/1.49 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[825, 824])).
% 1.32/1.49 tff(827,plain,
% 1.32/1.49 ($false),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[826, 120, 599, 820, 819, 818, 73])).
% 1.32/1.49 tff(828,plain,(hskp1 | (~c0_1(a1084)) | c3_1(a1084) | c1_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.49 tff(829,plain,
% 1.32/1.49 (hskp1),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[828, 242, 234, 228])).
% 1.32/1.49 tff(830,plain,
% 1.32/1.49 (((~hskp1) | (~c0_1(a1023))) <=> ((~hskp1) | (~c0_1(a1023)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(831,plain,
% 1.32/1.49 (((~c0_1(a1023)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1023)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(832,axiom,((~c0_1(a1023)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause259')).
% 1.32/1.49 tff(833,plain,
% 1.32/1.49 ((~hskp1) | (~c0_1(a1023))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[832, 831])).
% 1.32/1.49 tff(834,plain,
% 1.32/1.49 ((~hskp1) | (~c0_1(a1023))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[833, 830])).
% 1.32/1.49 tff(835,plain,
% 1.32/1.49 (~c0_1(a1023)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[834, 829])).
% 1.32/1.49 tff(836,plain,
% 1.32/1.49 (((~hskp1) | (~c1_1(a1023))) <=> ((~hskp1) | (~c1_1(a1023)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(837,plain,
% 1.32/1.49 (((~c1_1(a1023)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1023)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(838,axiom,((~c1_1(a1023)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause258')).
% 1.32/1.49 tff(839,plain,
% 1.32/1.49 ((~hskp1) | (~c1_1(a1023))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.32/1.49 tff(840,plain,
% 1.32/1.49 ((~hskp1) | (~c1_1(a1023))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[839, 836])).
% 1.32/1.49 tff(841,plain,
% 1.32/1.49 (~c1_1(a1023)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[840, 829])).
% 1.32/1.49 tff(842,plain,
% 1.32/1.49 (hskp1),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[828, 253, 254, 255])).
% 1.32/1.49 tff(843,plain,
% 1.32/1.49 (~c0_1(a1023)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[834, 842])).
% 1.32/1.49 tff(844,plain,
% 1.32/1.49 (~c1_1(a1023)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[840, 842])).
% 1.32/1.49 tff(845,plain,
% 1.32/1.49 (((~hskp1) | c2_1(a1023)) <=> ((~hskp1) | c2_1(a1023))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(846,axiom,((~hskp1) | c2_1(a1023)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.32/1.49 tff(847,plain,
% 1.32/1.49 ((~hskp1) | c2_1(a1023)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[846, 845])).
% 1.32/1.49 tff(848,plain,
% 1.32/1.49 ((~hskp1) | c2_1(a1023)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[847, 845])).
% 1.32/1.49 tff(849,plain,
% 1.32/1.49 ((~hskp1) | c2_1(a1023)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[848, 845])).
% 1.32/1.49 tff(850,plain,
% 1.32/1.49 ((~hskp1) | c2_1(a1023)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[849, 845])).
% 1.32/1.49 tff(851,plain,
% 1.32/1.49 ((~hskp1) | c2_1(a1023)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[850, 845])).
% 1.32/1.49 tff(852,plain,
% 1.32/1.49 (c2_1(a1023)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[851, 842])).
% 1.32/1.49 tff(853,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(854,plain,
% 1.32/1.49 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084)) <=> (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(855,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[854])).
% 1.32/1.49 tff(856,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[855, 853])).
% 1.32/1.49 tff(857,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(858,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.32/1.49 tff(859,plain,
% 1.32/1.49 (c2_1(a1084)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[858, 120, 253, 852, 254, 255, 844, 843, 221])).
% 1.32/1.49 tff(860,plain,
% 1.32/1.49 (hskp33),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[769, 859, 255, 254, 253])).
% 1.32/1.49 tff(861,plain,
% 1.32/1.49 (c3_1(a1031)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[291, 860])).
% 1.32/1.49 tff(862,plain,
% 1.32/1.49 (c2_1(a1031)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[271, 860])).
% 1.32/1.49 tff(863,plain,
% 1.32/1.49 (hskp47),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[439, 859])).
% 1.32/1.49 tff(864,plain,
% 1.32/1.49 (c3_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[447, 863])).
% 1.32/1.49 tff(865,plain,
% 1.32/1.49 (c1_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[455, 863])).
% 1.32/1.49 tff(866,plain,
% 1.32/1.49 (c2_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[463, 863])).
% 1.32/1.49 tff(867,plain,
% 1.32/1.49 (~c0_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[470, 120, 866, 865, 864, 10])).
% 1.32/1.49 tff(868,plain,
% 1.32/1.49 (hskp43 | hskp10 | c0_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[783, 120, 866, 865, 63])).
% 1.32/1.49 tff(869,plain,
% 1.32/1.49 (hskp43),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[868, 53, 867])).
% 1.32/1.49 tff(870,plain,
% 1.32/1.49 (c1_1(a1049)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[194, 869])).
% 1.32/1.49 tff(871,plain,
% 1.32/1.49 (c2_1(a1049)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[202, 869])).
% 1.32/1.49 tff(872,plain,
% 1.32/1.49 (c0_1(a1049)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[210, 869])).
% 1.32/1.49 tff(873,plain,
% 1.32/1.49 (~c0_1(a1031)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[794, 120, 872, 871, 870, 861, 862, 10])).
% 1.32/1.49 tff(874,plain,
% 1.32/1.49 (~hskp20),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[805, 873, 862, 254, 255, 859, 861])).
% 1.32/1.49 tff(875,plain,
% 1.32/1.49 (hskp19),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[632, 874])).
% 1.32/1.49 tff(876,plain,
% 1.32/1.49 (~c2_1(a1079)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[79, 875])).
% 1.32/1.49 tff(877,plain,
% 1.32/1.49 (~c0_1(a1079)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[85, 875])).
% 1.32/1.49 tff(878,plain,
% 1.32/1.49 (c1_1(a1079)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[144, 875])).
% 1.32/1.49 tff(879,plain,
% 1.32/1.49 (hskp25),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[816, 120, 866, 865, 864, 878, 877, 876, 252])).
% 1.32/1.49 tff(880,plain,
% 1.32/1.49 (~c2_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[493, 879])).
% 1.32/1.49 tff(881,plain,
% 1.32/1.49 (~c0_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[499, 879])).
% 1.32/1.49 tff(882,plain,
% 1.32/1.49 (~c3_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[522, 879])).
% 1.32/1.49 tff(883,plain,
% 1.32/1.49 ($false),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[826, 120, 53, 882, 881, 880, 73])).
% 1.32/1.49 tff(884,plain,(hskp10 | (~c0_1(a1084)) | c3_1(a1084) | c1_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.49 tff(885,plain,
% 1.32/1.49 (hskp10),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[884, 242, 234, 228])).
% 1.32/1.49 tff(886,plain,
% 1.32/1.49 (~c0_1(a1039)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[407, 885])).
% 1.32/1.49 tff(887,plain,
% 1.32/1.49 (~c2_1(a1039)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[393, 885])).
% 1.32/1.49 tff(888,plain,
% 1.32/1.49 (c1_1(a1039)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[401, 885])).
% 1.32/1.49 tff(889,plain,
% 1.32/1.49 (c2_1(a1023)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[851, 829])).
% 1.32/1.49 tff(890,plain,
% 1.32/1.49 (c2_1(a1084)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[858, 120, 242, 889, 234, 228, 841, 835, 221])).
% 1.32/1.49 tff(891,plain,
% 1.32/1.49 (hskp47 | (~c2_1(a1084))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[438, 120, 242, 234, 228, 432])).
% 1.32/1.49 tff(892,plain,
% 1.32/1.49 (hskp47),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[891, 890])).
% 1.32/1.49 tff(893,plain,
% 1.32/1.49 (c3_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[447, 892])).
% 1.32/1.49 tff(894,plain,
% 1.32/1.49 (c1_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[455, 892])).
% 1.32/1.49 tff(895,plain,
% 1.32/1.49 (c2_1(a1056)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[463, 892])).
% 1.32/1.49 tff(896,plain,
% 1.32/1.49 (hskp25),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[487, 120, 895, 894, 893, 888, 887, 886, 252])).
% 1.32/1.49 tff(897,plain,
% 1.32/1.49 (~c2_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[493, 896])).
% 1.32/1.49 tff(898,plain,
% 1.32/1.49 (~c3_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[522, 896])).
% 1.32/1.49 tff(899,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(900,plain,
% 1.32/1.49 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1091) | c1_1(a1091) | c2_1(a1091)) <=> (c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(901,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1091) | c1_1(a1091) | c2_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[900])).
% 1.32/1.49 tff(902,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1091) | c1_1(a1091) | c2_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[901, 899])).
% 1.32/1.49 tff(903,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1091) | c1_1(a1091) | c2_1(a1091))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(904,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[903, 902])).
% 1.32/1.49 tff(905,plain,
% 1.32/1.49 (c1_1(a1091)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[904, 120, 242, 889, 234, 228, 898, 897, 841, 835, 221])).
% 1.32/1.49 tff(906,plain,
% 1.32/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W)))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(907,plain,
% 1.32/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[906])).
% 1.32/1.49 tff(908,plain,
% 1.32/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(909,plain,
% 1.32/1.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(910,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[909])).
% 1.32/1.50 tff(911,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause312')).
% 1.32/1.50 tff(912,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.32/1.50 tff(913,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[912, 908])).
% 1.32/1.50 tff(914,plain,(
% 1.32/1.50 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 1.32/1.50 inference(skolemize,[status(sab)],[913])).
% 1.32/1.50 tff(915,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[914, 907])).
% 1.32/1.50 tff(916,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(917,plain,
% 1.32/1.50 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c0_1(a1023) | c3_1(a1023) | c1_1(a1023)) <=> (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(918,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c0_1(a1023) | c3_1(a1023) | c1_1(a1023))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[917])).
% 1.32/1.50 tff(919,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c0_1(a1023) | c3_1(a1023) | c1_1(a1023))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[918, 916])).
% 1.32/1.50 tff(920,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c0_1(a1023) | c3_1(a1023) | c1_1(a1023))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(921,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[920, 919])).
% 1.32/1.50 tff(922,plain,
% 1.32/1.50 (c3_1(a1023)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[921, 120, 889, 234, 228, 841, 835, 915, 890])).
% 1.32/1.50 tff(923,plain,
% 1.32/1.50 (^[V: $i, U: $i] : refl((hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(924,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[923])).
% 1.32/1.50 tff(925,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(926,plain,
% 1.32/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp35) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp35))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp35) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp35) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(927,plain,
% 1.32/1.50 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp35) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[926])).
% 1.32/1.50 tff(928,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause298')).
% 1.32/1.50 tff(929,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[928, 927])).
% 1.32/1.50 tff(930,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[929, 925])).
% 1.32/1.50 tff(931,plain,(
% 1.32/1.50 ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(skolemize,[status(sab)],[930])).
% 1.32/1.50 tff(932,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[931, 924])).
% 1.32/1.50 tff(933,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(934,plain,
% 1.32/1.50 ((hskp35 | (~ndr1_0) | c2_1(a1091) | c3_1(a1091) | (~c1_1(a1091)) | c0_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023))) <=> (hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(935,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1091) | c3_1(a1091) | (~c1_1(a1091)) | c0_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[934])).
% 1.32/1.50 tff(936,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1091) | c3_1(a1091) | (~c1_1(a1091)) | c0_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[935, 933])).
% 1.32/1.50 tff(937,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1091) | c3_1(a1091) | (~c1_1(a1091)) | c0_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(938,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[937, 936])).
% 1.32/1.50 tff(939,plain,
% 1.32/1.50 (hskp35),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[938, 120, 889, 898, 897, 835, 932, 922, 905])).
% 1.32/1.50 tff(940,plain,
% 1.32/1.50 (((~hskp35) | c3_1(a1033)) <=> ((~hskp35) | c3_1(a1033))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(941,axiom,((~hskp35) | c3_1(a1033)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.32/1.50 tff(942,plain,
% 1.32/1.50 ((~hskp35) | c3_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[941, 940])).
% 1.32/1.50 tff(943,plain,
% 1.32/1.50 ((~hskp35) | c3_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[942, 940])).
% 1.32/1.50 tff(944,plain,
% 1.32/1.50 ((~hskp35) | c3_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[943, 940])).
% 1.32/1.50 tff(945,plain,
% 1.32/1.50 ((~hskp35) | c3_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[944, 940])).
% 1.32/1.50 tff(946,plain,
% 1.32/1.50 ((~hskp35) | c3_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[945, 940])).
% 1.32/1.50 tff(947,plain,
% 1.32/1.50 (c3_1(a1033)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[946, 939])).
% 1.32/1.50 tff(948,plain,
% 1.32/1.50 (((~hskp35) | c1_1(a1033)) <=> ((~hskp35) | c1_1(a1033))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(949,axiom,((~hskp35) | c1_1(a1033)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.32/1.50 tff(950,plain,
% 1.32/1.50 ((~hskp35) | c1_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[949, 948])).
% 1.32/1.50 tff(951,plain,
% 1.32/1.50 ((~hskp35) | c1_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[950, 948])).
% 1.32/1.50 tff(952,plain,
% 1.32/1.50 ((~hskp35) | c1_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[951, 948])).
% 1.32/1.50 tff(953,plain,
% 1.32/1.50 ((~hskp35) | c1_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[952, 948])).
% 1.32/1.50 tff(954,plain,
% 1.32/1.50 ((~hskp35) | c1_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[953, 948])).
% 1.32/1.50 tff(955,plain,
% 1.32/1.50 (c1_1(a1033)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[954, 939])).
% 1.32/1.50 tff(956,plain,
% 1.32/1.50 (((~hskp35) | c0_1(a1033)) <=> ((~hskp35) | c0_1(a1033))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(957,axiom,((~hskp35) | c0_1(a1033)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.32/1.50 tff(958,plain,
% 1.32/1.50 ((~hskp35) | c0_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.32/1.50 tff(959,plain,
% 1.32/1.50 ((~hskp35) | c0_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[958, 956])).
% 1.32/1.50 tff(960,plain,
% 1.32/1.50 ((~hskp35) | c0_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[959, 956])).
% 1.32/1.50 tff(961,plain,
% 1.32/1.50 ((~hskp35) | c0_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[960, 956])).
% 1.32/1.50 tff(962,plain,
% 1.32/1.50 ((~hskp35) | c0_1(a1033)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[961, 956])).
% 1.32/1.50 tff(963,plain,
% 1.32/1.50 (c0_1(a1033)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[962, 939])).
% 1.32/1.50 tff(964,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(965,plain,
% 1.32/1.50 (((~ndr1_0) | (~c1_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033))) <=> ((~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(966,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[965])).
% 1.32/1.50 tff(967,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[966, 964])).
% 1.32/1.50 tff(968,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(969,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[968, 967])).
% 1.32/1.50 tff(970,plain,
% 1.32/1.50 (~c2_1(a1033)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[969, 120, 963, 955, 947, 10])).
% 1.32/1.50 tff(971,plain,
% 1.32/1.50 (^[V: $i, U: $i] : refl((hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(972,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[971])).
% 1.32/1.50 tff(973,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(974,plain,
% 1.32/1.50 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp57) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp57))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp57) <=> (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp57) <=> (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(975,plain,
% 1.32/1.50 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp57) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[974])).
% 1.32/1.50 tff(976,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause304')).
% 1.32/1.50 tff(977,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[976, 975])).
% 1.32/1.50 tff(978,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[977, 973])).
% 1.32/1.50 tff(979,plain,(
% 1.32/1.50 ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.32/1.50 inference(skolemize,[status(sab)],[978])).
% 1.32/1.50 tff(980,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[979, 972])).
% 1.32/1.50 tff(981,plain,
% 1.32/1.50 (hskp33),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[769, 890, 228, 234, 242])).
% 1.32/1.50 tff(982,plain,
% 1.32/1.50 (~c1_1(a1031)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[263, 981])).
% 1.32/1.50 tff(983,plain,
% 1.32/1.50 (c2_1(a1031)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[271, 981])).
% 1.32/1.50 tff(984,plain,
% 1.32/1.50 (c3_1(a1031)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[291, 981])).
% 1.32/1.50 tff(985,assumption,(c3_1(a1023)), introduced(assumption)).
% 1.32/1.50 tff(986,assumption,(~c1_1(a1023)), introduced(assumption)).
% 1.32/1.50 tff(987,assumption,(c2_1(a1023)), introduced(assumption)).
% 1.32/1.50 tff(988,assumption,(hskp57), introduced(assumption)).
% 1.32/1.50 tff(989,plain,
% 1.32/1.50 (((~hskp57) | c3_1(a1085)) <=> ((~hskp57) | c3_1(a1085))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(990,axiom,((~hskp57) | c3_1(a1085)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.32/1.50 tff(991,plain,
% 1.32/1.50 ((~hskp57) | c3_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[990, 989])).
% 1.32/1.50 tff(992,plain,
% 1.32/1.50 ((~hskp57) | c3_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[991, 989])).
% 1.32/1.50 tff(993,plain,
% 1.32/1.50 ((~hskp57) | c3_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[992, 989])).
% 1.32/1.50 tff(994,plain,
% 1.32/1.50 ((~hskp57) | c3_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[993, 989])).
% 1.32/1.50 tff(995,plain,
% 1.32/1.50 ((~hskp57) | c3_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[994, 989])).
% 1.32/1.50 tff(996,plain,
% 1.32/1.50 (c3_1(a1085)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[995, 988])).
% 1.32/1.50 tff(997,plain,
% 1.32/1.50 (((~hskp57) | c0_1(a1085)) <=> ((~hskp57) | c0_1(a1085))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(998,axiom,((~hskp57) | c0_1(a1085)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.32/1.50 tff(999,plain,
% 1.32/1.50 ((~hskp57) | c0_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[998, 997])).
% 1.32/1.50 tff(1000,plain,
% 1.32/1.50 ((~hskp57) | c0_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[999, 997])).
% 1.32/1.50 tff(1001,plain,
% 1.32/1.50 ((~hskp57) | c0_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1000, 997])).
% 1.32/1.50 tff(1002,plain,
% 1.32/1.50 ((~hskp57) | c0_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1001, 997])).
% 1.32/1.50 tff(1003,plain,
% 1.32/1.50 ((~hskp57) | c0_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1002, 997])).
% 1.32/1.50 tff(1004,plain,
% 1.32/1.50 (c0_1(a1085)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1003, 988])).
% 1.32/1.50 tff(1005,plain,
% 1.32/1.50 (((~hskp57) | c2_1(a1085)) <=> ((~hskp57) | c2_1(a1085))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1006,axiom,((~hskp57) | c2_1(a1085)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.32/1.50 tff(1007,plain,
% 1.32/1.50 ((~hskp57) | c2_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 1.32/1.50 tff(1008,plain,
% 1.32/1.50 ((~hskp57) | c2_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1007, 1005])).
% 1.32/1.50 tff(1009,plain,
% 1.32/1.50 ((~hskp57) | c2_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1008, 1005])).
% 1.32/1.50 tff(1010,plain,
% 1.32/1.50 ((~hskp57) | c2_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1009, 1005])).
% 1.32/1.50 tff(1011,plain,
% 1.32/1.50 ((~hskp57) | c2_1(a1085)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1010, 1005])).
% 1.32/1.50 tff(1012,plain,
% 1.32/1.50 (c2_1(a1085)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1011, 988])).
% 1.32/1.50 tff(1013,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1014,plain,
% 1.32/1.50 ((hskp53 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> (hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1015,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1014])).
% 1.32/1.50 tff(1016,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[1015, 1013])).
% 1.32/1.50 tff(1017,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1018,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.32/1.50 tff(1019,plain,
% 1.32/1.50 (hskp53),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1018, 120, 1012, 1004, 996, 987, 986, 20, 985])).
% 1.32/1.50 tff(1020,plain,
% 1.32/1.50 (c0_1(a1073)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[307, 1019])).
% 1.32/1.50 tff(1021,plain,
% 1.32/1.50 (c2_1(a1073)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[315, 1019])).
% 1.32/1.50 tff(1022,plain,
% 1.32/1.50 (c1_1(a1073)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[323, 1019])).
% 1.32/1.50 tff(1023,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1024,plain,
% 1.32/1.50 (((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> ((~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1025,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1024])).
% 1.32/1.50 tff(1026,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[1025, 1023])).
% 1.32/1.50 tff(1027,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1028,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 1.32/1.50 tff(1029,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1028, 120, 1012, 1004, 996, 1022, 1021, 1020, 10])).
% 1.32/1.50 tff(1030,plain,((~hskp57) | (~c2_1(a1023)) | c1_1(a1023) | (~c3_1(a1023))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(1031,plain,
% 1.32/1.50 (~hskp57),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1030, 922, 841, 889])).
% 1.32/1.50 tff(1032,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1033,plain,
% 1.32/1.50 ((hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033))) <=> (hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1034,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1033])).
% 1.32/1.50 tff(1035,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[1034, 1032])).
% 1.32/1.50 tff(1036,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1037,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 1.32/1.50 tff(1038,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1037, 120, 1031, 963, 947, 984, 983, 982, 980, 970])).
% 1.32/1.50 tff(1039,plain,(~hskp56), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(1040,plain,
% 1.32/1.50 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1041,plain,
% 1.32/1.50 ((hskp56 | hskp22 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079))) <=> (hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1042,plain,
% 1.32/1.50 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1041])).
% 1.32/1.50 tff(1043,plain,
% 1.32/1.50 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[1042, 1040])).
% 1.32/1.50 tff(1044,plain,
% 1.32/1.50 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1045,plain,
% 1.32/1.50 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 1.32/1.50 tff(1046,plain,
% 1.32/1.50 (hskp22 | (~c3_1(a1079))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1045, 120, 1039, 145, 80, 31])).
% 1.32/1.51 tff(1047,plain,
% 1.32/1.51 (hskp22),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1046, 127])).
% 1.32/1.51 tff(1048,plain,
% 1.32/1.51 (((~hskp22) | c3_1(a1083)) <=> ((~hskp22) | c3_1(a1083))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1049,axiom,((~hskp22) | c3_1(a1083)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 1.32/1.51 tff(1050,plain,
% 1.32/1.51 ((~hskp22) | c3_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 1.32/1.51 tff(1051,plain,
% 1.32/1.51 ((~hskp22) | c3_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1050, 1048])).
% 1.32/1.51 tff(1052,plain,
% 1.32/1.51 ((~hskp22) | c3_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1051, 1048])).
% 1.32/1.51 tff(1053,plain,
% 1.32/1.51 ((~hskp22) | c3_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1052, 1048])).
% 1.32/1.51 tff(1054,plain,
% 1.32/1.51 ((~hskp22) | c3_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1053, 1048])).
% 1.32/1.51 tff(1055,plain,
% 1.32/1.51 (c3_1(a1083)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1054, 1047])).
% 1.32/1.51 tff(1056,plain,
% 1.32/1.51 (((~hskp22) | c2_1(a1083)) <=> ((~hskp22) | c2_1(a1083))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1057,axiom,((~hskp22) | c2_1(a1083)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 1.32/1.51 tff(1058,plain,
% 1.32/1.51 ((~hskp22) | c2_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 1.32/1.51 tff(1059,plain,
% 1.32/1.51 ((~hskp22) | c2_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1058, 1056])).
% 1.32/1.51 tff(1060,plain,
% 1.32/1.51 ((~hskp22) | c2_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1059, 1056])).
% 1.32/1.51 tff(1061,plain,
% 1.32/1.51 ((~hskp22) | c2_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1060, 1056])).
% 1.32/1.51 tff(1062,plain,
% 1.32/1.51 ((~hskp22) | c2_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1061, 1056])).
% 1.32/1.51 tff(1063,plain,
% 1.32/1.51 (c2_1(a1083)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1062, 1047])).
% 1.32/1.51 tff(1064,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1065,plain,
% 1.32/1.51 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1083))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1066,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1065])).
% 1.32/1.51 tff(1067,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[1066, 1064])).
% 1.32/1.51 tff(1068,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1083)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1069,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 1.32/1.51 tff(1070,plain,
% 1.32/1.51 (~c0_1(a1083)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1069, 120, 211, 203, 195, 1063, 1055, 10])).
% 1.32/1.51 tff(1071,plain,
% 1.32/1.51 (^[V: $i, U: $i] : refl((hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.32/1.51 inference(bind,[status(th)],[])).
% 1.32/1.51 tff(1072,plain,
% 1.32/1.51 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.32/1.51 inference(quant_intro,[status(thm)],[1071])).
% 1.32/1.51 tff(1073,plain,
% 1.32/1.51 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1074,plain,
% 1.32/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) | hskp42) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp42))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp42) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) | hskp42) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.32/1.51 inference(bind,[status(th)],[])).
% 1.32/1.51 tff(1075,plain,
% 1.32/1.51 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) | hskp42) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.32/1.51 inference(quant_intro,[status(thm)],[1074])).
% 1.32/1.51 tff(1076,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) | hskp42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause295')).
% 1.32/1.51 tff(1077,plain,
% 1.32/1.51 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 1.32/1.51 tff(1078,plain,
% 1.32/1.51 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1077, 1073])).
% 1.32/1.51 tff(1079,plain,(
% 1.32/1.51 ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.32/1.51 inference(skolemize,[status(sab)],[1078])).
% 1.32/1.51 tff(1080,plain,
% 1.32/1.51 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1079, 1072])).
% 1.32/1.51 tff(1081,plain,
% 1.32/1.51 (((~hskp22) | (~c1_1(a1083))) <=> ((~hskp22) | (~c1_1(a1083)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1082,plain,
% 1.32/1.51 (((~c1_1(a1083)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1083)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1083,axiom,((~c1_1(a1083)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause219')).
% 1.32/1.51 tff(1084,plain,
% 1.32/1.51 ((~hskp22) | (~c1_1(a1083))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 1.32/1.51 tff(1085,plain,
% 1.32/1.51 ((~hskp22) | (~c1_1(a1083))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1084, 1081])).
% 1.32/1.51 tff(1086,plain,
% 1.32/1.51 (~c1_1(a1083)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1085, 1047])).
% 1.32/1.51 tff(1087,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1088,plain,
% 1.32/1.51 ((hskp42 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)) | c0_1(a1083) | c1_1(a1083) | (~c2_1(a1083))) <=> (hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1089,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)) | c0_1(a1083) | c1_1(a1083) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083)))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1088])).
% 1.32/1.51 tff(1090,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)) | c0_1(a1083) | c1_1(a1083) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083))),
% 1.32/1.51 inference(transitivity,[status(thm)],[1089, 1087])).
% 1.32/1.51 tff(1091,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)) | c0_1(a1083) | c1_1(a1083) | (~c2_1(a1083)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1092,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 1.32/1.51 tff(1093,plain,
% 1.32/1.51 (hskp42),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1092, 120, 1063, 145, 1086, 80, 1080, 127, 1070])).
% 1.32/1.51 tff(1094,plain,
% 1.32/1.51 (((~hskp42) | (~c2_1(a1046))) <=> ((~hskp42) | (~c2_1(a1046)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1095,plain,
% 1.32/1.51 (((~c2_1(a1046)) | (~hskp42)) <=> ((~hskp42) | (~c2_1(a1046)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1096,axiom,((~c2_1(a1046)) | (~hskp42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.32/1.51 tff(1097,plain,
% 1.32/1.51 ((~hskp42) | (~c2_1(a1046))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.32/1.51 tff(1098,plain,
% 1.32/1.51 ((~hskp42) | (~c2_1(a1046))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1097, 1094])).
% 1.32/1.51 tff(1099,plain,
% 1.32/1.51 (~c2_1(a1046)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1098, 1093])).
% 1.32/1.51 tff(1100,plain,
% 1.32/1.51 (((~hskp42) | c1_1(a1046)) <=> ((~hskp42) | c1_1(a1046))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1101,axiom,((~hskp42) | c1_1(a1046)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.32/1.51 tff(1102,plain,
% 1.32/1.51 ((~hskp42) | c1_1(a1046)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 1.32/1.51 tff(1103,plain,
% 1.32/1.51 ((~hskp42) | c1_1(a1046)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1102, 1100])).
% 1.32/1.51 tff(1104,plain,
% 1.32/1.51 ((~hskp42) | c1_1(a1046)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1103, 1100])).
% 1.32/1.51 tff(1105,plain,
% 1.32/1.51 ((~hskp42) | c1_1(a1046)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1104, 1100])).
% 1.32/1.51 tff(1106,plain,
% 1.32/1.51 ((~hskp42) | c1_1(a1046)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1105, 1100])).
% 1.32/1.51 tff(1107,plain,
% 1.32/1.51 (c1_1(a1046)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1106, 1093])).
% 1.32/1.51 tff(1108,assumption,(hskp35), introduced(assumption)).
% 1.32/1.51 tff(1109,plain,
% 1.32/1.51 (c3_1(a1033)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[946, 1108])).
% 1.32/1.51 tff(1110,plain,
% 1.32/1.51 (c1_1(a1033)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[954, 1108])).
% 1.32/1.51 tff(1111,plain,
% 1.32/1.51 (c0_1(a1033)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[962, 1108])).
% 1.32/1.51 tff(1112,plain,
% 1.32/1.51 (~c2_1(a1033)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[969, 120, 1111, 1110, 1109, 10])).
% 1.32/1.51 tff(1113,plain,
% 1.32/1.51 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1114,plain,
% 1.32/1.51 ((hskp56 | hskp22 | (~ndr1_0) | c2_1(a1033) | (~c1_1(a1033)) | (~c3_1(a1033))) <=> (hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1115,plain,
% 1.32/1.51 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1033) | (~c1_1(a1033)) | (~c3_1(a1033)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033))))),
% 1.36/1.51 inference(monotonicity,[status(thm)],[1114])).
% 1.36/1.51 tff(1116,plain,
% 1.36/1.51 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1033) | (~c1_1(a1033)) | (~c3_1(a1033)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033)))),
% 1.36/1.51 inference(transitivity,[status(thm)],[1115, 1113])).
% 1.36/1.51 tff(1117,plain,
% 1.36/1.51 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1033) | (~c1_1(a1033)) | (~c3_1(a1033)))),
% 1.36/1.51 inference(quant_inst,[status(thm)],[])).
% 1.36/1.51 tff(1118,plain,
% 1.36/1.51 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033))),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 1.36/1.51 tff(1119,plain,
% 1.36/1.51 (hskp22),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1118, 120, 1039, 1110, 1109, 31, 1112])).
% 1.36/1.51 tff(1120,plain,
% 1.36/1.51 (~c1_1(a1083)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1085, 1119])).
% 1.36/1.51 tff(1121,plain,
% 1.36/1.51 (c3_1(a1083)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1054, 1119])).
% 1.36/1.51 tff(1122,plain,
% 1.36/1.51 (c2_1(a1083)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1062, 1119])).
% 1.36/1.51 tff(1123,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1124,plain,
% 1.36/1.51 ((hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033))) <=> (hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1125,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083))))),
% 1.36/1.51 inference(monotonicity,[status(thm)],[1124])).
% 1.36/1.51 tff(1126,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.36/1.51 inference(transitivity,[status(thm)],[1125, 1123])).
% 1.36/1.51 tff(1127,plain,
% 1.36/1.51 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))),
% 1.36/1.51 inference(quant_inst,[status(thm)],[])).
% 1.36/1.51 tff(1128,plain,
% 1.36/1.51 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083))),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 1.36/1.51 tff(1129,plain,
% 1.36/1.51 (hskp57),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1128, 120, 1111, 1109, 1122, 1121, 1120, 980, 1112])).
% 1.36/1.51 tff(1130,plain,
% 1.36/1.51 (c3_1(a1085)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[995, 1129])).
% 1.36/1.51 tff(1131,plain,
% 1.36/1.51 (c0_1(a1085)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1003, 1129])).
% 1.36/1.51 tff(1132,plain,
% 1.36/1.51 (c2_1(a1085)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1011, 1129])).
% 1.36/1.51 tff(1133,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1134,plain,
% 1.36/1.51 ((hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1135,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083))))),
% 1.36/1.51 inference(monotonicity,[status(thm)],[1134])).
% 1.36/1.51 tff(1136,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.36/1.51 inference(transitivity,[status(thm)],[1135, 1133])).
% 1.36/1.51 tff(1137,plain,
% 1.36/1.51 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 1.36/1.51 inference(quant_inst,[status(thm)],[])).
% 1.36/1.51 tff(1138,plain,
% 1.36/1.51 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083))),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.36/1.51 tff(1139,plain,
% 1.36/1.51 (hskp53),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1138, 120, 1132, 1131, 1130, 1122, 1121, 1120, 20])).
% 1.36/1.51 tff(1140,plain,
% 1.36/1.51 (c0_1(a1073)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[307, 1139])).
% 1.36/1.51 tff(1141,plain,
% 1.36/1.51 (c2_1(a1073)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[315, 1139])).
% 1.36/1.51 tff(1142,plain,
% 1.36/1.51 (c1_1(a1073)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[323, 1139])).
% 1.36/1.51 tff(1143,plain,
% 1.36/1.51 ($false),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1028, 120, 1132, 1131, 1130, 1142, 1141, 1140, 10])).
% 1.36/1.51 tff(1144,plain,(~hskp35), inference(lemma,lemma(discharge,[]))).
% 1.36/1.51 tff(1145,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1146,plain,
% 1.36/1.51 ((hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083))) <=> (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1147,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046))))),
% 1.36/1.51 inference(monotonicity,[status(thm)],[1146])).
% 1.36/1.51 tff(1148,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046)))),
% 1.36/1.51 inference(transitivity,[status(thm)],[1147, 1145])).
% 1.36/1.51 tff(1149,plain,
% 1.36/1.51 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.36/1.51 inference(quant_inst,[status(thm)],[])).
% 1.36/1.51 tff(1150,plain,
% 1.36/1.51 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046))),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 1.36/1.51 tff(1151,plain,
% 1.36/1.51 (c3_1(a1046)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1150, 120, 1144, 1107, 1063, 1055, 1099, 932, 1070])).
% 1.36/1.51 tff(1152,plain,
% 1.36/1.51 (((~hskp42) | c0_1(a1046)) <=> ((~hskp42) | c0_1(a1046))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1153,axiom,((~hskp42) | c0_1(a1046)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.36/1.51 tff(1154,plain,
% 1.36/1.51 ((~hskp42) | c0_1(a1046)),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 1.36/1.51 tff(1155,plain,
% 1.36/1.51 ((~hskp42) | c0_1(a1046)),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1154, 1152])).
% 1.36/1.51 tff(1156,plain,
% 1.36/1.51 ((~hskp42) | c0_1(a1046)),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1155, 1152])).
% 1.36/1.51 tff(1157,plain,
% 1.36/1.51 ((~hskp42) | c0_1(a1046)),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1156, 1152])).
% 1.36/1.51 tff(1158,plain,
% 1.36/1.51 ((~hskp42) | c0_1(a1046)),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1157, 1152])).
% 1.36/1.51 tff(1159,plain,
% 1.36/1.51 (c0_1(a1046)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1158, 1093])).
% 1.36/1.51 tff(1160,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1161,plain,
% 1.36/1.51 ((hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046))) <=> (hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1162,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046))))),
% 1.36/1.51 inference(monotonicity,[status(thm)],[1161])).
% 1.36/1.51 tff(1163,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 1.36/1.51 inference(transitivity,[status(thm)],[1162, 1160])).
% 1.36/1.51 tff(1164,plain,
% 1.36/1.51 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 1.36/1.51 inference(quant_inst,[status(thm)],[])).
% 1.36/1.51 tff(1165,plain,
% 1.36/1.51 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046))),
% 1.36/1.51 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 1.36/1.51 tff(1166,plain,
% 1.36/1.51 (hskp57 | (~c3_1(a1046))),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1165, 120, 1159, 1063, 1055, 1099, 1086, 980])).
% 1.36/1.51 tff(1167,plain,
% 1.36/1.51 (hskp57),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1166, 1151])).
% 1.36/1.51 tff(1168,plain,
% 1.36/1.51 (c3_1(a1085)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[995, 1167])).
% 1.36/1.51 tff(1169,plain,
% 1.36/1.51 (c0_1(a1085)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1003, 1167])).
% 1.36/1.51 tff(1170,plain,
% 1.36/1.51 (c2_1(a1085)),
% 1.36/1.51 inference(unit_resolution,[status(thm)],[1011, 1167])).
% 1.36/1.51 tff(1171,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1172,plain,
% 1.36/1.51 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 1.36/1.51 inference(rewrite,[status(thm)],[])).
% 1.36/1.51 tff(1173,plain,
% 1.36/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085))))),
% 1.36/1.52 inference(monotonicity,[status(thm)],[1172])).
% 1.36/1.52 tff(1174,plain,
% 1.36/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 1.36/1.52 inference(transitivity,[status(thm)],[1173, 1171])).
% 1.36/1.52 tff(1175,plain,
% 1.36/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 1.36/1.52 inference(quant_inst,[status(thm)],[])).
% 1.36/1.52 tff(1176,plain,
% 1.36/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.36/1.52 tff(1177,plain,
% 1.36/1.52 ($false),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1176, 120, 1170, 1169, 1168, 211, 203, 195, 10])).
% 1.36/1.52 tff(1178,plain,((~hskp19) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.36/1.52 tff(1179,plain,
% 1.36/1.52 (~hskp19),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1178, 53])).
% 1.36/1.52 tff(1180,plain,
% 1.36/1.52 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 1.36/1.52 inference(bind,[status(th)],[])).
% 1.36/1.52 tff(1181,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.36/1.52 inference(quant_intro,[status(thm)],[1180])).
% 1.36/1.52 tff(1182,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1183,plain,
% 1.36/1.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.36/1.52 inference(bind,[status(th)],[])).
% 1.36/1.52 tff(1184,plain,
% 1.36/1.52 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.36/1.52 inference(quant_intro,[status(thm)],[1183])).
% 1.36/1.52 tff(1185,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause307')).
% 1.36/1.52 tff(1186,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.36/1.52 tff(1187,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1186, 1182])).
% 1.36/1.52 tff(1188,plain,(
% 1.36/1.52 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.36/1.52 inference(skolemize,[status(sab)],[1187])).
% 1.36/1.52 tff(1189,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1188, 1181])).
% 1.36/1.52 tff(1190,assumption,(~hskp20), introduced(assumption)).
% 1.36/1.52 tff(1191,assumption,(~hskp19), introduced(assumption)).
% 1.36/1.52 tff(1192,assumption,(~hskp43), introduced(assumption)).
% 1.36/1.52 tff(1193,assumption,(hskp38), introduced(assumption)).
% 1.36/1.52 tff(1194,plain,
% 1.36/1.52 (((~hskp38) | c2_1(a1040)) <=> ((~hskp38) | c2_1(a1040))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1195,axiom,((~hskp38) | c2_1(a1040)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.36/1.52 tff(1196,plain,
% 1.36/1.52 ((~hskp38) | c2_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.36/1.52 tff(1197,plain,
% 1.36/1.52 ((~hskp38) | c2_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1196, 1194])).
% 1.36/1.52 tff(1198,plain,
% 1.36/1.52 ((~hskp38) | c2_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1197, 1194])).
% 1.36/1.52 tff(1199,plain,
% 1.36/1.52 ((~hskp38) | c2_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1198, 1194])).
% 1.36/1.52 tff(1200,plain,
% 1.36/1.52 ((~hskp38) | c2_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1199, 1194])).
% 1.36/1.52 tff(1201,plain,
% 1.36/1.52 (c2_1(a1040)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1200, 1193])).
% 1.36/1.52 tff(1202,plain,
% 1.36/1.52 (((~hskp38) | c3_1(a1040)) <=> ((~hskp38) | c3_1(a1040))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1203,axiom,((~hskp38) | c3_1(a1040)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.36/1.52 tff(1204,plain,
% 1.36/1.52 ((~hskp38) | c3_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 1.36/1.52 tff(1205,plain,
% 1.36/1.52 ((~hskp38) | c3_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1204, 1202])).
% 1.36/1.52 tff(1206,plain,
% 1.36/1.52 ((~hskp38) | c3_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1205, 1202])).
% 1.36/1.52 tff(1207,plain,
% 1.36/1.52 ((~hskp38) | c3_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1206, 1202])).
% 1.36/1.52 tff(1208,plain,
% 1.36/1.52 ((~hskp38) | c3_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1207, 1202])).
% 1.36/1.52 tff(1209,plain,
% 1.36/1.52 (c3_1(a1040)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1208, 1193])).
% 1.36/1.52 tff(1210,plain,
% 1.36/1.52 (((~hskp38) | c1_1(a1040)) <=> ((~hskp38) | c1_1(a1040))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1211,axiom,((~hskp38) | c1_1(a1040)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.36/1.52 tff(1212,plain,
% 1.36/1.52 ((~hskp38) | c1_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 1.36/1.52 tff(1213,plain,
% 1.36/1.52 ((~hskp38) | c1_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1212, 1210])).
% 1.36/1.52 tff(1214,plain,
% 1.36/1.52 ((~hskp38) | c1_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1213, 1210])).
% 1.36/1.52 tff(1215,plain,
% 1.36/1.52 ((~hskp38) | c1_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1214, 1210])).
% 1.36/1.52 tff(1216,plain,
% 1.36/1.52 ((~hskp38) | c1_1(a1040)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1215, 1210])).
% 1.36/1.52 tff(1217,plain,
% 1.36/1.52 (c1_1(a1040)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1216, 1193])).
% 1.36/1.52 tff(1218,plain,
% 1.36/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1219,plain,
% 1.36/1.52 (((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040))) <=> ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1220,plain,
% 1.36/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040))))),
% 1.36/1.52 inference(monotonicity,[status(thm)],[1219])).
% 1.36/1.52 tff(1221,plain,
% 1.36/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 1.36/1.52 inference(transitivity,[status(thm)],[1220, 1218])).
% 1.36/1.52 tff(1222,plain,
% 1.36/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)))),
% 1.36/1.52 inference(quant_inst,[status(thm)],[])).
% 1.36/1.52 tff(1223,plain,
% 1.36/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 1.36/1.52 tff(1224,plain,
% 1.36/1.52 (~c0_1(a1040)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1223, 120, 1217, 1209, 1201, 10])).
% 1.36/1.52 tff(1225,plain,
% 1.36/1.52 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1226,plain,
% 1.36/1.52 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)))),
% 1.36/1.52 inference(quant_inst,[status(thm)],[])).
% 1.36/1.52 tff(1227,plain,
% 1.36/1.52 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 1.36/1.52 tff(1228,plain,
% 1.36/1.52 ($false),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1227, 120, 1192, 53, 1217, 1201, 63, 1224])).
% 1.36/1.52 tff(1229,plain,((~hskp38) | hskp43 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.36/1.52 tff(1230,plain,
% 1.36/1.52 (~hskp38),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1229, 1192, 53])).
% 1.36/1.52 tff(1231,assumption,(~hskp38), introduced(assumption)).
% 1.36/1.52 tff(1232,assumption,(~hskp14), introduced(assumption)).
% 1.36/1.52 tff(1233,plain,
% 1.36/1.52 ((hskp46 | hskp38 | hskp14) <=> (hskp46 | hskp38 | hskp14)),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1234,plain,
% 1.36/1.52 (((hskp46 | hskp38) | hskp14) <=> (hskp46 | hskp38 | hskp14)),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1235,plain,
% 1.36/1.52 ((hskp46 | hskp38) <=> (hskp46 | hskp38)),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1236,plain,
% 1.36/1.52 (((hskp46 | hskp38) | hskp14) <=> ((hskp46 | hskp38) | hskp14)),
% 1.36/1.52 inference(monotonicity,[status(thm)],[1235])).
% 1.36/1.52 tff(1237,plain,
% 1.36/1.52 (((hskp46 | hskp38) | hskp14) <=> (hskp46 | hskp38 | hskp14)),
% 1.36/1.52 inference(transitivity,[status(thm)],[1236, 1234])).
% 1.36/1.52 tff(1238,axiom,((hskp46 | hskp38) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.36/1.52 tff(1239,plain,
% 1.36/1.52 (hskp46 | hskp38 | hskp14),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.36/1.52 tff(1240,plain,
% 1.36/1.52 (hskp46 | hskp38 | hskp14),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1239, 1233])).
% 1.36/1.52 tff(1241,plain,
% 1.36/1.52 (hskp46 | hskp38 | hskp14),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1240, 1233])).
% 1.36/1.52 tff(1242,plain,
% 1.36/1.52 (hskp46 | hskp38 | hskp14),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1241, 1233])).
% 1.36/1.52 tff(1243,plain,
% 1.36/1.52 (hskp46 | hskp38 | hskp14),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1242, 1233])).
% 1.36/1.52 tff(1244,plain,
% 1.36/1.52 (hskp46),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1243, 1231, 1232])).
% 1.36/1.52 tff(1245,assumption,(hskp46), introduced(assumption)).
% 1.36/1.52 tff(1246,plain,
% 1.36/1.52 (((~hskp46) | (~c1_1(a1053))) <=> ((~hskp46) | (~c1_1(a1053)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1247,plain,
% 1.36/1.52 (((~c1_1(a1053)) | (~hskp46)) <=> ((~hskp46) | (~c1_1(a1053)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1248,axiom,((~c1_1(a1053)) | (~hskp46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.36/1.52 tff(1249,plain,
% 1.36/1.52 ((~hskp46) | (~c1_1(a1053))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.36/1.52 tff(1250,plain,
% 1.36/1.52 ((~hskp46) | (~c1_1(a1053))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1249, 1246])).
% 1.36/1.52 tff(1251,plain,
% 1.36/1.52 (~c1_1(a1053)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1250, 1245])).
% 1.36/1.52 tff(1252,plain,
% 1.36/1.52 (((~hskp46) | c0_1(a1053)) <=> ((~hskp46) | c0_1(a1053))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1253,axiom,((~hskp46) | c0_1(a1053)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.36/1.52 tff(1254,plain,
% 1.36/1.52 ((~hskp46) | c0_1(a1053)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 1.36/1.52 tff(1255,plain,
% 1.36/1.52 ((~hskp46) | c0_1(a1053)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1254, 1252])).
% 1.36/1.52 tff(1256,plain,
% 1.36/1.52 ((~hskp46) | c0_1(a1053)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1255, 1252])).
% 1.36/1.52 tff(1257,plain,
% 1.36/1.52 ((~hskp46) | c0_1(a1053)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1256, 1252])).
% 1.36/1.52 tff(1258,plain,
% 1.36/1.52 ((~hskp46) | c0_1(a1053)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1257, 1252])).
% 1.36/1.52 tff(1259,plain,
% 1.36/1.52 (c0_1(a1053)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1258, 1245])).
% 1.36/1.52 tff(1260,plain,
% 1.36/1.52 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1261,plain,
% 1.36/1.52 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a1053) | c1_1(a1053) | (~c0_1(a1053))) <=> (hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1262,plain,
% 1.36/1.52 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1053) | c1_1(a1053) | (~c0_1(a1053)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053))))),
% 1.36/1.52 inference(monotonicity,[status(thm)],[1261])).
% 1.36/1.52 tff(1263,plain,
% 1.36/1.52 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1053) | c1_1(a1053) | (~c0_1(a1053)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053)))),
% 1.36/1.52 inference(transitivity,[status(thm)],[1262, 1260])).
% 1.36/1.52 tff(1264,plain,
% 1.36/1.52 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1053) | c1_1(a1053) | (~c0_1(a1053)))),
% 1.36/1.52 inference(quant_inst,[status(thm)],[])).
% 1.36/1.52 tff(1265,plain,
% 1.36/1.52 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 1.36/1.52 tff(1266,plain,
% 1.36/1.52 (c3_1(a1053)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1265, 120, 1190, 1191, 1259, 1251, 625])).
% 1.36/1.52 tff(1267,plain,
% 1.36/1.52 (^[V: $i, U: $i] : refl((hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.36/1.52 inference(bind,[status(th)],[])).
% 1.36/1.52 tff(1268,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.52 inference(quant_intro,[status(thm)],[1267])).
% 1.36/1.52 tff(1269,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1270,plain,
% 1.36/1.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp38) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp38))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp38) <=> (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.36/1.52 inference(bind,[status(th)],[])).
% 1.36/1.52 tff(1271,plain,
% 1.36/1.52 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp38) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.52 inference(quant_intro,[status(thm)],[1270])).
% 1.36/1.52 tff(1272,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause301')).
% 1.36/1.52 tff(1273,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 1.36/1.52 tff(1274,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1273, 1269])).
% 1.36/1.52 tff(1275,plain,(
% 1.36/1.52 ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.52 inference(skolemize,[status(sab)],[1274])).
% 1.36/1.52 tff(1276,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1275, 1268])).
% 1.36/1.52 tff(1277,plain,
% 1.36/1.52 (((~hskp46) | (~c2_1(a1053))) <=> ((~hskp46) | (~c2_1(a1053)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1278,plain,
% 1.36/1.52 (((~c2_1(a1053)) | (~hskp46)) <=> ((~hskp46) | (~c2_1(a1053)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1279,axiom,((~c2_1(a1053)) | (~hskp46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.36/1.52 tff(1280,plain,
% 1.36/1.52 ((~hskp46) | (~c2_1(a1053))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 1.36/1.52 tff(1281,plain,
% 1.36/1.52 ((~hskp46) | (~c2_1(a1053))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1280, 1277])).
% 1.36/1.52 tff(1282,plain,
% 1.36/1.52 (~c2_1(a1053)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1281, 1245])).
% 1.36/1.52 tff(1283,plain,
% 1.36/1.52 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1284,plain,
% 1.36/1.52 ((hskp38 | (~ndr1_0) | c1_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)) | c2_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053))) <=> (hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1285,plain,
% 1.36/1.52 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | (~ndr1_0) | c1_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)) | c2_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053))))),
% 1.36/1.52 inference(monotonicity,[status(thm)],[1284])).
% 1.36/1.52 tff(1286,plain,
% 1.36/1.52 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | (~ndr1_0) | c1_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)) | c2_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053)))),
% 1.36/1.52 inference(transitivity,[status(thm)],[1285, 1283])).
% 1.36/1.52 tff(1287,plain,
% 1.36/1.52 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | (~ndr1_0) | c1_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)) | c2_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)))),
% 1.36/1.52 inference(quant_inst,[status(thm)],[])).
% 1.36/1.52 tff(1288,plain,
% 1.36/1.52 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 1.36/1.52 tff(1289,plain,
% 1.36/1.52 ($false),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1288, 120, 1231, 1259, 1251, 1282, 1276, 1266])).
% 1.36/1.52 tff(1290,plain,((~hskp46) | hskp38 | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.36/1.52 tff(1291,plain,
% 1.36/1.52 ($false),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1290, 1244, 1231, 1190, 1191])).
% 1.36/1.52 tff(1292,plain,(hskp38 | hskp20 | hskp19 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.36/1.52 tff(1293,plain,
% 1.36/1.52 (hskp14),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1292, 1230, 1190, 1191])).
% 1.36/1.52 tff(1294,plain,
% 1.36/1.52 (((~hskp14) | (~c2_1(a1055))) <=> ((~hskp14) | (~c2_1(a1055)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1295,plain,
% 1.36/1.52 (((~c2_1(a1055)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1055)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1296,axiom,((~c2_1(a1055)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause235')).
% 1.36/1.52 tff(1297,plain,
% 1.36/1.52 ((~hskp14) | (~c2_1(a1055))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 1.36/1.52 tff(1298,plain,
% 1.36/1.52 ((~hskp14) | (~c2_1(a1055))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1297, 1294])).
% 1.36/1.52 tff(1299,plain,
% 1.36/1.52 (~c2_1(a1055)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1298, 1293])).
% 1.36/1.52 tff(1300,plain,
% 1.36/1.52 (((~hskp14) | (~c0_1(a1055))) <=> ((~hskp14) | (~c0_1(a1055)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1301,plain,
% 1.36/1.52 (((~c0_1(a1055)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a1055)))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1302,axiom,((~c0_1(a1055)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause233')).
% 1.36/1.52 tff(1303,plain,
% 1.36/1.52 ((~hskp14) | (~c0_1(a1055))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.36/1.52 tff(1304,plain,
% 1.36/1.52 ((~hskp14) | (~c0_1(a1055))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1303, 1300])).
% 1.36/1.52 tff(1305,plain,
% 1.36/1.52 (~c0_1(a1055)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1304, 1293])).
% 1.36/1.52 tff(1306,plain,
% 1.36/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1307,plain,
% 1.36/1.52 ((hskp10 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | c3_1(a1055)) <=> (hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1308,plain,
% 1.36/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | c3_1(a1055))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055)))),
% 1.36/1.52 inference(monotonicity,[status(thm)],[1307])).
% 1.36/1.52 tff(1309,plain,
% 1.36/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | c3_1(a1055))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055))),
% 1.36/1.52 inference(transitivity,[status(thm)],[1308, 1306])).
% 1.36/1.52 tff(1310,plain,
% 1.36/1.52 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | c3_1(a1055))),
% 1.36/1.52 inference(quant_inst,[status(thm)],[])).
% 1.36/1.52 tff(1311,plain,
% 1.36/1.52 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 1.36/1.52 tff(1312,plain,
% 1.36/1.52 (c3_1(a1055)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1311, 120, 53, 1305, 1299, 73])).
% 1.36/1.52 tff(1313,plain,
% 1.36/1.52 (^[V: $i, U: $i] : refl((hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)))),
% 1.36/1.52 inference(bind,[status(th)],[])).
% 1.36/1.52 tff(1314,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.36/1.52 inference(quant_intro,[status(thm)],[1313])).
% 1.36/1.52 tff(1315,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1316,plain,
% 1.36/1.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | 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) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp35) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) | hskp35))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) | hskp35) <=> (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp35) <=> (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))))),
% 1.36/1.52 inference(bind,[status(th)],[])).
% 1.36/1.52 tff(1317,plain,
% 1.36/1.52 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp35) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.36/1.52 inference(quant_intro,[status(thm)],[1316])).
% 1.36/1.52 tff(1318,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause286')).
% 1.36/1.52 tff(1319,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 1.36/1.52 tff(1320,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1319, 1315])).
% 1.36/1.52 tff(1321,plain,(
% 1.36/1.52 ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.36/1.52 inference(skolemize,[status(sab)],[1320])).
% 1.36/1.52 tff(1322,plain,
% 1.36/1.52 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1321, 1314])).
% 1.36/1.52 tff(1323,assumption,(hskp62), introduced(assumption)).
% 1.36/1.52 tff(1324,plain,
% 1.36/1.52 (((~hskp62) | c1_1(a1103)) <=> ((~hskp62) | c1_1(a1103))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1325,axiom,((~hskp62) | c1_1(a1103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.36/1.52 tff(1326,plain,
% 1.36/1.52 ((~hskp62) | c1_1(a1103)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 1.36/1.52 tff(1327,plain,
% 1.36/1.52 ((~hskp62) | c1_1(a1103)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1326, 1324])).
% 1.36/1.52 tff(1328,plain,
% 1.36/1.52 ((~hskp62) | c1_1(a1103)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1327, 1324])).
% 1.36/1.52 tff(1329,plain,
% 1.36/1.52 ((~hskp62) | c1_1(a1103)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1328, 1324])).
% 1.36/1.52 tff(1330,plain,
% 1.36/1.52 ((~hskp62) | c1_1(a1103)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1329, 1324])).
% 1.36/1.52 tff(1331,plain,
% 1.36/1.52 (c1_1(a1103)),
% 1.36/1.52 inference(unit_resolution,[status(thm)],[1330, 1323])).
% 1.36/1.52 tff(1332,plain,
% 1.36/1.52 (((~hskp62) | c2_1(a1103)) <=> ((~hskp62) | c2_1(a1103))),
% 1.36/1.52 inference(rewrite,[status(thm)],[])).
% 1.36/1.52 tff(1333,axiom,((~hskp62) | c2_1(a1103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.36/1.52 tff(1334,plain,
% 1.36/1.52 ((~hskp62) | c2_1(a1103)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.36/1.52 tff(1335,plain,
% 1.36/1.52 ((~hskp62) | c2_1(a1103)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1334, 1332])).
% 1.36/1.52 tff(1336,plain,
% 1.36/1.52 ((~hskp62) | c2_1(a1103)),
% 1.36/1.52 inference(modus_ponens,[status(thm)],[1335, 1332])).
% 1.36/1.52 tff(1337,plain,
% 1.36/1.52 ((~hskp62) | c2_1(a1103)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1336, 1332])).
% 1.36/1.53 tff(1338,plain,
% 1.36/1.53 ((~hskp62) | c2_1(a1103)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1337, 1332])).
% 1.36/1.53 tff(1339,plain,
% 1.36/1.53 (c2_1(a1103)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1338, 1323])).
% 1.36/1.53 tff(1340,plain,
% 1.36/1.53 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1341,plain,
% 1.36/1.53 ((hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c2_1(a1103))) <=> (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1342,plain,
% 1.36/1.53 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c2_1(a1103)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1341])).
% 1.36/1.53 tff(1343,plain,
% 1.36/1.53 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c2_1(a1103)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1342, 1340])).
% 1.36/1.53 tff(1344,plain,
% 1.36/1.53 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c2_1(a1103)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1345,plain,
% 1.36/1.53 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 1.36/1.53 tff(1346,plain,
% 1.36/1.53 (c0_1(a1103)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1345, 120, 1192, 53, 1339, 1331, 63])).
% 1.36/1.53 tff(1347,plain,
% 1.36/1.53 (((~hskp62) | c3_1(a1103)) <=> ((~hskp62) | c3_1(a1103))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1348,axiom,((~hskp62) | c3_1(a1103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.36/1.53 tff(1349,plain,
% 1.36/1.53 ((~hskp62) | c3_1(a1103)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 1.36/1.53 tff(1350,plain,
% 1.36/1.53 ((~hskp62) | c3_1(a1103)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1349, 1347])).
% 1.36/1.53 tff(1351,plain,
% 1.36/1.53 ((~hskp62) | c3_1(a1103)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1350, 1347])).
% 1.36/1.53 tff(1352,plain,
% 1.36/1.53 ((~hskp62) | c3_1(a1103)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1351, 1347])).
% 1.36/1.53 tff(1353,plain,
% 1.36/1.53 ((~hskp62) | c3_1(a1103)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1352, 1347])).
% 1.36/1.53 tff(1354,plain,
% 1.36/1.53 (c3_1(a1103)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1353, 1323])).
% 1.36/1.53 tff(1355,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1356,plain,
% 1.36/1.53 (((~ndr1_0) | (~c1_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103))) <=> ((~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1357,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1356])).
% 1.36/1.53 tff(1358,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1357, 1355])).
% 1.36/1.53 tff(1359,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1360,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.36/1.53 tff(1361,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1360, 120, 1339, 1354, 1331, 10, 1346])).
% 1.36/1.53 tff(1362,plain,((~hskp62) | hskp43 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(1363,plain,
% 1.36/1.53 (~hskp62),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1362, 1192, 53])).
% 1.36/1.53 tff(1364,plain,
% 1.36/1.53 (hskp63 | hskp62),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[118, 1039])).
% 1.36/1.53 tff(1365,plain,
% 1.36/1.53 (hskp63),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1364, 1363])).
% 1.36/1.53 tff(1366,plain,
% 1.36/1.53 (((~hskp63) | (~c2_1(a1105))) <=> ((~hskp63) | (~c2_1(a1105)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1367,plain,
% 1.36/1.53 (((~c2_1(a1105)) | (~hskp63)) <=> ((~hskp63) | (~c2_1(a1105)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1368,axiom,((~c2_1(a1105)) | (~hskp63)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.36/1.53 tff(1369,plain,
% 1.36/1.53 ((~hskp63) | (~c2_1(a1105))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 1.36/1.53 tff(1370,plain,
% 1.36/1.53 ((~hskp63) | (~c2_1(a1105))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1369, 1366])).
% 1.36/1.53 tff(1371,plain,
% 1.36/1.53 (~c2_1(a1105)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1370, 1365])).
% 1.36/1.53 tff(1372,plain,
% 1.36/1.53 (((~hskp63) | c3_1(a1105)) <=> ((~hskp63) | c3_1(a1105))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1373,axiom,((~hskp63) | c3_1(a1105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.36/1.53 tff(1374,plain,
% 1.36/1.53 ((~hskp63) | c3_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.36/1.53 tff(1375,plain,
% 1.36/1.53 ((~hskp63) | c3_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1374, 1372])).
% 1.36/1.53 tff(1376,plain,
% 1.36/1.53 ((~hskp63) | c3_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1375, 1372])).
% 1.36/1.53 tff(1377,plain,
% 1.36/1.53 ((~hskp63) | c3_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1376, 1372])).
% 1.36/1.53 tff(1378,plain,
% 1.36/1.53 ((~hskp63) | c3_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1377, 1372])).
% 1.36/1.53 tff(1379,plain,
% 1.36/1.53 (c3_1(a1105)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1378, 1365])).
% 1.36/1.53 tff(1380,plain,
% 1.36/1.53 (((~hskp63) | c1_1(a1105)) <=> ((~hskp63) | c1_1(a1105))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1381,axiom,((~hskp63) | c1_1(a1105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.36/1.53 tff(1382,plain,
% 1.36/1.53 ((~hskp63) | c1_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 1.36/1.53 tff(1383,plain,
% 1.36/1.53 ((~hskp63) | c1_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1382, 1380])).
% 1.36/1.53 tff(1384,plain,
% 1.36/1.53 ((~hskp63) | c1_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1383, 1380])).
% 1.36/1.53 tff(1385,plain,
% 1.36/1.53 ((~hskp63) | c1_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1384, 1380])).
% 1.36/1.53 tff(1386,plain,
% 1.36/1.53 ((~hskp63) | c1_1(a1105)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1385, 1380])).
% 1.36/1.53 tff(1387,plain,
% 1.36/1.53 (c1_1(a1105)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1386, 1365])).
% 1.36/1.53 tff(1388,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1389,plain,
% 1.36/1.53 ((hskp59 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105))) <=> (hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1390,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1389])).
% 1.36/1.53 tff(1391,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1390, 1388])).
% 1.36/1.53 tff(1392,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1393,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 1.36/1.53 tff(1394,plain,
% 1.36/1.53 (hskp59),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1393, 120, 1387, 1379, 1371, 1305, 1299, 137, 1312])).
% 1.36/1.53 tff(1395,plain,
% 1.36/1.53 (~c3_1(a1095)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[158, 1394])).
% 1.36/1.53 tff(1396,plain,
% 1.36/1.53 (~c0_1(a1095)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[164, 1394])).
% 1.36/1.53 tff(1397,assumption,(~hskp35), introduced(assumption)).
% 1.36/1.53 tff(1398,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1399,plain,
% 1.36/1.53 ((hskp35 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095)) <=> (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1400,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095)))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1399])).
% 1.36/1.53 tff(1401,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1400, 1398])).
% 1.36/1.53 tff(1402,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1403,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 1.36/1.53 tff(1404,plain,
% 1.36/1.53 (c2_1(a1095)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1403, 120, 1397, 1396, 1395, 1305, 1299, 1322, 1312])).
% 1.36/1.53 tff(1405,plain,
% 1.36/1.53 (c1_1(a1095)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[179, 1394])).
% 1.36/1.53 tff(1406,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[186, 120, 1192, 53, 1405, 1396, 63, 1404])).
% 1.36/1.53 tff(1407,plain,(hskp43 | hskp10 | hskp35 | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(1408,plain,
% 1.36/1.53 (hskp43 | hskp10 | hskp20 | hskp19),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1407, 1144])).
% 1.36/1.53 tff(1409,plain,
% 1.36/1.53 (hskp43),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1408, 1191, 53, 1190])).
% 1.36/1.53 tff(1410,plain,
% 1.36/1.53 (c0_1(a1049)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[210, 1409])).
% 1.36/1.53 tff(1411,plain,
% 1.36/1.53 (c2_1(a1049)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[202, 1409])).
% 1.36/1.53 tff(1412,plain,
% 1.36/1.53 (c1_1(a1049)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[194, 1409])).
% 1.36/1.53 tff(1413,assumption,(c3_1(a1049)), introduced(assumption)).
% 1.36/1.53 tff(1414,assumption,(c1_1(a1049)), introduced(assumption)).
% 1.36/1.53 tff(1415,assumption,(c2_1(a1049)), introduced(assumption)).
% 1.36/1.53 tff(1416,assumption,(c0_1(a1049)), introduced(assumption)).
% 1.36/1.53 tff(1417,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1418,plain,
% 1.36/1.53 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1419,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1418])).
% 1.36/1.53 tff(1420,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1419, 1417])).
% 1.36/1.53 tff(1421,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1422,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.36/1.53 tff(1423,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1422, 120, 1416, 1415, 1414, 10, 1413])).
% 1.36/1.53 tff(1424,plain,((~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(1425,plain,
% 1.36/1.53 (~c3_1(a1049)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1424, 1412, 1411, 1410])).
% 1.36/1.53 tff(1426,plain,
% 1.36/1.53 (^[U: $i] : refl((hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.36/1.53 inference(bind,[status(th)],[])).
% 1.36/1.53 tff(1427,plain,
% 1.36/1.53 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.36/1.53 inference(quant_intro,[status(thm)],[1426])).
% 1.36/1.53 tff(1428,plain,
% 1.36/1.53 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1429,plain,
% 1.36/1.53 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp12) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp12))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp12) <=> (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.36/1.53 inference(bind,[status(th)],[])).
% 1.36/1.53 tff(1430,plain,
% 1.36/1.53 (![U: $i] : ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp12) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.36/1.53 inference(quant_intro,[status(thm)],[1429])).
% 1.36/1.53 tff(1431,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause278')).
% 1.36/1.53 tff(1432,plain,
% 1.36/1.53 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 1.36/1.53 tff(1433,plain,
% 1.36/1.53 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1432, 1428])).
% 1.36/1.53 tff(1434,plain,(
% 1.36/1.53 ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.36/1.53 inference(skolemize,[status(sab)],[1433])).
% 1.36/1.53 tff(1435,plain,
% 1.36/1.53 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1434, 1427])).
% 1.36/1.53 tff(1436,assumption,(hskp12), introduced(assumption)).
% 1.36/1.53 tff(1437,plain,
% 1.36/1.53 (((~hskp12) | (~c3_1(a1043))) <=> ((~hskp12) | (~c3_1(a1043)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1438,plain,
% 1.36/1.53 (((~c3_1(a1043)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1043)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1439,axiom,((~c3_1(a1043)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause238')).
% 1.36/1.53 tff(1440,plain,
% 1.36/1.53 ((~hskp12) | (~c3_1(a1043))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 1.36/1.53 tff(1441,plain,
% 1.36/1.53 ((~hskp12) | (~c3_1(a1043))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1440, 1437])).
% 1.36/1.53 tff(1442,plain,
% 1.36/1.53 (~c3_1(a1043)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1441, 1436])).
% 1.36/1.53 tff(1443,plain,
% 1.36/1.53 (((~hskp12) | (~c1_1(a1043))) <=> ((~hskp12) | (~c1_1(a1043)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1444,plain,
% 1.36/1.53 (((~c1_1(a1043)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a1043)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1445,axiom,((~c1_1(a1043)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause237')).
% 1.36/1.53 tff(1446,plain,
% 1.36/1.53 ((~hskp12) | (~c1_1(a1043))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 1.36/1.53 tff(1447,plain,
% 1.36/1.53 ((~hskp12) | (~c1_1(a1043))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1446, 1443])).
% 1.36/1.53 tff(1448,plain,
% 1.36/1.53 (~c1_1(a1043)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1447, 1436])).
% 1.36/1.53 tff(1449,plain,
% 1.36/1.53 (((~hskp12) | c0_1(a1043)) <=> ((~hskp12) | c0_1(a1043))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1450,axiom,((~hskp12) | c0_1(a1043)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.36/1.53 tff(1451,plain,
% 1.36/1.53 ((~hskp12) | c0_1(a1043)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 1.36/1.53 tff(1452,plain,
% 1.36/1.53 ((~hskp12) | c0_1(a1043)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1451, 1449])).
% 1.36/1.53 tff(1453,plain,
% 1.36/1.53 ((~hskp12) | c0_1(a1043)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1452, 1449])).
% 1.36/1.53 tff(1454,plain,
% 1.36/1.53 ((~hskp12) | c0_1(a1043)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1453, 1449])).
% 1.36/1.53 tff(1455,plain,
% 1.36/1.53 ((~hskp12) | c0_1(a1043)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1454, 1449])).
% 1.36/1.53 tff(1456,plain,
% 1.36/1.53 (c0_1(a1043)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1455, 1436])).
% 1.36/1.53 tff(1457,plain,
% 1.36/1.53 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1458,plain,
% 1.36/1.53 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043))) <=> (hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1459,plain,
% 1.36/1.53 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1458])).
% 1.36/1.53 tff(1460,plain,
% 1.36/1.53 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1459, 1457])).
% 1.36/1.53 tff(1461,plain,
% 1.36/1.53 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1462,plain,
% 1.36/1.53 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 1.36/1.53 tff(1463,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1462, 120, 1190, 1191, 1456, 1448, 1442, 625])).
% 1.36/1.53 tff(1464,plain,((~hskp12) | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(1465,plain,
% 1.36/1.53 (~hskp12),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1464, 1191, 1190])).
% 1.36/1.53 tff(1466,plain,
% 1.36/1.53 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1467,plain,
% 1.36/1.53 ((hskp12 | hskp7 | (~ndr1_0) | c3_1(a1049) | (~c1_1(a1049)) | (~c2_1(a1049))) <=> (hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1468,plain,
% 1.36/1.53 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1049) | (~c1_1(a1049)) | (~c2_1(a1049)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049)))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1467])).
% 1.36/1.53 tff(1469,plain,
% 1.36/1.53 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1049) | (~c1_1(a1049)) | (~c2_1(a1049)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1468, 1466])).
% 1.36/1.53 tff(1470,plain,
% 1.36/1.53 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1049) | (~c1_1(a1049)) | (~c2_1(a1049)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1471,plain,
% 1.36/1.53 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 1.36/1.53 tff(1472,plain,
% 1.36/1.53 (hskp7),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1471, 120, 1465, 1411, 1412, 1435, 1425])).
% 1.36/1.53 tff(1473,plain,
% 1.36/1.53 (((~hskp7) | (~c2_1(a1035))) <=> ((~hskp7) | (~c2_1(a1035)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1474,plain,
% 1.36/1.53 (((~c2_1(a1035)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1035)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1475,axiom,((~c2_1(a1035)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause247')).
% 1.36/1.53 tff(1476,plain,
% 1.36/1.53 ((~hskp7) | (~c2_1(a1035))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 1.36/1.53 tff(1477,plain,
% 1.36/1.53 ((~hskp7) | (~c2_1(a1035))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1476, 1473])).
% 1.36/1.53 tff(1478,plain,
% 1.36/1.53 (~c2_1(a1035)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1477, 1472])).
% 1.36/1.53 tff(1479,plain,
% 1.36/1.53 (((~hskp7) | c0_1(a1035)) <=> ((~hskp7) | c0_1(a1035))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1480,axiom,((~hskp7) | c0_1(a1035)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.36/1.53 tff(1481,plain,
% 1.36/1.53 ((~hskp7) | c0_1(a1035)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.36/1.53 tff(1482,plain,
% 1.36/1.53 ((~hskp7) | c0_1(a1035)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1481, 1479])).
% 1.36/1.53 tff(1483,plain,
% 1.36/1.53 ((~hskp7) | c0_1(a1035)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1482, 1479])).
% 1.36/1.53 tff(1484,plain,
% 1.36/1.53 ((~hskp7) | c0_1(a1035)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1483, 1479])).
% 1.36/1.53 tff(1485,plain,
% 1.36/1.53 ((~hskp7) | c0_1(a1035)),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1484, 1479])).
% 1.36/1.53 tff(1486,plain,
% 1.36/1.53 (c0_1(a1035)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1485, 1472])).
% 1.36/1.53 tff(1487,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1488,plain,
% 1.36/1.53 ((hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049))) <=> (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1489,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1488])).
% 1.36/1.53 tff(1490,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1489, 1487])).
% 1.36/1.53 tff(1491,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1492,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 1.36/1.53 tff(1493,plain,
% 1.36/1.53 (~c3_1(a1035)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1492, 120, 1465, 1410, 1411, 1412, 1486, 1478, 1189])).
% 1.36/1.53 tff(1494,assumption,(c3_1(a1059)), introduced(assumption)).
% 1.36/1.53 tff(1495,plain,
% 1.36/1.53 (hskp43),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1407, 1397, 53, 1190, 1191])).
% 1.36/1.53 tff(1496,plain,
% 1.36/1.53 (c1_1(a1049)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[194, 1495])).
% 1.36/1.53 tff(1497,plain,
% 1.36/1.53 (c2_1(a1049)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[202, 1495])).
% 1.36/1.53 tff(1498,plain,
% 1.38/1.54 (c0_1(a1049)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[210, 1495])).
% 1.38/1.54 tff(1499,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1500,plain,
% 1.38/1.54 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1501,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1500])).
% 1.38/1.54 tff(1502,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1501, 1499])).
% 1.38/1.54 tff(1503,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1504,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 1.38/1.54 tff(1505,plain,
% 1.38/1.54 (~c0_1(a1059)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1504, 120, 1498, 1497, 1496, 1494, 351, 10])).
% 1.38/1.54 tff(1506,plain,
% 1.38/1.54 (~c3_1(a1049)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1424, 1496, 1497, 1498])).
% 1.38/1.54 tff(1507,plain,
% 1.38/1.54 (hskp7),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1471, 120, 1465, 1497, 1496, 1435, 1506])).
% 1.38/1.54 tff(1508,plain,
% 1.38/1.54 (~c2_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1477, 1507])).
% 1.38/1.54 tff(1509,plain,
% 1.38/1.54 (((~hskp7) | c1_1(a1035)) <=> ((~hskp7) | c1_1(a1035))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1510,axiom,((~hskp7) | c1_1(a1035)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.38/1.54 tff(1511,plain,
% 1.38/1.54 ((~hskp7) | c1_1(a1035)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.38/1.54 tff(1512,plain,
% 1.38/1.54 ((~hskp7) | c1_1(a1035)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1511, 1509])).
% 1.38/1.54 tff(1513,plain,
% 1.38/1.54 ((~hskp7) | c1_1(a1035)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1512, 1509])).
% 1.38/1.54 tff(1514,plain,
% 1.38/1.54 ((~hskp7) | c1_1(a1035)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1513, 1509])).
% 1.38/1.54 tff(1515,plain,
% 1.38/1.54 ((~hskp7) | c1_1(a1035)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1514, 1509])).
% 1.38/1.54 tff(1516,plain,
% 1.38/1.54 (c1_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1515, 1507])).
% 1.38/1.54 tff(1517,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1518,plain,
% 1.38/1.54 ((hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059))) <=> (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1519,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1518])).
% 1.38/1.54 tff(1520,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1519, 1517])).
% 1.38/1.54 tff(1521,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1522,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.38/1.54 tff(1523,plain,
% 1.38/1.54 (c3_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1522, 120, 1397, 1494, 351, 1516, 1508, 932, 1505])).
% 1.38/1.54 tff(1524,plain,
% 1.38/1.54 (c0_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1485, 1507])).
% 1.38/1.54 tff(1525,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1492, 120, 1465, 1498, 1497, 1496, 1524, 1508, 1189, 1523])).
% 1.38/1.54 tff(1526,plain,(hskp35 | (~c3_1(a1059)) | (~c2_1(a1059)) | hskp10 | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1527,plain,
% 1.38/1.54 ((~c3_1(a1059)) | (~c2_1(a1059)) | hskp10 | hskp20 | hskp19),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1526, 1144])).
% 1.38/1.54 tff(1528,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1527, 348, 368, 53, 1190, 1191])).
% 1.38/1.54 tff(1529,plain,((~hskp15) | hskp10 | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1530,plain,
% 1.38/1.54 (~hskp15),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1529, 1191, 1190, 53])).
% 1.38/1.54 tff(1531,assumption,(hskp14), introduced(assumption)).
% 1.38/1.54 tff(1532,plain,
% 1.38/1.54 (~c0_1(a1055)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1304, 1531])).
% 1.38/1.54 tff(1533,plain,
% 1.38/1.54 (~c2_1(a1055)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1298, 1531])).
% 1.38/1.54 tff(1534,assumption,(~c0_1(a1055)), introduced(assumption)).
% 1.38/1.54 tff(1535,assumption,(~c2_1(a1055)), introduced(assumption)).
% 1.38/1.54 tff(1536,plain,
% 1.38/1.54 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1537,plain,
% 1.38/1.54 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055))) <=> (hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1538,plain,
% 1.38/1.54 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1537])).
% 1.38/1.54 tff(1539,plain,
% 1.38/1.54 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1538, 1536])).
% 1.38/1.54 tff(1540,plain,
% 1.38/1.54 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1541,plain,
% 1.38/1.54 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 1.38/1.54 tff(1542,plain,
% 1.38/1.54 (c0_1(a1055) | (~c3_1(a1055))),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1541, 120, 21, 42, 1535, 52])).
% 1.38/1.54 tff(1543,plain,
% 1.38/1.54 (~c3_1(a1055)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1542, 1534])).
% 1.38/1.54 tff(1544,plain,
% 1.38/1.54 (c0_1(a1055) | c3_1(a1055)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1311, 120, 53, 1535, 73])).
% 1.38/1.54 tff(1545,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1544, 1543, 1534])).
% 1.38/1.54 tff(1546,plain,(c0_1(a1055) | hskp10 | c2_1(a1055) | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1547,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1546, 1533, 1532, 53, 21, 42])).
% 1.38/1.54 tff(1548,plain,((~hskp14) | hskp10 | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1549,plain,
% 1.38/1.54 (~hskp14),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1548, 42, 21, 53])).
% 1.38/1.54 tff(1550,plain,
% 1.38/1.54 (~hskp19),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[614, 42, 21, 53])).
% 1.38/1.54 tff(1551,plain,
% 1.38/1.54 (hskp38),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1292, 1190, 1550, 1549])).
% 1.38/1.54 tff(1552,plain,
% 1.38/1.54 (hskp43),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1229, 1551, 53])).
% 1.38/1.54 tff(1553,plain,
% 1.38/1.54 (c1_1(a1049)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[194, 1552])).
% 1.38/1.54 tff(1554,plain,
% 1.38/1.54 (c2_1(a1049)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[202, 1552])).
% 1.38/1.54 tff(1555,plain,
% 1.38/1.54 (c0_1(a1049)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[210, 1552])).
% 1.38/1.54 tff(1556,plain,
% 1.38/1.54 (~hskp12),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1464, 1190, 1550])).
% 1.38/1.54 tff(1557,plain,
% 1.38/1.54 (c2_1(a1040)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1200, 1551])).
% 1.38/1.54 tff(1558,plain,
% 1.38/1.54 (c3_1(a1040)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1208, 1551])).
% 1.38/1.54 tff(1559,plain,
% 1.38/1.54 (c1_1(a1040)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1216, 1551])).
% 1.38/1.54 tff(1560,plain,
% 1.38/1.54 (~c0_1(a1040)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1223, 120, 1559, 1558, 1557, 10])).
% 1.38/1.54 tff(1561,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1562,plain,
% 1.38/1.54 ((hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c2_1(a1040))) <=> (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1563,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c2_1(a1040)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1562])).
% 1.38/1.54 tff(1564,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c2_1(a1040)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1563, 1561])).
% 1.38/1.54 tff(1565,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c2_1(a1040)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1566,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 1.38/1.54 tff(1567,plain,
% 1.38/1.54 (hskp36),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1566, 120, 1559, 1558, 1557, 708, 1560])).
% 1.38/1.54 tff(1568,plain,
% 1.38/1.54 (~c0_1(a1034)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[720, 1567])).
% 1.38/1.54 tff(1569,plain,
% 1.38/1.54 (c3_1(a1034)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[760, 1567])).
% 1.38/1.54 tff(1570,plain,
% 1.38/1.54 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1571,plain,
% 1.38/1.54 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034))) <=> (hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1572,plain,
% 1.38/1.54 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034)))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1571])).
% 1.38/1.54 tff(1573,plain,
% 1.38/1.54 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1572, 1570])).
% 1.38/1.54 tff(1574,plain,
% 1.38/1.54 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1575,plain,
% 1.38/1.54 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 1.38/1.54 tff(1576,plain,
% 1.38/1.54 (c2_1(a1034)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1575, 120, 21, 42, 1569, 1568, 52])).
% 1.38/1.54 tff(1577,assumption,(hskp7), introduced(assumption)).
% 1.38/1.54 tff(1578,plain,
% 1.38/1.54 (~c2_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1477, 1577])).
% 1.38/1.54 tff(1579,plain,
% 1.38/1.54 (c0_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1485, 1577])).
% 1.38/1.54 tff(1580,assumption,(~hskp12), introduced(assumption)).
% 1.38/1.54 tff(1581,plain,
% 1.38/1.54 (~c3_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1492, 120, 1580, 1416, 1415, 1414, 1579, 1578, 1189])).
% 1.38/1.54 tff(1582,assumption,(c2_1(a1034)), introduced(assumption)).
% 1.38/1.54 tff(1583,assumption,(~c0_1(a1034)), introduced(assumption)).
% 1.38/1.54 tff(1584,plain,
% 1.38/1.54 (c1_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1515, 1577])).
% 1.38/1.54 tff(1585,assumption,(c3_1(a1034)), introduced(assumption)).
% 1.38/1.54 tff(1586,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1587,plain,
% 1.38/1.54 ((hskp12 | (~ndr1_0) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049))) <=> (hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1588,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1587])).
% 1.38/1.54 tff(1589,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1588, 1586])).
% 1.38/1.54 tff(1590,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1591,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 1.38/1.54 tff(1592,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1591, 120, 1580, 1416, 1415, 1414, 1111, 1109, 1189, 1112])).
% 1.38/1.54 tff(1593,plain,((~hskp35) | hskp12 | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1594,plain,
% 1.38/1.54 (~hskp35),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1593, 1416, 1580, 1415, 1414])).
% 1.38/1.54 tff(1595,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1596,plain,
% 1.38/1.54 ((hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034))) <=> (hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1597,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1596])).
% 1.38/1.54 tff(1598,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1597, 1595])).
% 1.38/1.54 tff(1599,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1600,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 1.38/1.54 tff(1601,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1600, 120, 1594, 1585, 1584, 1583, 1578, 932, 1582, 1581])).
% 1.38/1.54 tff(1602,plain,((~hskp7) | (~c3_1(a1034)) | c0_1(a1034) | (~c2_1(a1034)) | hskp12 | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1603,plain,
% 1.38/1.54 (~hskp7),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1602, 1569, 1568, 1576, 1556, 1555, 1554, 1553])).
% 1.38/1.54 tff(1604,plain,
% 1.38/1.54 (hskp7 | c3_1(a1049)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1471, 120, 1556, 1554, 1553, 1435])).
% 1.38/1.54 tff(1605,plain,
% 1.38/1.54 (c3_1(a1049)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1604, 1603])).
% 1.38/1.54 tff(1606,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1422, 120, 1555, 1554, 1553, 10, 1605])).
% 1.38/1.54 tff(1607,plain,(hskp20 | hskp33 | hskp15 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1608,plain,
% 1.38/1.54 (hskp33),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1607, 1530, 1190, 53])).
% 1.38/1.54 tff(1609,plain,
% 1.38/1.54 (c2_1(a1031)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[271, 1608])).
% 1.38/1.54 tff(1610,plain,
% 1.38/1.54 (c3_1(a1031)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[291, 1608])).
% 1.38/1.54 tff(1611,plain,
% 1.38/1.54 (~c0_1(a1031)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[794, 120, 1410, 1411, 1412, 1610, 1609, 10])).
% 1.38/1.54 tff(1612,plain,
% 1.38/1.54 (c1_1(a1035)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1515, 1472])).
% 1.38/1.54 tff(1613,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1614,plain,
% 1.38/1.54 ((hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031))) <=> (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1615,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031)))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1614])).
% 1.38/1.54 tff(1616,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1615, 1613])).
% 1.38/1.54 tff(1617,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1618,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.38/1.54 tff(1619,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1618, 120, 1144, 1610, 1609, 1612, 1478, 932, 1611, 1493])).
% 1.38/1.54 tff(1620,plain,(hskp19 | hskp20 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1621,plain,
% 1.38/1.54 (hskp20),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1620, 1179, 53])).
% 1.38/1.54 tff(1622,plain,
% 1.38/1.54 (~c2_1(a1080)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[639, 1621])).
% 1.38/1.54 tff(1623,plain,
% 1.38/1.54 (~c0_1(a1080)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[645, 1621])).
% 1.38/1.54 tff(1624,plain,
% 1.38/1.54 (c3_1(a1080)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[683, 120, 53, 1623, 1622, 73])).
% 1.38/1.54 tff(1625,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1626,plain,
% 1.38/1.54 ((hskp59 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105))) <=> (hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1627,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1626])).
% 1.38/1.54 tff(1628,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1627, 1625])).
% 1.38/1.55 tff(1629,plain,
% 1.38/1.55 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1630,plain,
% 1.38/1.55 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 1.38/1.55 tff(1631,plain,
% 1.38/1.55 (hskp59),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1630, 120, 1387, 1379, 1371, 1623, 1622, 137, 1624])).
% 1.38/1.55 tff(1632,plain,
% 1.38/1.55 (~c0_1(a1095)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[164, 1631])).
% 1.38/1.55 tff(1633,plain,
% 1.38/1.55 (c1_1(a1095)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[179, 1631])).
% 1.38/1.55 tff(1634,plain,
% 1.38/1.55 (~c2_1(a1095)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[186, 120, 1192, 53, 1633, 1632, 63])).
% 1.38/1.55 tff(1635,plain,
% 1.38/1.55 (~c3_1(a1095)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[158, 1631])).
% 1.38/1.55 tff(1636,plain,
% 1.38/1.55 ($false),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[171, 120, 53, 1632, 1635, 73, 1634])).
% 1.38/1.55 tff(1637,plain,(hskp43 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.38/1.55 tff(1638,plain,
% 1.38/1.55 (hskp43),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1637, 53])).
% 1.38/1.55 tff(1639,plain,
% 1.38/1.55 (c1_1(a1049)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[194, 1638])).
% 1.38/1.55 tff(1640,plain,
% 1.38/1.55 (c2_1(a1049)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[202, 1638])).
% 1.38/1.55 tff(1641,plain,
% 1.38/1.55 (c0_1(a1049)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[210, 1638])).
% 1.38/1.55 tff(1642,plain,
% 1.38/1.55 (~c1_1(a1080)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[667, 1621])).
% 1.38/1.55 tff(1643,plain,
% 1.38/1.55 (~c0_1(a1031)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[794, 120, 1416, 1415, 1414, 292, 272, 10])).
% 1.38/1.55 tff(1644,plain,
% 1.38/1.55 (~c3_1(a1049)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1424, 1414, 1415, 1416])).
% 1.38/1.55 tff(1645,plain,
% 1.38/1.55 (hskp12 | hskp7),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1471, 120, 1415, 1414, 1435, 1644])).
% 1.38/1.55 tff(1646,plain,
% 1.38/1.55 (hskp7),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1645, 1580])).
% 1.38/1.55 tff(1647,plain,
% 1.38/1.55 (~c2_1(a1035)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1477, 1646])).
% 1.38/1.55 tff(1648,plain,
% 1.38/1.55 (c0_1(a1035)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1485, 1646])).
% 1.38/1.55 tff(1649,plain,
% 1.38/1.55 (~c3_1(a1035)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1492, 120, 1580, 1416, 1415, 1414, 1648, 1647, 1189])).
% 1.38/1.55 tff(1650,plain,
% 1.38/1.55 (~c0_1(a1031)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[794, 120, 1416, 1415, 1414, 797, 275, 10])).
% 1.38/1.55 tff(1651,plain,
% 1.38/1.55 (c1_1(a1035)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1515, 1646])).
% 1.38/1.55 tff(1652,plain,
% 1.38/1.55 ($false),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1618, 120, 1144, 797, 275, 1651, 1647, 932, 1650, 1649])).
% 1.38/1.55 tff(1653,plain,(hskp12 | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.55 tff(1654,plain,
% 1.38/1.55 (hskp12),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1653, 292, 272, 1416, 1415, 1414])).
% 1.38/1.55 tff(1655,plain,
% 1.38/1.55 (~c3_1(a1043)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1441, 1654])).
% 1.38/1.55 tff(1656,plain,
% 1.38/1.55 (~c1_1(a1043)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1447, 1654])).
% 1.38/1.55 tff(1657,assumption,(~c1_1(a1080)), introduced(assumption)).
% 1.38/1.55 tff(1658,assumption,(~c2_1(a1080)), introduced(assumption)).
% 1.38/1.55 tff(1659,assumption,(~c0_1(a1080)), introduced(assumption)).
% 1.38/1.55 tff(1660,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1661,plain,
% 1.38/1.55 (((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080)) <=> (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1662,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031)))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1661])).
% 1.38/1.55 tff(1663,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1662, 1660])).
% 1.38/1.55 tff(1664,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1665,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.38/1.55 tff(1666,plain,
% 1.38/1.55 (~c2_1(a1043)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1665, 120, 292, 272, 1659, 1658, 1657, 1656, 1655, 481, 1643])).
% 1.38/1.55 tff(1667,plain,
% 1.38/1.55 (c0_1(a1043)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1455, 1654])).
% 1.38/1.55 tff(1668,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1669,plain,
% 1.38/1.55 (((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043)) <=> (c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1670,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031)))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1669])).
% 1.38/1.55 tff(1671,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1670, 1668])).
% 1.38/1.55 tff(1672,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1673,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 1.38/1.55 tff(1674,plain,
% 1.38/1.55 ($false),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1673, 120, 272, 1667, 264, 1656, 1655, 221, 1643, 1666])).
% 1.38/1.55 tff(1675,plain,((~hskp33) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.55 tff(1676,plain,
% 1.38/1.55 (~hskp33),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1675, 1623, 1622, 1642, 1641, 1640, 1639])).
% 1.38/1.55 tff(1677,plain,
% 1.38/1.55 (hskp20),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1607, 42, 21, 53])).
% 1.38/1.55 tff(1678,plain,
% 1.38/1.55 (~c2_1(a1080)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[639, 1677])).
% 1.38/1.55 tff(1679,plain,
% 1.38/1.55 (~c0_1(a1080)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[645, 1677])).
% 1.38/1.55 tff(1680,plain,
% 1.38/1.55 (~c3_1(a1080)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[659, 120, 21, 42, 1679, 1678, 52])).
% 1.38/1.55 tff(1681,plain,
% 1.38/1.55 ($false),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[683, 120, 53, 1679, 1678, 73, 1680])).
% 1.38/1.55 tff(1682,plain,(hskp15 | hskp10 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.38/1.55 tff(1683,plain,
% 1.38/1.55 (hskp15),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1682, 1676, 53])).
% 1.38/1.55 tff(1684,plain,
% 1.38/1.55 (c2_1(a1059)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[347, 1683])).
% 1.38/1.55 tff(1685,plain,
% 1.38/1.55 (c3_1(a1059)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[367, 1683])).
% 1.38/1.55 tff(1686,plain,
% 1.38/1.55 (~c0_1(a1059)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1504, 120, 1641, 1640, 1639, 1685, 1684, 10])).
% 1.38/1.55 tff(1687,plain,
% 1.38/1.55 (~c0_1(a1059)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1504, 120, 1416, 1415, 1414, 1494, 351, 10])).
% 1.38/1.55 tff(1688,plain,
% 1.38/1.55 ($false),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1522, 120, 1144, 1494, 351, 1651, 1647, 932, 1687, 1649])).
% 1.38/1.55 tff(1689,plain,(hskp12 | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.55 tff(1690,plain,
% 1.38/1.55 (hskp12),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1689, 1685, 1684, 1641, 1640, 1639])).
% 1.38/1.55 tff(1691,plain,
% 1.38/1.55 (~c3_1(a1043)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1441, 1690])).
% 1.38/1.55 tff(1692,plain,
% 1.38/1.55 (~c1_1(a1043)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1447, 1690])).
% 1.38/1.55 tff(1693,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1694,plain,
% 1.38/1.55 (((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080)) <=> (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1695,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1694])).
% 1.38/1.55 tff(1696,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1695, 1693])).
% 1.38/1.55 tff(1697,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1698,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1697, 1696])).
% 1.38/1.55 tff(1699,plain,
% 1.38/1.55 (~c2_1(a1043)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1698, 120, 1685, 1684, 1623, 1622, 1642, 1692, 1691, 481, 1686])).
% 1.38/1.55 tff(1700,plain,
% 1.38/1.55 (~c1_1(a1059)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[339, 1683])).
% 1.38/1.55 tff(1701,plain,
% 1.38/1.55 (c0_1(a1043)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1455, 1690])).
% 1.38/1.55 tff(1702,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1703,plain,
% 1.38/1.55 (((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043)) <=> (c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1704,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059)))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1703])).
% 1.38/1.55 tff(1705,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1704, 1702])).
% 1.38/1.55 tff(1706,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1707,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 1.38/1.55 tff(1708,plain,
% 1.38/1.55 ($false),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1707, 120, 1684, 1701, 1700, 1692, 1691, 221, 1686, 1699])).
% 1.38/1.55 tff(1709,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 1.38/1.55 tff(1710,plain,
% 1.38/1.55 (~c0_1(a1039)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[407, 1709])).
% 1.38/1.55 tff(1711,plain,
% 1.38/1.55 (~c2_1(a1039)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[393, 1709])).
% 1.38/1.55 tff(1712,plain,
% 1.38/1.55 (hskp33 | hskp15 | (~c3_1(a1039))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[583, 120, 1711, 1710, 52])).
% 1.38/1.55 tff(1713,plain,
% 1.38/1.55 (~c3_1(a1039)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1712, 42, 21])).
% 1.38/1.55 tff(1714,assumption,(hskp36), introduced(assumption)).
% 1.38/1.55 tff(1715,plain,
% 1.38/1.55 (~c0_1(a1034)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[720, 1714])).
% 1.38/1.55 tff(1716,plain,
% 1.38/1.55 (c3_1(a1034)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[760, 1714])).
% 1.38/1.55 tff(1717,plain,
% 1.38/1.55 (c2_1(a1034)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1575, 120, 21, 42, 1716, 1715, 52])).
% 1.38/1.55 tff(1718,plain,
% 1.38/1.55 (c1_1(a1039)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[401, 1709])).
% 1.38/1.55 tff(1719,plain,
% 1.38/1.55 (c1_1(a1034)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[728, 1714])).
% 1.38/1.55 tff(1720,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1721,plain,
% 1.38/1.55 ((hskp33 | (~ndr1_0) | (~c1_1(a1034)) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039))) <=> (hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1722,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1034)) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1721])).
% 1.38/1.55 tff(1723,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1034)) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1722, 1720])).
% 1.38/1.55 tff(1724,plain,
% 1.38/1.55 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1034)) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1725,plain,
% 1.38/1.55 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 1.38/1.55 tff(1726,plain,
% 1.38/1.55 ($false),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1725, 120, 21, 1716, 1719, 1718, 1711, 1710, 698, 1717])).
% 1.38/1.55 tff(1727,plain,((~hskp36) | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.38/1.55 tff(1728,plain,
% 1.38/1.55 (~hskp36),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1727, 42, 21])).
% 1.38/1.55 tff(1729,plain,
% 1.38/1.55 (^[U: $i] : refl((hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(1730,plain,
% 1.38/1.55 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[1729])).
% 1.38/1.55 tff(1731,plain,
% 1.38/1.55 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1732,plain,
% 1.38/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | 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) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp36))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) | hskp48) <=> ((hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp48))), rewrite(((hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp48) <=> (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) | hskp48) <=> (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(1733,plain,
% 1.38/1.55 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) | hskp48) <=> ![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[1732])).
% 1.38/1.55 tff(1734,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) | hskp48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause267')).
% 1.38/1.55 tff(1735,plain,
% 1.38/1.55 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.38/1.55 tff(1736,plain,
% 1.38/1.55 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1735, 1731])).
% 1.38/1.55 tff(1737,plain,(
% 1.38/1.55 ![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.38/1.55 inference(skolemize,[status(sab)],[1736])).
% 1.38/1.55 tff(1738,plain,
% 1.38/1.55 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1737, 1730])).
% 1.38/1.55 tff(1739,plain,
% 1.38/1.55 (((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1740,plain,
% 1.38/1.55 ((hskp48 | hskp36 | (~ndr1_0) | c0_1(a1039) | c3_1(a1039) | (~c1_1(a1039))) <=> (hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1741,plain,
% 1.38/1.55 (((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | (~ndr1_0) | c0_1(a1039) | c3_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1740])).
% 1.38/1.55 tff(1742,plain,
% 1.38/1.55 (((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | (~ndr1_0) | c0_1(a1039) | c3_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1741, 1739])).
% 1.38/1.55 tff(1743,plain,
% 1.38/1.55 ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | (~ndr1_0) | c0_1(a1039) | c3_1(a1039) | (~c1_1(a1039)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1744,plain,
% 1.38/1.55 ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 1.38/1.55 tff(1745,plain,
% 1.38/1.55 (hskp48 | hskp36 | c3_1(a1039)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1744, 120, 1718, 1710, 1738])).
% 1.38/1.55 tff(1746,plain,
% 1.38/1.55 (hskp48),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1745, 1728, 1713])).
% 1.38/1.55 tff(1747,plain,
% 1.38/1.55 (((~hskp48) | c0_1(a1062)) <=> ((~hskp48) | c0_1(a1062))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1748,axiom,((~hskp48) | c0_1(a1062)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.38/1.55 tff(1749,plain,
% 1.38/1.55 ((~hskp48) | c0_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 1.38/1.55 tff(1750,plain,
% 1.38/1.55 ((~hskp48) | c0_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1749, 1747])).
% 1.38/1.55 tff(1751,plain,
% 1.38/1.55 ((~hskp48) | c0_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1750, 1747])).
% 1.38/1.55 tff(1752,plain,
% 1.38/1.55 ((~hskp48) | c0_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1751, 1747])).
% 1.38/1.55 tff(1753,plain,
% 1.38/1.55 ((~hskp48) | c0_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1752, 1747])).
% 1.38/1.55 tff(1754,plain,
% 1.38/1.55 (c0_1(a1062)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1753, 1746])).
% 1.38/1.55 tff(1755,plain,
% 1.38/1.55 (((~hskp48) | c2_1(a1062)) <=> ((~hskp48) | c2_1(a1062))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1756,axiom,((~hskp48) | c2_1(a1062)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.38/1.55 tff(1757,plain,
% 1.38/1.55 ((~hskp48) | c2_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1756, 1755])).
% 1.38/1.55 tff(1758,plain,
% 1.38/1.55 ((~hskp48) | c2_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1757, 1755])).
% 1.38/1.55 tff(1759,plain,
% 1.38/1.55 ((~hskp48) | c2_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1758, 1755])).
% 1.38/1.55 tff(1760,plain,
% 1.38/1.55 ((~hskp48) | c2_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1759, 1755])).
% 1.38/1.55 tff(1761,plain,
% 1.38/1.55 ((~hskp48) | c2_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1760, 1755])).
% 1.38/1.55 tff(1762,plain,
% 1.38/1.55 (c2_1(a1062)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1761, 1746])).
% 1.38/1.55 tff(1763,plain,
% 1.38/1.55 (((~hskp48) | c3_1(a1062)) <=> ((~hskp48) | c3_1(a1062))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1764,axiom,((~hskp48) | c3_1(a1062)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.38/1.55 tff(1765,plain,
% 1.38/1.55 ((~hskp48) | c3_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 1.38/1.55 tff(1766,plain,
% 1.38/1.55 ((~hskp48) | c3_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1765, 1763])).
% 1.38/1.55 tff(1767,plain,
% 1.38/1.55 ((~hskp48) | c3_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1766, 1763])).
% 1.38/1.55 tff(1768,plain,
% 1.38/1.55 ((~hskp48) | c3_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1767, 1763])).
% 1.38/1.55 tff(1769,plain,
% 1.38/1.55 ((~hskp48) | c3_1(a1062)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1768, 1763])).
% 1.38/1.55 tff(1770,plain,
% 1.38/1.55 (c3_1(a1062)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1769, 1746])).
% 1.38/1.55 tff(1771,plain,
% 1.38/1.55 (((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)))) <=> ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1772,plain,
% 1.38/1.55 ((hskp33 | hskp23 | (~ndr1_0) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062))) <=> (hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1773,plain,
% 1.38/1.55 (((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1772])).
% 1.38/1.55 tff(1774,plain,
% 1.38/1.55 (((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1773, 1771])).
% 1.38/1.55 tff(1775,plain,
% 1.38/1.55 ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1776,plain,
% 1.38/1.55 ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 1.38/1.55 tff(1777,plain,
% 1.38/1.55 (hskp23),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1776, 120, 21, 1770, 1762, 1754, 41])).
% 1.38/1.55 tff(1778,plain,
% 1.38/1.55 (((~hskp23) | (~c2_1(a1088))) <=> ((~hskp23) | (~c2_1(a1088)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1779,plain,
% 1.38/1.55 (((~c2_1(a1088)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a1088)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1780,axiom,((~c2_1(a1088)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause218')).
% 1.38/1.55 tff(1781,plain,
% 1.38/1.55 ((~hskp23) | (~c2_1(a1088))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.38/1.55 tff(1782,plain,
% 1.38/1.55 ((~hskp23) | (~c2_1(a1088))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1781, 1778])).
% 1.38/1.55 tff(1783,plain,
% 1.38/1.55 (~c2_1(a1088)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1782, 1777])).
% 1.38/1.55 tff(1784,plain,
% 1.38/1.55 (((~hskp23) | c3_1(a1088)) <=> ((~hskp23) | c3_1(a1088))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1785,axiom,((~hskp23) | c3_1(a1088)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.38/1.56 tff(1786,plain,
% 1.38/1.56 ((~hskp23) | c3_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 1.38/1.56 tff(1787,plain,
% 1.38/1.56 ((~hskp23) | c3_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1786, 1784])).
% 1.38/1.56 tff(1788,plain,
% 1.38/1.56 ((~hskp23) | c3_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1787, 1784])).
% 1.38/1.56 tff(1789,plain,
% 1.38/1.56 ((~hskp23) | c3_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1788, 1784])).
% 1.38/1.56 tff(1790,plain,
% 1.38/1.56 ((~hskp23) | c3_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1789, 1784])).
% 1.38/1.56 tff(1791,plain,
% 1.38/1.56 (c3_1(a1088)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1790, 1777])).
% 1.38/1.56 tff(1792,plain,
% 1.38/1.56 (((~hskp23) | c1_1(a1088)) <=> ((~hskp23) | c1_1(a1088))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1793,axiom,((~hskp23) | c1_1(a1088)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.38/1.56 tff(1794,plain,
% 1.38/1.56 ((~hskp23) | c1_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1793, 1792])).
% 1.38/1.56 tff(1795,plain,
% 1.38/1.56 ((~hskp23) | c1_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1794, 1792])).
% 1.38/1.56 tff(1796,plain,
% 1.38/1.56 ((~hskp23) | c1_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1795, 1792])).
% 1.38/1.56 tff(1797,plain,
% 1.38/1.56 ((~hskp23) | c1_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1796, 1792])).
% 1.38/1.56 tff(1798,plain,
% 1.38/1.56 ((~hskp23) | c1_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1797, 1792])).
% 1.38/1.56 tff(1799,plain,
% 1.38/1.56 (c1_1(a1088)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1798, 1777])).
% 1.38/1.56 tff(1800,plain,
% 1.38/1.56 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1801,plain,
% 1.38/1.56 ((hskp56 | hskp22 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c3_1(a1088))) <=> (hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1802,plain,
% 1.38/1.56 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1801])).
% 1.38/1.56 tff(1803,plain,
% 1.38/1.56 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1802, 1800])).
% 1.38/1.56 tff(1804,plain,
% 1.38/1.56 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c3_1(a1088)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1805,plain,
% 1.38/1.56 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 1.38/1.56 tff(1806,plain,
% 1.38/1.56 (hskp22),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1805, 120, 1039, 1799, 1791, 1783, 31])).
% 1.38/1.56 tff(1807,plain,
% 1.38/1.56 (~c1_1(a1083)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1085, 1806])).
% 1.38/1.56 tff(1808,plain,
% 1.38/1.56 (c3_1(a1083)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1054, 1806])).
% 1.38/1.56 tff(1809,plain,
% 1.38/1.56 (c2_1(a1083)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1062, 1806])).
% 1.38/1.56 tff(1810,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1811,plain,
% 1.38/1.56 ((hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062))) <=> (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1812,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1811])).
% 1.38/1.56 tff(1813,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1812, 1810])).
% 1.38/1.56 tff(1814,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1815,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.38/1.56 tff(1816,plain,
% 1.38/1.56 (hskp53),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1815, 120, 1770, 1762, 1754, 1809, 1808, 1807, 20])).
% 1.38/1.56 tff(1817,plain,
% 1.38/1.56 (c0_1(a1073)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[307, 1816])).
% 1.38/1.56 tff(1818,plain,
% 1.38/1.56 (c2_1(a1073)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[315, 1816])).
% 1.38/1.56 tff(1819,plain,
% 1.38/1.56 (c1_1(a1073)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[323, 1816])).
% 1.38/1.56 tff(1820,plain,
% 1.38/1.56 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1821,plain,
% 1.38/1.56 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1088) | c2_1(a1088) | (~c3_1(a1088))) <=> (hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1822,plain,
% 1.38/1.56 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1088) | c2_1(a1088) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088)))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1821])).
% 1.38/1.56 tff(1823,plain,
% 1.38/1.56 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1088) | c2_1(a1088) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1822, 1820])).
% 1.38/1.56 tff(1824,plain,
% 1.38/1.56 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1088) | c2_1(a1088) | (~c3_1(a1088)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1825,plain,
% 1.38/1.56 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.38/1.56 tff(1826,plain,
% 1.38/1.56 (c0_1(a1088)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1825, 120, 21, 42, 1791, 1783, 52])).
% 1.38/1.56 tff(1827,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1828,plain,
% 1.38/1.56 ((hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088))) <=> (hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1829,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1828])).
% 1.38/1.56 tff(1830,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1829, 1827])).
% 1.38/1.56 tff(1831,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1832,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 1.38/1.56 tff(1833,plain,
% 1.38/1.56 (hskp57),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1832, 120, 1791, 1809, 1808, 1783, 1807, 980, 1826])).
% 1.38/1.56 tff(1834,plain,
% 1.38/1.56 (c3_1(a1085)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[995, 1833])).
% 1.38/1.56 tff(1835,plain,
% 1.38/1.56 (c0_1(a1085)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1003, 1833])).
% 1.38/1.56 tff(1836,plain,
% 1.38/1.56 (c2_1(a1085)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1011, 1833])).
% 1.38/1.56 tff(1837,plain,
% 1.38/1.56 ($false),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1028, 120, 1836, 1835, 1834, 1819, 1818, 1817, 10])).
% 1.38/1.56 tff(1838,plain,(hskp15 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.38/1.56 tff(1839,plain,
% 1.38/1.56 (hskp15),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1838, 21])).
% 1.38/1.56 tff(1840,plain,
% 1.38/1.56 (c2_1(a1059)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[347, 1839])).
% 1.38/1.56 tff(1841,plain,
% 1.38/1.56 (~c1_1(a1059)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[339, 1839])).
% 1.38/1.56 tff(1842,plain,
% 1.38/1.56 (c3_1(a1059)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[367, 1839])).
% 1.38/1.56 tff(1843,assumption,(c0_1(a1059)), introduced(assumption)).
% 1.38/1.56 tff(1844,plain,
% 1.38/1.56 (hskp53 | (~c0_1(a1059))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[374, 120, 1494, 351, 350, 20])).
% 1.38/1.56 tff(1845,plain,
% 1.38/1.56 (hskp53),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1844, 1843])).
% 1.38/1.56 tff(1846,plain,
% 1.38/1.56 (c0_1(a1073)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[307, 1845])).
% 1.38/1.56 tff(1847,plain,
% 1.38/1.56 (c2_1(a1073)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[315, 1845])).
% 1.38/1.56 tff(1848,plain,
% 1.38/1.56 (c1_1(a1073)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[323, 1845])).
% 1.38/1.56 tff(1849,plain,
% 1.38/1.56 ($false),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[384, 120, 1848, 1847, 1846, 1494, 351, 10, 1843])).
% 1.38/1.56 tff(1850,plain,((~c0_1(a1059)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c1_1(a1059)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.56 tff(1851,plain,
% 1.38/1.56 (~c0_1(a1059)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1850, 1842, 1840, 1841])).
% 1.38/1.56 tff(1852,assumption,(~c2_1(a1043)), introduced(assumption)).
% 1.38/1.56 tff(1853,assumption,(~hskp7), introduced(assumption)).
% 1.38/1.56 tff(1854,assumption,(c3_1(a1039)), introduced(assumption)).
% 1.38/1.56 tff(1855,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1856,plain,
% 1.38/1.56 ((hskp59 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039))) <=> (hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1857,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1856])).
% 1.38/1.56 tff(1858,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1857, 1855])).
% 1.38/1.56 tff(1859,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1860,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 1.38/1.56 tff(1861,plain,
% 1.38/1.56 (hskp59 | (~c3_1(a1039))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1860, 120, 1718, 1711, 1710, 137])).
% 1.38/1.56 tff(1862,plain,
% 1.38/1.56 (hskp59),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1861, 1854])).
% 1.38/1.56 tff(1863,plain,
% 1.38/1.56 (~c3_1(a1095)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[158, 1862])).
% 1.38/1.56 tff(1864,plain,
% 1.38/1.56 (c1_1(a1095)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[179, 1862])).
% 1.38/1.56 tff(1865,plain,
% 1.38/1.56 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1866,plain,
% 1.38/1.56 ((hskp12 | hskp7 | (~ndr1_0) | c3_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095))) <=> (hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1867,plain,
% 1.38/1.56 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1866])).
% 1.38/1.56 tff(1868,plain,
% 1.38/1.56 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1867, 1865])).
% 1.38/1.56 tff(1869,plain,
% 1.38/1.56 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1870,plain,
% 1.38/1.56 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 1.38/1.56 tff(1871,plain,
% 1.38/1.56 (~c2_1(a1095)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1870, 120, 1580, 1853, 1864, 1863, 1435])).
% 1.38/1.56 tff(1872,plain,
% 1.38/1.56 (~c0_1(a1095)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[164, 1862])).
% 1.38/1.56 tff(1873,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1874,plain,
% 1.38/1.56 ((hskp35 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095)) <=> (hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1875,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095)))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1874])).
% 1.38/1.56 tff(1876,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1875, 1873])).
% 1.38/1.56 tff(1877,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1878,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 1.38/1.56 tff(1879,plain,
% 1.38/1.56 ($false),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1878, 120, 1144, 1872, 1863, 1711, 1710, 1322, 1854, 1871])).
% 1.38/1.56 tff(1880,plain,((~c3_1(a1039)) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.38/1.56 tff(1881,plain,
% 1.38/1.56 (~c3_1(a1039)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1880, 1853, 1580])).
% 1.38/1.56 tff(1882,plain,
% 1.38/1.56 (^[U: $i] : refl((hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(1883,plain,
% 1.38/1.56 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[1882])).
% 1.38/1.56 tff(1884,plain,
% 1.38/1.56 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1885,plain,
% 1.38/1.56 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp36))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp7) <=> ((hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp7) <=> (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp7) <=> (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(1886,plain,
% 1.38/1.56 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp7) <=> ![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[1885])).
% 1.38/1.56 tff(1887,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause265')).
% 1.38/1.56 tff(1888,plain,
% 1.38/1.56 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.38/1.56 tff(1889,plain,
% 1.38/1.56 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1888, 1884])).
% 1.38/1.56 tff(1890,plain,(
% 1.38/1.56 ![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.38/1.56 inference(skolemize,[status(sab)],[1889])).
% 1.38/1.56 tff(1891,plain,
% 1.38/1.56 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1890, 1883])).
% 1.38/1.56 tff(1892,plain,
% 1.38/1.56 (((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1893,plain,
% 1.38/1.56 ((hskp36 | hskp7 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039))) <=> (hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1894,plain,
% 1.38/1.56 (((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1893])).
% 1.38/1.56 tff(1895,plain,
% 1.38/1.56 (((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1894, 1892])).
% 1.38/1.56 tff(1896,plain,
% 1.38/1.56 ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1897,plain,
% 1.38/1.56 ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 1.38/1.56 tff(1898,plain,
% 1.38/1.56 (hskp36 | hskp7),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1897, 120, 1718, 1711, 1710, 1891])).
% 1.38/1.56 tff(1899,plain,
% 1.38/1.56 (hskp36),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1898, 1853])).
% 1.38/1.56 tff(1900,plain,
% 1.38/1.56 (~c0_1(a1034)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[720, 1899])).
% 1.38/1.56 tff(1901,plain,
% 1.38/1.56 (c3_1(a1034)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[760, 1899])).
% 1.38/1.56 tff(1902,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1903,plain,
% 1.38/1.56 ((hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034))) <=> (hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1904,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1903])).
% 1.38/1.56 tff(1905,plain,
% 1.38/1.56 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1904, 1902])).
% 1.38/1.56 tff(1906,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1907,plain,
% 1.38/1.56 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 1.38/1.57 tff(1908,plain,
% 1.38/1.57 (c3_1(a1039) | (~c2_1(a1034))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1907, 120, 1144, 1901, 1718, 1900, 1711, 932])).
% 1.38/1.57 tff(1909,plain,
% 1.38/1.57 (~c2_1(a1034)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1908, 1881])).
% 1.38/1.57 tff(1910,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1911,plain,
% 1.38/1.57 ((hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039)) <=> (hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1912,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034)))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1911])).
% 1.38/1.57 tff(1913,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1912, 1910])).
% 1.38/1.57 tff(1914,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1915,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034)),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.38/1.57 tff(1916,plain,
% 1.38/1.57 (c3_1(a1039) | c2_1(a1034)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1915, 120, 1144, 1901, 1900, 1711, 1710, 1322])).
% 1.38/1.57 tff(1917,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1916, 1909, 1881])).
% 1.38/1.57 tff(1918,plain,(hskp7 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(1919,plain,
% 1.38/1.57 (hskp7),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1918, 1580])).
% 1.38/1.57 tff(1920,plain,
% 1.38/1.57 (~c2_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1477, 1919])).
% 1.38/1.57 tff(1921,plain,
% 1.38/1.57 (c0_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1485, 1919])).
% 1.38/1.57 tff(1922,plain,
% 1.38/1.57 (c1_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1515, 1919])).
% 1.38/1.57 tff(1923,plain,
% 1.38/1.57 (c1_1(a1034)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[728, 1899])).
% 1.38/1.57 tff(1924,plain,
% 1.38/1.57 (~c2_1(a1034)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1725, 120, 21, 1901, 1923, 1718, 1711, 1710, 698])).
% 1.38/1.57 tff(1925,plain,
% 1.38/1.57 (c3_1(a1039)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1915, 120, 1144, 1901, 1900, 1711, 1710, 1322, 1924])).
% 1.38/1.57 tff(1926,plain,
% 1.38/1.57 (hskp59),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1861, 1925])).
% 1.38/1.57 tff(1927,plain,
% 1.38/1.57 (~c3_1(a1095)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[158, 1926])).
% 1.38/1.57 tff(1928,plain,
% 1.38/1.57 (c1_1(a1095)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[179, 1926])).
% 1.38/1.57 tff(1929,plain,
% 1.38/1.57 (~c2_1(a1095)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1870, 120, 1580, 1853, 1928, 1927, 1435])).
% 1.38/1.57 tff(1930,plain,
% 1.38/1.57 (~c0_1(a1095)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[164, 1926])).
% 1.38/1.57 tff(1931,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1932,plain,
% 1.38/1.57 ((hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095)) <=> (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1933,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095)))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1932])).
% 1.38/1.57 tff(1934,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1933, 1931])).
% 1.38/1.57 tff(1935,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1936,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095)),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 1.38/1.57 tff(1937,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1936, 120, 1144, 1901, 1930, 1927, 1900, 1322, 1924, 1929])).
% 1.38/1.57 tff(1938,plain,(hskp7 | hskp12 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(1939,plain,
% 1.38/1.57 (hskp7),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1938, 21, 1580])).
% 1.38/1.57 tff(1940,plain,
% 1.38/1.57 (c1_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1515, 1939])).
% 1.38/1.57 tff(1941,plain,
% 1.38/1.57 (~c2_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1477, 1939])).
% 1.38/1.57 tff(1942,plain,
% 1.38/1.57 (c0_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1485, 1939])).
% 1.38/1.57 tff(1943,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1944,plain,
% 1.38/1.57 ((hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059))) <=> (hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1945,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1944])).
% 1.38/1.57 tff(1946,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1945, 1943])).
% 1.38/1.57 tff(1947,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1948,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 1.38/1.57 tff(1949,plain,
% 1.38/1.57 (c3_1(a1039)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1948, 120, 1144, 1494, 351, 1718, 1711, 932, 349])).
% 1.38/1.57 tff(1950,plain,
% 1.38/1.57 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1951,plain,
% 1.38/1.57 ((hskp56 | hskp22 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039))) <=> (hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1952,plain,
% 1.38/1.57 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1951])).
% 1.38/1.57 tff(1953,plain,
% 1.38/1.57 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1952, 1950])).
% 1.38/1.57 tff(1954,plain,
% 1.38/1.57 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1955,plain,
% 1.38/1.57 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1954, 1953])).
% 1.38/1.57 tff(1956,plain,
% 1.38/1.57 (hskp22 | (~c3_1(a1039))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1955, 120, 1039, 1718, 1711, 31])).
% 1.38/1.57 tff(1957,plain,
% 1.38/1.57 (hskp22),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1956, 1949])).
% 1.38/1.57 tff(1958,plain,
% 1.38/1.57 (~c1_1(a1083)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1085, 1957])).
% 1.38/1.57 tff(1959,plain,
% 1.38/1.57 (c3_1(a1083)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1054, 1957])).
% 1.38/1.57 tff(1960,plain,
% 1.38/1.57 (c2_1(a1083)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1062, 1957])).
% 1.38/1.57 tff(1961,assumption,(~c2_1(a1035)), introduced(assumption)).
% 1.38/1.57 tff(1962,assumption,(c1_1(a1035)), introduced(assumption)).
% 1.38/1.57 tff(1963,plain,
% 1.38/1.57 (c3_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1522, 120, 1144, 1494, 351, 1962, 1961, 932, 349])).
% 1.38/1.57 tff(1964,assumption,(c0_1(a1035)), introduced(assumption)).
% 1.38/1.57 tff(1965,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1966,plain,
% 1.38/1.57 ((hskp57 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035))) <=> (hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1967,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1966])).
% 1.38/1.57 tff(1968,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1967, 1965])).
% 1.38/1.57 tff(1969,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1970,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 1.38/1.57 tff(1971,plain,
% 1.38/1.57 (hskp57 | (~c3_1(a1035))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1970, 120, 1494, 351, 1964, 350, 1961, 980])).
% 1.38/1.57 tff(1972,plain,
% 1.38/1.57 (hskp57),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1971, 1963])).
% 1.38/1.57 tff(1973,plain,
% 1.38/1.57 (c3_1(a1085)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[995, 1972])).
% 1.38/1.57 tff(1974,plain,
% 1.38/1.57 (c0_1(a1085)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1003, 1972])).
% 1.38/1.57 tff(1975,plain,
% 1.38/1.57 (c2_1(a1085)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1011, 1972])).
% 1.38/1.57 tff(1976,plain,
% 1.38/1.57 (hskp53),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1138, 120, 1975, 1974, 1973, 1960, 1959, 1958, 20])).
% 1.38/1.57 tff(1977,plain,
% 1.38/1.57 (c0_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[307, 1976])).
% 1.38/1.57 tff(1978,plain,
% 1.38/1.57 (c2_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[315, 1976])).
% 1.38/1.57 tff(1979,plain,
% 1.38/1.57 (c1_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[323, 1976])).
% 1.38/1.57 tff(1980,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1028, 120, 1975, 1974, 1973, 1979, 1978, 1977, 10])).
% 1.38/1.57 tff(1981,plain,(c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1035)) | c1_1(a1059) | c2_1(a1035) | (~c1_1(a1035))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(1982,plain,
% 1.38/1.57 (c0_1(a1059)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1981, 1842, 1840, 1942, 1841, 1941, 1940])).
% 1.38/1.57 tff(1983,plain,
% 1.38/1.57 (hskp53 | (~c0_1(a1059))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[374, 120, 1842, 1840, 1841, 20])).
% 1.38/1.57 tff(1984,plain,
% 1.38/1.57 (hskp53),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1983, 1982])).
% 1.38/1.57 tff(1985,plain,
% 1.38/1.57 (c0_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[307, 1984])).
% 1.38/1.57 tff(1986,plain,
% 1.38/1.57 (c2_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[315, 1984])).
% 1.38/1.57 tff(1987,plain,
% 1.38/1.57 (c1_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[323, 1984])).
% 1.38/1.57 tff(1988,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[384, 120, 1987, 1986, 1985, 1842, 1840, 10, 1982])).
% 1.38/1.57 tff(1989,plain,(hskp33 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(1990,plain,
% 1.38/1.57 (hskp33),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1989, 1580])).
% 1.38/1.57 tff(1991,plain,
% 1.38/1.57 (~c1_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[263, 1990])).
% 1.38/1.57 tff(1992,plain,
% 1.38/1.57 (c2_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[271, 1990])).
% 1.38/1.57 tff(1993,plain,
% 1.38/1.57 (c3_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[291, 1990])).
% 1.38/1.57 tff(1994,assumption,(~hskp53), introduced(assumption)).
% 1.38/1.57 tff(1995,plain,
% 1.38/1.57 (hskp53 | (~c0_1(a1031))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[298, 120, 797, 275, 274, 20])).
% 1.38/1.57 tff(1996,plain,
% 1.38/1.57 (~c0_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1995, 1994])).
% 1.38/1.57 tff(1997,plain,
% 1.38/1.57 (c3_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1618, 120, 1144, 797, 275, 1962, 1961, 932, 1996])).
% 1.38/1.57 tff(1998,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1999,plain,
% 1.38/1.57 ((hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035))) <=> (hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(2000,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1999])).
% 1.38/1.57 tff(2001,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[2000, 1998])).
% 1.38/1.57 tff(2002,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(2003,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 1.38/1.57 tff(2004,plain,
% 1.38/1.57 (hskp57 | (~c3_1(a1035))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2003, 120, 797, 275, 1964, 274, 1961, 980])).
% 1.38/1.57 tff(2005,plain,
% 1.38/1.57 (hskp57),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2004, 1997])).
% 1.38/1.57 tff(2006,plain,
% 1.38/1.57 (c3_1(a1085)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[995, 2005])).
% 1.38/1.57 tff(2007,plain,
% 1.38/1.57 (c0_1(a1085)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1003, 2005])).
% 1.38/1.57 tff(2008,plain,
% 1.38/1.57 (c2_1(a1085)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1011, 2005])).
% 1.38/1.57 tff(2009,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(2010,plain,
% 1.38/1.57 ((hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(2011,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[2010])).
% 1.38/1.57 tff(2012,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[2011, 2009])).
% 1.38/1.57 tff(2013,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(2014,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 1.38/1.57 tff(2015,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2014, 120, 1994, 2008, 2007, 2006, 797, 275, 274, 20])).
% 1.38/1.57 tff(2016,plain,(hskp53 | (~c3_1(a1031)) | (~c2_1(a1031)) | c1_1(a1031) | (~c0_1(a1035)) | c2_1(a1035) | (~c1_1(a1035))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(2017,plain,
% 1.38/1.57 (hskp53),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2016, 1993, 1992, 1991, 1921, 1920, 1922])).
% 1.38/1.57 tff(2018,plain,
% 1.38/1.57 (c0_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[307, 2017])).
% 1.38/1.57 tff(2019,plain,
% 1.38/1.57 (c2_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[315, 2017])).
% 1.38/1.57 tff(2020,plain,
% 1.38/1.57 (c1_1(a1073)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[323, 2017])).
% 1.38/1.57 tff(2021,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(2022,plain,
% 1.38/1.57 ((hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))) <=> (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(2023,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[2022])).
% 1.38/1.57 tff(2024,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[2023, 2021])).
% 1.38/1.57 tff(2025,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(2026,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 1.38/1.57 tff(2027,plain,
% 1.38/1.57 (~c3_1(a1035)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2026, 120, 1580, 2020, 2019, 2018, 1921, 1920, 1189])).
% 1.38/1.57 tff(2028,plain,
% 1.38/1.57 (~c0_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[330, 120, 2020, 2019, 2018, 1993, 1992, 10])).
% 1.38/1.57 tff(2029,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1618, 120, 1144, 1993, 1992, 1922, 1920, 932, 2028, 2027])).
% 1.38/1.57 tff(2030,plain,(hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(2031,plain,
% 1.38/1.57 (~c3_1(a1043)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1441, 2030])).
% 1.38/1.57 tff(2032,plain,
% 1.38/1.57 (~c1_1(a1043)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1447, 2030])).
% 1.38/1.57 tff(2033,plain,
% 1.38/1.57 (c0_1(a1043)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1455, 2030])).
% 1.38/1.57 tff(2034,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1707, 120, 351, 2033, 350, 2032, 2031, 221, 349, 1852])).
% 1.38/1.57 tff(2035,plain,(c0_1(a1059) | (~c2_1(a1059)) | c1_1(a1059) | c2_1(a1043)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(2036,plain,
% 1.38/1.57 (c2_1(a1043)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2035, 1851, 1841, 1840])).
% 1.38/1.57 tff(2037,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(2038,plain,
% 1.38/1.57 ((hskp47 | (~ndr1_0) | c3_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)) | c1_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043))) <=> (hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(2039,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)) | c1_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[2038])).
% 1.38/1.57 tff(2040,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)) | c1_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[2039, 2037])).
% 1.38/1.57 tff(2041,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)) | c1_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(2042,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 1.38/1.57 tff(2043,plain,
% 1.38/1.57 (hskp47 | (~c2_1(a1043))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2042, 120, 2033, 2032, 2031, 432])).
% 1.38/1.57 tff(2044,plain,
% 1.38/1.57 (hskp47),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2043, 2036])).
% 1.38/1.57 tff(2045,plain,
% 1.38/1.57 (c3_1(a1056)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[447, 2044])).
% 1.38/1.57 tff(2046,plain,
% 1.38/1.57 (c1_1(a1056)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[455, 2044])).
% 1.38/1.57 tff(2047,plain,
% 1.38/1.57 (c2_1(a1056)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[463, 2044])).
% 1.38/1.57 tff(2048,plain,
% 1.38/1.57 (~hskp19),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[748, 2047, 21, 2046, 2045])).
% 1.38/1.57 tff(2049,plain,
% 1.38/1.57 (hskp20),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1464, 2048, 2030])).
% 1.38/1.57 tff(2050,plain,
% 1.38/1.57 (~c1_1(a1080)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[667, 2049])).
% 1.38/1.57 tff(2051,plain,
% 1.38/1.57 (~c2_1(a1080)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[639, 2049])).
% 1.38/1.57 tff(2052,plain,
% 1.38/1.57 (~c0_1(a1080)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[645, 2049])).
% 1.38/1.57 tff(2053,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1698, 120, 1842, 1840, 2052, 2051, 2050, 2032, 2031, 481, 1851, 2036])).
% 1.38/1.57 tff(2054,plain,(hskp33), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(2055,plain,
% 1.38/1.57 (~c1_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[263, 2054])).
% 1.38/1.57 tff(2056,plain,
% 1.38/1.57 (c2_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[271, 2054])).
% 1.38/1.57 tff(2057,plain,
% 1.38/1.57 (c3_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[291, 2054])).
% 1.38/1.57 tff(2058,plain,
% 1.38/1.57 (hskp53 | (~c0_1(a1031))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[298, 120, 2057, 2056, 2055, 20])).
% 1.38/1.57 tff(2059,plain,
% 1.38/1.57 (~c0_1(a1031)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[2058, 1994])).
% 1.38/1.57 tff(2060,assumption,(hskp48), introduced(assumption)).
% 1.38/1.57 tff(2061,plain,
% 1.38/1.57 (c0_1(a1062)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1753, 2060])).
% 1.38/1.57 tff(2062,plain,
% 1.38/1.57 (c2_1(a1062)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1761, 2060])).
% 1.38/1.57 tff(2063,plain,
% 1.38/1.57 (c3_1(a1062)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1769, 2060])).
% 1.38/1.57 tff(2064,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2065,plain,
% 1.38/1.58 ((hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062))) <=> (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2066,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[2065])).
% 1.38/1.58 tff(2067,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[2066, 2064])).
% 1.38/1.58 tff(2068,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(2069,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[2068, 2067])).
% 1.38/1.58 tff(2070,plain,
% 1.38/1.58 (hskp53),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2069, 120, 2063, 2062, 2061, 797, 275, 274, 20])).
% 1.38/1.58 tff(2071,plain,
% 1.38/1.58 (c0_1(a1073)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[307, 2070])).
% 1.38/1.58 tff(2072,plain,
% 1.38/1.58 (c2_1(a1073)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[315, 2070])).
% 1.38/1.58 tff(2073,plain,
% 1.38/1.58 (c1_1(a1073)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[323, 2070])).
% 1.38/1.58 tff(2074,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2075,plain,
% 1.38/1.58 (((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062))) <=> ((~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2076,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[2075])).
% 1.38/1.58 tff(2077,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[2076, 2074])).
% 1.38/1.58 tff(2078,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(2079,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 1.38/1.58 tff(2080,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2079, 120, 2073, 2072, 2071, 2063, 2062, 2061, 10])).
% 1.38/1.58 tff(2081,plain,((~hskp48) | (~c3_1(a1031)) | (~c2_1(a1031)) | c1_1(a1031)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.58 tff(2082,plain,
% 1.38/1.58 (~hskp48),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2081, 2057, 2056, 2055])).
% 1.38/1.58 tff(2083,assumption,(~c3_1(a1039)), introduced(assumption)).
% 1.38/1.58 tff(2084,assumption,(~hskp48), introduced(assumption)).
% 1.38/1.58 tff(2085,plain,
% 1.38/1.58 (hskp36),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1745, 2083, 2084])).
% 1.38/1.58 tff(2086,plain,
% 1.38/1.58 (~c0_1(a1034)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[720, 2085])).
% 1.38/1.58 tff(2087,plain,
% 1.38/1.58 (c3_1(a1034)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[760, 2085])).
% 1.38/1.58 tff(2088,plain,
% 1.38/1.58 (~c2_1(a1034)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1907, 120, 1144, 2087, 1718, 2086, 1711, 932, 2083])).
% 1.38/1.58 tff(2089,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1915, 120, 1144, 2087, 2086, 1711, 1710, 1322, 2083, 2088])).
% 1.38/1.58 tff(2090,plain,(c3_1(a1039) | hskp48), inference(lemma,lemma(discharge,[]))).
% 1.38/1.58 tff(2091,plain,
% 1.38/1.58 (c3_1(a1039)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2090, 2082])).
% 1.38/1.58 tff(2092,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2093,plain,
% 1.38/1.58 ((hskp42 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031))) <=> (hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2094,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031)))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[2093])).
% 1.38/1.58 tff(2095,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031))),
% 1.38/1.58 inference(transitivity,[status(thm)],[2094, 2092])).
% 1.38/1.58 tff(2096,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(2097,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 1.38/1.58 tff(2098,plain,
% 1.38/1.58 (hskp42),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2097, 120, 2056, 1718, 2055, 1711, 1080, 2091, 2059])).
% 1.38/1.58 tff(2099,plain,
% 1.38/1.58 (~c2_1(a1046)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1098, 2098])).
% 1.38/1.58 tff(2100,plain,
% 1.38/1.58 (c1_1(a1046)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1106, 2098])).
% 1.38/1.58 tff(2101,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2102,plain,
% 1.38/1.58 ((hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031))) <=> (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2103,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[2102])).
% 1.38/1.58 tff(2104,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[2103, 2101])).
% 1.38/1.58 tff(2105,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(2106,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 1.38/1.58 tff(2107,plain,
% 1.38/1.58 (c3_1(a1046)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2106, 120, 1144, 2100, 2057, 2056, 2099, 932, 2059])).
% 1.38/1.58 tff(2108,plain,
% 1.38/1.58 (c0_1(a1046)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1158, 2098])).
% 1.38/1.58 tff(2109,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2110,plain,
% 1.38/1.58 ((hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046))) <=> (hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(2111,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[2110])).
% 1.38/1.58 tff(2112,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[2111, 2109])).
% 1.38/1.58 tff(2113,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(2114,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[2113, 2112])).
% 1.38/1.58 tff(2115,plain,
% 1.38/1.58 (hskp57 | (~c3_1(a1046))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2114, 120, 2108, 2057, 2056, 2099, 2055, 980])).
% 1.38/1.58 tff(2116,plain,
% 1.38/1.58 (hskp57),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2115, 2107])).
% 1.38/1.58 tff(2117,plain,
% 1.38/1.58 (c3_1(a1085)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[995, 2116])).
% 1.38/1.58 tff(2118,plain,
% 1.38/1.58 (c0_1(a1085)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1003, 2116])).
% 1.38/1.58 tff(2119,plain,
% 1.38/1.58 (c2_1(a1085)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1011, 2116])).
% 1.38/1.58 tff(2120,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2014, 120, 1994, 2119, 2118, 2117, 2057, 2056, 2055, 20])).
% 1.38/1.58 tff(2121,plain,(hskp53), inference(lemma,lemma(discharge,[]))).
% 1.38/1.58 tff(2122,plain,
% 1.38/1.58 (c0_1(a1073)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[307, 2121])).
% 1.38/1.58 tff(2123,plain,
% 1.38/1.58 (c2_1(a1073)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[315, 2121])).
% 1.38/1.58 tff(2124,plain,
% 1.38/1.58 (c1_1(a1073)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[323, 2121])).
% 1.38/1.58 tff(2125,plain,
% 1.38/1.58 (~c0_1(a1031)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[330, 120, 2124, 2123, 2122, 2057, 2056, 10])).
% 1.38/1.58 tff(2126,plain,
% 1.38/1.58 (hskp42),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2097, 120, 2056, 1718, 2055, 1711, 1080, 2091, 2125])).
% 1.38/1.58 tff(2127,plain,
% 1.38/1.58 (~c2_1(a1046)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1098, 2126])).
% 1.38/1.58 tff(2128,plain,
% 1.38/1.58 (c1_1(a1046)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1106, 2126])).
% 1.38/1.58 tff(2129,plain,
% 1.38/1.58 (c3_1(a1046)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2106, 120, 1144, 2128, 2057, 2056, 2127, 932, 2125])).
% 1.38/1.58 tff(2130,plain,
% 1.38/1.58 (c0_1(a1046)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1158, 2126])).
% 1.38/1.58 tff(2131,plain,
% 1.38/1.58 (hskp57 | (~c3_1(a1046))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2114, 120, 2130, 2057, 2056, 2127, 2055, 980])).
% 1.38/1.58 tff(2132,plain,
% 1.38/1.58 (hskp57),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[2131, 2129])).
% 1.38/1.58 tff(2133,plain,
% 1.38/1.58 (c3_1(a1085)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[995, 2132])).
% 1.38/1.58 tff(2134,plain,
% 1.38/1.58 (c0_1(a1085)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1003, 2132])).
% 1.38/1.58 tff(2135,plain,
% 1.38/1.58 (c2_1(a1085)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1011, 2132])).
% 1.38/1.58 tff(2136,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1028, 120, 2135, 2134, 2133, 2124, 2123, 2122, 10])).
% 1.38/1.58 % SZS output end Proof
% 1.38/1.59 % E exiting
%------------------------------------------------------------------------------