%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN499-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:39:21 AM UTC 2025
% Result : Unsatisfiable 0.79s 0.97s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN499-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:37:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.79/0.97 % SZS status Unsatisfiable
% 0.79/0.97 % SZS output start Proof
% 0.79/0.97 tff(c2_1_type, type, (
% 0.79/0.97 c2_1: $i > $o)).
% 0.79/0.97 tff(a142_type, type, (
% 0.79/0.97 a142: $i)).
% 0.79/0.97 tff(c0_1_type, type, (
% 0.79/0.97 c0_1: $i > $o)).
% 0.79/0.97 tff(c1_1_type, type, (
% 0.79/0.97 c1_1: $i > $o)).
% 0.79/0.97 tff(c3_1_type, type, (
% 0.79/0.97 c3_1: $i > $o)).
% 0.79/0.97 tff(ndr1_0_type, type, (
% 0.79/0.97 ndr1_0: $o)).
% 0.79/0.97 tff(a123_type, type, (
% 0.79/0.97 a123: $i)).
% 0.79/0.97 tff(hskp0_type, type, (
% 0.79/0.97 hskp0: $o)).
% 0.79/0.97 tff(a131_type, type, (
% 0.79/0.97 a131: $i)).
% 0.79/0.97 tff(hskp6_type, type, (
% 0.79/0.97 hskp6: $o)).
% 0.79/0.97 tff(hskp18_type, type, (
% 0.79/0.97 hskp18: $o)).
% 0.79/0.97 tff(a182_type, type, (
% 0.79/0.97 a182: $i)).
% 0.79/0.97 tff(a140_type, type, (
% 0.79/0.97 a140: $i)).
% 0.79/0.97 tff(hskp10_type, type, (
% 0.79/0.97 hskp10: $o)).
% 0.79/0.97 tff(a138_type, type, (
% 0.79/0.97 a138: $i)).
% 0.79/0.97 tff(hskp9_type, type, (
% 0.79/0.97 hskp9: $o)).
% 0.79/0.97 tff(a143_type, type, (
% 0.79/0.97 a143: $i)).
% 0.79/0.97 tff(a167_type, type, (
% 0.79/0.97 a167: $i)).
% 0.79/0.97 tff(hskp30_type, type, (
% 0.79/0.97 hskp30: $o)).
% 0.79/0.97 tff(a164_type, type, (
% 0.79/0.97 a164: $i)).
% 0.79/0.97 tff(hskp17_type, type, (
% 0.79/0.97 hskp17: $o)).
% 0.79/0.97 tff(hskp19_type, type, (
% 0.79/0.97 hskp19: $o)).
% 0.79/0.97 tff(a176_type, type, (
% 0.79/0.97 a176: $i)).
% 0.79/0.97 tff(hskp22_type, type, (
% 0.79/0.97 hskp22: $o)).
% 0.79/0.97 tff(a124_type, type, (
% 0.79/0.97 a124: $i)).
% 0.79/0.97 tff(hskp1_type, type, (
% 0.79/0.97 hskp1: $o)).
% 0.79/0.97 tff(hskp2_type, type, (
% 0.79/0.97 hskp2: $o)).
% 0.79/0.97 tff(a125_type, type, (
% 0.79/0.97 a125: $i)).
% 0.79/0.97 tff(a132_type, type, (
% 0.79/0.97 a132: $i)).
% 0.79/0.97 tff(hskp7_type, type, (
% 0.79/0.97 hskp7: $o)).
% 0.79/0.97 tff(a155_type, type, (
% 0.79/0.97 a155: $i)).
% 0.79/0.97 tff(a147_type, type, (
% 0.79/0.97 a147: $i)).
% 0.79/0.97 tff(hskp12_type, type, (
% 0.79/0.97 hskp12: $o)).
% 0.79/0.97 tff(hskp14_type, type, (
% 0.79/0.97 hskp14: $o)).
% 0.79/0.97 tff(a160_type, type, (
% 0.79/0.97 a160: $i)).
% 0.79/0.97 tff(a168_type, type, (
% 0.79/0.97 a168: $i)).
% 0.79/0.97 tff(hskp20_type, type, (
% 0.79/0.97 hskp20: $o)).
% 0.79/0.97 tff(a122_type, type, (
% 0.79/0.97 a122: $i)).
% 0.79/0.97 tff(hskp27_type, type, (
% 0.79/0.97 hskp27: $o)).
% 0.79/0.97 tff(hskp13_type, type, (
% 0.79/0.97 hskp13: $o)).
% 0.79/0.97 tff(a136_type, type, (
% 0.79/0.97 a136: $i)).
% 0.79/0.97 tff(hskp29_type, type, (
% 0.79/0.97 hskp29: $o)).
% 0.79/0.97 tff(a170_type, type, (
% 0.79/0.97 a170: $i)).
% 0.79/0.97 tff(hskp21_type, type, (
% 0.79/0.97 hskp21: $o)).
% 0.79/0.97 tff(hskp24_type, type, (
% 0.79/0.97 hskp24: $o)).
% 0.79/0.97 tff(a134_type, type, (
% 0.79/0.97 a134: $i)).
% 0.79/0.97 tff(hskp8_type, type, (
% 0.79/0.97 hskp8: $o)).
% 0.79/0.97 tff(a127_type, type, (
% 0.79/0.97 a127: $i)).
% 0.79/0.97 tff(hskp3_type, type, (
% 0.79/0.97 hskp3: $o)).
% 0.79/0.97 tff(a153_type, type, (
% 0.79/0.97 a153: $i)).
% 0.79/0.97 tff(hskp15_type, type, (
% 0.79/0.97 hskp15: $o)).
% 0.79/0.97 tff(a133_type, type, (
% 0.79/0.97 a133: $i)).
% 0.79/0.97 tff(hskp28_type, type, (
% 0.79/0.97 hskp28: $o)).
% 0.79/0.97 tff(1,plain,
% 0.79/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(2,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[1])).
% 0.79/0.97 tff(3,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(4,plain,
% 0.79/0.97 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(5,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[4])).
% 0.79/0.97 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 0.79/0.98 tff(7,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.79/0.98 tff(8,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.79/0.98 tff(9,plain,(
% 0.79/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[8])).
% 0.79/0.98 tff(10,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.79/0.98 tff(11,assumption,(~hskp0), introduced(assumption)).
% 0.79/0.98 tff(12,plain,
% 0.79/0.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(13,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[12])).
% 0.79/0.98 tff(14,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(15,plain,
% 0.79/0.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(16,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[15])).
% 0.79/0.98 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.79/0.98 tff(18,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.79/0.98 tff(19,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.79/0.98 tff(20,plain,(
% 0.79/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.98 inference(skolemize,[status(sab)],[19])).
% 0.79/0.98 tff(21,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.79/0.98 tff(22,assumption,(~hskp18), introduced(assumption)).
% 0.79/0.98 tff(23,plain,
% 0.79/0.98 (^[U: $i] : refl((hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(24,plain,
% 0.79/0.98 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[23])).
% 0.79/0.98 tff(25,plain,
% 0.79/0.98 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(26,plain,
% 0.79/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp18) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp18) <=> (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(27,plain,
% 0.79/0.98 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp18) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[26])).
% 0.79/0.98 tff(28,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.79/0.98 tff(29,plain,
% 0.79/0.98 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.79/0.98 tff(30,plain,
% 0.79/0.98 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.79/0.98 tff(31,plain,(
% 0.79/0.98 ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[30])).
% 0.79/0.98 tff(32,plain,
% 0.79/0.98 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.79/0.98 tff(33,assumption,(~hskp9), introduced(assumption)).
% 0.79/0.98 tff(34,plain,
% 0.79/0.98 (^[U: $i] : refl((hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(35,plain,
% 0.79/0.98 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[34])).
% 0.79/0.98 tff(36,plain,
% 0.79/0.98 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(37,plain,
% 0.79/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> ((hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0))), rewrite(((hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(38,plain,
% 0.79/0.98 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[37])).
% 0.79/0.98 tff(39,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.79/0.98 tff(40,plain,
% 0.79/0.98 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.79/0.98 tff(41,plain,
% 0.79/0.98 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.79/0.98 tff(42,plain,(
% 0.79/0.98 ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[41])).
% 0.79/0.98 tff(43,plain,
% 0.79/0.98 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.79/0.98 tff(44,plain,
% 0.79/0.98 (^[U: $i] : refl((hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(45,plain,
% 0.79/0.98 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[44])).
% 0.79/0.98 tff(46,plain,
% 0.79/0.98 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(47,plain,
% 0.79/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp17) <=> ((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp17) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(48,plain,
% 0.79/0.98 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp17) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[47])).
% 0.79/0.98 tff(49,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.79/0.98 tff(50,plain,
% 0.79/0.98 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.79/0.98 tff(51,plain,
% 0.79/0.98 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.79/0.98 tff(52,plain,(
% 0.79/0.98 ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[51])).
% 0.79/0.98 tff(53,plain,
% 0.79/0.98 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.79/0.98 tff(54,assumption,(~hskp30), introduced(assumption)).
% 0.79/0.98 tff(55,plain,
% 0.79/0.98 ((hskp30 | hskp9 | hskp6) <=> (hskp30 | hskp9 | hskp6)),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(56,plain,
% 0.79/0.98 (((hskp30 | hskp9) | hskp6) <=> (hskp30 | hskp9 | hskp6)),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(57,axiom,((hskp30 | hskp9) | hskp6), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.79/0.98 tff(58,plain,
% 0.79/0.98 (hskp30 | hskp9 | hskp6),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.79/0.98 tff(59,plain,
% 0.79/0.98 (hskp30 | hskp9 | hskp6),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.79/0.98 tff(60,plain,
% 0.79/0.98 (hskp30 | hskp9 | hskp6),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.79/0.98 tff(61,plain,
% 0.79/0.98 (hskp30 | hskp9 | hskp6),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.79/0.98 tff(62,plain,
% 0.79/0.98 (hskp30 | hskp9 | hskp6),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[61, 55])).
% 0.79/0.98 tff(63,plain,
% 0.79/0.98 (hskp6),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[62, 54, 33])).
% 0.79/0.98 tff(64,plain,
% 0.79/0.98 (((~hskp6) | (~c2_1(a131))) <=> ((~hskp6) | (~c2_1(a131)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(65,plain,
% 0.79/0.98 (((~c2_1(a131)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a131)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(66,axiom,((~c2_1(a131)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.79/0.98 tff(67,plain,
% 0.79/0.98 ((~hskp6) | (~c2_1(a131))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.79/0.98 tff(68,plain,
% 0.79/0.98 ((~hskp6) | (~c2_1(a131))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.79/0.98 tff(69,plain,
% 0.79/0.98 (~c2_1(a131)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[68, 63])).
% 0.79/0.98 tff(70,plain,
% 0.79/0.98 (((~hskp6) | (~c1_1(a131))) <=> ((~hskp6) | (~c1_1(a131)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(71,plain,
% 0.79/0.98 (((~c1_1(a131)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a131)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(72,axiom,((~c1_1(a131)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.79/0.98 tff(73,plain,
% 0.79/0.98 ((~hskp6) | (~c1_1(a131))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.79/0.98 tff(74,plain,
% 0.79/0.98 ((~hskp6) | (~c1_1(a131))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.79/0.98 tff(75,plain,
% 0.79/0.98 (~c1_1(a131)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[74, 63])).
% 0.79/0.98 tff(76,plain,
% 0.79/0.98 (((~hskp6) | (~c0_1(a131))) <=> ((~hskp6) | (~c0_1(a131)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(77,plain,
% 0.79/0.98 (((~c0_1(a131)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a131)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(78,axiom,((~c0_1(a131)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.79/0.98 tff(79,plain,
% 0.79/0.98 ((~hskp6) | (~c0_1(a131))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.79/0.98 tff(80,plain,
% 0.79/0.98 ((~hskp6) | (~c0_1(a131))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.79/0.98 tff(81,plain,
% 0.79/0.98 (~c0_1(a131)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[80, 63])).
% 0.79/0.98 tff(82,plain,
% 0.79/0.98 (^[U: $i] : refl((hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(83,plain,
% 0.79/0.98 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[82])).
% 0.79/0.98 tff(84,plain,
% 0.79/0.98 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(85,plain,
% 0.79/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp7) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7) <=> (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp7) <=> (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(86,plain,
% 0.79/0.98 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp7) <=> ![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[85])).
% 0.79/0.98 tff(87,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.79/0.98 tff(88,plain,
% 0.79/0.98 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.79/0.98 tff(89,plain,
% 0.79/0.98 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.79/0.98 tff(90,plain,(
% 0.79/0.98 ![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.79/0.98 inference(skolemize,[status(sab)],[89])).
% 0.79/0.98 tff(91,plain,
% 0.79/0.98 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.79/0.98 tff(92,assumption,(~c2_1(a131)), introduced(assumption)).
% 0.79/0.98 tff(93,assumption,(~hskp7), introduced(assumption)).
% 0.79/0.98 tff(94,assumption,(~c0_1(a131)), introduced(assumption)).
% 0.79/0.98 tff(95,assumption,(~ndr1_0), introduced(assumption)).
% 0.79/0.98 tff(96,plain,
% 0.79/0.98 ((ndr1_0 | (~hskp6)) <=> (ndr1_0 | (~hskp6))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(97,plain,
% 0.79/0.98 (((~hskp6) | ndr1_0) <=> (ndr1_0 | (~hskp6))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(98,axiom,((~hskp6) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause25')).
% 0.79/0.98 tff(99,plain,
% 0.79/0.98 (ndr1_0 | (~hskp6)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.79/0.98 tff(100,plain,
% 0.79/0.98 (ndr1_0 | (~hskp6)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.79/0.98 tff(101,plain,
% 0.79/0.98 (~hskp6),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[100, 95])).
% 0.79/0.98 tff(102,plain,
% 0.79/0.98 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(103,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.79/0.98 tff(104,plain,
% 0.79/0.98 ((~hskp30) | ndr1_0),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.79/0.98 tff(105,plain,
% 0.79/0.98 ((~hskp30) | ndr1_0),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[104, 102])).
% 0.79/0.98 tff(106,plain,
% 0.79/0.98 ((~hskp30) | ndr1_0),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.79/0.98 tff(107,plain,
% 0.79/0.98 ((~hskp30) | ndr1_0),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.79/0.98 tff(108,plain,
% 0.79/0.98 ((~hskp30) | ndr1_0),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[107, 102])).
% 0.79/0.98 tff(109,plain,
% 0.79/0.98 (~hskp30),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[108, 95])).
% 0.79/0.98 tff(110,plain,
% 0.79/0.98 ((ndr1_0 | (~hskp9)) <=> (ndr1_0 | (~hskp9))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(111,plain,
% 0.79/0.98 (((~hskp9) | ndr1_0) <=> (ndr1_0 | (~hskp9))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(112,axiom,((~hskp9) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.79/0.98 tff(113,plain,
% 0.79/0.98 (ndr1_0 | (~hskp9)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.79/0.98 tff(114,plain,
% 0.79/0.98 (ndr1_0 | (~hskp9)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.79/0.98 tff(115,plain,
% 0.79/0.98 (~hskp9),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[114, 95])).
% 0.79/0.98 tff(116,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[62, 115, 109, 101])).
% 0.79/0.98 tff(117,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(118,plain,
% 0.79/0.98 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(119,plain,
% 0.79/0.98 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | c3_1(a131)) <=> (hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(120,plain,
% 0.79/0.98 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | c3_1(a131))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131)))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[119])).
% 0.79/0.98 tff(121,plain,
% 0.79/0.98 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | c3_1(a131))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131))),
% 0.79/0.98 inference(transitivity,[status(thm)],[120, 118])).
% 0.79/0.98 tff(122,plain,
% 0.79/0.98 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | c3_1(a131))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(123,plain,
% 0.79/0.98 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.79/0.98 tff(124,plain,
% 0.79/0.98 (hskp7 | c3_1(a131)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[123, 117, 33, 94, 92, 91])).
% 0.79/0.98 tff(125,plain,
% 0.79/0.98 (c3_1(a131)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[124, 93])).
% 0.79/0.98 tff(126,assumption,(~c1_1(a131)), introduced(assumption)).
% 0.79/0.98 tff(127,assumption,(c3_1(a131)), introduced(assumption)).
% 0.79/0.98 tff(128,assumption,(~hskp17), introduced(assumption)).
% 0.79/0.98 tff(129,plain,
% 0.79/0.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(130,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[129])).
% 0.79/0.98 tff(131,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(132,plain,
% 0.79/0.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_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) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(133,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[132])).
% 0.79/0.98 tff(134,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.79/0.98 tff(135,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.79/0.98 tff(136,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.79/0.98 tff(137,plain,(
% 0.79/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[136])).
% 0.79/0.98 tff(138,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.79/0.98 tff(139,assumption,(hskp12), introduced(assumption)).
% 0.79/0.98 tff(140,plain,
% 0.79/0.98 (((~hskp12) | (~c1_1(a142))) <=> ((~hskp12) | (~c1_1(a142)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(141,plain,
% 0.79/0.98 (((~c1_1(a142)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a142)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(142,axiom,((~c1_1(a142)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.79/0.98 tff(143,plain,
% 0.79/0.98 ((~hskp12) | (~c1_1(a142))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.79/0.98 tff(144,plain,
% 0.79/0.98 ((~hskp12) | (~c1_1(a142))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[143, 140])).
% 0.79/0.98 tff(145,plain,
% 0.79/0.98 (~c1_1(a142)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[144, 139])).
% 0.79/0.98 tff(146,plain,
% 0.79/0.98 (((~hskp12) | c3_1(a142)) <=> ((~hskp12) | c3_1(a142))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(147,axiom,((~hskp12) | c3_1(a142)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.79/0.98 tff(148,plain,
% 0.79/0.98 ((~hskp12) | c3_1(a142)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.79/0.98 tff(149,plain,
% 0.79/0.98 ((~hskp12) | c3_1(a142)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[148, 146])).
% 0.79/0.98 tff(150,plain,
% 0.79/0.98 ((~hskp12) | c3_1(a142)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[149, 146])).
% 0.79/0.98 tff(151,plain,
% 0.79/0.98 ((~hskp12) | c3_1(a142)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.79/0.98 tff(152,plain,
% 0.79/0.98 ((~hskp12) | c3_1(a142)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[151, 146])).
% 0.79/0.98 tff(153,plain,
% 0.79/0.98 (c3_1(a142)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[152, 139])).
% 0.79/0.98 tff(154,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(155,plain,
% 0.79/0.98 (((~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(156,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[155])).
% 0.79/0.99 tff(157,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[156, 154])).
% 0.79/0.99 tff(158,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(159,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.79/0.99 tff(160,plain,
% 0.79/0.99 (~c2_1(a142)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[159, 117, 153, 145, 94, 126, 92, 138, 127])).
% 0.79/0.99 tff(161,plain,
% 0.79/0.99 (^[U: $i] : refl((hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(162,plain,
% 0.79/0.99 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[161])).
% 0.79/0.99 tff(163,plain,
% 0.79/0.99 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(164,plain,
% 0.79/0.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp7) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp7) <=> (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(165,plain,
% 0.79/0.99 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp7) <=> ![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[164])).
% 0.79/0.99 tff(166,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.79/0.99 tff(167,plain,
% 0.79/0.99 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.79/0.99 tff(168,plain,
% 0.79/0.99 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.79/0.99 tff(169,plain,(
% 0.79/0.99 ![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.99 inference(skolemize,[status(sab)],[168])).
% 0.79/0.99 tff(170,plain,
% 0.79/0.99 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.79/0.99 tff(171,plain,
% 0.79/0.99 (((~hskp12) | c0_1(a142)) <=> ((~hskp12) | c0_1(a142))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(172,axiom,((~hskp12) | c0_1(a142)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.79/0.99 tff(173,plain,
% 0.79/0.99 ((~hskp12) | c0_1(a142)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.79/0.99 tff(174,plain,
% 0.79/0.99 ((~hskp12) | c0_1(a142)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[173, 171])).
% 0.79/0.99 tff(175,plain,
% 0.79/0.99 ((~hskp12) | c0_1(a142)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[174, 171])).
% 0.79/0.99 tff(176,plain,
% 0.79/0.99 ((~hskp12) | c0_1(a142)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.79/0.99 tff(177,plain,
% 0.79/0.99 ((~hskp12) | c0_1(a142)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[176, 171])).
% 0.79/0.99 tff(178,plain,
% 0.79/0.99 (c0_1(a142)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[177, 139])).
% 0.79/0.99 tff(179,plain,
% 0.79/0.99 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(180,plain,
% 0.79/0.99 ((hskp7 | hskp0 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142))) <=> (hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(181,plain,
% 0.79/0.99 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[180])).
% 0.79/0.99 tff(182,plain,
% 0.79/0.99 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[181, 179])).
% 0.79/0.99 tff(183,plain,
% 0.79/0.99 ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(184,plain,
% 0.79/0.99 ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.79/0.99 tff(185,plain,
% 0.79/0.99 (hskp0),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[184, 117, 93, 178, 153, 145, 170])).
% 0.79/0.99 tff(186,plain,
% 0.79/0.99 (((~hskp0) | (~c1_1(a123))) <=> ((~hskp0) | (~c1_1(a123)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(187,plain,
% 0.79/0.99 (((~c1_1(a123)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a123)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(188,axiom,((~c1_1(a123)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.79/0.99 tff(189,plain,
% 0.79/0.99 ((~hskp0) | (~c1_1(a123))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.79/0.99 tff(190,plain,
% 0.79/0.99 ((~hskp0) | (~c1_1(a123))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[189, 186])).
% 0.79/0.99 tff(191,plain,
% 0.79/0.99 (~c1_1(a123)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[190, 185])).
% 0.79/0.99 tff(192,plain,
% 0.79/0.99 (((~hskp0) | c2_1(a123)) <=> ((~hskp0) | c2_1(a123))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(193,axiom,((~hskp0) | c2_1(a123)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.79/0.99 tff(194,plain,
% 0.79/0.99 ((~hskp0) | c2_1(a123)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.79/0.99 tff(195,plain,
% 0.79/0.99 ((~hskp0) | c2_1(a123)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[194, 192])).
% 0.79/0.99 tff(196,plain,
% 0.79/0.99 ((~hskp0) | c2_1(a123)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[195, 192])).
% 0.79/0.99 tff(197,plain,
% 0.79/0.99 ((~hskp0) | c2_1(a123)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.79/0.99 tff(198,plain,
% 0.79/0.99 ((~hskp0) | c2_1(a123)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[197, 192])).
% 0.79/0.99 tff(199,plain,
% 0.79/0.99 (c2_1(a123)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[198, 185])).
% 0.79/0.99 tff(200,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(201,plain,
% 0.79/0.99 (((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(202,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[201])).
% 0.79/0.99 tff(203,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[202, 200])).
% 0.79/0.99 tff(204,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(205,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.79/0.99 tff(206,plain,
% 0.79/0.99 (~c3_1(a123)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[205, 117, 153, 199, 145, 94, 126, 191, 138, 127, 160])).
% 0.79/0.99 tff(207,plain,
% 0.79/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(208,plain,
% 0.79/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[207])).
% 0.79/0.99 tff(209,plain,
% 0.79/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(210,plain,
% 0.79/0.99 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(211,plain,
% 0.79/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[210])).
% 0.79/0.99 tff(212,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.79/0.99 tff(213,plain,
% 0.79/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.79/0.99 tff(214,plain,
% 0.79/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.79/0.99 tff(215,plain,(
% 0.79/0.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.99 inference(skolemize,[status(sab)],[214])).
% 0.79/0.99 tff(216,plain,
% 0.79/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.79/0.99 tff(217,plain,
% 0.79/0.99 (((~hskp0) | (~c0_1(a123))) <=> ((~hskp0) | (~c0_1(a123)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(218,plain,
% 0.79/0.99 (((~c0_1(a123)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a123)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(219,axiom,((~c0_1(a123)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.79/0.99 tff(220,plain,
% 0.79/0.99 ((~hskp0) | (~c0_1(a123))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.79/0.99 tff(221,plain,
% 0.79/0.99 ((~hskp0) | (~c0_1(a123))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.79/0.99 tff(222,plain,
% 0.79/0.99 (~c0_1(a123)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[221, 185])).
% 0.79/0.99 tff(223,plain,
% 0.79/0.99 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(224,plain,
% 0.79/0.99 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a142) | c1_1(a142) | (~c0_1(a142))) <=> (hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(225,plain,
% 0.79/0.99 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a142) | c1_1(a142) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[224])).
% 0.79/0.99 tff(226,plain,
% 0.79/0.99 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a142) | c1_1(a142) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[225, 223])).
% 0.79/0.99 tff(227,plain,
% 0.79/0.99 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a142) | c1_1(a142) | (~c0_1(a142)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(228,plain,
% 0.79/0.99 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.79/0.99 tff(229,plain,
% 0.79/0.99 (hskp19 | c2_1(a142)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[228, 117, 128, 178, 145, 53])).
% 0.79/0.99 tff(230,plain,
% 0.79/0.99 (hskp19),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[229, 160])).
% 0.79/0.99 tff(231,plain,
% 0.79/0.99 (((~hskp19) | (~c2_1(a164))) <=> ((~hskp19) | (~c2_1(a164)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(232,plain,
% 0.79/0.99 (((~c2_1(a164)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a164)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(233,axiom,((~c2_1(a164)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.79/0.99 tff(234,plain,
% 0.79/0.99 ((~hskp19) | (~c2_1(a164))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.79/0.99 tff(235,plain,
% 0.79/0.99 ((~hskp19) | (~c2_1(a164))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[234, 231])).
% 0.79/0.99 tff(236,plain,
% 0.79/0.99 (~c2_1(a164)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[235, 230])).
% 0.79/0.99 tff(237,plain,
% 0.79/0.99 (((~hskp19) | c3_1(a164)) <=> ((~hskp19) | c3_1(a164))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(238,axiom,((~hskp19) | c3_1(a164)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.79/0.99 tff(239,plain,
% 0.79/0.99 ((~hskp19) | c3_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.79/0.99 tff(240,plain,
% 0.79/0.99 ((~hskp19) | c3_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[239, 237])).
% 0.79/0.99 tff(241,plain,
% 0.79/0.99 ((~hskp19) | c3_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[240, 237])).
% 0.79/0.99 tff(242,plain,
% 0.79/0.99 ((~hskp19) | c3_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[241, 237])).
% 0.79/0.99 tff(243,plain,
% 0.79/0.99 ((~hskp19) | c3_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[242, 237])).
% 0.79/0.99 tff(244,plain,
% 0.79/0.99 (c3_1(a164)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[243, 230])).
% 0.79/0.99 tff(245,plain,
% 0.79/0.99 (((~hskp19) | c1_1(a164)) <=> ((~hskp19) | c1_1(a164))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(246,axiom,((~hskp19) | c1_1(a164)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.79/0.99 tff(247,plain,
% 0.79/0.99 ((~hskp19) | c1_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.79/0.99 tff(248,plain,
% 0.79/0.99 ((~hskp19) | c1_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[247, 245])).
% 0.79/0.99 tff(249,plain,
% 0.79/0.99 ((~hskp19) | c1_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[248, 245])).
% 0.79/0.99 tff(250,plain,
% 0.79/0.99 ((~hskp19) | c1_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.79/0.99 tff(251,plain,
% 0.79/0.99 ((~hskp19) | c1_1(a164)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[250, 245])).
% 0.79/0.99 tff(252,plain,
% 0.79/0.99 (c1_1(a164)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[251, 230])).
% 0.79/0.99 tff(253,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(254,plain,
% 0.79/0.99 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(255,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[254])).
% 0.79/0.99 tff(256,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[255, 253])).
% 0.79/0.99 tff(257,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(258,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.79/0.99 tff(259,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[258, 117, 252, 244, 236, 94, 126, 92, 222, 191, 216, 206])).
% 0.79/0.99 tff(260,plain,((~hskp12) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~c3_1(a131)) | hskp17 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(261,plain,
% 0.79/0.99 (~hskp12),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[260, 128, 126, 92, 127, 94, 93])).
% 0.79/0.99 tff(262,plain,
% 0.79/0.99 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(263,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[262])).
% 0.79/0.99 tff(264,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(265,plain,
% 0.79/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(266,plain,
% 0.79/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[265])).
% 0.79/0.99 tff(267,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.79/0.99 tff(268,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.79/0.99 tff(269,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[268, 264])).
% 0.79/0.99 tff(270,plain,(
% 0.79/0.99 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.99 inference(skolemize,[status(sab)],[269])).
% 0.79/0.99 tff(271,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[270, 263])).
% 0.79/0.99 tff(272,plain,
% 0.79/0.99 (^[U: $i] : refl((hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(273,plain,
% 0.79/0.99 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[272])).
% 0.79/0.99 tff(274,plain,
% 0.79/0.99 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(275,plain,
% 0.79/0.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp7) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp7) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(276,plain,
% 0.79/1.00 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp7) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[275])).
% 0.79/1.00 tff(277,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.79/1.00 tff(278,plain,
% 0.79/1.00 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.79/1.00 tff(279,plain,
% 0.79/1.00 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[278, 274])).
% 0.79/1.00 tff(280,plain,(
% 0.79/1.00 ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.79/1.00 inference(skolemize,[status(sab)],[279])).
% 0.79/1.00 tff(281,plain,
% 0.79/1.00 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[280, 273])).
% 0.79/1.00 tff(282,plain,
% 0.79/1.00 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(283,plain,
% 0.79/1.00 ((hskp14 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(284,plain,
% 0.79/1.00 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[283])).
% 0.79/1.00 tff(285,plain,
% 0.79/1.00 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[284, 282])).
% 0.79/1.00 tff(286,plain,
% 0.79/1.00 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(287,plain,
% 0.79/1.00 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.79/1.00 tff(288,plain,
% 0.79/1.00 (hskp14 | hskp7 | (~c3_1(a131))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[287, 117, 94, 92, 281])).
% 0.79/1.00 tff(289,plain,
% 0.79/1.00 (hskp14),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[288, 93, 127])).
% 0.79/1.00 tff(290,plain,
% 0.79/1.00 (((~hskp14) | (~c3_1(a147))) <=> ((~hskp14) | (~c3_1(a147)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(291,plain,
% 0.79/1.00 (((~c3_1(a147)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a147)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(292,axiom,((~c3_1(a147)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.79/1.00 tff(293,plain,
% 0.79/1.00 ((~hskp14) | (~c3_1(a147))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.79/1.00 tff(294,plain,
% 0.79/1.00 ((~hskp14) | (~c3_1(a147))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[293, 290])).
% 0.79/1.00 tff(295,plain,
% 0.79/1.00 (~c3_1(a147)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[294, 289])).
% 0.79/1.00 tff(296,plain,
% 0.79/1.00 (((~hskp14) | c0_1(a147)) <=> ((~hskp14) | c0_1(a147))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(297,axiom,((~hskp14) | c0_1(a147)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.79/1.00 tff(298,plain,
% 0.79/1.00 ((~hskp14) | c0_1(a147)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.79/1.00 tff(299,plain,
% 0.79/1.00 ((~hskp14) | c0_1(a147)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[298, 296])).
% 0.79/1.00 tff(300,plain,
% 0.79/1.00 ((~hskp14) | c0_1(a147)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[299, 296])).
% 0.79/1.00 tff(301,plain,
% 0.79/1.00 ((~hskp14) | c0_1(a147)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.79/1.00 tff(302,plain,
% 0.79/1.00 ((~hskp14) | c0_1(a147)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[301, 296])).
% 0.79/1.00 tff(303,plain,
% 0.79/1.00 (c0_1(a147)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[302, 289])).
% 0.79/1.00 tff(304,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(305,plain,
% 0.79/1.00 ((hskp12 | (~ndr1_0) | c3_1(a147) | (~c0_1(a147)) | (~c2_1(a147)) | c2_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(306,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a147) | (~c0_1(a147)) | (~c2_1(a147)) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[305])).
% 0.79/1.00 tff(307,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a147) | (~c0_1(a147)) | (~c2_1(a147)) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[306, 304])).
% 0.79/1.00 tff(308,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a147) | (~c0_1(a147)) | (~c2_1(a147)) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(309,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.79/1.00 tff(310,plain,
% 0.79/1.00 (hskp12 | (~c2_1(a147))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[309, 117, 303, 295, 94, 92, 271, 127])).
% 0.79/1.00 tff(311,plain,
% 0.79/1.00 (~c2_1(a147)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[310, 261])).
% 0.79/1.00 tff(312,plain,
% 0.79/1.00 (((~hskp14) | (~c1_1(a147))) <=> ((~hskp14) | (~c1_1(a147)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(313,plain,
% 0.79/1.00 (((~c1_1(a147)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a147)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(314,axiom,((~c1_1(a147)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.79/1.00 tff(315,plain,
% 0.79/1.00 ((~hskp14) | (~c1_1(a147))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.79/1.00 tff(316,plain,
% 0.79/1.00 ((~hskp14) | (~c1_1(a147))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[315, 312])).
% 0.79/1.00 tff(317,plain,
% 0.79/1.00 (~c1_1(a147)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[316, 289])).
% 0.79/1.00 tff(318,plain,
% 0.79/1.00 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(319,plain,
% 0.79/1.00 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a147) | c1_1(a147) | (~c0_1(a147))) <=> (hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(320,plain,
% 0.79/1.00 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a147) | c1_1(a147) | (~c0_1(a147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[319])).
% 0.79/1.00 tff(321,plain,
% 0.79/1.00 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a147) | c1_1(a147) | (~c0_1(a147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[320, 318])).
% 0.79/1.00 tff(322,plain,
% 0.79/1.00 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a147) | c1_1(a147) | (~c0_1(a147)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(323,plain,
% 0.79/1.00 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.79/1.00 tff(324,plain,
% 0.79/1.00 (hskp19 | hskp17 | c2_1(a147)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[323, 117, 303, 317, 53])).
% 0.79/1.00 tff(325,plain,
% 0.79/1.00 (hskp19),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[324, 311, 128])).
% 0.79/1.00 tff(326,plain,
% 0.79/1.00 (~c2_1(a164)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[235, 325])).
% 0.79/1.00 tff(327,plain,
% 0.79/1.00 (c1_1(a164)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[251, 325])).
% 0.79/1.00 tff(328,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(329,plain,
% 0.79/1.00 (((~ndr1_0) | c2_1(a147) | c3_1(a147) | (~c0_1(a147)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(330,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a147) | c3_1(a147) | (~c0_1(a147)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[329])).
% 0.79/1.00 tff(331,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a147) | c3_1(a147) | (~c0_1(a147)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[330, 328])).
% 0.79/1.00 tff(332,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a147) | c3_1(a147) | (~c0_1(a147)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(333,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.79/1.00 tff(334,plain,
% 0.79/1.00 (c0_1(a164)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[333, 117, 327, 303, 326, 295, 94, 126, 92, 21, 311])).
% 0.79/1.00 tff(335,plain,
% 0.79/1.00 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(336,plain,
% 0.79/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[335])).
% 0.79/1.00 tff(337,plain,
% 0.79/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(338,plain,
% 0.79/1.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(339,plain,
% 0.79/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[338])).
% 0.79/1.00 tff(340,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.79/1.00 tff(341,plain,
% 0.79/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.79/1.00 tff(342,plain,
% 0.79/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[341, 337])).
% 0.79/1.00 tff(343,plain,(
% 0.79/1.00 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/1.00 inference(skolemize,[status(sab)],[342])).
% 0.79/1.00 tff(344,plain,
% 0.79/1.00 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[343, 336])).
% 0.79/1.00 tff(345,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(346,plain,
% 0.79/1.00 ((hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(347,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[346])).
% 0.79/1.00 tff(348,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[347, 345])).
% 0.79/1.00 tff(349,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(350,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.79/1.00 tff(351,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[350, 117, 93, 327, 326, 94, 126, 344, 127, 334])).
% 0.79/1.00 tff(352,plain,(hskp17 | hskp7 | c0_1(a131) | c1_1(a131) | (~c3_1(a131)) | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(353,plain,
% 0.79/1.00 (hskp17),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[352, 93, 94, 126, 125, 92])).
% 0.79/1.00 tff(354,plain,
% 0.79/1.00 (((~hskp17) | (~c2_1(a155))) <=> ((~hskp17) | (~c2_1(a155)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(355,plain,
% 0.79/1.00 (((~c2_1(a155)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a155)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(356,axiom,((~c2_1(a155)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.79/1.00 tff(357,plain,
% 0.79/1.00 ((~hskp17) | (~c2_1(a155))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.79/1.00 tff(358,plain,
% 0.79/1.00 ((~hskp17) | (~c2_1(a155))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[357, 354])).
% 0.79/1.00 tff(359,plain,
% 0.79/1.00 (~c2_1(a155)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[358, 353])).
% 0.79/1.00 tff(360,plain,
% 0.79/1.00 (((~hskp17) | (~c0_1(a155))) <=> ((~hskp17) | (~c0_1(a155)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(361,plain,
% 0.79/1.00 (((~c0_1(a155)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a155)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(362,axiom,((~c0_1(a155)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.79/1.00 tff(363,plain,
% 0.79/1.00 ((~hskp17) | (~c0_1(a155))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.79/1.00 tff(364,plain,
% 0.79/1.00 ((~hskp17) | (~c0_1(a155))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[363, 360])).
% 0.79/1.00 tff(365,plain,
% 0.79/1.00 (~c0_1(a155)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[364, 353])).
% 0.79/1.00 tff(366,plain,
% 0.79/1.00 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(367,plain,
% 0.79/1.00 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | c3_1(a155)) <=> (hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(368,plain,
% 0.79/1.00 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | c3_1(a155))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155)))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[367])).
% 0.79/1.00 tff(369,plain,
% 0.79/1.00 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | c3_1(a155))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155))),
% 0.79/1.00 inference(transitivity,[status(thm)],[368, 366])).
% 0.79/1.00 tff(370,plain,
% 0.79/1.00 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | c3_1(a155))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(371,plain,
% 0.79/1.00 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.79/1.00 tff(372,plain,
% 0.79/1.00 (c3_1(a155)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[371, 117, 33, 93, 365, 359, 91])).
% 0.79/1.00 tff(373,plain,
% 0.79/1.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(374,plain,
% 0.79/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[373])).
% 0.79/1.00 tff(375,plain,
% 0.79/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(376,plain,
% 0.79/1.00 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(377,plain,
% 0.79/1.00 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[376])).
% 0.79/1.00 tff(378,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.79/1.00 tff(379,plain,
% 0.79/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.79/1.00 tff(380,plain,
% 0.79/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[379, 375])).
% 0.79/1.00 tff(381,plain,(
% 0.79/1.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/1.00 inference(skolemize,[status(sab)],[380])).
% 0.79/1.00 tff(382,plain,
% 0.79/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[381, 374])).
% 0.79/1.00 tff(383,plain,
% 0.79/1.00 (((~hskp17) | c1_1(a155)) <=> ((~hskp17) | c1_1(a155))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(384,axiom,((~hskp17) | c1_1(a155)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.79/1.00 tff(385,plain,
% 0.79/1.00 ((~hskp17) | c1_1(a155)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.79/1.00 tff(386,plain,
% 0.79/1.00 ((~hskp17) | c1_1(a155)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[385, 383])).
% 0.79/1.00 tff(387,plain,
% 0.79/1.00 ((~hskp17) | c1_1(a155)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[386, 383])).
% 0.79/1.00 tff(388,plain,
% 0.79/1.00 ((~hskp17) | c1_1(a155)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[387, 383])).
% 0.79/1.00 tff(389,plain,
% 0.79/1.00 ((~hskp17) | c1_1(a155)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[388, 383])).
% 0.79/1.00 tff(390,plain,
% 0.79/1.00 (c1_1(a155)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[389, 353])).
% 0.79/1.00 tff(391,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(392,plain,
% 0.79/1.00 (((~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(393,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[392])).
% 0.79/1.00 tff(394,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[393, 391])).
% 0.79/1.00 tff(395,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(396,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.79/1.00 tff(397,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[396, 117, 390, 365, 359, 94, 126, 92, 382, 372])).
% 0.79/1.00 tff(398,plain,(hskp7 | c0_1(a131) | c1_1(a131) | c2_1(a131) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(399,plain,
% 0.79/1.00 (hskp7),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[398, 81, 75, 69, 33])).
% 0.79/1.01 tff(400,plain,
% 0.79/1.01 (((~hskp7) | (~c0_1(a132))) <=> ((~hskp7) | (~c0_1(a132)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(401,plain,
% 0.79/1.01 (((~c0_1(a132)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a132)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(402,axiom,((~c0_1(a132)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.79/1.01 tff(403,plain,
% 0.79/1.01 ((~hskp7) | (~c0_1(a132))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.79/1.01 tff(404,plain,
% 0.79/1.01 ((~hskp7) | (~c0_1(a132))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[403, 400])).
% 0.79/1.01 tff(405,plain,
% 0.79/1.01 (~c0_1(a132)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[404, 399])).
% 0.79/1.01 tff(406,assumption,(~c0_1(a125)), introduced(assumption)).
% 0.79/1.01 tff(407,assumption,(~c0_1(a132)), introduced(assumption)).
% 0.79/1.01 tff(408,assumption,(~c3_1(a124)), introduced(assumption)).
% 0.79/1.01 tff(409,assumption,(~c2_1(a132)), introduced(assumption)).
% 0.79/1.01 tff(410,assumption,(~c3_1(a132)), introduced(assumption)).
% 0.79/1.01 tff(411,plain,
% 0.79/1.01 (((~hskp7) | c3_1(a132)) <=> ((~hskp7) | c3_1(a132))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(412,axiom,((~hskp7) | c3_1(a132)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.79/1.01 tff(413,plain,
% 0.79/1.01 ((~hskp7) | c3_1(a132)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.79/1.01 tff(414,plain,
% 0.79/1.01 ((~hskp7) | c3_1(a132)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[413, 411])).
% 0.79/1.01 tff(415,plain,
% 0.79/1.01 ((~hskp7) | c3_1(a132)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[414, 411])).
% 0.79/1.01 tff(416,plain,
% 0.79/1.01 ((~hskp7) | c3_1(a132)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[415, 411])).
% 0.79/1.01 tff(417,plain,
% 0.79/1.01 ((~hskp7) | c3_1(a132)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[416, 411])).
% 0.79/1.01 tff(418,plain,
% 0.79/1.01 (~hskp7),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[417, 410])).
% 0.79/1.01 tff(419,plain,
% 0.79/1.01 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(420,plain,
% 0.79/1.01 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | c3_1(a132)) <=> (hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(421,plain,
% 0.79/1.01 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0)))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[420])).
% 0.79/1.01 tff(422,plain,
% 0.79/1.01 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0))),
% 0.79/1.01 inference(transitivity,[status(thm)],[421, 419])).
% 0.79/1.01 tff(423,plain,
% 0.79/1.01 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | c3_1(a132))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(424,plain,
% 0.79/1.01 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.79/1.01 tff(425,plain,
% 0.79/1.01 (hskp7 | c3_1(a132) | c0_1(a132)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[424, 117, 33, 409, 91])).
% 0.79/1.01 tff(426,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[425, 418, 410, 407])).
% 0.79/1.01 tff(427,plain,(c3_1(a132) | c0_1(a132) | hskp9 | c2_1(a132)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(428,plain,
% 0.79/1.01 (c3_1(a132)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[427, 409, 33, 407])).
% 0.79/1.01 tff(429,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(430,plain,
% 0.79/1.01 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(431,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[430])).
% 0.79/1.01 tff(432,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[431, 429])).
% 0.79/1.01 tff(433,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(434,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.79/1.01 tff(435,plain,
% 0.79/1.01 (~c1_1(a132)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[434, 117, 428, 407, 409, 81, 75, 69, 382])).
% 0.79/1.01 tff(436,assumption,(~c1_1(a132)), introduced(assumption)).
% 0.79/1.01 tff(437,assumption,(hskp17), introduced(assumption)).
% 0.79/1.01 tff(438,plain,
% 0.79/1.01 (~c2_1(a155)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[358, 437])).
% 0.79/1.01 tff(439,plain,
% 0.79/1.01 (~c0_1(a155)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[364, 437])).
% 0.79/1.01 tff(440,assumption,(c3_1(a132)), introduced(assumption)).
% 0.79/1.01 tff(441,plain,
% 0.79/1.01 (c1_1(a155)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[389, 437])).
% 0.79/1.01 tff(442,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(443,plain,
% 0.79/1.01 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(444,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[443])).
% 0.79/1.01 tff(445,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[444, 442])).
% 0.79/1.01 tff(446,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(447,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.79/1.01 tff(448,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[447, 117, 441, 440, 439, 438, 407, 409, 382, 436])).
% 0.79/1.01 tff(449,plain,((~hskp17) | (~c3_1(a132)) | c0_1(a132) | c2_1(a132) | c1_1(a132)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(450,plain,
% 0.79/1.01 (~hskp17),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[449, 435, 407, 409, 428])).
% 0.79/1.01 tff(451,plain,
% 0.79/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(452,plain,
% 0.79/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[451])).
% 0.79/1.01 tff(453,plain,
% 0.79/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(454,plain,
% 0.79/1.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(455,plain,
% 0.79/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[454])).
% 0.79/1.01 tff(456,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 0.79/1.01 tff(457,plain,
% 0.79/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.79/1.01 tff(458,plain,
% 0.79/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[457, 453])).
% 0.79/1.01 tff(459,plain,(
% 0.79/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.79/1.01 inference(skolemize,[status(sab)],[458])).
% 0.79/1.01 tff(460,plain,
% 0.79/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[459, 452])).
% 0.79/1.01 tff(461,assumption,(hskp0), introduced(assumption)).
% 0.79/1.01 tff(462,plain,
% 0.79/1.01 (~c1_1(a123)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[190, 461])).
% 0.79/1.01 tff(463,plain,
% 0.79/1.01 (~c0_1(a123)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[221, 461])).
% 0.79/1.01 tff(464,plain,
% 0.79/1.01 (c2_1(a123)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[198, 461])).
% 0.79/1.01 tff(465,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(466,plain,
% 0.79/1.01 (((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(467,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132)))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[466])).
% 0.79/1.01 tff(468,plain,
% 0.79/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 0.79/1.01 inference(transitivity,[status(thm)],[467, 465])).
% 0.79/1.01 tff(469,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(470,plain,
% 0.79/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132)),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.79/1.01 tff(471,plain,
% 0.79/1.01 (~c3_1(a123)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[470, 117, 440, 464, 409, 463, 462, 138, 436])).
% 0.85/1.01 tff(472,plain,
% 0.85/1.01 (^[U: $i] : refl((hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(473,plain,
% 0.85/1.01 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[472])).
% 0.85/1.01 tff(474,plain,
% 0.85/1.01 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(475,plain,
% 0.85/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp20) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp20))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(476,plain,
% 0.85/1.01 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp20) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[475])).
% 0.85/1.01 tff(477,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.85/1.01 tff(478,plain,
% 0.85/1.01 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.85/1.01 tff(479,plain,
% 0.85/1.01 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[478, 474])).
% 0.85/1.01 tff(480,plain,(
% 0.85/1.01 ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.01 inference(skolemize,[status(sab)],[479])).
% 0.85/1.01 tff(481,plain,
% 0.85/1.01 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[480, 473])).
% 0.85/1.01 tff(482,plain,
% 0.85/1.01 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(483,plain,
% 0.85/1.01 ((hskp30 | hskp20 | (~ndr1_0) | c1_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(484,plain,
% 0.85/1.01 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[483])).
% 0.85/1.01 tff(485,plain,
% 0.85/1.01 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[484, 482])).
% 0.85/1.01 tff(486,plain,
% 0.85/1.01 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(487,plain,
% 0.85/1.01 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.85/1.01 tff(488,plain,
% 0.85/1.01 (hskp20 | c3_1(a123)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[487, 54, 117, 464, 462, 481])).
% 0.85/1.01 tff(489,plain,
% 0.85/1.01 (hskp20),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[488, 471])).
% 0.85/1.01 tff(490,plain,
% 0.85/1.01 (((~hskp20) | (~c3_1(a168))) <=> ((~hskp20) | (~c3_1(a168)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(491,plain,
% 0.85/1.01 (((~c3_1(a168)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a168)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(492,axiom,((~c3_1(a168)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.85/1.01 tff(493,plain,
% 0.85/1.01 ((~hskp20) | (~c3_1(a168))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.85/1.01 tff(494,plain,
% 0.85/1.01 ((~hskp20) | (~c3_1(a168))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[493, 490])).
% 0.85/1.01 tff(495,plain,
% 0.85/1.01 (~c3_1(a168)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[494, 489])).
% 0.85/1.01 tff(496,plain,
% 0.85/1.01 (((~hskp20) | (~c0_1(a168))) <=> ((~hskp20) | (~c0_1(a168)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(497,plain,
% 0.85/1.01 (((~c0_1(a168)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a168)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(498,axiom,((~c0_1(a168)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.85/1.01 tff(499,plain,
% 0.85/1.01 ((~hskp20) | (~c0_1(a168))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.85/1.01 tff(500,plain,
% 0.85/1.01 ((~hskp20) | (~c0_1(a168))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[499, 496])).
% 0.85/1.01 tff(501,plain,
% 0.85/1.01 (~c0_1(a168)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[500, 489])).
% 0.85/1.01 tff(502,plain,
% 0.85/1.01 (((~hskp20) | c1_1(a168)) <=> ((~hskp20) | c1_1(a168))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(503,axiom,((~hskp20) | c1_1(a168)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.85/1.01 tff(504,plain,
% 0.85/1.01 ((~hskp20) | c1_1(a168)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.85/1.01 tff(505,plain,
% 0.85/1.01 ((~hskp20) | c1_1(a168)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[504, 502])).
% 0.85/1.01 tff(506,plain,
% 0.85/1.01 ((~hskp20) | c1_1(a168)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[505, 502])).
% 0.85/1.01 tff(507,plain,
% 0.85/1.01 ((~hskp20) | c1_1(a168)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[506, 502])).
% 0.85/1.01 tff(508,plain,
% 0.85/1.01 ((~hskp20) | c1_1(a168)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[507, 502])).
% 0.85/1.01 tff(509,plain,
% 0.85/1.01 (c1_1(a168)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[508, 489])).
% 0.85/1.01 tff(510,plain,
% 0.85/1.01 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(511,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[510])).
% 0.85/1.01 tff(512,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(513,plain,
% 0.85/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(514,plain,
% 0.85/1.02 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[513])).
% 0.85/1.02 tff(515,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.85/1.02 tff(516,plain,
% 0.85/1.02 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.85/1.02 tff(517,plain,
% 0.85/1.02 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[516, 512])).
% 0.85/1.02 tff(518,plain,(
% 0.85/1.02 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.02 inference(skolemize,[status(sab)],[517])).
% 0.85/1.02 tff(519,plain,
% 0.85/1.02 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[518, 511])).
% 0.85/1.02 tff(520,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(521,plain,
% 0.85/1.02 ((hskp27 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(522,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132)))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[521])).
% 0.85/1.02 tff(523,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132))),
% 0.85/1.02 inference(transitivity,[status(thm)],[522, 520])).
% 0.85/1.02 tff(524,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(525,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.85/1.02 tff(526,plain,
% 0.85/1.02 (hskp27 | c3_1(a123)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[525, 117, 464, 407, 409, 463, 519, 436])).
% 0.85/1.02 tff(527,plain,
% 0.85/1.02 (hskp27),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[526, 471])).
% 0.85/1.02 tff(528,plain,
% 0.85/1.02 (((~hskp27) | c3_1(a122)) <=> ((~hskp27) | c3_1(a122))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(529,axiom,((~hskp27) | c3_1(a122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.85/1.02 tff(530,plain,
% 0.85/1.02 ((~hskp27) | c3_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.85/1.02 tff(531,plain,
% 0.85/1.02 ((~hskp27) | c3_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[530, 528])).
% 0.85/1.02 tff(532,plain,
% 0.85/1.02 ((~hskp27) | c3_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[531, 528])).
% 0.85/1.02 tff(533,plain,
% 0.85/1.02 ((~hskp27) | c3_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[532, 528])).
% 0.85/1.02 tff(534,plain,
% 0.85/1.02 ((~hskp27) | c3_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[533, 528])).
% 0.85/1.02 tff(535,plain,
% 0.85/1.02 (c3_1(a122)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[534, 527])).
% 0.85/1.02 tff(536,plain,
% 0.85/1.02 (((~hskp27) | c2_1(a122)) <=> ((~hskp27) | c2_1(a122))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(537,axiom,((~hskp27) | c2_1(a122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.85/1.02 tff(538,plain,
% 0.85/1.02 ((~hskp27) | c2_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.85/1.02 tff(539,plain,
% 0.85/1.02 ((~hskp27) | c2_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[538, 536])).
% 0.85/1.02 tff(540,plain,
% 0.85/1.02 ((~hskp27) | c2_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[539, 536])).
% 0.85/1.02 tff(541,plain,
% 0.85/1.02 ((~hskp27) | c2_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[540, 536])).
% 0.85/1.02 tff(542,plain,
% 0.85/1.02 ((~hskp27) | c2_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[541, 536])).
% 0.85/1.02 tff(543,plain,
% 0.85/1.02 (c2_1(a122)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[542, 527])).
% 0.85/1.02 tff(544,plain,
% 0.85/1.02 (((~hskp27) | c0_1(a122)) <=> ((~hskp27) | c0_1(a122))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(545,axiom,((~hskp27) | c0_1(a122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.85/1.02 tff(546,plain,
% 0.85/1.02 ((~hskp27) | c0_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.85/1.02 tff(547,plain,
% 0.85/1.02 ((~hskp27) | c0_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[546, 544])).
% 0.85/1.02 tff(548,plain,
% 0.85/1.02 ((~hskp27) | c0_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[547, 544])).
% 0.85/1.02 tff(549,plain,
% 0.85/1.02 ((~hskp27) | c0_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[548, 544])).
% 0.85/1.02 tff(550,plain,
% 0.85/1.02 ((~hskp27) | c0_1(a122)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[549, 544])).
% 0.85/1.02 tff(551,plain,
% 0.85/1.02 (c0_1(a122)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[550, 527])).
% 0.85/1.02 tff(552,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(553,plain,
% 0.85/1.02 (((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a168) | (~c2_1(a168)) | (~c1_1(a168)) | c0_1(a168) | c3_1(a168) | (~c1_1(a168))) <=> (c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(554,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a168) | (~c2_1(a168)) | (~c1_1(a168)) | c0_1(a168) | c3_1(a168) | (~c1_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[553])).
% 0.85/1.02 tff(555,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a168) | (~c2_1(a168)) | (~c1_1(a168)) | c0_1(a168) | c3_1(a168) | (~c1_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[554, 552])).
% 0.85/1.02 tff(556,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a168) | (~c2_1(a168)) | (~c1_1(a168)) | c0_1(a168) | c3_1(a168) | (~c1_1(a168)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(557,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.85/1.02 tff(558,plain,
% 0.85/1.02 (~c2_1(a168)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[557, 117, 551, 543, 535, 509, 501, 495, 460])).
% 0.85/1.02 tff(559,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(560,plain,
% 0.85/1.02 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a168) | c0_1(a168) | (~c1_1(a168)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(561,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a168) | c0_1(a168) | (~c1_1(a168)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168)))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[560])).
% 0.85/1.02 tff(562,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a168) | c0_1(a168) | (~c1_1(a168)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168))),
% 0.85/1.02 inference(transitivity,[status(thm)],[561, 559])).
% 0.85/1.02 tff(563,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a168) | c0_1(a168) | (~c1_1(a168)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(564,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.85/1.02 tff(565,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[564, 117, 509, 440, 501, 407, 409, 382, 436, 558])).
% 0.85/1.02 tff(566,plain,((~hskp0) | (~c3_1(a132)) | c0_1(a132) | c2_1(a132) | c1_1(a132) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(567,plain,
% 0.85/1.02 (~hskp0),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[566, 435, 407, 409, 428, 54])).
% 0.85/1.02 tff(568,assumption,(~hskp22), introduced(assumption)).
% 0.85/1.02 tff(569,assumption,(hskp1), introduced(assumption)).
% 0.85/1.02 tff(570,plain,
% 0.85/1.02 (((~hskp1) | c1_1(a124)) <=> ((~hskp1) | c1_1(a124))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(571,axiom,((~hskp1) | c1_1(a124)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.85/1.02 tff(572,plain,
% 0.85/1.02 ((~hskp1) | c1_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.85/1.02 tff(573,plain,
% 0.85/1.02 ((~hskp1) | c1_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[572, 570])).
% 0.85/1.02 tff(574,plain,
% 0.85/1.02 ((~hskp1) | c1_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[573, 570])).
% 0.85/1.02 tff(575,plain,
% 0.85/1.02 ((~hskp1) | c1_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[574, 570])).
% 0.85/1.02 tff(576,plain,
% 0.85/1.02 ((~hskp1) | c1_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[575, 570])).
% 0.85/1.02 tff(577,plain,
% 0.85/1.02 (c1_1(a124)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[576, 569])).
% 0.85/1.02 tff(578,plain,
% 0.85/1.02 (((~hskp1) | c2_1(a124)) <=> ((~hskp1) | c2_1(a124))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(579,axiom,((~hskp1) | c2_1(a124)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.85/1.02 tff(580,plain,
% 0.85/1.02 ((~hskp1) | c2_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.85/1.02 tff(581,plain,
% 0.85/1.02 ((~hskp1) | c2_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[580, 578])).
% 0.85/1.02 tff(582,plain,
% 0.85/1.02 ((~hskp1) | c2_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[581, 578])).
% 0.85/1.02 tff(583,plain,
% 0.85/1.02 ((~hskp1) | c2_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[582, 578])).
% 0.85/1.02 tff(584,plain,
% 0.85/1.02 ((~hskp1) | c2_1(a124)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[583, 578])).
% 0.85/1.02 tff(585,plain,
% 0.85/1.02 (c2_1(a124)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[584, 569])).
% 0.85/1.02 tff(586,plain,
% 0.85/1.02 (^[U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(587,plain,
% 0.85/1.02 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[586])).
% 0.85/1.02 tff(588,plain,
% 0.85/1.02 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(589,plain,
% 0.85/1.02 (^[U: $i] : 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)) | 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)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(590,plain,
% 0.85/1.02 (![U: $i] : (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[589])).
% 0.85/1.02 tff(591,axiom,(![U: $i] : (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.85/1.02 tff(592,plain,
% 0.85/1.02 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.85/1.02 tff(593,plain,
% 0.85/1.02 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.85/1.02 tff(594,plain,(
% 0.85/1.02 ![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.02 inference(skolemize,[status(sab)],[593])).
% 0.85/1.02 tff(595,plain,
% 0.85/1.02 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[594, 587])).
% 0.85/1.02 tff(596,plain,
% 0.85/1.02 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(597,plain,
% 0.85/1.02 ((hskp22 | (~ndr1_0) | c3_1(a124) | (~c1_1(a124)) | (~c2_1(a124))) <=> (hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(598,plain,
% 0.85/1.02 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a124) | (~c1_1(a124)) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[597])).
% 0.85/1.02 tff(599,plain,
% 0.85/1.02 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a124) | (~c1_1(a124)) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[598, 596])).
% 0.85/1.02 tff(600,plain,
% 0.85/1.02 ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a124) | (~c1_1(a124)) | (~c2_1(a124)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(601,plain,
% 0.85/1.02 ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.85/1.02 tff(602,plain,
% 0.85/1.02 (hskp22 | (~c2_1(a124)) | (~c1_1(a124))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[601, 117, 408, 595])).
% 0.85/1.02 tff(603,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[602, 585, 577, 568])).
% 0.85/1.02 tff(604,plain,((~hskp1) | hskp22 | c3_1(a124)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(605,plain,
% 0.85/1.02 (~hskp1),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[604, 568, 408])).
% 0.85/1.02 tff(606,plain,
% 0.85/1.02 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(607,plain,
% 0.85/1.02 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[606])).
% 0.85/1.02 tff(608,plain,
% 0.85/1.02 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(609,plain,
% 0.85/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(610,plain,
% 0.85/1.02 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[609])).
% 0.85/1.02 tff(611,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.85/1.02 tff(612,plain,
% 0.85/1.02 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.85/1.02 tff(613,plain,
% 0.85/1.02 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[612, 608])).
% 0.85/1.02 tff(614,plain,(
% 0.85/1.02 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.85/1.02 inference(skolemize,[status(sab)],[613])).
% 0.85/1.02 tff(615,plain,
% 0.85/1.02 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[614, 607])).
% 0.85/1.02 tff(616,plain,
% 0.85/1.02 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(617,plain,
% 0.85/1.02 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(618,plain,
% 0.85/1.02 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0)))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[617])).
% 0.85/1.02 tff(619,plain,
% 0.85/1.02 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.85/1.02 inference(transitivity,[status(thm)],[618, 616])).
% 0.85/1.02 tff(620,plain,
% 0.85/1.02 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(621,plain,
% 0.85/1.02 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.85/1.02 tff(622,plain,
% 0.85/1.02 (hskp2 | hskp1),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[621, 117, 94, 126, 92, 615])).
% 0.85/1.02 tff(623,plain,
% 0.85/1.02 (hskp2),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[622, 605])).
% 0.85/1.02 tff(624,plain,
% 0.85/1.02 (((~hskp2) | c1_1(a125)) <=> ((~hskp2) | c1_1(a125))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(625,axiom,((~hskp2) | c1_1(a125)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.85/1.02 tff(626,plain,
% 0.85/1.02 ((~hskp2) | c1_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.85/1.02 tff(627,plain,
% 0.85/1.02 ((~hskp2) | c1_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[626, 624])).
% 0.85/1.02 tff(628,plain,
% 0.85/1.02 ((~hskp2) | c1_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[627, 624])).
% 0.85/1.02 tff(629,plain,
% 0.85/1.02 ((~hskp2) | c1_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[628, 624])).
% 0.85/1.02 tff(630,plain,
% 0.85/1.02 ((~hskp2) | c1_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[629, 624])).
% 0.85/1.02 tff(631,plain,
% 0.85/1.02 (c1_1(a125)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[630, 623])).
% 0.85/1.02 tff(632,plain,
% 0.85/1.02 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(633,plain,
% 0.85/1.02 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a125) | (~c3_1(a125)) | (~c1_1(a125))) <=> (hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(634,plain,
% 0.85/1.02 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a125) | (~c3_1(a125)) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[633])).
% 0.85/1.02 tff(635,plain,
% 0.85/1.02 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a125) | (~c3_1(a125)) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[634, 632])).
% 0.85/1.02 tff(636,plain,
% 0.85/1.02 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a125) | (~c3_1(a125)) | (~c1_1(a125)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(637,plain,
% 0.85/1.02 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.85/1.02 tff(638,plain,
% 0.85/1.02 (hskp17 | hskp0 | (~c1_1(a125)) | (~c3_1(a125))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[637, 117, 406, 43])).
% 0.85/1.02 tff(639,plain,
% 0.85/1.02 (~c3_1(a125)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[638, 631, 128, 11])).
% 0.85/1.02 tff(640,plain,
% 0.85/1.02 (((~hskp2) | c2_1(a125)) <=> ((~hskp2) | c2_1(a125))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(641,axiom,((~hskp2) | c2_1(a125)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.85/1.02 tff(642,plain,
% 0.85/1.02 ((~hskp2) | c2_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.85/1.02 tff(643,plain,
% 0.85/1.02 ((~hskp2) | c2_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[642, 640])).
% 0.85/1.02 tff(644,plain,
% 0.85/1.02 ((~hskp2) | c2_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[643, 640])).
% 0.85/1.02 tff(645,plain,
% 0.85/1.02 ((~hskp2) | c2_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[644, 640])).
% 0.85/1.02 tff(646,plain,
% 0.85/1.02 ((~hskp2) | c2_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[645, 640])).
% 0.85/1.02 tff(647,plain,
% 0.85/1.02 (c2_1(a125)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[646, 623])).
% 0.85/1.02 tff(648,plain,
% 0.85/1.02 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(649,plain,
% 0.85/1.02 ((hskp22 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c2_1(a125))) <=> (hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(650,plain,
% 0.85/1.02 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c2_1(a125)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125)))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[649])).
% 0.85/1.02 tff(651,plain,
% 0.85/1.02 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c2_1(a125)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125))),
% 0.85/1.02 inference(transitivity,[status(thm)],[650, 648])).
% 0.85/1.02 tff(652,plain,
% 0.85/1.02 ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c2_1(a125)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(653,plain,
% 0.85/1.02 ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.85/1.02 tff(654,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[653, 117, 568, 631, 647, 595, 639])).
% 0.85/1.02 tff(655,plain,(hskp22 | hskp17 | hskp0 | c0_1(a125) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c3_1(a124)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(656,plain,
% 0.85/1.02 (hskp22),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[655, 567, 450, 406, 81, 75, 69, 408])).
% 0.85/1.02 tff(657,plain,
% 0.85/1.02 (((~hskp22) | (~c2_1(a176))) <=> ((~hskp22) | (~c2_1(a176)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(658,plain,
% 0.85/1.02 (((~c2_1(a176)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a176)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(659,axiom,((~c2_1(a176)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.85/1.02 tff(660,plain,
% 0.85/1.02 ((~hskp22) | (~c2_1(a176))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.85/1.02 tff(661,plain,
% 0.85/1.02 ((~hskp22) | (~c2_1(a176))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[660, 657])).
% 0.85/1.02 tff(662,plain,
% 0.85/1.02 (~c2_1(a176)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[661, 656])).
% 0.85/1.02 tff(663,plain,
% 0.85/1.02 (((~hskp22) | (~c1_1(a176))) <=> ((~hskp22) | (~c1_1(a176)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(664,plain,
% 0.85/1.02 (((~c1_1(a176)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a176)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(665,axiom,((~c1_1(a176)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.85/1.02 tff(666,plain,
% 0.85/1.02 ((~hskp22) | (~c1_1(a176))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.85/1.02 tff(667,plain,
% 0.85/1.02 ((~hskp22) | (~c1_1(a176))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[666, 663])).
% 0.85/1.02 tff(668,plain,
% 0.85/1.02 (~c1_1(a176)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[667, 656])).
% 0.85/1.02 tff(669,plain,
% 0.85/1.02 (((~hskp22) | c0_1(a176)) <=> ((~hskp22) | c0_1(a176))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(670,axiom,((~hskp22) | c0_1(a176)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.85/1.02 tff(671,plain,
% 0.85/1.02 ((~hskp22) | c0_1(a176)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.85/1.02 tff(672,plain,
% 0.85/1.02 ((~hskp22) | c0_1(a176)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[671, 669])).
% 0.85/1.02 tff(673,plain,
% 0.85/1.02 ((~hskp22) | c0_1(a176)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[672, 669])).
% 0.85/1.02 tff(674,plain,
% 0.85/1.02 ((~hskp22) | c0_1(a176)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[673, 669])).
% 0.85/1.02 tff(675,plain,
% 0.85/1.02 ((~hskp22) | c0_1(a176)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[674, 669])).
% 0.85/1.02 tff(676,plain,
% 0.85/1.02 (c0_1(a176)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[675, 656])).
% 0.85/1.02 tff(677,plain,
% 0.85/1.02 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(678,plain,
% 0.85/1.02 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176))) <=> (hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(679,plain,
% 0.85/1.03 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[678])).
% 0.85/1.03 tff(680,plain,
% 0.85/1.03 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[679, 677])).
% 0.85/1.03 tff(681,plain,
% 0.85/1.03 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(682,plain,
% 0.85/1.03 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.85/1.03 tff(683,plain,
% 0.85/1.03 (hskp19),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[682, 117, 450, 676, 668, 662, 53])).
% 0.85/1.03 tff(684,plain,
% 0.85/1.03 (c3_1(a164)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[243, 683])).
% 0.85/1.03 tff(685,plain,
% 0.85/1.03 (c1_1(a164)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[251, 683])).
% 0.85/1.03 tff(686,plain,
% 0.85/1.03 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(687,plain,
% 0.85/1.03 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a164) | (~c3_1(a164)) | (~c1_1(a164))) <=> (hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(688,plain,
% 0.85/1.03 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[687])).
% 0.85/1.03 tff(689,plain,
% 0.85/1.03 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[688, 686])).
% 0.85/1.03 tff(690,plain,
% 0.85/1.03 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(691,plain,
% 0.85/1.03 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.85/1.03 tff(692,plain,
% 0.85/1.03 (c0_1(a164)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[691, 117, 450, 567, 685, 684, 43])).
% 0.85/1.03 tff(693,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(694,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[693])).
% 0.85/1.03 tff(695,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(696,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(697,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[696])).
% 0.85/1.03 tff(698,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 0.85/1.03 tff(699,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.85/1.03 tff(700,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[699, 695])).
% 0.85/1.03 tff(701,plain,(
% 0.85/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[700])).
% 0.85/1.03 tff(702,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[701, 694])).
% 0.85/1.03 tff(703,plain,
% 0.85/1.03 (^[U: $i] : refl((hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(704,plain,
% 0.85/1.03 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[703])).
% 0.85/1.03 tff(705,plain,
% 0.85/1.03 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(706,plain,
% 0.85/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp13) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp13) <=> (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(707,plain,
% 0.85/1.03 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp13) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[706])).
% 0.85/1.03 tff(708,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.85/1.03 tff(709,plain,
% 0.85/1.03 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.85/1.03 tff(710,plain,
% 0.85/1.03 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[709, 705])).
% 0.85/1.03 tff(711,plain,(
% 0.85/1.03 ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[710])).
% 0.85/1.03 tff(712,plain,
% 0.85/1.03 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[711, 704])).
% 0.85/1.03 tff(713,plain,
% 0.85/1.03 (~c2_1(a164)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[235, 683])).
% 0.85/1.03 tff(714,plain,
% 0.85/1.03 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(715,plain,
% 0.85/1.03 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164))) <=> (hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(716,plain,
% 0.85/1.03 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[715])).
% 0.85/1.03 tff(717,plain,
% 0.85/1.03 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[716, 714])).
% 0.85/1.03 tff(718,plain,
% 0.85/1.03 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(719,plain,
% 0.85/1.03 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.85/1.03 tff(720,plain,
% 0.85/1.03 (hskp13),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[719, 117, 450, 685, 684, 713, 712])).
% 0.85/1.03 tff(721,plain,
% 0.85/1.03 (((~hskp13) | (~c1_1(a143))) <=> ((~hskp13) | (~c1_1(a143)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(722,plain,
% 0.85/1.03 (((~c1_1(a143)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a143)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(723,axiom,((~c1_1(a143)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.85/1.03 tff(724,plain,
% 0.85/1.03 ((~hskp13) | (~c1_1(a143))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[723, 722])).
% 0.85/1.03 tff(725,plain,
% 0.85/1.03 ((~hskp13) | (~c1_1(a143))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[724, 721])).
% 0.85/1.03 tff(726,plain,
% 0.85/1.03 (~c1_1(a143)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[725, 720])).
% 0.85/1.03 tff(727,assumption,(hskp2), introduced(assumption)).
% 0.85/1.03 tff(728,plain,
% 0.85/1.03 (c1_1(a125)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[630, 727])).
% 0.85/1.03 tff(729,plain,
% 0.85/1.03 (~c3_1(a125)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[638, 728, 128, 11])).
% 0.85/1.03 tff(730,plain,
% 0.85/1.03 (c2_1(a125)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[646, 727])).
% 0.85/1.03 tff(731,assumption,(~c1_1(a176)), introduced(assumption)).
% 0.85/1.03 tff(732,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(733,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[732])).
% 0.85/1.03 tff(734,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(735,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(736,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[735])).
% 0.85/1.03 tff(737,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.85/1.03 tff(738,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.85/1.03 tff(739,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[738, 734])).
% 0.85/1.03 tff(740,plain,(
% 0.85/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[739])).
% 0.85/1.03 tff(741,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[740, 733])).
% 0.85/1.03 tff(742,assumption,(~c2_1(a176)), introduced(assumption)).
% 0.85/1.03 tff(743,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(744,plain,
% 0.85/1.03 (((~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)) | c0_1(a125) | (~c2_1(a125)) | (~c1_1(a125)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(745,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)) | c0_1(a125) | (~c2_1(a125)) | (~c1_1(a125)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[744])).
% 0.85/1.03 tff(746,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)) | c0_1(a125) | (~c2_1(a125)) | (~c1_1(a125)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[745, 743])).
% 0.85/1.03 tff(747,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)) | c0_1(a125) | (~c2_1(a125)) | (~c1_1(a125)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(748,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.85/1.03 tff(749,plain,
% 0.85/1.03 (c1_1(a176) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[748, 117, 742, 407, 409, 406, 741])).
% 0.85/1.03 tff(750,plain,
% 0.85/1.03 (~c0_1(a176)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[749, 728, 440, 730, 731])).
% 0.85/1.03 tff(751,plain,
% 0.85/1.03 (~hskp22),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[675, 750])).
% 0.85/1.03 tff(752,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[653, 117, 751, 728, 730, 595, 729])).
% 0.85/1.03 tff(753,plain,((~hskp2) | hskp17 | hskp0 | c0_1(a125) | (~c3_1(a132)) | c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(754,plain,
% 0.85/1.03 (~hskp2),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[753, 662, 567, 406, 428, 450, 668, 407, 409])).
% 0.85/1.03 tff(755,plain,
% 0.85/1.03 (hskp2 | hskp1),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[621, 117, 81, 75, 69, 615])).
% 0.85/1.03 tff(756,plain,
% 0.85/1.03 (hskp1),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[755, 754])).
% 0.85/1.03 tff(757,plain,
% 0.85/1.03 (c2_1(a124)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[584, 756])).
% 0.85/1.03 tff(758,plain,
% 0.85/1.03 (c1_1(a124)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[576, 756])).
% 0.85/1.03 tff(759,plain,
% 0.85/1.03 (((~hskp13) | c3_1(a143)) <=> ((~hskp13) | c3_1(a143))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(760,axiom,((~hskp13) | c3_1(a143)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.85/1.03 tff(761,plain,
% 0.85/1.03 ((~hskp13) | c3_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.85/1.03 tff(762,plain,
% 0.85/1.03 ((~hskp13) | c3_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[761, 759])).
% 0.85/1.03 tff(763,plain,
% 0.85/1.03 ((~hskp13) | c3_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[762, 759])).
% 0.85/1.03 tff(764,plain,
% 0.85/1.03 ((~hskp13) | c3_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[763, 759])).
% 0.85/1.03 tff(765,plain,
% 0.85/1.03 ((~hskp13) | c3_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[764, 759])).
% 0.85/1.03 tff(766,plain,
% 0.85/1.03 (c3_1(a143)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[765, 720])).
% 0.85/1.03 tff(767,plain,
% 0.85/1.03 (((~hskp13) | c2_1(a143)) <=> ((~hskp13) | c2_1(a143))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(768,axiom,((~hskp13) | c2_1(a143)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.85/1.03 tff(769,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.85/1.03 tff(770,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[769, 767])).
% 0.85/1.03 tff(771,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[770, 767])).
% 0.85/1.03 tff(772,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[771, 767])).
% 0.85/1.03 tff(773,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a143)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[772, 767])).
% 0.85/1.03 tff(774,plain,
% 0.85/1.03 (c2_1(a143)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[773, 720])).
% 0.85/1.03 tff(775,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(776,plain,
% 0.85/1.03 (((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143))) <=> (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(777,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[776])).
% 0.85/1.03 tff(778,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[777, 775])).
% 0.85/1.03 tff(779,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(780,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.85/1.03 tff(781,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[780, 117, 685, 684, 774, 766, 758, 757, 726, 408, 702, 692])).
% 0.85/1.04 tff(782,plain,(c2_1(a132) | c3_1(a124) | c0_1(a125) | c0_1(a132) | hskp30 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(783,plain,
% 0.85/1.04 (c2_1(a132)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[782, 407, 406, 408, 54, 33])).
% 0.85/1.04 tff(784,assumption,(c2_1(a132)), introduced(assumption)).
% 0.85/1.04 tff(785,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(786,plain,
% 0.85/1.04 ((hskp27 | (~ndr1_0) | c0_1(a132) | c3_1(a132) | (~c2_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(787,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a132) | c3_1(a132) | (~c2_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[786])).
% 0.85/1.04 tff(788,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a132) | c3_1(a132) | (~c2_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.85/1.04 inference(transitivity,[status(thm)],[787, 785])).
% 0.85/1.04 tff(789,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a132) | c3_1(a132) | (~c2_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(790,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.85/1.04 tff(791,plain,
% 0.85/1.04 (hskp27 | c3_1(a132) | (~c2_1(a132))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[790, 117, 407, 81, 75, 69, 519])).
% 0.85/1.04 tff(792,plain,
% 0.85/1.04 (hskp27),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[791, 410, 784])).
% 0.85/1.04 tff(793,plain,
% 0.85/1.04 (c3_1(a122)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[534, 792])).
% 0.85/1.04 tff(794,plain,
% 0.85/1.04 (c2_1(a122)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[542, 792])).
% 0.85/1.04 tff(795,plain,
% 0.85/1.04 (c0_1(a122)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[550, 792])).
% 0.85/1.04 tff(796,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(797,plain,
% 0.85/1.04 (((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a132) | (~c2_1(a132)) | (~c1_1(a132)) | c0_1(a132) | c3_1(a132) | (~c1_1(a132))) <=> (c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(798,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a132) | (~c2_1(a132)) | (~c1_1(a132)) | c0_1(a132) | c3_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[797])).
% 0.85/1.04 tff(799,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a132) | (~c2_1(a132)) | (~c1_1(a132)) | c0_1(a132) | c3_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[798, 796])).
% 0.85/1.04 tff(800,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a132) | (~c2_1(a132)) | (~c1_1(a132)) | c0_1(a132) | c3_1(a132) | (~c1_1(a132)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(801,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.85/1.04 tff(802,plain,
% 0.85/1.04 (~c1_1(a132)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[801, 117, 795, 794, 793, 410, 407, 784, 460])).
% 0.85/1.04 tff(803,plain,
% 0.85/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_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)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(804,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_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)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[803])).
% 0.85/1.04 tff(805,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_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)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(806,plain,
% 0.85/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(807,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[806])).
% 0.85/1.04 tff(808,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 0.85/1.04 tff(809,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.85/1.04 tff(810,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[809, 805])).
% 0.85/1.04 tff(811,plain,(
% 0.85/1.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.85/1.04 inference(skolemize,[status(sab)],[810])).
% 0.85/1.04 tff(812,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[811, 804])).
% 0.85/1.04 tff(813,plain,
% 0.85/1.04 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(814,plain,
% 0.85/1.04 ((hskp30 | hskp20 | (~ndr1_0) | c1_1(a132) | c3_1(a132) | (~c2_1(a132))) <=> (hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(815,plain,
% 0.85/1.04 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[814])).
% 0.85/1.04 tff(816,plain,
% 0.85/1.04 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132))),
% 0.85/1.04 inference(transitivity,[status(thm)],[815, 813])).
% 0.85/1.04 tff(817,plain,
% 0.85/1.04 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(818,plain,
% 0.85/1.04 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.85/1.04 tff(819,plain,
% 0.85/1.04 (hskp20 | c3_1(a132) | c1_1(a132)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[818, 54, 117, 784, 481])).
% 0.85/1.04 tff(820,plain,
% 0.85/1.04 (hskp20),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[819, 802, 410])).
% 0.85/1.04 tff(821,plain,
% 0.85/1.04 (~c3_1(a168)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[494, 820])).
% 0.85/1.04 tff(822,plain,
% 0.85/1.04 (~c0_1(a168)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[500, 820])).
% 0.85/1.04 tff(823,plain,
% 0.85/1.04 (c1_1(a168)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[508, 820])).
% 0.85/1.04 tff(824,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(825,plain,
% 0.85/1.04 (((~ndr1_0) | c3_1(a168) | (~c1_1(a168)) | (~c2_1(a168)) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)) | c0_1(a168) | (~c1_1(a168)) | (~c2_1(a168))) <=> (c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(826,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a168) | (~c1_1(a168)) | (~c2_1(a168)) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)) | c0_1(a168) | (~c1_1(a168)) | (~c2_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[825])).
% 0.85/1.04 tff(827,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a168) | (~c1_1(a168)) | (~c2_1(a168)) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)) | c0_1(a168) | (~c1_1(a168)) | (~c2_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[826, 824])).
% 0.85/1.04 tff(828,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a168) | (~c1_1(a168)) | (~c2_1(a168)) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)) | c0_1(a168) | (~c1_1(a168)) | (~c2_1(a168)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(829,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[828, 827])).
% 0.85/1.04 tff(830,plain,
% 0.85/1.04 (~c2_1(a168)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[829, 117, 823, 410, 822, 821, 784, 812, 802])).
% 0.85/1.04 tff(831,plain,
% 0.85/1.04 (((~hskp7) | (~c2_1(a132))) <=> ((~hskp7) | (~c2_1(a132)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(832,plain,
% 0.85/1.04 (((~c2_1(a132)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a132)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(833,axiom,((~c2_1(a132)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.85/1.04 tff(834,plain,
% 0.85/1.04 ((~hskp7) | (~c2_1(a132))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[833, 832])).
% 0.85/1.04 tff(835,plain,
% 0.85/1.04 ((~hskp7) | (~c2_1(a132))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[834, 831])).
% 0.85/1.04 tff(836,plain,
% 0.85/1.04 (~hskp7),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[835, 784])).
% 0.85/1.04 tff(837,plain,
% 0.85/1.04 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(838,plain,
% 0.85/1.04 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a168) | c0_1(a168) | c3_1(a168)) <=> (hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(839,plain,
% 0.85/1.04 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a168) | c0_1(a168) | c3_1(a168))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[838])).
% 0.85/1.04 tff(840,plain,
% 0.85/1.04 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a168) | c0_1(a168) | c3_1(a168))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168))),
% 0.85/1.04 inference(transitivity,[status(thm)],[839, 837])).
% 0.85/1.04 tff(841,plain,
% 0.85/1.04 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a168) | c0_1(a168) | c3_1(a168))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(842,plain,
% 0.85/1.04 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.85/1.04 tff(843,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[842, 117, 33, 836, 822, 821, 91, 830])).
% 0.85/1.04 tff(844,plain,(c3_1(a132) | hskp9 | (~c2_1(a132)) | hskp30 | c0_1(a132)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(845,plain,
% 0.85/1.04 (c3_1(a132)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[844, 783, 33, 54, 407])).
% 0.85/1.04 tff(846,plain,
% 0.85/1.04 (~hskp7),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[835, 783])).
% 0.85/1.04 tff(847,plain,
% 0.85/1.04 (^[U: $i] : refl((hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(848,plain,
% 0.85/1.04 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[847])).
% 0.85/1.04 tff(849,plain,
% 0.85/1.04 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(850,plain,
% 0.85/1.04 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) | hskp7) <=> ((hskp29 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp7))), rewrite(((hskp29 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) | hskp7) <=> (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(851,plain,
% 0.85/1.04 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) | hskp7) <=> ![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[850])).
% 0.85/1.04 tff(852,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.85/1.04 tff(853,plain,
% 0.85/1.04 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.85/1.04 tff(854,plain,
% 0.85/1.04 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[853, 849])).
% 0.85/1.04 tff(855,plain,(
% 0.85/1.04 ![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(skolemize,[status(sab)],[854])).
% 0.85/1.04 tff(856,plain,
% 0.85/1.04 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[855, 848])).
% 0.85/1.04 tff(857,plain,
% 0.85/1.04 (((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(858,plain,
% 0.85/1.04 ((hskp29 | hskp7 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132))) <=> (hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(859,plain,
% 0.85/1.04 (((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[858])).
% 0.85/1.04 tff(860,plain,
% 0.85/1.04 (((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[859, 857])).
% 0.85/1.04 tff(861,plain,
% 0.85/1.04 ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(862,plain,
% 0.85/1.04 ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.85/1.04 tff(863,plain,
% 0.85/1.04 (hskp29 | hskp7 | (~c2_1(a132)) | (~c3_1(a132))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[862, 117, 407, 856])).
% 0.85/1.04 tff(864,plain,
% 0.85/1.04 (hskp29),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[863, 845, 846, 783])).
% 0.85/1.04 tff(865,plain,
% 0.85/1.04 (((~hskp29) | c2_1(a136)) <=> ((~hskp29) | c2_1(a136))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(866,axiom,((~hskp29) | c2_1(a136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.85/1.04 tff(867,plain,
% 0.85/1.04 ((~hskp29) | c2_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.85/1.04 tff(868,plain,
% 0.85/1.04 ((~hskp29) | c2_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[867, 865])).
% 0.85/1.04 tff(869,plain,
% 0.85/1.04 ((~hskp29) | c2_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[868, 865])).
% 0.85/1.04 tff(870,plain,
% 0.85/1.04 ((~hskp29) | c2_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[869, 865])).
% 0.85/1.04 tff(871,plain,
% 0.85/1.04 ((~hskp29) | c2_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[870, 865])).
% 0.85/1.04 tff(872,plain,
% 0.85/1.04 (c2_1(a136)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[871, 864])).
% 0.85/1.04 tff(873,plain,
% 0.85/1.04 (((~hskp29) | c1_1(a136)) <=> ((~hskp29) | c1_1(a136))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(874,axiom,((~hskp29) | c1_1(a136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.85/1.04 tff(875,plain,
% 0.85/1.04 ((~hskp29) | c1_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.85/1.04 tff(876,plain,
% 0.85/1.04 ((~hskp29) | c1_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[875, 873])).
% 0.85/1.04 tff(877,plain,
% 0.85/1.04 ((~hskp29) | c1_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[876, 873])).
% 0.85/1.04 tff(878,plain,
% 0.85/1.04 ((~hskp29) | c1_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[877, 873])).
% 0.85/1.04 tff(879,plain,
% 0.85/1.04 ((~hskp29) | c1_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[878, 873])).
% 0.85/1.04 tff(880,plain,
% 0.85/1.04 (c1_1(a136)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[879, 864])).
% 0.85/1.04 tff(881,plain,
% 0.85/1.04 (((~hskp29) | c0_1(a136)) <=> ((~hskp29) | c0_1(a136))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(882,axiom,((~hskp29) | c0_1(a136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.85/1.04 tff(883,plain,
% 0.85/1.04 ((~hskp29) | c0_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[882, 881])).
% 0.85/1.04 tff(884,plain,
% 0.85/1.04 ((~hskp29) | c0_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[883, 881])).
% 0.85/1.04 tff(885,plain,
% 0.85/1.04 ((~hskp29) | c0_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[884, 881])).
% 0.85/1.04 tff(886,plain,
% 0.85/1.04 ((~hskp29) | c0_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[885, 881])).
% 0.85/1.04 tff(887,plain,
% 0.85/1.04 ((~hskp29) | c0_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[886, 881])).
% 0.85/1.04 tff(888,plain,
% 0.85/1.04 (c0_1(a136)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[887, 864])).
% 0.85/1.04 tff(889,plain,
% 0.85/1.04 (hskp7 | c3_1(a131)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[123, 117, 33, 81, 69, 91])).
% 0.85/1.04 tff(890,plain,
% 0.85/1.04 (c3_1(a131)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[889, 846])).
% 0.85/1.04 tff(891,plain,
% 0.85/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(892,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[891])).
% 0.85/1.04 tff(893,plain,
% 0.85/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(894,plain,
% 0.85/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(895,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[894])).
% 0.85/1.05 tff(896,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 0.85/1.05 tff(897,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.85/1.05 tff(898,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[897, 893])).
% 0.85/1.05 tff(899,plain,(
% 0.85/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.05 inference(skolemize,[status(sab)],[898])).
% 0.85/1.05 tff(900,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[899, 892])).
% 0.85/1.05 tff(901,assumption,(c2_1(a136)), introduced(assumption)).
% 0.85/1.05 tff(902,assumption,(c1_1(a136)), introduced(assumption)).
% 0.85/1.05 tff(903,assumption,(c0_1(a136)), introduced(assumption)).
% 0.85/1.05 tff(904,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(905,plain,
% 0.85/1.05 (((~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(906,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[905])).
% 0.85/1.05 tff(907,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[906, 904])).
% 0.85/1.05 tff(908,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(909,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.85/1.05 tff(910,plain,
% 0.85/1.05 (c3_1(a123)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[909, 117, 903, 902, 901, 464, 126, 92, 463, 900, 127])).
% 0.85/1.05 tff(911,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(912,plain,
% 0.85/1.05 (((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(913,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[912])).
% 0.85/1.05 tff(914,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[913, 911])).
% 0.85/1.05 tff(915,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(916,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[915, 914])).
% 0.85/1.05 tff(917,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[916, 117, 464, 126, 92, 463, 462, 138, 127, 910])).
% 0.85/1.05 tff(918,plain,((~hskp0) | c1_1(a131) | c2_1(a131) | (~c3_1(a131)) | (~c0_1(a136)) | (~c1_1(a136)) | (~c2_1(a136))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(919,plain,
% 0.85/1.05 (~hskp0),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[918, 890, 69, 75, 888, 880, 872])).
% 0.85/1.05 tff(920,plain,
% 0.85/1.05 (^[U: $i] : refl((hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(921,plain,
% 0.85/1.05 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[920])).
% 0.85/1.05 tff(922,plain,
% 0.85/1.05 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(923,plain,
% 0.85/1.05 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp18) <=> ((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18))), rewrite(((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp18) <=> (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(924,plain,
% 0.85/1.05 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp18) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[923])).
% 0.85/1.05 tff(925,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.85/1.05 tff(926,plain,
% 0.85/1.05 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[925, 924])).
% 0.85/1.05 tff(927,plain,
% 0.85/1.05 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[926, 922])).
% 0.85/1.05 tff(928,plain,(
% 0.85/1.05 ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.05 inference(skolemize,[status(sab)],[927])).
% 0.85/1.05 tff(929,plain,
% 0.85/1.05 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[928, 921])).
% 0.85/1.05 tff(930,plain,
% 0.85/1.05 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(931,plain,
% 0.85/1.05 ((hskp18 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132))) <=> (hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(932,plain,
% 0.85/1.05 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[931])).
% 0.85/1.05 tff(933,plain,
% 0.85/1.05 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[932, 930])).
% 0.85/1.05 tff(934,plain,
% 0.85/1.05 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(935,plain,
% 0.85/1.05 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.85/1.05 tff(936,plain,
% 0.85/1.05 (hskp18 | hskp0 | (~c2_1(a132)) | (~c3_1(a132))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[935, 117, 407, 929])).
% 0.85/1.05 tff(937,plain,
% 0.85/1.05 (hskp18),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[936, 919, 783, 845])).
% 0.85/1.05 tff(938,plain,
% 0.85/1.05 (((~hskp18) | (~c1_1(a160))) <=> ((~hskp18) | (~c1_1(a160)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(939,plain,
% 0.85/1.05 (((~c1_1(a160)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a160)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(940,axiom,((~c1_1(a160)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.85/1.05 tff(941,plain,
% 0.85/1.05 ((~hskp18) | (~c1_1(a160))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.85/1.05 tff(942,plain,
% 0.85/1.05 ((~hskp18) | (~c1_1(a160))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[941, 938])).
% 0.85/1.05 tff(943,plain,
% 0.85/1.05 (~c1_1(a160)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[942, 937])).
% 0.85/1.05 tff(944,plain,
% 0.85/1.05 (((~hskp18) | c3_1(a160)) <=> ((~hskp18) | c3_1(a160))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(945,axiom,((~hskp18) | c3_1(a160)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.85/1.05 tff(946,plain,
% 0.85/1.05 ((~hskp18) | c3_1(a160)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.85/1.05 tff(947,plain,
% 0.85/1.05 ((~hskp18) | c3_1(a160)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[946, 944])).
% 0.85/1.05 tff(948,plain,
% 0.85/1.05 ((~hskp18) | c3_1(a160)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[947, 944])).
% 0.85/1.05 tff(949,plain,
% 0.85/1.05 ((~hskp18) | c3_1(a160)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[948, 944])).
% 0.85/1.05 tff(950,plain,
% 0.85/1.05 ((~hskp18) | c3_1(a160)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[949, 944])).
% 0.85/1.05 tff(951,plain,
% 0.85/1.05 (c3_1(a160)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[950, 937])).
% 0.85/1.05 tff(952,plain,
% 0.85/1.05 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(953,plain,
% 0.85/1.05 ((hskp7 | hskp0 | (~ndr1_0) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160))) <=> (hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(954,plain,
% 0.85/1.05 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[953])).
% 0.85/1.05 tff(955,plain,
% 0.85/1.05 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[954, 952])).
% 0.85/1.05 tff(956,plain,
% 0.85/1.05 ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(957,plain,
% 0.85/1.05 ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[956, 955])).
% 0.85/1.05 tff(958,plain,
% 0.85/1.05 (~c0_1(a160)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[957, 117, 846, 919, 951, 943, 170])).
% 0.85/1.05 tff(959,plain,
% 0.85/1.05 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(960,plain,
% 0.85/1.05 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c1_1(a132))) <=> (hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(961,plain,
% 0.85/1.05 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[960])).
% 0.85/1.05 tff(962,plain,
% 0.85/1.05 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[961, 959])).
% 0.85/1.05 tff(963,plain,
% 0.85/1.05 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(964,plain,
% 0.85/1.05 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.85/1.05 tff(965,plain,
% 0.85/1.05 (hskp17 | hskp0 | (~c3_1(a132)) | (~c1_1(a132))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[964, 117, 407, 43])).
% 0.85/1.05 tff(966,plain,
% 0.85/1.05 (~c1_1(a132)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[965, 11, 440, 128])).
% 0.85/1.05 tff(967,plain,
% 0.85/1.05 (hskp18),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[936, 11, 784, 440])).
% 0.85/1.05 tff(968,plain,
% 0.85/1.05 (((~hskp18) | (~c2_1(a160))) <=> ((~hskp18) | (~c2_1(a160)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(969,plain,
% 0.85/1.05 (((~c2_1(a160)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a160)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(970,axiom,((~c2_1(a160)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.85/1.05 tff(971,plain,
% 0.85/1.05 ((~hskp18) | (~c2_1(a160))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.85/1.05 tff(972,plain,
% 0.85/1.05 ((~hskp18) | (~c2_1(a160))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[971, 968])).
% 0.85/1.05 tff(973,plain,
% 0.85/1.05 (~c2_1(a160)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[972, 967])).
% 0.85/1.05 tff(974,plain,
% 0.85/1.05 (~c1_1(a160)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[942, 967])).
% 0.85/1.05 tff(975,plain,
% 0.85/1.05 (c3_1(a160)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[950, 967])).
% 0.85/1.05 tff(976,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(977,plain,
% 0.85/1.05 (((~ndr1_0) | c1_1(a132) | (~c3_1(a132)) | (~c2_1(a132)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(978,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a132) | (~c3_1(a132)) | (~c2_1(a132)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[977])).
% 0.85/1.05 tff(979,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a132) | (~c3_1(a132)) | (~c2_1(a132)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[978, 976])).
% 0.85/1.05 tff(980,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a132) | (~c3_1(a132)) | (~c2_1(a132)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(981,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.85/1.05 tff(982,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[981, 117, 975, 440, 974, 973, 407, 784, 138, 966])).
% 0.85/1.05 tff(983,plain,(hskp0 | (~c3_1(a132)) | c0_1(a132) | (~c2_1(a132)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(984,plain,
% 0.85/1.05 (hskp17),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[983, 919, 407, 783, 845])).
% 0.85/1.05 tff(985,plain,
% 0.85/1.05 (~c2_1(a155)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[358, 984])).
% 0.85/1.05 tff(986,plain,
% 0.85/1.05 (~c0_1(a155)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[364, 984])).
% 0.85/1.05 tff(987,plain,
% 0.85/1.05 (~c2_1(a160)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[972, 937])).
% 0.85/1.05 tff(988,plain,
% 0.85/1.05 (c1_1(a155)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[389, 984])).
% 0.85/1.05 tff(989,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(990,plain,
% 0.85/1.05 (((~ndr1_0) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a160) | c1_1(a160) | c0_1(a160)) <=> (c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(991,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a160) | c1_1(a160) | c0_1(a160))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[990])).
% 0.85/1.05 tff(992,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a160) | c1_1(a160) | c0_1(a160))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160))),
% 0.85/1.05 inference(transitivity,[status(thm)],[991, 989])).
% 0.85/1.05 tff(993,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a160) | c1_1(a160) | c0_1(a160))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(994,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[993, 992])).
% 0.85/1.05 tff(995,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[994, 117, 951, 988, 943, 987, 986, 985, 382, 958])).
% 0.85/1.05 tff(996,plain,(c0_1(a132) | hskp9 | hskp30 | c0_1(a125) | c3_1(a124)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(997,plain,
% 0.85/1.05 (c3_1(a124)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[996, 406, 54, 33, 405])).
% 0.85/1.05 tff(998,plain,
% 0.85/1.05 (((~hskp1) | (~c3_1(a124))) <=> ((~hskp1) | (~c3_1(a124)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(999,plain,
% 0.85/1.05 (((~c3_1(a124)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a124)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1000,axiom,((~c3_1(a124)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.85/1.05 tff(1001,plain,
% 0.85/1.05 ((~hskp1) | (~c3_1(a124))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.85/1.05 tff(1002,plain,
% 0.85/1.05 ((~hskp1) | (~c3_1(a124))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1001, 998])).
% 0.85/1.05 tff(1003,plain,
% 0.85/1.05 (~hskp1),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1002, 997])).
% 0.85/1.05 tff(1004,plain,
% 0.85/1.05 (hskp2),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[755, 1003])).
% 0.85/1.05 tff(1005,plain,
% 0.85/1.05 (c3_1(a132)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[417, 399])).
% 0.85/1.05 tff(1006,plain,
% 0.85/1.05 (~c2_1(a132)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[835, 399])).
% 0.85/1.05 tff(1007,plain,
% 0.85/1.05 (~c1_1(a132)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[434, 117, 1005, 405, 1006, 81, 75, 69, 382])).
% 0.85/1.06 tff(1008,plain,
% 0.85/1.06 (~hskp17),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[449, 1007, 405, 1006, 1005])).
% 0.85/1.06 tff(1009,plain,
% 0.85/1.06 (~hskp0),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[566, 1007, 405, 1006, 1005, 54])).
% 0.85/1.06 tff(1010,plain,
% 0.85/1.06 (c1_1(a125)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[630, 1004])).
% 0.85/1.06 tff(1011,plain,
% 0.85/1.06 (~c3_1(a125)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[637, 117, 1008, 1009, 1010, 406, 43])).
% 0.85/1.06 tff(1012,plain,
% 0.85/1.06 (c2_1(a125)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[646, 1004])).
% 0.85/1.06 tff(1013,plain,
% 0.85/1.06 (hskp22),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[653, 117, 1010, 1012, 595, 1011])).
% 0.85/1.06 tff(1014,plain,
% 0.85/1.06 (~c1_1(a176)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[667, 1013])).
% 0.85/1.06 tff(1015,plain,
% 0.85/1.06 (~c2_1(a176)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[661, 1013])).
% 0.85/1.06 tff(1016,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[753, 1015, 1014, 1006, 1009, 1005, 1008, 406, 405, 1004])).
% 0.85/1.06 tff(1017,plain,(c0_1(a125) | hskp30 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1018,plain,
% 0.85/1.06 (c0_1(a125)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1017, 54, 33])).
% 0.85/1.06 tff(1019,plain,
% 0.85/1.06 (((~hskp2) | (~c0_1(a125))) <=> ((~hskp2) | (~c0_1(a125)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1020,plain,
% 0.85/1.06 (((~c0_1(a125)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a125)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1021,axiom,((~c0_1(a125)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.85/1.06 tff(1022,plain,
% 0.85/1.06 ((~hskp2) | (~c0_1(a125))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 0.85/1.06 tff(1023,plain,
% 0.85/1.06 ((~hskp2) | (~c0_1(a125))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1022, 1019])).
% 0.85/1.06 tff(1024,plain,
% 0.85/1.06 (~hskp2),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1023, 1018])).
% 0.85/1.06 tff(1025,plain,
% 0.85/1.06 (hskp1),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[755, 1024])).
% 0.85/1.06 tff(1026,plain,
% 0.85/1.06 (~c3_1(a124)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1002, 1025])).
% 0.85/1.06 tff(1027,plain,
% 0.85/1.06 (hskp22),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[604, 1025, 1026])).
% 0.85/1.06 tff(1028,plain,
% 0.85/1.06 (~c2_1(a176)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[661, 1027])).
% 0.85/1.06 tff(1029,plain,
% 0.85/1.06 (~c1_1(a176)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[667, 1027])).
% 0.85/1.06 tff(1030,plain,
% 0.85/1.06 (c0_1(a176)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[675, 1027])).
% 0.85/1.06 tff(1031,plain,
% 0.85/1.06 (hskp19),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[682, 117, 1008, 1030, 1029, 1028, 53])).
% 0.85/1.06 tff(1032,plain,
% 0.85/1.06 (c3_1(a164)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[243, 1031])).
% 0.85/1.06 tff(1033,plain,
% 0.85/1.06 (c1_1(a164)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[251, 1031])).
% 0.85/1.06 tff(1034,plain,
% 0.85/1.06 (c0_1(a164)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[691, 117, 1008, 1009, 1033, 1032, 43])).
% 0.85/1.06 tff(1035,plain,
% 0.85/1.06 (~c2_1(a164)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[235, 1031])).
% 0.85/1.06 tff(1036,plain,
% 0.85/1.06 (hskp13),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[719, 117, 1008, 1033, 1032, 1035, 712])).
% 0.85/1.06 tff(1037,plain,
% 0.85/1.06 (~c1_1(a143)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[725, 1036])).
% 0.85/1.06 tff(1038,plain,
% 0.85/1.06 (c2_1(a124)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[584, 1025])).
% 0.85/1.06 tff(1039,plain,
% 0.85/1.06 (c1_1(a124)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[576, 1025])).
% 0.85/1.06 tff(1040,plain,
% 0.85/1.06 (c3_1(a143)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[765, 1036])).
% 0.85/1.06 tff(1041,plain,
% 0.85/1.06 (c2_1(a143)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[773, 1036])).
% 0.85/1.06 tff(1042,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[780, 117, 1033, 1032, 1041, 1040, 1039, 1038, 1037, 1026, 702, 1034])).
% 0.85/1.06 tff(1043,plain,(hskp30 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1044,plain,
% 0.85/1.06 (hskp30),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1043, 33])).
% 0.85/1.06 tff(1045,plain,
% 0.85/1.06 (((~hskp30) | c0_1(a167)) <=> ((~hskp30) | c0_1(a167))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1046,axiom,((~hskp30) | c0_1(a167)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.85/1.06 tff(1047,plain,
% 0.85/1.06 ((~hskp30) | c0_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.85/1.06 tff(1048,plain,
% 0.85/1.06 ((~hskp30) | c0_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1047, 1045])).
% 0.85/1.06 tff(1049,plain,
% 0.85/1.06 ((~hskp30) | c0_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1048, 1045])).
% 0.85/1.06 tff(1050,plain,
% 0.85/1.06 ((~hskp30) | c0_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1049, 1045])).
% 0.85/1.06 tff(1051,plain,
% 0.85/1.06 ((~hskp30) | c0_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1050, 1045])).
% 0.85/1.06 tff(1052,plain,
% 0.85/1.06 (c0_1(a167)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1051, 1044])).
% 0.85/1.06 tff(1053,plain,
% 0.85/1.06 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1054,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1053])).
% 0.85/1.06 tff(1055,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1056,plain,
% 0.85/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_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)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_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)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_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)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1057,plain,
% 0.85/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1056])).
% 0.85/1.06 tff(1058,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.85/1.06 tff(1059,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.85/1.06 tff(1060,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1059, 1055])).
% 0.85/1.06 tff(1061,plain,(
% 0.85/1.06 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[1060])).
% 0.85/1.06 tff(1062,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1061, 1054])).
% 0.85/1.06 tff(1063,plain,
% 0.85/1.06 (^[U: $i] : refl((hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1064,plain,
% 0.85/1.06 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1063])).
% 0.85/1.06 tff(1065,plain,
% 0.85/1.06 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1066,plain,
% 0.85/1.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp6) <=> ((hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp6) <=> (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1067,plain,
% 0.85/1.06 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp6) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1066])).
% 0.85/1.06 tff(1068,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.85/1.06 tff(1069,plain,
% 0.85/1.06 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 0.85/1.06 tff(1070,plain,
% 0.85/1.06 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1069, 1065])).
% 0.85/1.06 tff(1071,plain,(
% 0.85/1.06 ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[1070])).
% 0.85/1.06 tff(1072,plain,
% 0.85/1.06 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1071, 1064])).
% 0.85/1.06 tff(1073,plain,
% 0.85/1.06 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1074,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1073])).
% 0.85/1.06 tff(1075,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1076,plain,
% 0.85/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1077,plain,
% 0.85/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1076])).
% 0.85/1.06 tff(1078,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.85/1.06 tff(1079,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 0.85/1.06 tff(1080,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1079, 1075])).
% 0.85/1.06 tff(1081,plain,(
% 0.85/1.06 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[1080])).
% 0.85/1.06 tff(1082,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1081, 1074])).
% 0.85/1.06 tff(1083,plain,
% 0.85/1.06 (hskp7),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[398, 94, 126, 92, 33])).
% 0.85/1.06 tff(1084,plain,
% 0.85/1.06 (~c2_1(a132)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[835, 1083])).
% 0.85/1.06 tff(1085,plain,
% 0.85/1.06 (~c0_1(a132)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[404, 1083])).
% 0.85/1.06 tff(1086,plain,
% 0.85/1.06 (c3_1(a132)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[417, 1083])).
% 0.85/1.06 tff(1087,plain,
% 0.85/1.06 (~c1_1(a132)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[434, 117, 1086, 1085, 1084, 94, 126, 92, 382])).
% 0.85/1.06 tff(1088,plain,
% 0.85/1.06 (((~hskp30) | c3_1(a167)) <=> ((~hskp30) | c3_1(a167))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1089,axiom,((~hskp30) | c3_1(a167)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.85/1.06 tff(1090,plain,
% 0.85/1.06 ((~hskp30) | c3_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 0.85/1.06 tff(1091,plain,
% 0.85/1.06 ((~hskp30) | c3_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1090, 1088])).
% 0.85/1.06 tff(1092,plain,
% 0.85/1.06 ((~hskp30) | c3_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1091, 1088])).
% 0.85/1.06 tff(1093,plain,
% 0.85/1.06 ((~hskp30) | c3_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1092, 1088])).
% 0.85/1.06 tff(1094,plain,
% 0.85/1.06 ((~hskp30) | c3_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1093, 1088])).
% 0.85/1.06 tff(1095,plain,
% 0.85/1.06 (c3_1(a167)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1094, 1044])).
% 0.85/1.06 tff(1096,plain,
% 0.85/1.06 (((~hskp30) | c1_1(a167)) <=> ((~hskp30) | c1_1(a167))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1097,axiom,((~hskp30) | c1_1(a167)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.85/1.06 tff(1098,plain,
% 0.85/1.06 ((~hskp30) | c1_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 0.85/1.06 tff(1099,plain,
% 0.85/1.06 ((~hskp30) | c1_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1098, 1096])).
% 0.85/1.06 tff(1100,plain,
% 0.85/1.06 ((~hskp30) | c1_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1099, 1096])).
% 0.85/1.06 tff(1101,plain,
% 0.85/1.06 ((~hskp30) | c1_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1100, 1096])).
% 0.85/1.06 tff(1102,plain,
% 0.85/1.06 ((~hskp30) | c1_1(a167)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1101, 1096])).
% 0.85/1.06 tff(1103,plain,
% 0.85/1.06 (c1_1(a167)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1102, 1044])).
% 0.85/1.06 tff(1104,plain,
% 0.85/1.06 (~hskp17),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[449, 1087, 1085, 1084, 1086])).
% 0.85/1.06 tff(1105,assumption,(~hskp2), introduced(assumption)).
% 0.85/1.06 tff(1106,plain,
% 0.85/1.06 (hskp2 | hskp1 | c0_1(a131) | c1_1(a131)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[621, 117, 92, 615])).
% 0.85/1.06 tff(1107,plain,
% 0.85/1.06 (hskp1),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1106, 1105, 94, 126])).
% 0.85/1.06 tff(1108,plain,
% 0.85/1.06 (~c3_1(a124)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1002, 1107])).
% 0.85/1.06 tff(1109,plain,
% 0.85/1.06 (^[U: $i] : refl((hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1110,plain,
% 0.85/1.06 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1109])).
% 0.85/1.06 tff(1111,plain,
% 0.85/1.06 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1112,plain,
% 0.85/1.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp19) <=> ((hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp19) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1113,plain,
% 0.85/1.06 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp19) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1112])).
% 0.85/1.06 tff(1114,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.85/1.06 tff(1115,plain,
% 0.85/1.06 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.85/1.06 tff(1116,plain,
% 0.85/1.06 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1115, 1111])).
% 0.85/1.06 tff(1117,plain,(
% 0.85/1.06 ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[1116])).
% 0.85/1.06 tff(1118,plain,
% 0.85/1.06 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1117, 1110])).
% 0.85/1.06 tff(1119,assumption,(c3_1(a167)), introduced(assumption)).
% 0.85/1.06 tff(1120,assumption,(c1_1(a167)), introduced(assumption)).
% 0.85/1.06 tff(1121,assumption,(c0_1(a167)), introduced(assumption)).
% 0.85/1.06 tff(1122,plain,
% 0.85/1.06 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1123,plain,
% 0.85/1.06 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1124,plain,
% 0.85/1.06 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 0.85/1.06 tff(1125,plain,
% 0.85/1.06 (hskp19 | hskp2),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1124, 117, 1121, 1120, 1119, 1118])).
% 0.85/1.06 tff(1126,plain,
% 0.85/1.06 (hskp19),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1125, 1105])).
% 0.85/1.06 tff(1127,plain,
% 0.85/1.06 (~c2_1(a164)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[235, 1126])).
% 0.85/1.06 tff(1128,plain,
% 0.85/1.06 (c3_1(a164)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[243, 1126])).
% 0.85/1.06 tff(1129,plain,
% 0.85/1.06 (c1_1(a164)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[251, 1126])).
% 0.85/1.06 tff(1130,plain,
% 0.85/1.06 (hskp13),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[719, 117, 128, 1129, 1128, 1127, 712])).
% 0.85/1.06 tff(1131,plain,
% 0.85/1.06 (~c1_1(a143)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[725, 1130])).
% 0.85/1.06 tff(1132,plain,
% 0.85/1.06 (c2_1(a124)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[584, 1107])).
% 0.85/1.06 tff(1133,plain,
% 0.85/1.06 (c1_1(a124)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[576, 1107])).
% 0.85/1.06 tff(1134,plain,
% 0.85/1.06 (c3_1(a143)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[765, 1130])).
% 0.85/1.06 tff(1135,plain,
% 0.85/1.06 (c2_1(a143)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[773, 1130])).
% 0.85/1.06 tff(1136,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1137,plain,
% 0.85/1.06 (((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143))) <=> (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1138,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1137])).
% 0.85/1.06 tff(1139,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1138, 1136])).
% 0.85/1.06 tff(1140,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1141,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.85/1.06 tff(1142,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1141, 117, 1121, 1120, 1119, 1135, 1134, 1133, 1132, 1131, 1108, 702])).
% 0.85/1.06 tff(1143,plain,(hskp2 | (~c0_1(a167)) | (~c1_1(a167)) | (~c3_1(a167)) | hskp17 | c0_1(a131) | c1_1(a131) | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1144,plain,
% 0.85/1.06 (hskp2),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1143, 1104, 1103, 1095, 1052, 94, 126, 92])).
% 0.85/1.06 tff(1145,plain,
% 0.85/1.06 (~c0_1(a125)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1023, 1144])).
% 0.85/1.06 tff(1146,plain,
% 0.85/1.06 (~hskp17),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[449, 436, 407, 409, 440])).
% 0.85/1.06 tff(1147,plain,
% 0.85/1.06 ((~c1_1(a125)) | (~c3_1(a125))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[637, 117, 1146, 11, 406, 43])).
% 0.85/1.06 tff(1148,plain,
% 0.85/1.06 (~c3_1(a125)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1147, 728])).
% 0.85/1.06 tff(1149,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1150,plain,
% 0.85/1.06 (((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a125) | c3_1(a125) | (~c2_1(a125))) <=> (c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1151,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a125) | c3_1(a125) | (~c2_1(a125)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1150])).
% 0.85/1.06 tff(1152,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a125) | c3_1(a125) | (~c2_1(a125)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1151, 1149])).
% 0.85/1.06 tff(1153,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a125) | c3_1(a125) | (~c2_1(a125)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1154,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 0.85/1.06 tff(1155,plain,
% 0.85/1.06 ((~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1154, 117, 1052, 1103, 440, 409, 406, 900, 436])).
% 0.85/1.06 tff(1156,plain,
% 0.85/1.06 (~c2_1(a167)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1155, 730, 1148])).
% 0.85/1.06 tff(1157,plain,
% 0.85/1.06 (^[U: $i] : refl((hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1158,plain,
% 0.85/1.07 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1157])).
% 0.85/1.07 tff(1159,plain,
% 0.85/1.07 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1160,plain,
% 0.85/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp22) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp22) <=> (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1161,plain,
% 0.85/1.07 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp22) <=> ![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1160])).
% 0.85/1.07 tff(1162,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.85/1.07 tff(1163,plain,
% 0.85/1.07 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.85/1.07 tff(1164,plain,
% 0.85/1.07 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1163, 1159])).
% 0.85/1.07 tff(1165,plain,(
% 0.85/1.07 ![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(skolemize,[status(sab)],[1164])).
% 0.85/1.07 tff(1166,plain,
% 0.85/1.07 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1165, 1158])).
% 0.85/1.07 tff(1167,plain,
% 0.85/1.07 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1168,plain,
% 0.85/1.07 ((hskp22 | hskp9 | (~ndr1_0) | c2_1(a167) | (~c1_1(a167)) | (~c0_1(a167))) <=> (hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1169,plain,
% 0.85/1.07 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a167) | (~c1_1(a167)) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1168])).
% 0.85/1.07 tff(1170,plain,
% 0.85/1.07 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a167) | (~c1_1(a167)) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1169, 1167])).
% 0.85/1.07 tff(1171,plain,
% 0.85/1.07 ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a167) | (~c1_1(a167)) | (~c0_1(a167)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1172,plain,
% 0.85/1.07 ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 0.85/1.07 tff(1173,plain,
% 0.85/1.07 (hskp22 | c2_1(a167)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1172, 117, 33, 1052, 1103, 1166])).
% 0.85/1.07 tff(1174,plain,
% 0.85/1.07 (hskp22),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1173, 1156])).
% 0.85/1.07 tff(1175,plain,
% 0.85/1.07 (~c1_1(a176)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[667, 1174])).
% 0.85/1.07 tff(1176,plain,
% 0.85/1.07 (~c2_1(a176)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[661, 1174])).
% 0.85/1.07 tff(1177,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[753, 1176, 1175, 409, 11, 440, 1146, 406, 407, 727])).
% 0.85/1.07 tff(1178,plain,((~hskp2) | c2_1(a132) | hskp0 | (~c3_1(a132)) | c0_1(a125) | c0_1(a132) | hskp9 | c1_1(a132)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1179,plain,
% 0.85/1.07 (hskp0),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1178, 1145, 1144, 1086, 1084, 1085, 33, 1087])).
% 0.85/1.07 tff(1180,plain,
% 0.85/1.07 (~c1_1(a123)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[190, 1179])).
% 0.85/1.07 tff(1181,plain,
% 0.85/1.07 (~c0_1(a123)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[221, 1179])).
% 0.85/1.07 tff(1182,plain,
% 0.85/1.07 (c2_1(a123)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[198, 1179])).
% 0.85/1.07 tff(1183,plain,
% 0.85/1.07 (~c3_1(a123)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[470, 117, 1086, 1182, 1084, 1181, 1180, 138, 1087])).
% 0.85/1.07 tff(1184,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1185,plain,
% 0.85/1.07 (((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1186,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1185])).
% 0.85/1.07 tff(1187,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1186, 1184])).
% 0.85/1.07 tff(1188,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1189,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.85/1.07 tff(1190,plain,
% 0.85/1.07 (~c2_1(a167)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1189, 117, 1052, 1103, 1086, 1182, 1084, 1181, 900, 1087, 1183])).
% 0.85/1.07 tff(1191,plain,
% 0.85/1.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1192,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1191])).
% 0.85/1.07 tff(1193,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1194,plain,
% 0.85/1.07 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1195,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1194])).
% 0.85/1.07 tff(1196,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.85/1.07 tff(1197,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 0.85/1.07 tff(1198,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1197, 1193])).
% 0.85/1.07 tff(1199,plain,(
% 0.85/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.85/1.07 inference(skolemize,[status(sab)],[1198])).
% 0.85/1.07 tff(1200,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1199, 1192])).
% 0.85/1.07 tff(1201,plain,
% 0.85/1.07 (^[U: $i] : refl((hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1202,plain,
% 0.85/1.07 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1201])).
% 0.85/1.07 tff(1203,plain,
% 0.85/1.07 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1204,plain,
% 0.85/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp24) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp24) <=> (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1205,plain,
% 0.85/1.07 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp24) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1204])).
% 0.85/1.07 tff(1206,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.85/1.07 tff(1207,plain,
% 0.85/1.07 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 0.85/1.07 tff(1208,plain,
% 0.85/1.07 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1207, 1203])).
% 0.85/1.07 tff(1209,plain,(
% 0.85/1.07 ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.07 inference(skolemize,[status(sab)],[1208])).
% 0.85/1.07 tff(1210,plain,
% 0.85/1.07 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1209, 1202])).
% 0.85/1.07 tff(1211,plain,
% 0.85/1.07 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1212,plain,
% 0.85/1.07 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167))) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1213,plain,
% 0.85/1.07 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1212])).
% 0.85/1.07 tff(1214,plain,
% 0.85/1.07 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1213, 1211])).
% 0.85/1.07 tff(1215,plain,
% 0.85/1.07 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1216,plain,
% 0.85/1.07 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 0.85/1.07 tff(1217,plain,
% 0.85/1.07 (hskp24 | hskp17 | c2_1(a167)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1216, 117, 1103, 1095, 1210])).
% 0.85/1.07 tff(1218,plain,
% 0.85/1.07 (hskp24),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1217, 1190, 1104])).
% 0.85/1.07 tff(1219,plain,
% 0.85/1.07 (((~hskp24) | (~c3_1(a182))) <=> ((~hskp24) | (~c3_1(a182)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1220,plain,
% 0.85/1.07 (((~c3_1(a182)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a182)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1221,axiom,((~c3_1(a182)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.85/1.07 tff(1222,plain,
% 0.85/1.07 ((~hskp24) | (~c3_1(a182))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 0.85/1.07 tff(1223,plain,
% 0.85/1.07 ((~hskp24) | (~c3_1(a182))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1222, 1219])).
% 0.85/1.07 tff(1224,plain,
% 0.85/1.07 (~c3_1(a182)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1223, 1218])).
% 0.85/1.07 tff(1225,plain,
% 0.85/1.07 (((~hskp24) | (~c2_1(a182))) <=> ((~hskp24) | (~c2_1(a182)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1226,plain,
% 0.85/1.07 (((~c2_1(a182)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a182)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1227,axiom,((~c2_1(a182)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.85/1.07 tff(1228,plain,
% 0.85/1.07 ((~hskp24) | (~c2_1(a182))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.85/1.07 tff(1229,plain,
% 0.85/1.07 ((~hskp24) | (~c2_1(a182))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1228, 1225])).
% 0.85/1.07 tff(1230,plain,
% 0.85/1.07 (~c2_1(a182)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1229, 1218])).
% 0.85/1.07 tff(1231,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1232,plain,
% 0.85/1.07 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132))) <=> (c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1233,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1232])).
% 0.85/1.07 tff(1234,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1233, 1231])).
% 0.85/1.07 tff(1235,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1236,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 0.85/1.07 tff(1237,plain,
% 0.85/1.07 (~c1_1(a182)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1236, 117, 1052, 1095, 1086, 1230, 1224, 1084, 1200, 1087, 1190])).
% 0.85/1.07 tff(1238,plain,
% 0.85/1.07 (((~hskp24) | (~c0_1(a182))) <=> ((~hskp24) | (~c0_1(a182)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1239,plain,
% 0.85/1.07 (((~c0_1(a182)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a182)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1240,axiom,((~c0_1(a182)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.85/1.07 tff(1241,plain,
% 0.85/1.07 ((~hskp24) | (~c0_1(a182))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 0.85/1.07 tff(1242,plain,
% 0.85/1.07 ((~hskp24) | (~c0_1(a182))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1241, 1238])).
% 0.85/1.07 tff(1243,plain,
% 0.85/1.07 (~c0_1(a182)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1242, 1218])).
% 0.85/1.07 tff(1244,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1245,plain,
% 0.85/1.07 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1246,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1245])).
% 0.85/1.07 tff(1247,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1246, 1244])).
% 0.85/1.07 tff(1248,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1249,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.85/1.07 tff(1250,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1249, 117, 1103, 1095, 1243, 1230, 1181, 1180, 216, 1190, 1183, 1237])).
% 0.85/1.07 tff(1251,plain,(c0_1(a131) | hskp9 | c1_1(a131) | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1252,plain,
% 0.85/1.07 (c0_1(a131)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1251, 126, 33, 92])).
% 0.85/1.07 tff(1253,plain,
% 0.85/1.07 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.85/1.08 inference(bind,[status(th)],[])).
% 0.85/1.08 tff(1254,plain,
% 0.85/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.85/1.08 inference(quant_intro,[status(thm)],[1253])).
% 0.85/1.08 tff(1255,plain,
% 0.85/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1256,plain,
% 0.85/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.85/1.08 inference(bind,[status(th)],[])).
% 0.85/1.08 tff(1257,plain,
% 0.85/1.08 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.85/1.08 inference(quant_intro,[status(thm)],[1256])).
% 0.85/1.08 tff(1258,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.85/1.08 tff(1259,plain,
% 0.85/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.85/1.08 tff(1260,plain,
% 0.85/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1259, 1255])).
% 0.85/1.08 tff(1261,plain,(
% 0.85/1.08 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.85/1.08 inference(skolemize,[status(sab)],[1260])).
% 0.85/1.08 tff(1262,plain,
% 0.85/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1261, 1254])).
% 0.85/1.08 tff(1263,plain,
% 0.85/1.08 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1264,plain,
% 0.85/1.08 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131))) <=> (hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1265,plain,
% 0.85/1.08 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1264])).
% 0.91/1.08 tff(1266,plain,
% 0.91/1.08 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1265, 1263])).
% 0.91/1.08 tff(1267,plain,
% 0.91/1.08 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1268,plain,
% 0.91/1.08 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 0.91/1.08 tff(1269,plain,
% 0.91/1.08 (hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1268, 117, 92, 53])).
% 0.91/1.08 tff(1270,plain,
% 0.91/1.08 (hskp19),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1269, 128, 1252, 126])).
% 0.91/1.08 tff(1271,plain,
% 0.91/1.08 (~c2_1(a164)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[235, 1270])).
% 0.91/1.08 tff(1272,plain,
% 0.91/1.08 (c3_1(a164)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[243, 1270])).
% 0.91/1.08 tff(1273,plain,
% 0.91/1.08 (c1_1(a164)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[251, 1270])).
% 0.91/1.08 tff(1274,plain,
% 0.91/1.08 (hskp13),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[719, 117, 128, 1273, 1272, 1271, 712])).
% 0.91/1.08 tff(1275,plain,
% 0.91/1.08 (~c1_1(a143)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[725, 1274])).
% 0.91/1.08 tff(1276,plain,
% 0.91/1.08 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1277,plain,
% 0.91/1.08 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164))) <=> (hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1278,plain,
% 0.91/1.08 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1277])).
% 0.91/1.08 tff(1279,plain,
% 0.91/1.08 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1278, 1276])).
% 0.91/1.08 tff(1280,plain,
% 0.91/1.08 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1281,plain,
% 0.91/1.08 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.91/1.08 tff(1282,plain,
% 0.91/1.08 (hskp24),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1281, 117, 128, 1273, 1272, 1271, 1210])).
% 0.91/1.08 tff(1283,plain,
% 0.91/1.08 (~c3_1(a182)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1223, 1282])).
% 0.91/1.08 tff(1284,plain,
% 0.91/1.08 (~c2_1(a182)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1229, 1282])).
% 0.91/1.08 tff(1285,plain,
% 0.91/1.08 (~c0_1(a182)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1242, 1282])).
% 0.91/1.08 tff(1286,plain,
% 0.91/1.08 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1287,plain,
% 0.91/1.08 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a182) | c0_1(a182) | c3_1(a182)) <=> (hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1288,plain,
% 0.91/1.08 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1287])).
% 0.91/1.08 tff(1289,plain,
% 0.91/1.08 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1288, 1286])).
% 0.91/1.08 tff(1290,plain,
% 0.91/1.08 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a182) | c0_1(a182) | c3_1(a182))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1291,plain,
% 0.91/1.08 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 0.91/1.08 tff(1292,plain,
% 0.91/1.08 (hskp7),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1291, 117, 33, 1285, 1284, 1283, 91])).
% 0.91/1.08 tff(1293,plain,
% 0.91/1.08 (~c2_1(a132)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[835, 1292])).
% 0.91/1.08 tff(1294,plain,
% 0.91/1.08 (c3_1(a132)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[417, 1292])).
% 0.91/1.08 tff(1295,plain,
% 0.91/1.08 (c3_1(a143)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[765, 1274])).
% 0.91/1.08 tff(1296,plain,
% 0.91/1.08 (~hskp6),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[80, 1252])).
% 0.91/1.08 tff(1297,plain,
% 0.91/1.08 (c2_1(a143)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[773, 1274])).
% 0.91/1.08 tff(1298,assumption,(~c1_1(a143)), introduced(assumption)).
% 0.91/1.08 tff(1299,assumption,(c3_1(a143)), introduced(assumption)).
% 0.91/1.08 tff(1300,assumption,(c2_1(a143)), introduced(assumption)).
% 0.91/1.08 tff(1301,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1302,plain,
% 0.91/1.08 (((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143))) <=> (c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1303,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1302])).
% 0.91/1.08 tff(1304,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1303, 1301])).
% 0.91/1.08 tff(1305,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1306,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 0.91/1.08 tff(1307,plain,
% 0.91/1.08 (c1_1(a132) | c0_1(a143)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1306, 117, 1300, 1299, 440, 1298, 409, 138])).
% 0.91/1.08 tff(1308,plain,
% 0.91/1.08 (c0_1(a143)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1307, 436])).
% 0.91/1.08 tff(1309,plain,
% 0.91/1.08 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.91/1.08 inference(bind,[status(th)],[])).
% 0.91/1.08 tff(1310,plain,
% 0.91/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.91/1.08 inference(quant_intro,[status(thm)],[1309])).
% 0.91/1.08 tff(1311,plain,
% 0.91/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1312,plain,
% 0.91/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.91/1.08 inference(bind,[status(th)],[])).
% 0.91/1.08 tff(1313,plain,
% 0.91/1.08 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.91/1.08 inference(quant_intro,[status(thm)],[1312])).
% 0.91/1.08 tff(1314,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.91/1.08 tff(1315,plain,
% 0.91/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.91/1.08 tff(1316,plain,
% 0.91/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1315, 1311])).
% 0.91/1.08 tff(1317,plain,(
% 0.91/1.08 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.91/1.08 inference(skolemize,[status(sab)],[1316])).
% 0.91/1.08 tff(1318,plain,
% 0.91/1.08 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1317, 1310])).
% 0.91/1.08 tff(1319,assumption,(~hskp6), introduced(assumption)).
% 0.91/1.08 tff(1320,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1321,plain,
% 0.91/1.08 ((hskp6 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132))) <=> (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1322,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1321])).
% 0.91/1.08 tff(1323,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1322, 1320])).
% 0.91/1.08 tff(1324,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1325,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 0.91/1.08 tff(1326,plain,
% 0.91/1.08 (c1_1(a132) | (~c0_1(a143))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1325, 117, 1319, 1300, 1299, 440, 409, 1318])).
% 0.91/1.08 tff(1327,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1326, 1308, 436])).
% 0.91/1.08 tff(1328,plain,(c1_1(a132) | hskp6 | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a132)) | c2_1(a132) | c1_1(a143)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(1329,plain,
% 0.91/1.08 (c1_1(a132)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1328, 1297, 1296, 1295, 1294, 1293, 1275])).
% 0.91/1.08 tff(1330,plain,
% 0.91/1.08 (~c0_1(a132)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[404, 1292])).
% 0.91/1.08 tff(1331,plain,
% 0.91/1.08 (hskp0 | (~c1_1(a132))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[964, 117, 128, 1294, 1330, 43])).
% 0.91/1.08 tff(1332,plain,
% 0.91/1.08 (hskp0),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1331, 1329])).
% 0.91/1.08 tff(1333,plain,
% 0.91/1.08 (~c1_1(a123)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[190, 1332])).
% 0.91/1.08 tff(1334,plain,
% 0.91/1.08 (~c0_1(a123)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[221, 1332])).
% 0.91/1.08 tff(1335,plain,
% 0.91/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.91/1.08 inference(bind,[status(th)],[])).
% 0.91/1.08 tff(1336,plain,
% 0.91/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.91/1.08 inference(quant_intro,[status(thm)],[1335])).
% 0.91/1.08 tff(1337,plain,
% 0.91/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1338,plain,
% 0.91/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.91/1.08 inference(bind,[status(th)],[])).
% 0.91/1.08 tff(1339,plain,
% 0.91/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.91/1.08 inference(quant_intro,[status(thm)],[1338])).
% 0.91/1.08 tff(1340,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.91/1.08 tff(1341,plain,
% 0.91/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 0.91/1.08 tff(1342,plain,
% 0.91/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1341, 1337])).
% 0.91/1.08 tff(1343,plain,(
% 0.91/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.91/1.08 inference(skolemize,[status(sab)],[1342])).
% 0.91/1.08 tff(1344,plain,
% 0.91/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1343, 1336])).
% 0.91/1.08 tff(1345,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1346,plain,
% 0.91/1.08 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c0_1(a164)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132))) <=> (c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1347,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c0_1(a164)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1346])).
% 0.91/1.08 tff(1348,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c0_1(a164)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1347, 1345])).
% 0.91/1.09 tff(1349,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c0_1(a164)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1350,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 0.91/1.09 tff(1351,plain,
% 0.91/1.09 ((~c1_1(a132)) | (~c0_1(a164))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1350, 117, 1272, 1294, 1271, 1330, 1293, 1344])).
% 0.91/1.09 tff(1352,plain,
% 0.91/1.09 (~c0_1(a164)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1351, 1329])).
% 0.91/1.09 tff(1353,plain,
% 0.91/1.09 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1354,plain,
% 0.91/1.09 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1353])).
% 0.91/1.09 tff(1355,plain,
% 0.91/1.09 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1356,plain,
% 0.91/1.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1357,plain,
% 0.91/1.09 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1356])).
% 0.91/1.09 tff(1358,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.91/1.09 tff(1359,plain,
% 0.91/1.09 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 0.91/1.09 tff(1360,plain,
% 0.91/1.09 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1359, 1355])).
% 0.91/1.09 tff(1361,plain,(
% 0.91/1.09 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.91/1.09 inference(skolemize,[status(sab)],[1360])).
% 0.91/1.09 tff(1362,plain,
% 0.91/1.09 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1361, 1354])).
% 0.91/1.09 tff(1363,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1364,plain,
% 0.91/1.09 ((hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132))) <=> (hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1365,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164)))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1364])).
% 0.91/1.09 tff(1366,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1365, 1363])).
% 0.91/1.09 tff(1367,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1368,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 0.91/1.09 tff(1369,plain,
% 0.91/1.09 (hskp12 | (~c1_1(a132)) | c0_1(a164)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1368, 117, 1272, 1271, 1330, 1293, 1362])).
% 0.91/1.09 tff(1370,plain,
% 0.91/1.09 (hskp12),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1369, 1329, 1352])).
% 0.91/1.09 tff(1371,plain,
% 0.91/1.09 (~c1_1(a142)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[144, 1370])).
% 0.91/1.09 tff(1372,plain,
% 0.91/1.09 (c3_1(a142)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[152, 1370])).
% 0.91/1.09 tff(1373,plain,
% 0.91/1.09 (c0_1(a142)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[177, 1370])).
% 0.91/1.09 tff(1374,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1375,plain,
% 0.91/1.09 ((hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1376,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1375])).
% 0.91/1.09 tff(1377,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1376, 1374])).
% 0.91/1.09 tff(1378,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1379,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.91/1.09 tff(1380,plain,
% 0.91/1.09 (~c3_1(a123)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1379, 117, 1296, 1373, 1372, 1371, 1334, 1333, 1262])).
% 0.91/1.09 tff(1381,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1382,plain,
% 0.91/1.09 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1383,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182)))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1382])).
% 0.91/1.09 tff(1384,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1383, 1381])).
% 0.91/1.09 tff(1385,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1386,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 0.91/1.09 tff(1387,plain,
% 0.91/1.09 ((~c1_1(a132)) | c1_1(a182)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1386, 117, 1294, 1285, 1284, 1330, 1293, 382])).
% 0.91/1.09 tff(1388,plain,
% 0.91/1.09 (c1_1(a182)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1387, 1329])).
% 0.91/1.09 tff(1389,plain,
% 0.91/1.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1390,plain,
% 0.91/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1389])).
% 0.91/1.09 tff(1391,plain,
% 0.91/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1392,plain,
% 0.91/1.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1393,plain,
% 0.91/1.09 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1392])).
% 0.91/1.09 tff(1394,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.91/1.09 tff(1395,plain,
% 0.91/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 0.91/1.09 tff(1396,plain,
% 0.91/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1395, 1391])).
% 0.91/1.09 tff(1397,plain,(
% 0.91/1.09 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.91/1.09 inference(skolemize,[status(sab)],[1396])).
% 0.91/1.09 tff(1398,plain,
% 0.91/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1397, 1390])).
% 0.91/1.09 tff(1399,plain,
% 0.91/1.09 (c2_1(a123)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[198, 1332])).
% 0.91/1.09 tff(1400,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1401,plain,
% 0.91/1.09 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1402,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1401])).
% 0.91/1.09 tff(1403,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1402, 1400])).
% 0.91/1.09 tff(1404,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1405,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.91/1.09 tff(1406,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1405, 117, 1273, 1272, 1399, 1284, 1283, 1271, 1334, 1398, 1388, 1380])).
% 0.91/1.09 tff(1407,plain,(hskp17 | hskp9 | c1_1(a131) | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(1408,plain,
% 0.91/1.09 (hskp17),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1407, 126, 33, 92])).
% 0.91/1.09 tff(1409,plain,
% 0.91/1.09 (~c2_1(a155)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[358, 1408])).
% 0.91/1.09 tff(1410,plain,
% 0.91/1.09 (~c0_1(a155)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[364, 1408])).
% 0.91/1.09 tff(1411,plain,
% 0.91/1.09 (c1_1(a155)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[389, 1408])).
% 0.91/1.09 tff(1412,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1413,plain,
% 0.91/1.09 ((hskp13 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1414,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1413])).
% 0.91/1.09 tff(1415,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1414, 1412])).
% 0.91/1.09 tff(1416,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1417,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.91/1.09 tff(1418,plain,
% 0.91/1.09 (hskp13),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1417, 117, 1411, 1410, 1409, 1252, 126, 92, 1082])).
% 0.91/1.09 tff(1419,plain,
% 0.91/1.09 (~c1_1(a143)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[725, 1418])).
% 0.91/1.09 tff(1420,assumption,(~c2_1(a155)), introduced(assumption)).
% 0.91/1.09 tff(1421,assumption,(~c0_1(a155)), introduced(assumption)).
% 0.91/1.09 tff(1422,plain,
% 0.91/1.09 (hskp7 | c3_1(a155)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[371, 117, 33, 1421, 1420, 91])).
% 0.91/1.09 tff(1423,plain,
% 0.91/1.09 (c3_1(a155)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1422, 93])).
% 0.91/1.09 tff(1424,assumption,(c1_1(a155)), introduced(assumption)).
% 0.91/1.09 tff(1425,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1426,plain,
% 0.91/1.09 ((hskp12 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1427,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1426])).
% 0.91/1.09 tff(1428,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1427, 1425])).
% 0.91/1.09 tff(1429,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1430,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1429, 1428])).
% 0.91/1.09 tff(1431,plain,
% 0.91/1.09 (hskp12 | (~c3_1(a155))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1430, 117, 1424, 1421, 1420, 1362])).
% 0.91/1.09 tff(1432,plain,
% 0.91/1.09 (hskp12),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1431, 1423])).
% 0.91/1.09 tff(1433,plain,
% 0.91/1.09 (~c1_1(a142)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[144, 1432])).
% 0.91/1.09 tff(1434,plain,
% 0.91/1.09 (c3_1(a142)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[152, 1432])).
% 0.91/1.09 tff(1435,plain,
% 0.91/1.09 (c0_1(a142)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[177, 1432])).
% 0.91/1.09 tff(1436,plain,
% 0.91/1.09 (hskp0),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[184, 117, 93, 1435, 1434, 1433, 170])).
% 0.91/1.09 tff(1437,plain,
% 0.91/1.09 (~c1_1(a123)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[190, 1436])).
% 0.91/1.09 tff(1438,plain,
% 0.91/1.09 (~c0_1(a123)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[221, 1436])).
% 0.91/1.09 tff(1439,plain,
% 0.91/1.09 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1440,plain,
% 0.91/1.09 ((hskp21 | hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142))) <=> (hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1441,plain,
% 0.91/1.09 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1440])).
% 0.91/1.09 tff(1442,plain,
% 0.91/1.09 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1441, 1439])).
% 0.91/1.09 tff(1443,plain,
% 0.91/1.09 ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1444,plain,
% 0.91/1.09 ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 0.91/1.10 tff(1445,plain,
% 0.91/1.10 (hskp21),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1444, 117, 1319, 1435, 1434, 1433, 1072])).
% 0.91/1.10 tff(1446,plain,
% 0.91/1.10 (((~hskp21) | (~c1_1(a170))) <=> ((~hskp21) | (~c1_1(a170)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1447,plain,
% 0.91/1.10 (((~c1_1(a170)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a170)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1448,axiom,((~c1_1(a170)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.91/1.10 tff(1449,plain,
% 0.91/1.10 ((~hskp21) | (~c1_1(a170))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 0.91/1.10 tff(1450,plain,
% 0.91/1.10 ((~hskp21) | (~c1_1(a170))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1449, 1446])).
% 0.91/1.10 tff(1451,plain,
% 0.91/1.10 (~c1_1(a170)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1450, 1445])).
% 0.91/1.10 tff(1452,plain,
% 0.91/1.10 (c2_1(a123)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[198, 1436])).
% 0.91/1.10 tff(1453,plain,
% 0.91/1.10 (((~hskp21) | c2_1(a170)) <=> ((~hskp21) | c2_1(a170))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1454,axiom,((~hskp21) | c2_1(a170)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.91/1.10 tff(1455,plain,
% 0.91/1.10 ((~hskp21) | c2_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 0.91/1.10 tff(1456,plain,
% 0.91/1.10 ((~hskp21) | c2_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1455, 1453])).
% 0.91/1.10 tff(1457,plain,
% 0.91/1.10 ((~hskp21) | c2_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1456, 1453])).
% 0.91/1.10 tff(1458,plain,
% 0.91/1.10 ((~hskp21) | c2_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1457, 1453])).
% 0.91/1.10 tff(1459,plain,
% 0.91/1.10 ((~hskp21) | c2_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1458, 1453])).
% 0.91/1.10 tff(1460,plain,
% 0.91/1.10 (c2_1(a170)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1459, 1445])).
% 0.91/1.10 tff(1461,plain,
% 0.91/1.10 (((~hskp21) | c0_1(a170)) <=> ((~hskp21) | c0_1(a170))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1462,axiom,((~hskp21) | c0_1(a170)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.91/1.10 tff(1463,plain,
% 0.91/1.10 ((~hskp21) | c0_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.91/1.10 tff(1464,plain,
% 0.91/1.10 ((~hskp21) | c0_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1463, 1461])).
% 0.91/1.10 tff(1465,plain,
% 0.91/1.10 ((~hskp21) | c0_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1464, 1461])).
% 0.91/1.10 tff(1466,plain,
% 0.91/1.10 ((~hskp21) | c0_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1465, 1461])).
% 0.91/1.10 tff(1467,plain,
% 0.91/1.10 ((~hskp21) | c0_1(a170)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1466, 1461])).
% 0.91/1.10 tff(1468,plain,
% 0.91/1.10 (c0_1(a170)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1467, 1445])).
% 0.91/1.10 tff(1469,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1470,plain,
% 0.91/1.10 (((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123))) <=> (c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1471,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1470])).
% 0.91/1.10 tff(1472,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1471, 1469])).
% 0.91/1.10 tff(1473,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1474,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 0.91/1.10 tff(1475,plain,
% 0.91/1.10 (~c2_1(a167)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1474, 117, 1103, 1095, 1468, 1460, 1452, 1451, 1438, 1437, 10])).
% 0.91/1.10 tff(1476,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1477,plain,
% 0.91/1.10 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1478,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1477])).
% 0.91/1.10 tff(1479,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1478, 1476])).
% 0.91/1.10 tff(1480,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1481,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 0.91/1.10 tff(1482,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1481, 117, 1052, 1095, 1424, 1421, 1420, 1344, 1475, 1423])).
% 0.91/1.10 tff(1483,plain,(hskp7 | (~c1_1(a155)) | c0_1(a155) | c2_1(a155) | hskp6 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(1484,plain,
% 0.91/1.10 (hskp7),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1483, 1411, 1410, 1409, 1296, 33])).
% 0.91/1.10 tff(1485,plain,
% 0.91/1.10 (~c2_1(a132)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[835, 1484])).
% 0.91/1.10 tff(1486,plain,
% 0.91/1.10 (c2_1(a143)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[773, 1418])).
% 0.91/1.10 tff(1487,plain,
% 0.91/1.10 (c3_1(a143)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[765, 1418])).
% 0.91/1.10 tff(1488,plain,
% 0.91/1.10 (c3_1(a132)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[417, 1484])).
% 0.91/1.10 tff(1489,plain,
% 0.91/1.10 (c1_1(a132)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1328, 1488, 1296, 1487, 1486, 1485, 1419])).
% 0.91/1.10 tff(1490,plain,
% 0.91/1.10 (~c0_1(a132)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[404, 1484])).
% 0.91/1.10 tff(1491,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1492,plain,
% 0.91/1.10 ((hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132))) <=> (hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1493,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1492])).
% 0.91/1.10 tff(1494,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1493, 1491])).
% 0.91/1.10 tff(1495,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1496,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 0.91/1.10 tff(1497,plain,
% 0.91/1.10 (hskp12),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1496, 117, 1488, 1490, 1485, 1362, 1489])).
% 0.91/1.10 tff(1498,plain,
% 0.91/1.10 (~c1_1(a142)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[144, 1497])).
% 0.91/1.10 tff(1499,plain,
% 0.91/1.10 (c3_1(a142)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[152, 1497])).
% 0.91/1.10 tff(1500,plain,
% 0.91/1.10 (c0_1(a142)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[177, 1497])).
% 0.91/1.10 tff(1501,plain,
% 0.91/1.10 (hskp21),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1444, 117, 1296, 1500, 1499, 1498, 1072])).
% 0.91/1.10 tff(1502,plain,
% 0.91/1.10 (~c1_1(a170)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1450, 1501])).
% 0.91/1.10 tff(1503,plain,
% 0.91/1.10 (c2_1(a170)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1459, 1501])).
% 0.91/1.10 tff(1504,plain,
% 0.91/1.10 (c0_1(a170)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1467, 1501])).
% 0.91/1.10 tff(1505,assumption,(c2_1(a167)), introduced(assumption)).
% 0.91/1.10 tff(1506,plain,
% 0.91/1.10 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(1507,plain,
% 0.91/1.10 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[1506])).
% 0.91/1.10 tff(1508,plain,
% 0.91/1.10 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1509,plain,
% 0.91/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp9))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp8) <=> ((hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp8))), rewrite(((hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp8) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp8) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(1510,plain,
% 0.91/1.10 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp8) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[1509])).
% 0.91/1.10 tff(1511,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.91/1.10 tff(1512,plain,
% 0.91/1.10 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 0.91/1.10 tff(1513,plain,
% 0.91/1.10 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1512, 1508])).
% 0.91/1.10 tff(1514,plain,(
% 0.91/1.10 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.10 inference(skolemize,[status(sab)],[1513])).
% 0.91/1.10 tff(1515,plain,
% 0.91/1.10 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1514, 1507])).
% 0.91/1.10 tff(1516,plain,
% 0.91/1.10 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp9 | hskp8 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1517,plain,
% 0.91/1.10 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1518,plain,
% 0.91/1.10 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp9 | hskp8 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 0.91/1.10 tff(1519,plain,
% 0.91/1.10 (hskp8 | (~c2_1(a167))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1518, 117, 33, 1103, 1095, 1515])).
% 0.91/1.10 tff(1520,plain,
% 0.91/1.10 (hskp8),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1519, 1505])).
% 0.91/1.10 tff(1521,plain,
% 0.91/1.10 (((~hskp8) | (~c3_1(a134))) <=> ((~hskp8) | (~c3_1(a134)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1522,plain,
% 0.91/1.10 (((~c3_1(a134)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a134)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1523,axiom,((~c3_1(a134)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.91/1.10 tff(1524,plain,
% 0.91/1.10 ((~hskp8) | (~c3_1(a134))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.91/1.10 tff(1525,plain,
% 0.91/1.10 ((~hskp8) | (~c3_1(a134))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1524, 1521])).
% 0.91/1.10 tff(1526,plain,
% 0.91/1.10 (~c3_1(a134)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1525, 1520])).
% 0.91/1.10 tff(1527,plain,
% 0.91/1.10 (((~hskp8) | (~c0_1(a134))) <=> ((~hskp8) | (~c0_1(a134)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1528,plain,
% 0.91/1.10 (((~c0_1(a134)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a134)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1529,axiom,((~c0_1(a134)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.91/1.10 tff(1530,plain,
% 0.91/1.10 ((~hskp8) | (~c0_1(a134))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 0.91/1.10 tff(1531,plain,
% 0.91/1.10 ((~hskp8) | (~c0_1(a134))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1530, 1527])).
% 0.91/1.10 tff(1532,plain,
% 0.91/1.10 (~c0_1(a134)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1531, 1520])).
% 0.91/1.10 tff(1533,plain,
% 0.91/1.10 (((~hskp8) | c2_1(a134)) <=> ((~hskp8) | c2_1(a134))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1534,axiom,((~hskp8) | c2_1(a134)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.91/1.10 tff(1535,plain,
% 0.91/1.10 ((~hskp8) | c2_1(a134)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 0.91/1.10 tff(1536,plain,
% 0.91/1.10 ((~hskp8) | c2_1(a134)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1535, 1533])).
% 0.91/1.10 tff(1537,plain,
% 0.91/1.10 ((~hskp8) | c2_1(a134)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1536, 1533])).
% 0.91/1.10 tff(1538,plain,
% 0.91/1.10 ((~hskp8) | c2_1(a134)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1537, 1533])).
% 0.91/1.10 tff(1539,plain,
% 0.91/1.10 ((~hskp8) | c2_1(a134)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1538, 1533])).
% 0.91/1.10 tff(1540,plain,
% 0.91/1.10 (c2_1(a134)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1539, 1520])).
% 0.91/1.10 tff(1541,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1542,plain,
% 0.91/1.10 (((~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a134) | (~c2_1(a134)) | (~c1_1(a134)) | c0_1(a134) | c3_1(a134) | (~c1_1(a134))) <=> (c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1543,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a134) | (~c2_1(a134)) | (~c1_1(a134)) | c0_1(a134) | c3_1(a134) | (~c1_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1542])).
% 0.91/1.10 tff(1544,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a134) | (~c2_1(a134)) | (~c1_1(a134)) | c0_1(a134) | c3_1(a134) | (~c1_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1543, 1541])).
% 0.91/1.10 tff(1545,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a134) | (~c2_1(a134)) | (~c1_1(a134)) | c0_1(a134) | c3_1(a134) | (~c1_1(a134)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1546,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.91/1.10 tff(1547,plain,
% 0.91/1.10 (~c1_1(a134)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1546, 117, 1052, 1095, 1540, 1532, 1526, 460, 1505])).
% 0.91/1.10 tff(1548,assumption,(~c1_1(a170)), introduced(assumption)).
% 0.91/1.10 tff(1549,assumption,(c2_1(a170)), introduced(assumption)).
% 0.91/1.10 tff(1550,assumption,(c0_1(a170)), introduced(assumption)).
% 0.91/1.10 tff(1551,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1552,plain,
% 0.91/1.10 (((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a134) | c0_1(a134) | (~c2_1(a134))) <=> (c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1553,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a134) | c0_1(a134) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1552])).
% 0.91/1.10 tff(1554,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a134) | c0_1(a134) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1553, 1551])).
% 0.91/1.10 tff(1555,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a134) | c0_1(a134) | (~c2_1(a134)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1556,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 0.91/1.10 tff(1557,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1556, 117, 1103, 1095, 1550, 1549, 1540, 1548, 1532, 10, 1505, 1547])).
% 0.91/1.10 tff(1558,plain,((~c2_1(a167)) | (~c0_1(a170)) | (~c2_1(a170)) | c1_1(a170) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(1559,plain,
% 0.91/1.10 (~c2_1(a167)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1558, 1504, 1503, 1502, 33])).
% 0.91/1.10 tff(1560,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1561,plain,
% 0.91/1.10 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1562,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1561])).
% 0.91/1.10 tff(1563,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1562, 1560])).
% 0.91/1.10 tff(1564,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1565,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 0.91/1.11 tff(1566,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1565, 117, 1052, 1095, 1411, 1488, 1410, 1409, 1490, 1485, 1344, 1559])).
% 0.91/1.11 tff(1567,plain,(c1_1(a131) | hskp9 | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(1568,plain,
% 0.91/1.11 (c1_1(a131)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1567, 92, 33])).
% 0.91/1.11 tff(1569,plain,
% 0.91/1.11 (~hskp6),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[74, 1568])).
% 0.91/1.11 tff(1570,plain,
% 0.91/1.11 (hskp7),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1483, 439, 441, 438, 1319, 33])).
% 0.91/1.11 tff(1571,plain,
% 0.91/1.11 (~c2_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[835, 1570])).
% 0.91/1.11 tff(1572,plain,
% 0.91/1.11 (~c0_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[404, 1570])).
% 0.91/1.11 tff(1573,plain,
% 0.91/1.11 (c3_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[417, 1570])).
% 0.91/1.11 tff(1574,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1575,plain,
% 0.91/1.11 ((hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1576,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1575])).
% 0.91/1.11 tff(1577,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1576, 1574])).
% 0.91/1.11 tff(1578,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1579,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 0.91/1.11 tff(1580,plain,
% 0.91/1.11 (hskp12),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1579, 117, 441, 1573, 439, 438, 1572, 1571, 1362])).
% 0.91/1.11 tff(1581,plain,
% 0.91/1.11 (~c1_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[144, 1580])).
% 0.91/1.11 tff(1582,plain,
% 0.91/1.11 (c3_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[152, 1580])).
% 0.91/1.11 tff(1583,plain,
% 0.91/1.11 (c0_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[177, 1580])).
% 0.91/1.11 tff(1584,plain,
% 0.91/1.11 (hskp21),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1444, 117, 1319, 1583, 1582, 1581, 1072])).
% 0.91/1.11 tff(1585,plain,
% 0.91/1.11 (~c1_1(a170)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1450, 1584])).
% 0.91/1.11 tff(1586,plain,
% 0.91/1.11 (c2_1(a170)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1459, 1584])).
% 0.91/1.11 tff(1587,plain,
% 0.91/1.11 (c0_1(a170)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1467, 1584])).
% 0.91/1.11 tff(1588,plain,
% 0.91/1.11 (~c2_1(a167)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1558, 1587, 1586, 1585, 33])).
% 0.91/1.11 tff(1589,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1565, 117, 1052, 1095, 441, 1573, 439, 438, 1572, 1571, 1344, 1588])).
% 0.91/1.11 tff(1590,plain,((~hskp17) | hskp9 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(1591,plain,
% 0.91/1.11 (~hskp17),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1590, 1569, 33])).
% 0.91/1.11 tff(1592,plain,
% 0.91/1.11 (hskp7 | c0_1(a131) | c3_1(a131)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[123, 117, 33, 92, 91])).
% 0.91/1.11 tff(1593,plain,
% 0.91/1.11 (c3_1(a131)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1592, 93, 94])).
% 0.91/1.11 tff(1594,plain,
% 0.91/1.11 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1595,plain,
% 0.91/1.11 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131))) <=> (hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1596,plain,
% 0.91/1.11 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1595])).
% 0.91/1.11 tff(1597,plain,
% 0.91/1.11 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1596, 1594])).
% 0.91/1.11 tff(1598,plain,
% 0.91/1.11 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1599,plain,
% 0.91/1.11 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 0.91/1.11 tff(1600,plain,
% 0.91/1.11 (hskp24 | hskp17 | (~c1_1(a131)) | (~c3_1(a131))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1599, 117, 92, 1210])).
% 0.91/1.11 tff(1601,plain,
% 0.91/1.11 (hskp24),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1600, 1593, 1568, 128])).
% 0.91/1.11 tff(1602,plain,
% 0.91/1.11 (~c3_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1223, 1601])).
% 0.91/1.11 tff(1603,plain,
% 0.91/1.11 (~c2_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1229, 1601])).
% 0.91/1.11 tff(1604,plain,
% 0.91/1.11 (~c0_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1242, 1601])).
% 0.91/1.11 tff(1605,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1291, 117, 33, 93, 1604, 1603, 1602, 91])).
% 0.91/1.11 tff(1606,plain,(hskp7 | hskp9 | hskp17 | c2_1(a131) | c0_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(1607,plain,
% 0.91/1.11 (hskp7),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1606, 128, 33, 92, 94])).
% 0.91/1.11 tff(1608,plain,
% 0.91/1.11 (~c2_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[835, 1607])).
% 0.91/1.11 tff(1609,plain,
% 0.91/1.11 (~c0_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[404, 1607])).
% 0.91/1.11 tff(1610,plain,
% 0.91/1.11 (c3_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[417, 1607])).
% 0.91/1.11 tff(1611,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1612,plain,
% 0.91/1.11 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a131) | c0_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1613,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a131) | c0_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132)))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1612])).
% 0.91/1.11 tff(1614,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a131) | c0_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1613, 1611])).
% 0.91/1.11 tff(1615,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a131) | c0_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1616,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 0.91/1.11 tff(1617,plain,
% 0.91/1.11 (c1_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1616, 117, 1610, 1609, 1608, 94, 1568, 92, 382])).
% 0.91/1.11 tff(1618,plain,
% 0.91/1.11 (hskp0 | (~c1_1(a132))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[964, 117, 128, 1610, 1609, 43])).
% 0.91/1.11 tff(1619,plain,
% 0.91/1.11 (hskp0),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1618, 1617])).
% 0.91/1.11 tff(1620,plain,
% 0.91/1.11 (~c1_1(a123)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[190, 1619])).
% 0.91/1.11 tff(1621,plain,
% 0.91/1.11 (~c0_1(a123)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[221, 1619])).
% 0.91/1.11 tff(1622,plain,
% 0.91/1.11 (hskp12),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1496, 117, 1610, 1609, 1608, 1362, 1617])).
% 0.91/1.11 tff(1623,plain,
% 0.91/1.11 (~c1_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[144, 1622])).
% 0.91/1.11 tff(1624,plain,
% 0.91/1.11 (c3_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[152, 1622])).
% 0.91/1.11 tff(1625,plain,
% 0.91/1.11 (c0_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[177, 1622])).
% 0.91/1.11 tff(1626,plain,
% 0.91/1.11 (~c3_1(a123)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1379, 117, 1569, 1625, 1624, 1623, 1621, 1620, 1262])).
% 0.91/1.11 tff(1627,plain,
% 0.91/1.11 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1628,plain,
% 0.91/1.11 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132))) <=> (hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1629,plain,
% 0.91/1.11 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1628])).
% 0.91/1.11 tff(1630,plain,
% 0.91/1.11 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1629, 1627])).
% 0.91/1.11 tff(1631,plain,
% 0.91/1.11 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1632,plain,
% 0.91/1.11 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 0.91/1.11 tff(1633,plain,
% 0.91/1.11 (hskp24 | (~c1_1(a132))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1632, 117, 128, 1610, 1608, 1210])).
% 0.91/1.11 tff(1634,plain,
% 0.91/1.11 (hskp24),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1633, 1617])).
% 0.91/1.11 tff(1635,plain,
% 0.91/1.11 (~c2_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1229, 1634])).
% 0.91/1.11 tff(1636,plain,
% 0.91/1.11 (~c0_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1242, 1634])).
% 0.91/1.11 tff(1637,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1638,plain,
% 0.91/1.11 (((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1639,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182)))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1638])).
% 0.91/1.11 tff(1640,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1639, 1637])).
% 0.91/1.11 tff(1641,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1642,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 0.91/1.11 tff(1643,plain,
% 0.91/1.11 (c1_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1642, 117, 1610, 1636, 1635, 1608, 1621, 1620, 216, 1617, 1626])).
% 0.91/1.11 tff(1644,plain,
% 0.91/1.11 (~c3_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1223, 1634])).
% 0.91/1.11 tff(1645,plain,
% 0.91/1.11 (c2_1(a123)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[198, 1619])).
% 0.91/1.11 tff(1646,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1647,plain,
% 0.91/1.11 (((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1648,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1647])).
% 0.91/1.11 tff(1649,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1648, 1646])).
% 0.91/1.11 tff(1650,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1651,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.91/1.11 tff(1652,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1651, 117, 1610, 1645, 1635, 1644, 1608, 1621, 1398, 1617, 1626, 1643])).
% 0.91/1.11 tff(1653,plain,(hskp17 | c0_1(a131) | c2_1(a131) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(1654,plain,
% 0.91/1.11 (c0_1(a131)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1653, 1591, 92, 33])).
% 0.91/1.11 tff(1655,plain,
% 0.91/1.11 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1656,plain,
% 0.91/1.11 ((hskp22 | hskp9 | (~ndr1_0) | c2_1(a131) | (~c1_1(a131)) | (~c0_1(a131))) <=> (hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1657,plain,
% 0.91/1.11 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a131) | (~c1_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0)))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1656])).
% 0.91/1.11 tff(1658,plain,
% 0.91/1.11 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a131) | (~c1_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1657, 1655])).
% 0.91/1.11 tff(1659,plain,
% 0.91/1.11 ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a131) | (~c1_1(a131)) | (~c0_1(a131)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1660,plain,
% 0.91/1.11 ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 0.91/1.11 tff(1661,plain,
% 0.91/1.11 (hskp22 | (~c0_1(a131)) | (~c1_1(a131))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1660, 117, 33, 92, 1166])).
% 0.91/1.11 tff(1662,plain,
% 0.91/1.11 (hskp22),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1661, 1654, 1568])).
% 0.91/1.11 tff(1663,plain,
% 0.91/1.11 (~c2_1(a176)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[661, 1662])).
% 0.91/1.11 tff(1664,plain,
% 0.91/1.11 (~c1_1(a176)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[667, 1662])).
% 0.91/1.11 tff(1665,plain,
% 0.91/1.11 (c0_1(a176)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[675, 1662])).
% 0.91/1.11 tff(1666,plain,
% 0.91/1.11 (hskp19),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[682, 117, 1591, 1665, 1664, 1663, 53])).
% 0.91/1.11 tff(1667,plain,
% 0.91/1.11 (~c2_1(a164)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[235, 1666])).
% 0.91/1.11 tff(1668,plain,
% 0.91/1.11 (c3_1(a164)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[243, 1666])).
% 0.91/1.11 tff(1669,plain,
% 0.91/1.11 (c1_1(a164)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[251, 1666])).
% 0.91/1.11 tff(1670,plain,
% 0.91/1.11 (hskp13),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[719, 117, 1591, 1669, 1668, 1667, 712])).
% 0.91/1.11 tff(1671,plain,
% 0.91/1.11 (~c1_1(a143)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[725, 1670])).
% 0.91/1.11 tff(1672,plain,
% 0.91/1.11 (hskp24),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1281, 117, 1591, 1669, 1668, 1667, 1210])).
% 0.91/1.11 tff(1673,plain,
% 0.91/1.11 (~c3_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1223, 1672])).
% 0.91/1.11 tff(1674,plain,
% 0.91/1.11 (~c2_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1229, 1672])).
% 0.91/1.11 tff(1675,plain,
% 0.91/1.11 (~c0_1(a182)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1242, 1672])).
% 0.91/1.11 tff(1676,plain,
% 0.91/1.11 (hskp7),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1291, 117, 33, 1675, 1674, 1673, 91])).
% 0.91/1.11 tff(1677,plain,
% 0.91/1.11 (~c2_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[835, 1676])).
% 0.91/1.11 tff(1678,plain,
% 0.91/1.11 (c2_1(a143)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[773, 1670])).
% 0.91/1.11 tff(1679,plain,
% 0.91/1.11 (c3_1(a143)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[765, 1670])).
% 0.91/1.11 tff(1680,plain,
% 0.91/1.11 (c3_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[417, 1676])).
% 0.91/1.11 tff(1681,plain,
% 0.91/1.11 (c1_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1328, 1680, 1569, 1679, 1678, 1677, 1671])).
% 0.91/1.11 tff(1682,plain,
% 0.91/1.11 (~c0_1(a132)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[404, 1676])).
% 0.91/1.11 tff(1683,plain,
% 0.91/1.11 (~c0_1(a164)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1350, 117, 1668, 1680, 1667, 1682, 1677, 1344, 1681])).
% 0.91/1.11 tff(1684,assumption,(~c0_1(a164)), introduced(assumption)).
% 0.91/1.11 tff(1685,assumption,(~c2_1(a167)), introduced(assumption)).
% 0.91/1.11 tff(1686,assumption,(~c2_1(a164)), introduced(assumption)).
% 0.91/1.11 tff(1687,assumption,(c3_1(a164)), introduced(assumption)).
% 0.91/1.11 tff(1688,assumption,(c1_1(a164)), introduced(assumption)).
% 0.91/1.11 tff(1689,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1690,plain,
% 0.91/1.11 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164))) <=> (c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1691,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1690])).
% 0.91/1.11 tff(1692,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1691, 1689])).
% 0.91/1.11 tff(1693,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1694,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 0.91/1.11 tff(1695,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1694, 117, 1121, 1119, 1688, 1687, 1686, 1344, 1685, 1684])).
% 0.91/1.11 tff(1696,plain,(c2_1(a167) | (~c0_1(a167)) | (~c3_1(a167)) | (~c1_1(a164)) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(1697,plain,
% 0.91/1.11 (c2_1(a167)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1696, 1683, 1095, 1669, 1668, 1667, 1052])).
% 0.91/1.11 tff(1698,plain,
% 0.91/1.11 (hskp0),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[964, 117, 1591, 1680, 1682, 43, 1681])).
% 0.91/1.11 tff(1699,plain,
% 0.91/1.11 (~c1_1(a123)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[190, 1698])).
% 0.91/1.11 tff(1700,plain,
% 0.91/1.11 (~c0_1(a123)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[221, 1698])).
% 0.91/1.11 tff(1701,plain,
% 0.91/1.11 (c2_1(a123)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[198, 1698])).
% 0.91/1.11 tff(1702,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1703,plain,
% 0.91/1.11 (((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a143) | (~c2_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123))) <=> (c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1704,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a143) | (~c2_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1703])).
% 0.91/1.11 tff(1705,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a143) | (~c2_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1704, 1702])).
% 0.91/1.11 tff(1706,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a143) | (~c2_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1707,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 0.91/1.11 tff(1708,plain,
% 0.91/1.11 (~c0_1(a143)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1707, 117, 1103, 1095, 1678, 1701, 1671, 1700, 1699, 10, 1697])).
% 0.91/1.11 tff(1709,plain,
% 0.91/1.11 (hskp12),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1368, 117, 1668, 1667, 1682, 1677, 1362, 1681, 1683])).
% 0.91/1.11 tff(1710,plain,
% 0.91/1.11 (~c1_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[144, 1709])).
% 0.91/1.11 tff(1711,plain,
% 0.91/1.11 (c3_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[152, 1709])).
% 0.91/1.11 tff(1712,plain,
% 0.91/1.11 (c0_1(a142)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[177, 1709])).
% 0.91/1.11 tff(1713,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1714,plain,
% 0.91/1.12 ((hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143))) <=> (hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1715,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143)))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[1714])).
% 0.91/1.12 tff(1716,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.12 inference(transitivity,[status(thm)],[1715, 1713])).
% 0.91/1.12 tff(1717,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(1718,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 0.91/1.12 tff(1719,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1718, 117, 1569, 1679, 1712, 1711, 1671, 1710, 1262, 1708])).
% 0.91/1.12 tff(1720,plain,(c2_1(a131) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(1721,plain,
% 0.91/1.12 (c2_1(a131)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1720, 33])).
% 0.91/1.12 tff(1722,plain,
% 0.91/1.12 (~hskp6),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[68, 1721])).
% 0.91/1.12 tff(1723,plain,
% 0.91/1.12 (~hskp17),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1590, 1722, 33])).
% 0.91/1.12 tff(1724,assumption,(~hskp19), introduced(assumption)).
% 0.91/1.12 tff(1725,assumption,(hskp22), introduced(assumption)).
% 0.91/1.12 tff(1726,plain,
% 0.91/1.12 (~c2_1(a176)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[661, 1725])).
% 0.91/1.12 tff(1727,plain,
% 0.91/1.12 (~c1_1(a176)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[667, 1725])).
% 0.91/1.12 tff(1728,plain,
% 0.91/1.12 (c0_1(a176)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[675, 1725])).
% 0.91/1.12 tff(1729,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[682, 117, 1724, 128, 1728, 1727, 1726, 53])).
% 0.91/1.12 tff(1730,plain,((~hskp22) | hskp19 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(1731,plain,
% 0.91/1.12 (~hskp22),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1730, 1724, 1723])).
% 0.91/1.12 tff(1732,plain,
% 0.91/1.12 (^[U: $i] : refl((hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.91/1.12 inference(bind,[status(th)],[])).
% 0.91/1.12 tff(1733,plain,
% 0.91/1.12 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.91/1.12 inference(quant_intro,[status(thm)],[1732])).
% 0.91/1.12 tff(1734,plain,
% 0.91/1.12 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1735,plain,
% 0.91/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp10) <=> ((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp10) <=> (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.91/1.12 inference(bind,[status(th)],[])).
% 0.91/1.12 tff(1736,plain,
% 0.91/1.12 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp10) <=> ![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.91/1.12 inference(quant_intro,[status(thm)],[1735])).
% 0.91/1.12 tff(1737,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.91/1.12 tff(1738,plain,
% 0.91/1.12 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 0.91/1.12 tff(1739,plain,
% 0.91/1.12 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1738, 1734])).
% 0.91/1.12 tff(1740,plain,(
% 0.91/1.12 ![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.91/1.12 inference(skolemize,[status(sab)],[1739])).
% 0.91/1.12 tff(1741,plain,
% 0.91/1.12 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1740, 1733])).
% 0.91/1.12 tff(1742,plain,
% 0.91/1.12 (((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1743,plain,
% 0.91/1.12 ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(1744,plain,
% 0.91/1.12 ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 0.91/1.12 tff(1745,plain,
% 0.91/1.12 (hskp22 | hskp10),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1744, 117, 1052, 1103, 1095, 1741])).
% 0.91/1.12 tff(1746,plain,
% 0.91/1.12 (hskp10),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1745, 1731])).
% 0.91/1.12 tff(1747,plain,
% 0.91/1.12 (((~hskp10) | (~c3_1(a140))) <=> ((~hskp10) | (~c3_1(a140)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1748,plain,
% 0.91/1.12 (((~c3_1(a140)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a140)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1749,axiom,((~c3_1(a140)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.91/1.12 tff(1750,plain,
% 0.91/1.12 ((~hskp10) | (~c3_1(a140))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 0.91/1.12 tff(1751,plain,
% 0.91/1.12 ((~hskp10) | (~c3_1(a140))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1750, 1747])).
% 0.91/1.12 tff(1752,plain,
% 0.91/1.12 (~c3_1(a140)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1751, 1746])).
% 0.91/1.12 tff(1753,plain,
% 0.91/1.12 (((~hskp10) | (~c2_1(a140))) <=> ((~hskp10) | (~c2_1(a140)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1754,plain,
% 0.91/1.12 (((~c2_1(a140)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a140)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1755,axiom,((~c2_1(a140)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.91/1.12 tff(1756,plain,
% 0.91/1.12 ((~hskp10) | (~c2_1(a140))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 0.91/1.12 tff(1757,plain,
% 0.91/1.12 ((~hskp10) | (~c2_1(a140))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1756, 1753])).
% 0.91/1.12 tff(1758,plain,
% 0.91/1.12 (~c2_1(a140)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1757, 1746])).
% 0.91/1.12 tff(1759,plain,
% 0.91/1.12 (((~hskp10) | c0_1(a140)) <=> ((~hskp10) | c0_1(a140))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1760,axiom,((~hskp10) | c0_1(a140)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.91/1.12 tff(1761,plain,
% 0.91/1.12 ((~hskp10) | c0_1(a140)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 0.91/1.12 tff(1762,plain,
% 0.91/1.12 ((~hskp10) | c0_1(a140)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1761, 1759])).
% 0.91/1.12 tff(1763,plain,
% 0.91/1.12 ((~hskp10) | c0_1(a140)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1762, 1759])).
% 0.91/1.12 tff(1764,plain,
% 0.91/1.12 ((~hskp10) | c0_1(a140)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1763, 1759])).
% 0.91/1.12 tff(1765,plain,
% 0.91/1.12 ((~hskp10) | c0_1(a140)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1764, 1759])).
% 0.91/1.12 tff(1766,plain,
% 0.91/1.12 (c0_1(a140)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1765, 1746])).
% 0.91/1.12 tff(1767,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1768,plain,
% 0.91/1.12 ((hskp9 | (~ndr1_0) | c3_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c2_1(a140) | c3_1(a140) | (~c1_1(a140))) <=> (hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1769,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c2_1(a140) | c3_1(a140) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[1768])).
% 0.91/1.12 tff(1770,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c2_1(a140) | c3_1(a140) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[1769, 1767])).
% 0.91/1.12 tff(1771,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c2_1(a140) | c3_1(a140) | (~c1_1(a140)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(1772,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 0.91/1.12 tff(1773,plain,
% 0.91/1.12 (~c1_1(a140)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1772, 117, 33, 1766, 1758, 1752, 1062])).
% 0.91/1.12 tff(1774,plain,
% 0.91/1.12 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1775,plain,
% 0.91/1.12 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a140) | c1_1(a140) | (~c0_1(a140))) <=> (hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1776,plain,
% 0.91/1.12 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[1775])).
% 0.91/1.12 tff(1777,plain,
% 0.91/1.12 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[1776, 1774])).
% 0.91/1.12 tff(1778,plain,
% 0.91/1.12 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(1779,plain,
% 0.91/1.12 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 0.91/1.12 tff(1780,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1779, 117, 1724, 1723, 1766, 1758, 53, 1773])).
% 0.91/1.12 tff(1781,plain,(hskp19 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(1782,plain,
% 0.91/1.12 (hskp19),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1781, 33])).
% 0.91/1.12 tff(1783,plain,
% 0.91/1.12 (~c2_1(a164)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[235, 1782])).
% 0.91/1.12 tff(1784,plain,
% 0.91/1.12 (c3_1(a164)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[243, 1782])).
% 0.91/1.12 tff(1785,plain,
% 0.91/1.12 (c1_1(a164)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[251, 1782])).
% 0.91/1.12 tff(1786,assumption,(hskp19), introduced(assumption)).
% 0.91/1.12 tff(1787,plain,
% 0.91/1.12 (~c2_1(a164)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[235, 1786])).
% 0.91/1.12 tff(1788,plain,
% 0.91/1.12 (c3_1(a164)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[243, 1786])).
% 0.91/1.12 tff(1789,plain,
% 0.91/1.12 (c1_1(a164)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[251, 1786])).
% 0.91/1.12 tff(1790,assumption,(~hskp24), introduced(assumption)).
% 0.91/1.12 tff(1791,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1281, 117, 1790, 128, 1789, 1788, 1787, 1210])).
% 0.91/1.12 tff(1792,plain,((~hskp19) | hskp24 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(1793,plain,
% 0.91/1.12 (hskp24),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1792, 1782, 1723])).
% 0.91/1.12 tff(1794,assumption,(hskp24), introduced(assumption)).
% 0.91/1.12 tff(1795,plain,
% 0.91/1.12 (~c3_1(a182)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1223, 1794])).
% 0.91/1.12 tff(1796,plain,
% 0.91/1.12 (~c2_1(a182)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1229, 1794])).
% 0.91/1.12 tff(1797,plain,
% 0.91/1.12 (~c0_1(a182)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1242, 1794])).
% 0.91/1.12 tff(1798,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1291, 117, 33, 93, 1797, 1796, 1795, 91])).
% 0.91/1.12 tff(1799,plain,((~hskp24) | hskp9 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(1800,plain,
% 0.91/1.12 (hskp7),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1799, 1793, 33])).
% 0.91/1.12 tff(1801,plain,
% 0.91/1.12 (~c2_1(a132)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[835, 1800])).
% 0.91/1.12 tff(1802,plain,
% 0.91/1.12 (c3_1(a132)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[417, 1800])).
% 0.91/1.12 tff(1803,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1804,plain,
% 0.91/1.12 ((hskp6 | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132))) <=> (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1805,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132)))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[1804])).
% 0.91/1.12 tff(1806,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132))),
% 0.91/1.12 inference(transitivity,[status(thm)],[1805, 1803])).
% 0.91/1.12 tff(1807,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(1808,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 0.91/1.12 tff(1809,plain,
% 0.91/1.12 ((~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1808, 117, 1319, 1121, 1119, 409, 1318])).
% 0.91/1.12 tff(1810,plain,
% 0.91/1.12 (~c2_1(a167)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1809, 436, 440])).
% 0.91/1.12 tff(1811,plain,
% 0.91/1.12 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1812,plain,
% 0.91/1.12 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167))) <=> (hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1813,plain,
% 0.91/1.12 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167)))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[1812])).
% 0.91/1.12 tff(1814,plain,
% 0.91/1.12 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 0.91/1.12 inference(transitivity,[status(thm)],[1813, 1811])).
% 0.91/1.12 tff(1815,plain,
% 0.91/1.12 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(1816,plain,
% 0.91/1.12 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 0.91/1.12 tff(1817,plain,
% 0.91/1.12 (hskp17 | hskp13 | c2_1(a167)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1816, 117, 1120, 1119, 712])).
% 0.91/1.12 tff(1818,plain,
% 0.91/1.12 (hskp13),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1817, 1810, 128])).
% 0.91/1.12 tff(1819,plain,
% 0.91/1.12 (~c1_1(a143)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[725, 1818])).
% 0.91/1.12 tff(1820,plain,
% 0.91/1.12 (c2_1(a143)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[773, 1818])).
% 0.91/1.12 tff(1821,plain,
% 0.91/1.12 (c3_1(a143)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[765, 1818])).
% 0.91/1.12 tff(1822,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1328, 1821, 1820, 1319, 440, 436, 409, 1819])).
% 0.91/1.12 tff(1823,plain,(c1_1(a132) | hskp6 | (~c3_1(a132)) | c2_1(a132) | hskp17 | (~c1_1(a167)) | (~c3_1(a167)) | (~c0_1(a167))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(1824,plain,
% 0.91/1.12 (c1_1(a132)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1823, 1802, 1722, 1801, 1723, 1103, 1095, 1052])).
% 0.91/1.12 tff(1825,plain,
% 0.91/1.12 (~c0_1(a132)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[404, 1800])).
% 0.91/1.12 tff(1826,plain,
% 0.91/1.12 (~c0_1(a164)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1350, 117, 1784, 1802, 1783, 1825, 1801, 1344, 1824])).
% 0.91/1.12 tff(1827,plain,
% 0.91/1.12 (c2_1(a167)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1696, 1826, 1095, 1785, 1784, 1783, 1052])).
% 0.91/1.12 tff(1828,plain,
% 0.91/1.12 (hskp0),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[964, 117, 1723, 1802, 1825, 43, 1824])).
% 0.91/1.12 tff(1829,plain,
% 0.91/1.12 (~c1_1(a123)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[190, 1828])).
% 0.91/1.12 tff(1830,plain,
% 0.91/1.12 (~c0_1(a123)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[221, 1828])).
% 0.91/1.12 tff(1831,plain,
% 0.91/1.12 (hskp13),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[719, 117, 1723, 1785, 1784, 1783, 712])).
% 0.91/1.12 tff(1832,plain,
% 0.91/1.12 (~c1_1(a143)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[725, 1831])).
% 0.91/1.12 tff(1833,plain,
% 0.91/1.12 (c2_1(a123)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[198, 1828])).
% 0.91/1.12 tff(1834,plain,
% 0.91/1.12 (c2_1(a143)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[773, 1831])).
% 0.91/1.12 tff(1835,plain,
% 0.91/1.12 (~c0_1(a143)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1707, 117, 1103, 1095, 1834, 1833, 1832, 1830, 1829, 10, 1827])).
% 0.91/1.12 tff(1836,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1837,plain,
% 0.91/1.12 ((hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164))) <=> (hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1838,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[1837])).
% 0.91/1.12 tff(1839,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[1838, 1836])).
% 0.91/1.12 tff(1840,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(1841,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 0.91/1.12 tff(1842,plain,
% 0.91/1.12 (hskp12),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1841, 117, 1785, 1784, 1783, 1362, 1826])).
% 0.91/1.12 tff(1843,plain,
% 0.91/1.12 (~c1_1(a142)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[144, 1842])).
% 0.91/1.12 tff(1844,plain,
% 0.91/1.12 (c3_1(a142)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[152, 1842])).
% 0.91/1.12 tff(1845,plain,
% 0.91/1.12 (c0_1(a142)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[177, 1842])).
% 0.91/1.12 tff(1846,plain,
% 0.91/1.12 (c3_1(a143)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[765, 1831])).
% 0.91/1.12 tff(1847,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1718, 117, 1722, 1846, 1845, 1844, 1832, 1843, 1262, 1835])).
% 0.91/1.12 tff(1848,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(1849,plain,
% 0.91/1.12 (((~hskp9) | (~c2_1(a138))) <=> ((~hskp9) | (~c2_1(a138)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1850,plain,
% 0.91/1.12 (((~c2_1(a138)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a138)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1851,axiom,((~c2_1(a138)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.91/1.12 tff(1852,plain,
% 0.91/1.12 ((~hskp9) | (~c2_1(a138))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 0.91/1.12 tff(1853,plain,
% 0.91/1.12 ((~hskp9) | (~c2_1(a138))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1852, 1849])).
% 0.91/1.12 tff(1854,plain,
% 0.91/1.12 (~c2_1(a138)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1853, 1848])).
% 0.91/1.12 tff(1855,plain,
% 0.91/1.12 (((~hskp9) | c1_1(a138)) <=> ((~hskp9) | c1_1(a138))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1856,axiom,((~hskp9) | c1_1(a138)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.91/1.12 tff(1857,plain,
% 0.91/1.12 ((~hskp9) | c1_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 0.91/1.12 tff(1858,plain,
% 0.91/1.12 ((~hskp9) | c1_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1857, 1855])).
% 0.91/1.12 tff(1859,plain,
% 0.91/1.12 ((~hskp9) | c1_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1858, 1855])).
% 0.91/1.12 tff(1860,plain,
% 0.91/1.12 ((~hskp9) | c1_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1859, 1855])).
% 0.91/1.12 tff(1861,plain,
% 0.91/1.12 ((~hskp9) | c1_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1860, 1855])).
% 0.91/1.12 tff(1862,plain,
% 0.91/1.12 (c1_1(a138)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1861, 1848])).
% 0.91/1.12 tff(1863,plain,
% 0.91/1.12 (((~hskp9) | c0_1(a138)) <=> ((~hskp9) | c0_1(a138))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1864,axiom,((~hskp9) | c0_1(a138)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.91/1.12 tff(1865,plain,
% 0.91/1.12 ((~hskp9) | c0_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 0.91/1.12 tff(1866,plain,
% 0.91/1.12 ((~hskp9) | c0_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1865, 1863])).
% 0.91/1.12 tff(1867,plain,
% 0.91/1.12 ((~hskp9) | c0_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1866, 1863])).
% 0.91/1.12 tff(1868,plain,
% 0.91/1.12 ((~hskp9) | c0_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1867, 1863])).
% 0.91/1.12 tff(1869,plain,
% 0.91/1.12 ((~hskp9) | c0_1(a138)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[1868, 1863])).
% 0.91/1.12 tff(1870,plain,
% 0.91/1.12 (c0_1(a138)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1869, 1848])).
% 0.91/1.12 tff(1871,plain,
% 0.91/1.12 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1872,plain,
% 0.91/1.12 ((hskp18 | hskp10 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138))) <=> (hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(1873,plain,
% 0.91/1.12 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[1872])).
% 0.91/1.12 tff(1874,plain,
% 0.91/1.12 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[1873, 1871])).
% 0.91/1.12 tff(1875,plain,
% 0.91/1.12 ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(1876,plain,
% 0.91/1.13 ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 0.91/1.13 tff(1877,plain,
% 0.91/1.13 (hskp18 | hskp10),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1876, 117, 1870, 1862, 1854, 32])).
% 0.91/1.13 tff(1878,plain,
% 0.91/1.13 (hskp10),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1877, 22])).
% 0.91/1.13 tff(1879,plain,
% 0.91/1.13 (~c3_1(a140)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1751, 1878])).
% 0.91/1.13 tff(1880,plain,
% 0.91/1.13 (~c2_1(a140)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1757, 1878])).
% 0.91/1.13 tff(1881,plain,
% 0.91/1.13 (^[U: $i] : refl((hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.91/1.13 inference(bind,[status(th)],[])).
% 0.91/1.13 tff(1882,plain,
% 0.91/1.13 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.13 inference(quant_intro,[status(thm)],[1881])).
% 0.91/1.13 tff(1883,plain,
% 0.91/1.13 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1884,plain,
% 0.91/1.13 (^[U: $i] : 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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) | hskp7) <=> ((hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp7))), rewrite(((hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) | hskp7) <=> (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.91/1.13 inference(bind,[status(th)],[])).
% 0.91/1.13 tff(1885,plain,
% 0.91/1.13 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) | hskp7) <=> ![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.13 inference(quant_intro,[status(thm)],[1884])).
% 0.91/1.13 tff(1886,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.91/1.13 tff(1887,plain,
% 0.91/1.13 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 0.91/1.13 tff(1888,plain,
% 0.91/1.13 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1887, 1883])).
% 0.91/1.13 tff(1889,plain,(
% 0.91/1.13 ![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.13 inference(skolemize,[status(sab)],[1888])).
% 0.91/1.13 tff(1890,plain,
% 0.91/1.13 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1889, 1882])).
% 0.91/1.13 tff(1891,plain,
% 0.91/1.13 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.91/1.13 inference(bind,[status(th)],[])).
% 0.91/1.13 tff(1892,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.91/1.13 inference(quant_intro,[status(thm)],[1891])).
% 0.91/1.13 tff(1893,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1894,plain,
% 0.91/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.91/1.13 inference(bind,[status(th)],[])).
% 0.91/1.13 tff(1895,plain,
% 0.91/1.13 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.91/1.13 inference(quant_intro,[status(thm)],[1894])).
% 0.91/1.13 tff(1896,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.91/1.13 tff(1897,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 0.91/1.13 tff(1898,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1897, 1893])).
% 0.91/1.13 tff(1899,plain,(
% 0.91/1.13 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.91/1.13 inference(skolemize,[status(sab)],[1898])).
% 0.91/1.13 tff(1900,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1899, 1892])).
% 0.91/1.13 tff(1901,assumption,(hskp13), introduced(assumption)).
% 0.91/1.13 tff(1902,plain,
% 0.91/1.13 (~c1_1(a143)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[725, 1901])).
% 0.91/1.13 tff(1903,plain,
% 0.91/1.13 (c3_1(a143)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[765, 1901])).
% 0.91/1.13 tff(1904,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1905,plain,
% 0.91/1.13 ((hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143))) <=> (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1906,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[1905])).
% 0.91/1.13 tff(1907,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[1906, 1904])).
% 0.91/1.13 tff(1908,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(1909,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 0.91/1.13 tff(1910,plain,
% 0.91/1.13 (~c0_1(a143)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1909, 117, 93, 1903, 1870, 1862, 1902, 1854, 1900])).
% 0.91/1.13 tff(1911,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1912,plain,
% 0.91/1.13 ((hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143))) <=> (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1913,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143)))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[1912])).
% 0.91/1.13 tff(1914,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143))),
% 0.91/1.13 inference(transitivity,[status(thm)],[1913, 1911])).
% 0.91/1.13 tff(1915,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(1916,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143)),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 0.91/1.13 tff(1917,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1916, 117, 93, 1903, 1870, 1862, 1902, 1854, 344, 1910])).
% 0.91/1.13 tff(1918,plain,((~hskp13) | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(1919,plain,
% 0.91/1.13 (~hskp13),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1918, 93])).
% 0.91/1.13 tff(1920,assumption,(~hskp13), introduced(assumption)).
% 0.91/1.13 tff(1921,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[719, 117, 128, 1920, 1789, 1788, 1787, 712])).
% 0.91/1.13 tff(1922,plain,((~hskp19) | hskp17 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(1923,plain,
% 0.91/1.13 (~hskp19),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1922, 1919, 128])).
% 0.91/1.13 tff(1924,plain,
% 0.91/1.13 ((hskp19 | hskp13 | hskp12) <=> (hskp19 | hskp13 | hskp12)),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1925,plain,
% 0.91/1.13 (((hskp12 | hskp19) | hskp13) <=> (hskp19 | hskp13 | hskp12)),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1926,axiom,((hskp12 | hskp19) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.91/1.13 tff(1927,plain,
% 0.91/1.13 (hskp19 | hskp13 | hskp12),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 0.91/1.13 tff(1928,plain,
% 0.91/1.13 (hskp19 | hskp13 | hskp12),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1927, 1924])).
% 0.91/1.13 tff(1929,plain,
% 0.91/1.13 (hskp19 | hskp13 | hskp12),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1928, 1924])).
% 0.91/1.13 tff(1930,plain,
% 0.91/1.13 (hskp19 | hskp13 | hskp12),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1929, 1924])).
% 0.91/1.13 tff(1931,plain,
% 0.91/1.13 (hskp19 | hskp13 | hskp12),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1930, 1924])).
% 0.91/1.13 tff(1932,plain,
% 0.91/1.13 (hskp12),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1931, 1923, 1919])).
% 0.91/1.13 tff(1933,plain,
% 0.91/1.13 (~c1_1(a142)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[144, 1932])).
% 0.91/1.13 tff(1934,plain,
% 0.91/1.13 (c3_1(a142)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[152, 1932])).
% 0.91/1.13 tff(1935,plain,
% 0.91/1.13 (~hskp22),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1730, 1923, 128])).
% 0.91/1.13 tff(1936,plain,
% 0.91/1.13 (((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142)))) <=> ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1937,plain,
% 0.91/1.13 ((hskp22 | hskp7 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142))) <=> (hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1938,plain,
% 0.91/1.13 (((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)))) <=> ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[1937])).
% 0.91/1.13 tff(1939,plain,
% 0.91/1.13 (((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)))) <=> ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[1938, 1936])).
% 0.91/1.13 tff(1940,plain,
% 0.91/1.13 ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(1941,plain,
% 0.91/1.13 ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 0.91/1.13 tff(1942,plain,
% 0.91/1.13 (~c2_1(a142)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1941, 117, 1935, 93, 1934, 1933, 1890])).
% 0.91/1.13 tff(1943,plain,
% 0.91/1.13 (c0_1(a142)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[177, 1932])).
% 0.91/1.13 tff(1944,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[228, 117, 1923, 128, 1943, 1933, 53, 1942])).
% 0.91/1.13 tff(1945,plain,(hskp7 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(1946,plain,
% 0.91/1.13 (hskp7),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1945, 128])).
% 0.91/1.13 tff(1947,plain,
% 0.91/1.13 (c3_1(a132)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[417, 1946])).
% 0.91/1.13 tff(1948,plain,
% 0.91/1.13 (~c2_1(a132)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[835, 1946])).
% 0.91/1.13 tff(1949,plain,
% 0.91/1.13 (~c0_1(a132)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[404, 1946])).
% 0.91/1.13 tff(1950,assumption,(c1_1(a131)), introduced(assumption)).
% 0.91/1.13 tff(1951,plain,
% 0.91/1.13 (hskp0 | (~c1_1(a132))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[964, 117, 128, 1947, 1949, 43])).
% 0.91/1.13 tff(1952,plain,
% 0.91/1.13 (~c1_1(a132)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1951, 11])).
% 0.91/1.13 tff(1953,plain,
% 0.91/1.13 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.91/1.13 inference(bind,[status(th)],[])).
% 0.91/1.13 tff(1954,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.13 inference(quant_intro,[status(thm)],[1953])).
% 0.91/1.13 tff(1955,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1956,plain,
% 0.91/1.13 (^[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(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.91/1.13 inference(bind,[status(th)],[])).
% 0.91/1.13 tff(1957,plain,
% 0.91/1.13 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.13 inference(quant_intro,[status(thm)],[1956])).
% 0.91/1.13 tff(1958,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.91/1.13 tff(1959,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 0.91/1.13 tff(1960,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1959, 1955])).
% 0.91/1.13 tff(1961,plain,(
% 0.91/1.13 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.13 inference(skolemize,[status(sab)],[1960])).
% 0.91/1.13 tff(1962,plain,
% 0.91/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1961, 1954])).
% 0.91/1.13 tff(1963,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1964,plain,
% 0.91/1.13 ((hskp0 | (~ndr1_0) | c2_1(a131) | c3_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1965,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a131) | c3_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132)))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[1964])).
% 0.91/1.13 tff(1966,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a131) | c3_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132))),
% 0.91/1.13 inference(transitivity,[status(thm)],[1965, 1963])).
% 0.91/1.13 tff(1967,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a131) | c3_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(1968,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132)),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 0.91/1.13 tff(1969,plain,
% 0.91/1.13 (hskp0 | (~c1_1(a131)) | c3_1(a131) | c1_1(a132)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1968, 117, 1949, 1948, 92, 1962])).
% 0.91/1.13 tff(1970,plain,
% 0.91/1.13 (c3_1(a131)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1969, 11, 1950, 1952])).
% 0.91/1.13 tff(1971,plain,
% 0.91/1.13 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1972,plain,
% 0.91/1.13 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131))) <=> (hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1973,plain,
% 0.91/1.13 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[1972])).
% 0.91/1.13 tff(1974,plain,
% 0.91/1.13 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[1973, 1971])).
% 0.91/1.13 tff(1975,plain,
% 0.91/1.13 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(1976,plain,
% 0.91/1.13 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 0.91/1.13 tff(1977,plain,
% 0.91/1.13 (hskp13 | (~c1_1(a131)) | (~c3_1(a131))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1976, 117, 128, 92, 712])).
% 0.91/1.13 tff(1978,plain,
% 0.91/1.13 (hskp13),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1977, 1970, 1950])).
% 0.91/1.13 tff(1979,plain,
% 0.91/1.13 (c2_1(a143)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[773, 1978])).
% 0.91/1.13 tff(1980,plain,
% 0.91/1.13 (~hskp6),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[74, 1950])).
% 0.91/1.13 tff(1981,plain,
% 0.91/1.13 (c3_1(a143)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[765, 1978])).
% 0.91/1.13 tff(1982,plain,
% 0.91/1.13 (~c1_1(a143)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[725, 1978])).
% 0.91/1.13 tff(1983,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1328, 1982, 1981, 1947, 1980, 1952, 1948, 1979])).
% 0.91/1.13 tff(1984,plain,(hskp0 | (~c1_1(a131)) | hskp17 | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(1985,plain,
% 0.91/1.13 (hskp0),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1984, 1950, 128, 92])).
% 0.91/1.13 tff(1986,plain,
% 0.91/1.13 (c2_1(a123)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[198, 1985])).
% 0.91/1.13 tff(1987,plain,
% 0.91/1.13 (~c1_1(a123)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[190, 1985])).
% 0.91/1.13 tff(1988,plain,
% 0.91/1.13 (~c0_1(a123)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[221, 1985])).
% 0.91/1.13 tff(1989,assumption,(c1_1(a132)), introduced(assumption)).
% 0.91/1.13 tff(1990,plain,
% 0.91/1.13 (hskp12 | (~c1_1(a132))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1496, 117, 1947, 1949, 1948, 1362])).
% 0.91/1.13 tff(1991,plain,
% 0.91/1.13 (hskp12),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1990, 1989])).
% 0.91/1.13 tff(1992,plain,
% 0.91/1.13 (~c1_1(a142)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[144, 1991])).
% 0.91/1.13 tff(1993,plain,
% 0.91/1.13 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1994,plain,
% 0.91/1.13 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132))) <=> (hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(1995,plain,
% 0.91/1.13 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[1994])).
% 0.91/1.13 tff(1996,plain,
% 0.91/1.13 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[1995, 1993])).
% 0.91/1.13 tff(1997,plain,
% 0.91/1.13 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(1998,plain,
% 0.91/1.13 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 0.91/1.13 tff(1999,plain,
% 0.91/1.13 (hskp13 | (~c1_1(a132))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1998, 117, 128, 1947, 1948, 712])).
% 0.91/1.13 tff(2000,plain,
% 0.91/1.13 (hskp13),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1999, 1989])).
% 0.91/1.13 tff(2001,plain,
% 0.91/1.13 (~c1_1(a143)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[725, 2000])).
% 0.91/1.13 tff(2002,plain,
% 0.91/1.13 (c3_1(a142)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[152, 1991])).
% 0.91/1.13 tff(2003,plain,
% 0.91/1.13 (c0_1(a142)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[177, 1991])).
% 0.91/1.13 tff(2004,plain,
% 0.91/1.13 (c3_1(a143)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[765, 2000])).
% 0.91/1.14 tff(2005,plain,
% 0.91/1.14 (c0_1(a143)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1718, 117, 1319, 2004, 2003, 2002, 2001, 1992, 1262])).
% 0.91/1.14 tff(2006,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2007,plain,
% 0.91/1.14 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132))) <=> (c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2008,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2007])).
% 0.91/1.14 tff(2009,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2008, 2006])).
% 0.91/1.14 tff(2010,plain,
% 0.91/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2011,plain,
% 0.91/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 0.91/1.14 tff(2012,plain,
% 0.91/1.14 ((~c1_1(a132)) | (~c3_1(a138))),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2011, 117, 1870, 1947, 1854, 1949, 1948, 1344])).
% 0.91/1.14 tff(2013,plain,
% 0.91/1.14 (~c3_1(a138)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2012, 1989])).
% 0.91/1.14 tff(2014,assumption,(~c0_1(a123)), introduced(assumption)).
% 0.91/1.14 tff(2015,assumption,(c2_1(a123)), introduced(assumption)).
% 0.91/1.14 tff(2016,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2017,plain,
% 0.91/1.14 (((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2018,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2017])).
% 0.91/1.14 tff(2019,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2018, 2016])).
% 0.91/1.14 tff(2020,plain,
% 0.91/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2021,plain,
% 0.91/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 0.91/1.14 tff(2022,plain,
% 0.91/1.14 (c3_1(a123) | (~c1_1(a132)) | c3_1(a138)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2021, 117, 1862, 1947, 2015, 1854, 1948, 2014, 1398])).
% 0.91/1.14 tff(2023,plain,
% 0.91/1.14 (c3_1(a123)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2022, 2013, 1989])).
% 0.91/1.14 tff(2024,assumption,(~c1_1(a123)), introduced(assumption)).
% 0.91/1.14 tff(2025,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2026,plain,
% 0.91/1.14 ((hskp6 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2027,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2026])).
% 0.91/1.14 tff(2028,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2027, 2025])).
% 0.91/1.14 tff(2029,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2030,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 0.91/1.14 tff(2031,plain,
% 0.91/1.14 ($false),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2030, 117, 1319, 2004, 2001, 2014, 2024, 1262, 2023, 2005])).
% 0.91/1.14 tff(2032,plain,((~c1_1(a132)) | hskp6 | c0_1(a123) | c1_1(a123) | (~c2_1(a123)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.91/1.14 tff(2033,plain,
% 0.91/1.14 (~c1_1(a132)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2032, 1980, 1988, 1987, 1986, 128])).
% 0.91/1.14 tff(2034,plain,
% 0.91/1.14 (hskp30),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[566, 2033, 1949, 1948, 1947, 1985])).
% 0.91/1.14 tff(2035,plain,
% 0.91/1.14 (c0_1(a167)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1051, 2034])).
% 0.91/1.14 tff(2036,plain,
% 0.91/1.14 (c1_1(a167)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1102, 2034])).
% 0.91/1.14 tff(2037,plain,
% 0.91/1.14 (c3_1(a167)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1094, 2034])).
% 0.91/1.14 tff(2038,plain,
% 0.91/1.14 ($false),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1823, 2037, 2036, 1947, 1948, 128, 1980, 2033, 2035])).
% 0.91/1.14 tff(2039,plain,((~c1_1(a131)) | hskp17 | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.14 tff(2040,plain,
% 0.91/1.14 (~c1_1(a131)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2039, 92, 128])).
% 0.91/1.14 tff(2041,plain,
% 0.91/1.14 (hskp19 | (~c0_1(a131)) | c1_1(a131)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1268, 117, 128, 92, 53])).
% 0.91/1.14 tff(2042,plain,
% 0.91/1.14 (~c0_1(a131)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2041, 126, 1724])).
% 0.91/1.14 tff(2043,plain,
% 0.91/1.14 (c0_1(a131) | c1_1(a131) | (~c1_1(a132))),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[434, 117, 1947, 1949, 1948, 92, 382])).
% 0.91/1.14 tff(2044,plain,
% 0.91/1.14 (~c1_1(a132)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2043, 2042, 126])).
% 0.91/1.14 tff(2045,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2046,plain,
% 0.91/1.14 ((hskp0 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2047,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2046])).
% 0.91/1.14 tff(2048,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2047, 2045])).
% 0.91/1.14 tff(2049,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2050,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 0.91/1.14 tff(2051,plain,
% 0.91/1.14 (hskp0 | c1_1(a132) | c3_1(a138)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2050, 117, 1862, 1854, 1949, 1948, 1962])).
% 0.91/1.14 tff(2052,plain,
% 0.91/1.14 (c3_1(a138)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2051, 11, 2044])).
% 0.91/1.14 tff(2053,plain,
% 0.91/1.14 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2054,plain,
% 0.91/1.14 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138))) <=> (hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2055,plain,
% 0.91/1.14 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2054])).
% 0.91/1.14 tff(2056,plain,
% 0.91/1.14 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2055, 2053])).
% 0.91/1.14 tff(2057,plain,
% 0.91/1.14 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2058,plain,
% 0.91/1.14 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 0.91/1.14 tff(2059,plain,
% 0.91/1.14 (hskp24 | hskp17 | (~c3_1(a138))),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2058, 117, 1862, 1854, 1210])).
% 0.91/1.14 tff(2060,plain,
% 0.91/1.14 (hskp24),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2059, 2052, 128])).
% 0.91/1.14 tff(2061,plain,
% 0.91/1.14 (~c3_1(a182)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1223, 2060])).
% 0.91/1.14 tff(2062,plain,
% 0.91/1.14 (~c2_1(a182)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1229, 2060])).
% 0.91/1.14 tff(2063,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2064,plain,
% 0.91/1.14 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132))) <=> (c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2065,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2064])).
% 0.91/1.14 tff(2066,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2065, 2063])).
% 0.91/1.14 tff(2067,plain,
% 0.91/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2068,plain,
% 0.91/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 0.91/1.14 tff(2069,plain,
% 0.91/1.14 (~c1_1(a182)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2068, 117, 1870, 1947, 2062, 2061, 1854, 1948, 1200, 2044, 2052])).
% 0.91/1.14 tff(2070,plain,
% 0.91/1.14 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.91/1.14 inference(bind,[status(th)],[])).
% 0.91/1.14 tff(2071,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.14 inference(quant_intro,[status(thm)],[2070])).
% 0.91/1.14 tff(2072,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2073,plain,
% 0.91/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_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)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.91/1.14 inference(bind,[status(th)],[])).
% 0.91/1.14 tff(2074,plain,
% 0.91/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.14 inference(quant_intro,[status(thm)],[2073])).
% 0.91/1.14 tff(2075,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.91/1.14 tff(2076,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 0.91/1.14 tff(2077,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2076, 2072])).
% 0.91/1.14 tff(2078,plain,(
% 0.91/1.14 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.14 inference(skolemize,[status(sab)],[2077])).
% 0.91/1.14 tff(2079,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2078, 2071])).
% 0.91/1.14 tff(2080,plain,
% 0.91/1.14 (~hskp22),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1730, 1724, 128])).
% 0.91/1.14 tff(2081,plain,
% 0.91/1.14 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2082,plain,
% 0.91/1.14 ((hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138))) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2083,plain,
% 0.91/1.14 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2082])).
% 0.91/1.14 tff(2084,plain,
% 0.91/1.14 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2083, 2081])).
% 0.91/1.14 tff(2085,plain,
% 0.91/1.14 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2086,plain,
% 0.91/1.14 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 0.91/1.14 tff(2087,plain,
% 0.91/1.14 (hskp19 | hskp2 | (~c3_1(a138))),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2086, 117, 1870, 1862, 1118])).
% 0.91/1.14 tff(2088,plain,
% 0.91/1.14 (hskp2),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2087, 2052, 1724])).
% 0.91/1.14 tff(2089,plain,
% 0.91/1.14 (~c0_1(a125)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1023, 2088])).
% 0.91/1.14 tff(2090,plain,
% 0.91/1.14 (c3_1(a124)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[655, 2089, 128, 2080, 2042, 126, 92, 11])).
% 0.91/1.14 tff(2091,plain,
% 0.91/1.14 (~hskp1),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1002, 2090])).
% 0.91/1.14 tff(2092,plain,
% 0.91/1.14 (^[U: $i] : refl((hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.91/1.14 inference(bind,[status(th)],[])).
% 0.91/1.14 tff(2093,plain,
% 0.91/1.14 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.91/1.14 inference(quant_intro,[status(thm)],[2092])).
% 0.91/1.14 tff(2094,plain,
% 0.91/1.14 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2095,plain,
% 0.91/1.14 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp3) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.91/1.14 inference(bind,[status(th)],[])).
% 0.91/1.14 tff(2096,plain,
% 0.91/1.14 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp3) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.91/1.14 inference(quant_intro,[status(thm)],[2095])).
% 0.91/1.14 tff(2097,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.91/1.14 tff(2098,plain,
% 0.91/1.14 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2097, 2096])).
% 0.91/1.14 tff(2099,plain,
% 0.91/1.14 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2098, 2094])).
% 0.91/1.14 tff(2100,plain,(
% 0.91/1.14 ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.91/1.15 inference(skolemize,[status(sab)],[2099])).
% 0.91/1.15 tff(2101,plain,
% 0.91/1.15 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2100, 2093])).
% 0.91/1.15 tff(2102,plain,
% 0.91/1.15 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2103,plain,
% 0.91/1.15 ((hskp3 | hskp1 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138))) <=> (hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2104,plain,
% 0.91/1.15 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2103])).
% 0.91/1.15 tff(2105,plain,
% 0.91/1.15 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2104, 2102])).
% 0.91/1.15 tff(2106,plain,
% 0.91/1.15 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2107,plain,
% 0.91/1.15 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 0.91/1.15 tff(2108,plain,
% 0.91/1.15 (hskp3 | hskp1 | (~c3_1(a138))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2107, 117, 1870, 1854, 2101])).
% 0.91/1.15 tff(2109,plain,
% 0.91/1.15 (hskp3),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2108, 2091, 2052])).
% 0.91/1.15 tff(2110,plain,
% 0.91/1.15 (((~hskp3) | (~c3_1(a127))) <=> ((~hskp3) | (~c3_1(a127)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2111,plain,
% 0.91/1.15 (((~c3_1(a127)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a127)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2112,axiom,((~c3_1(a127)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.91/1.15 tff(2113,plain,
% 0.91/1.15 ((~hskp3) | (~c3_1(a127))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 0.91/1.15 tff(2114,plain,
% 0.91/1.15 ((~hskp3) | (~c3_1(a127))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2113, 2110])).
% 0.91/1.15 tff(2115,plain,
% 0.91/1.15 (~c3_1(a127)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2114, 2109])).
% 0.91/1.15 tff(2116,plain,
% 0.91/1.15 (((~hskp3) | c1_1(a127)) <=> ((~hskp3) | c1_1(a127))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2117,axiom,((~hskp3) | c1_1(a127)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.91/1.15 tff(2118,plain,
% 0.91/1.15 ((~hskp3) | c1_1(a127)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 0.91/1.15 tff(2119,plain,
% 0.91/1.15 ((~hskp3) | c1_1(a127)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2118, 2116])).
% 0.91/1.15 tff(2120,plain,
% 0.91/1.15 ((~hskp3) | c1_1(a127)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2119, 2116])).
% 0.91/1.15 tff(2121,plain,
% 0.91/1.15 ((~hskp3) | c1_1(a127)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2120, 2116])).
% 0.91/1.15 tff(2122,plain,
% 0.91/1.15 ((~hskp3) | c1_1(a127)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2121, 2116])).
% 0.91/1.15 tff(2123,plain,
% 0.91/1.15 (c1_1(a127)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2122, 2109])).
% 0.91/1.15 tff(2124,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2125,plain,
% 0.91/1.15 ((hskp1 | (~ndr1_0) | c3_1(a127) | (~c1_1(a127)) | (~c0_1(a127)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2126,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a127) | (~c1_1(a127)) | (~c0_1(a127)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132)))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2125])).
% 0.91/1.15 tff(2127,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a127) | (~c1_1(a127)) | (~c0_1(a127)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2126, 2124])).
% 0.91/1.15 tff(2128,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a127) | (~c1_1(a127)) | (~c0_1(a127)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2129,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.91/1.15 tff(2130,plain,
% 0.91/1.15 (~c0_1(a127)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2129, 117, 2091, 2123, 1949, 1948, 2115, 2079, 2044])).
% 0.91/1.15 tff(2131,plain,
% 0.91/1.15 (((~hskp3) | (~c2_1(a127))) <=> ((~hskp3) | (~c2_1(a127)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2132,plain,
% 0.91/1.15 (((~c2_1(a127)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a127)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2133,axiom,((~c2_1(a127)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.91/1.15 tff(2134,plain,
% 0.91/1.15 ((~hskp3) | (~c2_1(a127))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 0.91/1.15 tff(2135,plain,
% 0.91/1.15 ((~hskp3) | (~c2_1(a127))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2134, 2131])).
% 0.91/1.15 tff(2136,plain,
% 0.91/1.15 (~c2_1(a127)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2135, 2109])).
% 0.91/1.15 tff(2137,plain,
% 0.91/1.15 (((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2138,plain,
% 0.91/1.15 ((hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138))) <=> (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2139,plain,
% 0.91/1.15 (((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2138])).
% 0.91/1.15 tff(2140,plain,
% 0.91/1.15 (((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2139, 2137])).
% 0.91/1.15 tff(2141,plain,
% 0.91/1.15 ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2142,plain,
% 0.91/1.15 ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 0.91/1.15 tff(2143,plain,
% 0.91/1.15 (hskp22 | hskp10 | (~c3_1(a138))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2142, 117, 1870, 1862, 1741])).
% 0.91/1.15 tff(2144,plain,
% 0.91/1.15 (hskp10),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2143, 2052, 2080])).
% 0.91/1.15 tff(2145,plain,
% 0.91/1.15 (~c3_1(a140)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1751, 2144])).
% 0.91/1.15 tff(2146,plain,
% 0.91/1.15 (~c2_1(a140)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1757, 2144])).
% 0.91/1.15 tff(2147,plain,
% 0.91/1.15 (~c0_1(a182)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1242, 2060])).
% 0.91/1.15 tff(2148,plain,
% 0.91/1.15 (c0_1(a140)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1765, 2144])).
% 0.91/1.15 tff(2149,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2150,plain,
% 0.91/1.15 (((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a127) | c0_1(a127) | (~c1_1(a127)) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2151,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a127) | c0_1(a127) | (~c1_1(a127)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182)))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2150])).
% 0.91/1.15 tff(2152,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a127) | c0_1(a127) | (~c1_1(a127)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2151, 2149])).
% 0.91/1.15 tff(2153,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a127) | c0_1(a127) | (~c1_1(a127)) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2154,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2153, 2152])).
% 0.91/1.15 tff(2155,plain,
% 0.91/1.15 ($false),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2154, 117, 2148, 2123, 2147, 2062, 2146, 2145, 2136, 21, 2130, 2069])).
% 0.91/1.15 tff(2156,plain,(hskp0 | hskp17 | c1_1(a131) | c2_1(a131) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.91/1.15 tff(2157,plain,
% 0.91/1.15 (hskp0),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2156, 126, 128, 92, 1724])).
% 0.91/1.15 tff(2158,plain,
% 0.91/1.15 (hskp30),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[566, 2157, 1949, 1948, 1947, 2044])).
% 0.91/1.15 tff(2159,plain,
% 0.91/1.15 (c0_1(a167)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1051, 2158])).
% 0.91/1.15 tff(2160,plain,
% 0.91/1.15 (c3_1(a167)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1094, 2158])).
% 0.91/1.15 tff(2161,plain,
% 0.91/1.15 (c1_1(a167)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1102, 2158])).
% 0.91/1.15 tff(2162,plain,
% 0.91/1.15 (hskp2),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1143, 2161, 92, 2160, 2159, 126, 128, 2042])).
% 0.91/1.15 tff(2163,plain,
% 0.91/1.15 (c2_1(a125)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[646, 2162])).
% 0.91/1.15 tff(2164,plain,
% 0.91/1.15 (c1_1(a125)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[630, 2162])).
% 0.91/1.15 tff(2165,plain,
% 0.91/1.15 (c3_1(a125)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[653, 117, 2080, 2164, 2163, 595])).
% 0.91/1.15 tff(2166,plain,
% 0.91/1.15 (~c1_1(a123)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[190, 2157])).
% 0.91/1.15 tff(2167,plain,
% 0.91/1.15 (~c0_1(a123)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[221, 2157])).
% 0.91/1.15 tff(2168,plain,
% 0.91/1.15 (c2_1(a123)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[198, 2157])).
% 0.91/1.15 tff(2169,plain,
% 0.91/1.15 (~c3_1(a123)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[470, 117, 1947, 2168, 1948, 2167, 2166, 138, 2044])).
% 0.91/1.15 tff(2170,plain,
% 0.91/1.15 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(2171,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[2170])).
% 0.91/1.15 tff(2172,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2173,plain,
% 0.91/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(2174,plain,
% 0.91/1.15 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[2173])).
% 0.91/1.15 tff(2175,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.91/1.15 tff(2176,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 0.91/1.15 tff(2177,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2176, 2172])).
% 0.91/1.15 tff(2178,plain,(
% 0.91/1.15 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.91/1.15 inference(skolemize,[status(sab)],[2177])).
% 0.91/1.15 tff(2179,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2178, 2171])).
% 0.91/1.15 tff(2180,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2181,plain,
% 0.91/1.15 ((hskp14 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2182,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2181])).
% 0.91/1.15 tff(2183,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2182, 2180])).
% 0.91/1.15 tff(2184,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2185,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2184, 2183])).
% 0.91/1.15 tff(2186,plain,
% 0.91/1.15 (hskp14 | c3_1(a123)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2185, 117, 1947, 2168, 1949, 1948, 2167, 2179])).
% 0.91/1.15 tff(2187,plain,
% 0.91/1.15 (hskp14),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2186, 2169])).
% 0.91/1.15 tff(2188,plain,
% 0.91/1.15 (~c1_1(a147)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[316, 2187])).
% 0.91/1.15 tff(2189,plain,
% 0.91/1.15 (c0_1(a147)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[302, 2187])).
% 0.91/1.15 tff(2190,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2191,plain,
% 0.91/1.15 (((~ndr1_0) | (~c3_1(a125)) | (~c1_1(a125)) | (~c2_1(a125)) | c1_1(a147) | (~c2_1(a147)) | (~c0_1(a147)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123))) <=> (c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2192,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a125)) | (~c1_1(a125)) | (~c2_1(a125)) | c1_1(a147) | (~c2_1(a147)) | (~c0_1(a147)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2191])).
% 0.91/1.15 tff(2193,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a125)) | (~c1_1(a125)) | (~c2_1(a125)) | c1_1(a147) | (~c2_1(a147)) | (~c0_1(a147)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2192, 2190])).
% 0.91/1.15 tff(2194,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a125)) | (~c1_1(a125)) | (~c2_1(a125)) | c1_1(a147) | (~c2_1(a147)) | (~c0_1(a147)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2195,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 0.91/1.15 tff(2196,plain,
% 0.91/1.15 (~c2_1(a147)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2195, 117, 2189, 2164, 2163, 2168, 2188, 2167, 2166, 10, 2165])).
% 0.91/1.15 tff(2197,plain,
% 0.91/1.15 ($false),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[323, 117, 1724, 128, 2189, 2188, 53, 2196])).
% 0.91/1.15 tff(2198,plain,(c1_1(a131) | hskp19 | hskp17 | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.15 tff(2199,plain,
% 0.91/1.15 (hskp19),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2198, 2040, 128, 92])).
% 0.91/1.15 tff(2200,plain,
% 0.91/1.15 (hskp13),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1922, 2199, 128])).
% 0.91/1.15 tff(2201,plain,
% 0.91/1.15 (~c1_1(a143)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[725, 2200])).
% 0.91/1.15 tff(2202,plain,
% 0.91/1.15 (c3_1(a143)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[765, 2200])).
% 0.91/1.15 tff(2203,plain,
% 0.91/1.15 (c2_1(a143)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[773, 2200])).
% 0.91/1.15 tff(2204,plain,
% 0.91/1.15 (~c2_1(a164)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[235, 2199])).
% 0.91/1.15 tff(2205,plain,
% 0.91/1.15 (hskp24),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1792, 2199, 128])).
% 0.91/1.15 tff(2206,plain,
% 0.91/1.15 (~c2_1(a182)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1229, 2205])).
% 0.91/1.15 tff(2207,plain,
% 0.91/1.15 (~c0_1(a182)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1242, 2205])).
% 0.91/1.15 tff(2208,plain,
% 0.91/1.15 (c3_1(a164)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[243, 2199])).
% 0.91/1.15 tff(2209,plain,
% 0.91/1.15 (c1_1(a164)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[251, 2199])).
% 0.91/1.15 tff(2210,assumption,(~c2_1(a182)), introduced(assumption)).
% 0.91/1.15 tff(2211,assumption,(~c0_1(a182)), introduced(assumption)).
% 0.91/1.15 tff(2212,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2213,plain,
% 0.91/1.15 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a182) | c0_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2214,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a182) | c0_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2213])).
% 0.91/1.15 tff(2215,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a182) | c0_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2214, 2212])).
% 0.91/1.15 tff(2216,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a182) | c0_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2217,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 0.91/1.15 tff(2218,plain,
% 0.91/1.15 (c1_1(a132) | (~c1_1(a182))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2217, 117, 440, 2211, 2210, 407, 409, 382])).
% 0.91/1.15 tff(2219,plain,
% 0.91/1.15 (~c1_1(a182)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2218, 436])).
% 0.91/1.15 tff(2220,plain,
% 0.91/1.15 (hskp6),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1328, 436, 440, 1299, 1298, 409, 1300])).
% 0.91/1.15 tff(2221,plain,
% 0.91/1.15 (~c0_1(a131)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[80, 2220])).
% 0.91/1.15 tff(2222,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2223,plain,
% 0.91/1.15 (((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2224,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2223])).
% 0.91/1.15 tff(2225,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2224, 2222])).
% 0.91/1.15 tff(2226,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2227,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 0.91/1.15 tff(2228,plain,
% 0.91/1.15 (c0_1(a131) | (~c3_1(a131)) | c1_1(a132)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2227, 117, 1300, 1299, 440, 1298, 409, 126, 138])).
% 0.91/1.15 tff(2229,plain,
% 0.91/1.15 (~c3_1(a131)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2228, 2221, 436])).
% 0.91/1.15 tff(2230,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2231,plain,
% 0.91/1.16 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a131) | c0_1(a131) | c3_1(a131) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2232,plain,
% 0.91/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a131) | c0_1(a131) | c3_1(a131) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182)))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[2231])).
% 0.91/1.16 tff(2233,plain,
% 0.91/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a131) | c0_1(a131) | c3_1(a131) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182))),
% 0.91/1.16 inference(transitivity,[status(thm)],[2232, 2230])).
% 0.91/1.16 tff(2234,plain,
% 0.91/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a131) | c0_1(a131) | c3_1(a131) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(2235,plain,
% 0.91/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182)),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 0.91/1.16 tff(2236,plain,
% 0.91/1.16 (c0_1(a131) | c3_1(a131) | c1_1(a182)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2235, 117, 1688, 1687, 2211, 2210, 1686, 126, 216])).
% 0.91/1.16 tff(2237,plain,
% 0.91/1.16 ($false),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2236, 2229, 2221, 2219])).
% 0.91/1.16 tff(2238,plain,(c1_1(a132) | (~c1_1(a164)) | (~c3_1(a164)) | c0_1(a182) | c2_1(a182) | c2_1(a164) | c1_1(a131) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a132)) | c1_1(a143) | c2_1(a132) | c0_1(a132)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.16 tff(2239,plain,
% 0.91/1.16 (c1_1(a132)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2238, 2209, 2208, 2207, 2206, 2204, 2040, 2203, 2202, 1947, 2201, 1948, 1949])).
% 0.91/1.16 tff(2240,plain,
% 0.91/1.16 (hskp0),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1951, 2239])).
% 0.91/1.16 tff(2241,plain,
% 0.91/1.16 (c2_1(a123)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[198, 2240])).
% 0.91/1.16 tff(2242,plain,
% 0.91/1.16 (~c1_1(a123)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[190, 2240])).
% 0.91/1.16 tff(2243,plain,
% 0.91/1.16 (~c0_1(a123)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[221, 2240])).
% 0.91/1.16 tff(2244,plain,
% 0.91/1.16 (c0_1(a131)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2043, 2239, 2040])).
% 0.91/1.16 tff(2245,plain,
% 0.91/1.16 (~hskp6),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[80, 2244])).
% 0.91/1.16 tff(2246,plain,
% 0.91/1.16 ($false),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2032, 2245, 2243, 2239, 2242, 2241, 128])).
% 0.91/1.16 tff(2247,plain,(c2_1(a131) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.91/1.16 tff(2248,plain,
% 0.91/1.16 (c2_1(a131)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2247, 128])).
% 0.91/1.16 tff(2249,plain,
% 0.91/1.16 (~hskp6),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[68, 2248])).
% 0.91/1.16 tff(2250,plain,
% 0.91/1.16 (~c1_1(a132)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2032, 463, 2249, 462, 464, 128])).
% 0.91/1.16 tff(2251,plain,
% 0.91/1.16 (hskp30),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[566, 2250, 1949, 1948, 1947, 461])).
% 0.91/1.16 tff(2252,plain,
% 0.91/1.16 (c0_1(a167)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1051, 2251])).
% 0.91/1.16 tff(2253,plain,
% 0.91/1.16 (c1_1(a167)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1102, 2251])).
% 0.91/1.16 tff(2254,plain,
% 0.91/1.16 (c3_1(a167)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1094, 2251])).
% 0.91/1.16 tff(2255,plain,
% 0.91/1.16 ($false),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1823, 2254, 2253, 1947, 1948, 128, 2249, 2250, 2252])).
% 0.91/1.16 tff(2256,plain,((~hskp0) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.91/1.16 tff(2257,plain,
% 0.91/1.16 (~hskp0),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2256, 128])).
% 0.91/1.16 tff(2258,plain,
% 0.91/1.16 (~c1_1(a132)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1951, 2257])).
% 0.91/1.16 tff(2259,plain,
% 0.91/1.16 (c3_1(a138)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2051, 2257, 2258])).
% 0.91/1.16 tff(2260,plain,
% 0.91/1.16 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2261,plain,
% 0.91/1.16 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138))) <=> (hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2262,plain,
% 0.91/1.16 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[2261])).
% 0.91/1.16 tff(2263,plain,
% 0.91/1.16 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.91/1.16 inference(transitivity,[status(thm)],[2262, 2260])).
% 0.91/1.16 tff(2264,plain,
% 0.91/1.16 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(2265,plain,
% 0.91/1.16 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 0.91/1.16 tff(2266,plain,
% 0.91/1.16 (hskp17 | hskp13 | (~c3_1(a138))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2265, 117, 1862, 1854, 712])).
% 0.91/1.16 tff(2267,plain,
% 0.91/1.16 (hskp13),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2266, 2259, 128])).
% 0.91/1.16 tff(2268,plain,
% 0.91/1.16 (c2_1(a143)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[773, 2267])).
% 0.91/1.16 tff(2269,plain,
% 0.91/1.16 (c3_1(a143)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[765, 2267])).
% 0.91/1.16 tff(2270,plain,
% 0.91/1.16 (~c1_1(a143)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[725, 2267])).
% 0.91/1.16 tff(2271,plain,
% 0.91/1.16 ($false),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1328, 2270, 2269, 1947, 2249, 2258, 1948, 2268])).
% 0.91/1.16 tff(2272,plain,(hskp17), inference(lemma,lemma(discharge,[]))).
% 0.91/1.16 tff(2273,plain,
% 0.91/1.16 (~c2_1(a155)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[358, 2272])).
% 0.91/1.16 tff(2274,plain,
% 0.91/1.16 (~c0_1(a155)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[364, 2272])).
% 0.91/1.16 tff(2275,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2276,plain,
% 0.91/1.16 ((hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142))) <=> (hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2277,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[2276])).
% 0.91/1.16 tff(2278,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.16 inference(transitivity,[status(thm)],[2277, 2275])).
% 0.91/1.16 tff(2279,plain,
% 0.91/1.16 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(2280,plain,
% 0.91/1.16 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 0.91/1.16 tff(2281,plain,
% 0.91/1.16 ($false),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2280, 117, 93, 178, 153, 1870, 1862, 145, 1854, 1900])).
% 0.91/1.16 tff(2282,plain,((~hskp12) | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.91/1.16 tff(2283,plain,
% 0.91/1.16 (~hskp12),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2282, 93])).
% 0.91/1.16 tff(2284,plain,
% 0.91/1.16 (c1_1(a155)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[389, 2272])).
% 0.91/1.16 tff(2285,plain,
% 0.91/1.16 (hskp12 | (~c3_1(a155))),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1430, 117, 2284, 2274, 2273, 1362])).
% 0.91/1.16 tff(2286,plain,
% 0.91/1.16 (~c3_1(a155)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2285, 2283])).
% 0.91/1.16 tff(2287,plain,
% 0.91/1.16 (hskp19),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1931, 2283, 1919])).
% 0.91/1.16 tff(2288,plain,
% 0.91/1.16 (~c2_1(a164)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[235, 2287])).
% 0.91/1.16 tff(2289,plain,
% 0.91/1.16 (c3_1(a164)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[243, 2287])).
% 0.91/1.16 tff(2290,plain,
% 0.91/1.16 (c1_1(a164)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[251, 2287])).
% 0.91/1.16 tff(2291,plain,
% 0.91/1.16 (c0_1(a164)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1841, 117, 2283, 2290, 2289, 2288, 1362])).
% 0.91/1.16 tff(2292,assumption,(hskp18), introduced(assumption)).
% 0.91/1.16 tff(2293,plain,
% 0.91/1.16 (~c1_1(a160)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[942, 2292])).
% 0.91/1.16 tff(2294,plain,
% 0.91/1.16 (c3_1(a160)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[950, 2292])).
% 0.91/1.16 tff(2295,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2296,plain,
% 0.91/1.16 ((hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160))) <=> (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2297,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[2296])).
% 0.91/1.16 tff(2298,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.91/1.16 inference(transitivity,[status(thm)],[2297, 2295])).
% 0.91/1.16 tff(2299,plain,
% 0.91/1.16 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(2300,plain,
% 0.91/1.16 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 0.91/1.16 tff(2301,plain,
% 0.91/1.16 (~c0_1(a160)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2300, 117, 93, 2290, 2294, 2288, 2293, 1900, 2291])).
% 0.91/1.16 tff(2302,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2303,plain,
% 0.91/1.16 ((hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160))) <=> (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2304,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[2303])).
% 0.91/1.16 tff(2305,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[2304, 2302])).
% 1.00/1.16 tff(2306,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(2307,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 1.00/1.16 tff(2308,plain,
% 1.00/1.16 ($false),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2307, 117, 93, 2290, 2294, 2288, 2293, 344, 2291, 2301])).
% 1.00/1.16 tff(2309,plain,((~hskp18) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.00/1.16 tff(2310,plain,
% 1.00/1.16 (~hskp18),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2309, 93])).
% 1.00/1.16 tff(2311,plain,
% 1.00/1.16 (^[U: $i] : refl((hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(2312,plain,
% 1.00/1.16 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[2311])).
% 1.00/1.16 tff(2313,plain,
% 1.00/1.16 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2314,plain,
% 1.00/1.16 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp13) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp13) <=> (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(2315,plain,
% 1.00/1.16 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp13) <=> ![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[2314])).
% 1.00/1.16 tff(2316,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.00/1.16 tff(2317,plain,
% 1.00/1.16 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 1.00/1.16 tff(2318,plain,
% 1.00/1.16 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2317, 2313])).
% 1.00/1.16 tff(2319,plain,(
% 1.00/1.16 ![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.00/1.16 inference(skolemize,[status(sab)],[2318])).
% 1.00/1.16 tff(2320,plain,
% 1.00/1.16 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2319, 2312])).
% 1.00/1.16 tff(2321,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2322,plain,
% 1.00/1.16 ((hskp15 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164))) <=> (hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2323,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[2322])).
% 1.00/1.16 tff(2324,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[2323, 2321])).
% 1.00/1.16 tff(2325,plain,
% 1.00/1.16 ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(2326,plain,
% 1.00/1.16 ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 1.00/1.16 tff(2327,plain,
% 1.00/1.16 (hskp15),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2326, 117, 1919, 2290, 2289, 2288, 2320])).
% 1.00/1.16 tff(2328,plain,
% 1.00/1.16 (((~hskp15) | (~c0_1(a153))) <=> ((~hskp15) | (~c0_1(a153)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2329,plain,
% 1.00/1.16 (((~c0_1(a153)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a153)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2330,axiom,((~c0_1(a153)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.00/1.16 tff(2331,plain,
% 1.00/1.16 ((~hskp15) | (~c0_1(a153))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2330, 2329])).
% 1.00/1.16 tff(2332,plain,
% 1.00/1.16 ((~hskp15) | (~c0_1(a153))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2331, 2328])).
% 1.00/1.16 tff(2333,plain,
% 1.00/1.16 (~c0_1(a153)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2332, 2327])).
% 1.00/1.16 tff(2334,plain,
% 1.00/1.16 (((~hskp15) | c3_1(a153)) <=> ((~hskp15) | c3_1(a153))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2335,axiom,((~hskp15) | c3_1(a153)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.00/1.16 tff(2336,plain,
% 1.00/1.16 ((~hskp15) | c3_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 1.00/1.16 tff(2337,plain,
% 1.00/1.16 ((~hskp15) | c3_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2336, 2334])).
% 1.00/1.16 tff(2338,plain,
% 1.00/1.16 ((~hskp15) | c3_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2337, 2334])).
% 1.00/1.16 tff(2339,plain,
% 1.00/1.16 ((~hskp15) | c3_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2338, 2334])).
% 1.00/1.16 tff(2340,plain,
% 1.00/1.16 ((~hskp15) | c3_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2339, 2334])).
% 1.00/1.16 tff(2341,plain,
% 1.00/1.16 (c3_1(a153)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2340, 2327])).
% 1.00/1.16 tff(2342,plain,
% 1.00/1.16 (((~hskp15) | c2_1(a153)) <=> ((~hskp15) | c2_1(a153))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2343,axiom,((~hskp15) | c2_1(a153)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.00/1.16 tff(2344,plain,
% 1.00/1.16 ((~hskp15) | c2_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 1.00/1.16 tff(2345,plain,
% 1.00/1.16 ((~hskp15) | c2_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2344, 2342])).
% 1.00/1.16 tff(2346,plain,
% 1.00/1.16 ((~hskp15) | c2_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2345, 2342])).
% 1.00/1.16 tff(2347,plain,
% 1.00/1.16 ((~hskp15) | c2_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2346, 2342])).
% 1.00/1.16 tff(2348,plain,
% 1.00/1.16 ((~hskp15) | c2_1(a153)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2347, 2342])).
% 1.00/1.16 tff(2349,plain,
% 1.00/1.16 (c2_1(a153)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2348, 2327])).
% 1.00/1.16 tff(2350,plain,
% 1.00/1.16 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2351,plain,
% 1.00/1.16 ((hskp18 | hskp0 | (~ndr1_0) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153))) <=> (hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2352,plain,
% 1.00/1.16 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[2351])).
% 1.00/1.16 tff(2353,plain,
% 1.00/1.16 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[2352, 2350])).
% 1.00/1.16 tff(2354,plain,
% 1.00/1.16 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(2355,plain,
% 1.00/1.16 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 1.00/1.16 tff(2356,plain,
% 1.00/1.16 (hskp18 | hskp0),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2355, 117, 2349, 2341, 2333, 929])).
% 1.00/1.16 tff(2357,plain,
% 1.00/1.16 (hskp0),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2356, 2310])).
% 1.00/1.16 tff(2358,plain,
% 1.00/1.16 (~c0_1(a123)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[221, 2357])).
% 1.00/1.16 tff(2359,plain,
% 1.00/1.16 (c2_1(a123)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[198, 2357])).
% 1.00/1.16 tff(2360,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2361,plain,
% 1.00/1.16 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2362,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[2361])).
% 1.00/1.16 tff(2363,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[2362, 2360])).
% 1.00/1.16 tff(2364,plain,
% 1.00/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(2365,plain,
% 1.00/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 1.00/1.16 tff(2366,plain,
% 1.00/1.16 (c3_1(a123)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[2365, 117, 2290, 2289, 2284, 2359, 2288, 2273, 2358, 1398, 2286])).
% 1.00/1.16 tff(2367,plain,
% 1.00/1.16 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(2368,plain,
% 1.00/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[2367])).
% 1.00/1.16 tff(2369,plain,
% 1.00/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(2370,plain,
% 1.00/1.16 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | 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(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(2371,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[2370])).
% 1.00/1.17 tff(2372,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 1.00/1.17 tff(2373,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 1.00/1.17 tff(2374,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2373, 2369])).
% 1.00/1.17 tff(2375,plain,(
% 1.00/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(skolemize,[status(sab)],[2374])).
% 1.00/1.17 tff(2376,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2375, 2368])).
% 1.00/1.17 tff(2377,plain,
% 1.00/1.17 (hskp10),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1877, 2310])).
% 1.00/1.17 tff(2378,plain,
% 1.00/1.17 (~c2_1(a140)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1757, 2377])).
% 1.00/1.17 tff(2379,plain,
% 1.00/1.17 (c0_1(a140)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1765, 2377])).
% 1.00/1.17 tff(2380,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2381,plain,
% 1.00/1.17 (((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153))) <=> (c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2382,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[2381])).
% 1.00/1.17 tff(2383,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.00/1.17 tff(2384,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(2385,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.00/1.17 tff(2386,plain,
% 1.00/1.17 (c1_1(a140)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2385, 117, 2290, 2289, 2349, 2341, 2379, 2333, 2378, 2376, 2291])).
% 1.00/1.17 tff(2387,plain,
% 1.00/1.17 (~c1_1(a123)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[190, 2357])).
% 1.00/1.17 tff(2388,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2389,plain,
% 1.00/1.17 ((hskp7 | (~ndr1_0) | c2_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2390,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[2389])).
% 1.00/1.17 tff(2391,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[2390, 2388])).
% 1.00/1.17 tff(2392,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(2393,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 1.00/1.17 tff(2394,plain,
% 1.00/1.17 ($false),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2393, 117, 93, 2379, 2378, 2358, 2387, 344, 2386, 2366])).
% 1.00/1.17 tff(2395,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 1.00/1.17 tff(2396,plain,
% 1.00/1.17 (~c0_1(a132)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[404, 2395])).
% 1.00/1.17 tff(2397,plain,
% 1.00/1.17 (~c2_1(a132)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[835, 2395])).
% 1.00/1.17 tff(2398,plain,
% 1.00/1.17 (c3_1(a132)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[417, 2395])).
% 1.00/1.17 tff(2399,plain,
% 1.00/1.17 ((~c3_1(a132)) | c0_1(a132) | c2_1(a132) | c1_1(a132)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[449, 2272])).
% 1.00/1.17 tff(2400,plain,
% 1.00/1.17 (c1_1(a132)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2399, 2398, 2397, 2396])).
% 1.00/1.17 tff(2401,plain,
% 1.00/1.17 (~c3_1(a138)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2011, 117, 1870, 2398, 1854, 2396, 2397, 1344, 2400])).
% 1.00/1.17 tff(2402,assumption,(hskp15), introduced(assumption)).
% 1.00/1.17 tff(2403,plain,
% 1.00/1.17 (~c0_1(a153)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2332, 2402])).
% 1.00/1.17 tff(2404,plain,
% 1.00/1.17 (c3_1(a153)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2340, 2402])).
% 1.00/1.17 tff(2405,plain,
% 1.00/1.17 (c2_1(a153)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2348, 2402])).
% 1.00/1.17 tff(2406,plain,
% 1.00/1.17 ($false),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2355, 117, 22, 11, 2405, 2404, 2403, 929])).
% 1.00/1.17 tff(2407,plain,((~hskp15) | hskp18 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.00/1.17 tff(2408,plain,
% 1.00/1.17 (~hskp15),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2407, 22, 11])).
% 1.00/1.17 tff(2409,plain,
% 1.00/1.17 (^[U: $i] : refl((hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(2410,plain,
% 1.00/1.17 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[2409])).
% 1.00/1.17 tff(2411,plain,
% 1.00/1.17 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2412,plain,
% 1.00/1.17 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp24) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp24))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(2413,plain,
% 1.00/1.17 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp24) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[2412])).
% 1.00/1.17 tff(2414,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.00/1.17 tff(2415,plain,
% 1.00/1.17 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.00/1.17 tff(2416,plain,
% 1.00/1.17 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2415, 2411])).
% 1.00/1.17 tff(2417,plain,(
% 1.00/1.17 ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.00/1.17 inference(skolemize,[status(sab)],[2416])).
% 1.00/1.17 tff(2418,plain,
% 1.00/1.17 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2417, 2410])).
% 1.00/1.17 tff(2419,plain,
% 1.00/1.17 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2420,plain,
% 1.00/1.17 ((hskp24 | hskp15 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138))) <=> (hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2421,plain,
% 1.00/1.17 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[2420])).
% 1.00/1.17 tff(2422,plain,
% 1.00/1.17 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[2421, 2419])).
% 1.00/1.17 tff(2423,plain,
% 1.00/1.17 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(2424,plain,
% 1.00/1.17 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 1.00/1.17 tff(2425,plain,
% 1.00/1.17 (hskp24 | hskp15 | c3_1(a138)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2424, 117, 1862, 1854, 2418])).
% 1.00/1.17 tff(2426,plain,
% 1.00/1.17 (hskp24),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2425, 2408, 2401])).
% 1.00/1.17 tff(2427,plain,
% 1.00/1.17 (~c2_1(a182)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1229, 2426])).
% 1.00/1.17 tff(2428,plain,
% 1.00/1.17 (~c0_1(a182)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1242, 2426])).
% 1.00/1.17 tff(2429,plain,
% 1.00/1.17 (c0_1(a140)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1765, 1878])).
% 1.00/1.17 tff(2430,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2431,plain,
% 1.00/1.17 (((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2432,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182)))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[2431])).
% 1.00/1.17 tff(2433,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182))),
% 1.00/1.17 inference(transitivity,[status(thm)],[2432, 2430])).
% 1.00/1.17 tff(2434,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(2435,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 1.00/1.17 tff(2436,plain,
% 1.00/1.17 (c1_1(a182)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2435, 117, 2284, 2429, 2428, 2427, 2274, 2273, 1880, 1879, 21])).
% 1.00/1.17 tff(2437,plain,
% 1.00/1.17 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(2438,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[2437])).
% 1.00/1.17 tff(2439,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2440,plain,
% 1.00/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(2441,plain,
% 1.00/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[2440])).
% 1.00/1.17 tff(2442,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.00/1.17 tff(2443,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 1.00/1.17 tff(2444,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2443, 2439])).
% 1.00/1.17 tff(2445,plain,(
% 1.00/1.17 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.17 inference(skolemize,[status(sab)],[2444])).
% 1.00/1.17 tff(2446,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2445, 2438])).
% 1.00/1.17 tff(2447,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2448,plain,
% 1.00/1.17 ((hskp28 | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2449,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[2448])).
% 1.00/1.17 tff(2450,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[2449, 2447])).
% 1.00/1.17 tff(2451,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(2452,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 1.00/1.17 tff(2453,plain,
% 1.00/1.17 (hskp28),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2452, 117, 2284, 1870, 1862, 2274, 2273, 2446, 2401])).
% 1.00/1.17 tff(2454,plain,
% 1.00/1.17 (((~hskp28) | c3_1(a133)) <=> ((~hskp28) | c3_1(a133))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2455,axiom,((~hskp28) | c3_1(a133)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.00/1.17 tff(2456,plain,
% 1.00/1.17 ((~hskp28) | c3_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 1.00/1.17 tff(2457,plain,
% 1.00/1.17 ((~hskp28) | c3_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2456, 2454])).
% 1.00/1.17 tff(2458,plain,
% 1.00/1.17 ((~hskp28) | c3_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2457, 2454])).
% 1.00/1.17 tff(2459,plain,
% 1.00/1.17 ((~hskp28) | c3_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2458, 2454])).
% 1.00/1.17 tff(2460,plain,
% 1.00/1.17 ((~hskp28) | c3_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2459, 2454])).
% 1.00/1.17 tff(2461,plain,
% 1.00/1.17 (c3_1(a133)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2460, 2453])).
% 1.00/1.17 tff(2462,plain,
% 1.00/1.17 (((~hskp28) | c2_1(a133)) <=> ((~hskp28) | c2_1(a133))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2463,axiom,((~hskp28) | c2_1(a133)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.00/1.17 tff(2464,plain,
% 1.00/1.17 ((~hskp28) | c2_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 1.00/1.17 tff(2465,plain,
% 1.00/1.17 ((~hskp28) | c2_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2464, 2462])).
% 1.00/1.17 tff(2466,plain,
% 1.00/1.17 ((~hskp28) | c2_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2465, 2462])).
% 1.00/1.17 tff(2467,plain,
% 1.00/1.17 ((~hskp28) | c2_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2466, 2462])).
% 1.00/1.17 tff(2468,plain,
% 1.00/1.17 ((~hskp28) | c2_1(a133)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2467, 2462])).
% 1.00/1.17 tff(2469,plain,
% 1.00/1.17 (c2_1(a133)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2468, 2453])).
% 1.00/1.17 tff(2470,plain,
% 1.00/1.17 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2471,plain,
% 1.00/1.17 ((hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c3_1(a133)) | (~c2_1(a133))) <=> (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2472,plain,
% 1.00/1.17 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c3_1(a133)) | (~c2_1(a133)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[2471])).
% 1.00/1.17 tff(2473,plain,
% 1.00/1.17 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c3_1(a133)) | (~c2_1(a133)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[2472, 2470])).
% 1.00/1.17 tff(2474,plain,
% 1.00/1.17 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c3_1(a133)) | (~c2_1(a133)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(2475,plain,
% 1.00/1.17 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[2474, 2473])).
% 1.00/1.17 tff(2476,plain,
% 1.00/1.17 (hskp18 | hskp0 | c0_1(a133)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2475, 117, 2469, 2461, 929])).
% 1.00/1.17 tff(2477,plain,
% 1.00/1.17 (c0_1(a133)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[2476, 22, 11])).
% 1.00/1.17 tff(2478,plain,
% 1.00/1.17 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(2479,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[2478])).
% 1.00/1.17 tff(2480,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(2481,plain,
% 1.00/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(2482,plain,
% 1.00/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[2481])).
% 1.00/1.18 tff(2483,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.00/1.18 tff(2484,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 1.00/1.18 tff(2485,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2484, 2480])).
% 1.00/1.18 tff(2486,plain,(
% 1.00/1.18 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.18 inference(skolemize,[status(sab)],[2485])).
% 1.00/1.18 tff(2487,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2486, 2479])).
% 1.00/1.18 tff(2488,plain,
% 1.00/1.18 (~c3_1(a182)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1223, 2426])).
% 1.00/1.18 tff(2489,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2490,plain,
% 1.00/1.18 ((hskp8 | (~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c2_1(a133)) | c2_1(a182) | c0_1(a182) | c3_1(a182)) <=> (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2491,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c2_1(a133)) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[2490])).
% 1.00/1.18 tff(2492,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c2_1(a133)) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[2491, 2489])).
% 1.00/1.18 tff(2493,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c2_1(a133)) | c2_1(a182) | c0_1(a182) | c3_1(a182))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(2494,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 1.00/1.18 tff(2495,plain,
% 1.00/1.18 (hskp8),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2494, 117, 2469, 2461, 2428, 2427, 2488, 2487, 2477])).
% 1.00/1.18 tff(2496,plain,
% 1.00/1.18 (~c3_1(a134)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1525, 2495])).
% 1.00/1.18 tff(2497,plain,
% 1.00/1.18 (~c0_1(a134)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1531, 2495])).
% 1.00/1.18 tff(2498,plain,
% 1.00/1.18 (c2_1(a134)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1539, 2495])).
% 1.00/1.18 tff(2499,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2500,plain,
% 1.00/1.18 (((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a134) | c3_1(a134) | (~c2_1(a134))) <=> (c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2501,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a134) | c3_1(a134) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[2500])).
% 1.00/1.18 tff(2502,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a134) | c3_1(a134) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[2501, 2499])).
% 1.00/1.18 tff(2503,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a134) | c3_1(a134) | (~c2_1(a134)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(2504,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 1.00/1.18 tff(2505,plain,
% 1.00/1.18 ($false),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2504, 117, 2498, 2398, 2427, 2488, 2497, 2496, 2397, 1398, 2400, 2436])).
% 1.00/1.18 tff(2506,plain,(hskp18 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.00/1.18 tff(2507,plain,
% 1.00/1.18 (hskp18),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2506, 11])).
% 1.00/1.18 tff(2508,plain,
% 1.00/1.18 (hskp12),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1496, 117, 2398, 2396, 2397, 1362, 2400])).
% 1.00/1.18 tff(2509,plain,
% 1.00/1.18 (~c1_1(a142)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[144, 2508])).
% 1.00/1.18 tff(2510,plain,
% 1.00/1.18 (c3_1(a142)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[152, 2508])).
% 1.00/1.18 tff(2511,plain,
% 1.00/1.18 (c0_1(a142)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[177, 2508])).
% 1.00/1.18 tff(2512,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2513,plain,
% 1.00/1.18 ((hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160))) <=> (hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2514,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160)))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[2513])).
% 1.00/1.18 tff(2515,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160))),
% 1.00/1.18 inference(transitivity,[status(thm)],[2514, 2512])).
% 1.00/1.18 tff(2516,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(2517,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2516, 2515])).
% 1.00/1.18 tff(2518,plain,
% 1.00/1.18 (c0_1(a160)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2517, 117, 1319, 2294, 2511, 2510, 2293, 2509, 1262])).
% 1.00/1.18 tff(2519,plain,
% 1.00/1.18 (~c2_1(a160)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[972, 2292])).
% 1.00/1.18 tff(2520,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2521,plain,
% 1.00/1.18 (((~ndr1_0) | c2_1(a160) | (~c3_1(a160)) | (~c0_1(a160)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160))) <=> (c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2522,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | (~c3_1(a160)) | (~c0_1(a160)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[2521])).
% 1.00/1.18 tff(2523,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | (~c3_1(a160)) | (~c0_1(a160)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[2522, 2520])).
% 1.00/1.18 tff(2524,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | (~c3_1(a160)) | (~c0_1(a160)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(2525,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 1.00/1.18 tff(2526,plain,
% 1.00/1.18 ($false),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2525, 117, 2294, 1862, 2293, 2519, 1854, 1200, 2401, 2518])).
% 1.00/1.18 tff(2527,plain,((~hskp18) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.00/1.18 tff(2528,plain,
% 1.00/1.18 (hskp6),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2527, 2507])).
% 1.00/1.18 tff(2529,plain,
% 1.00/1.18 (~c1_1(a131)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[74, 2528])).
% 1.00/1.18 tff(2530,plain,
% 1.00/1.18 (~c2_1(a131)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[68, 2528])).
% 1.00/1.18 tff(2531,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2532,plain,
% 1.00/1.18 (((~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2533,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[2532])).
% 1.00/1.18 tff(2534,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[2533, 2531])).
% 1.00/1.18 tff(2535,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(2536,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2535, 2534])).
% 1.00/1.18 tff(2537,plain,
% 1.00/1.18 (c0_1(a131) | c1_1(a131)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2536, 117, 2284, 1870, 2274, 2273, 1854, 92, 21, 2401])).
% 1.00/1.18 tff(2538,plain,
% 1.00/1.18 (c0_1(a131)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2537, 126])).
% 1.00/1.18 tff(2539,plain,
% 1.00/1.18 (((~hskp28) | c1_1(a133)) <=> ((~hskp28) | c1_1(a133))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2540,axiom,((~hskp28) | c1_1(a133)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.00/1.18 tff(2541,plain,
% 1.00/1.18 ((~hskp28) | c1_1(a133)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 1.00/1.18 tff(2542,plain,
% 1.00/1.18 ((~hskp28) | c1_1(a133)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2541, 2539])).
% 1.00/1.18 tff(2543,plain,
% 1.00/1.18 ((~hskp28) | c1_1(a133)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2542, 2539])).
% 1.00/1.18 tff(2544,plain,
% 1.00/1.18 ((~hskp28) | c1_1(a133)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2543, 2539])).
% 1.00/1.18 tff(2545,plain,
% 1.00/1.18 ((~hskp28) | c1_1(a133)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2544, 2539])).
% 1.00/1.18 tff(2546,plain,
% 1.00/1.18 (c1_1(a133)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2545, 2453])).
% 1.00/1.18 tff(2547,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2548,plain,
% 1.00/1.18 (((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153))) <=> (c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2549,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[2548])).
% 1.00/1.18 tff(2550,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.00/1.18 tff(2551,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(2552,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.00/1.18 tff(2553,plain,
% 1.00/1.18 (~c0_1(a133)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2552, 117, 2546, 2461, 2405, 2404, 2403, 2538, 126, 92, 2376])).
% 1.00/1.18 tff(2554,plain,
% 1.00/1.18 (hskp18),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2355, 117, 11, 2405, 2404, 2403, 929])).
% 1.00/1.18 tff(2555,plain,
% 1.00/1.18 (~c2_1(a160)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[972, 2554])).
% 1.00/1.18 tff(2556,plain,
% 1.00/1.18 (~c1_1(a160)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[942, 2554])).
% 1.00/1.18 tff(2557,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2558,plain,
% 1.00/1.18 (((~ndr1_0) | c2_1(a160) | c1_1(a160) | (~c0_1(a160)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2559,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | c1_1(a160) | (~c0_1(a160)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[2558])).
% 1.00/1.18 tff(2560,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | c1_1(a160) | (~c0_1(a160)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[2559, 2557])).
% 1.00/1.18 tff(2561,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | c1_1(a160) | (~c0_1(a160)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(2562,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 1.00/1.18 tff(2563,plain,
% 1.00/1.18 (~c0_1(a160)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[2562, 117, 2546, 2469, 2398, 2556, 2555, 2396, 2397, 741, 2553])).
% 1.00/1.18 tff(2564,plain,
% 1.00/1.18 (c3_1(a160)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[950, 2554])).
% 1.00/1.18 tff(2565,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2566,plain,
% 1.00/1.18 (((~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a160) | c0_1(a160) | (~c3_1(a160))) <=> (c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(2567,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160)))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[2566])).
% 1.00/1.18 tff(2568,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160))),
% 1.00/1.19 inference(transitivity,[status(thm)],[2567, 2565])).
% 1.00/1.19 tff(2569,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(2570,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.00/1.19 tff(2571,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2570, 117, 2546, 2469, 2564, 2555, 2538, 126, 92, 741, 2553, 2563])).
% 1.00/1.19 tff(2572,plain,((~hskp15) | c1_1(a131) | c2_1(a131) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(2573,plain,
% 1.00/1.19 (~hskp15),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2572, 126, 92, 11])).
% 1.00/1.19 tff(2574,plain,
% 1.00/1.19 (^[U: $i] : refl((hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(2575,plain,
% 1.00/1.19 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[2574])).
% 1.00/1.19 tff(2576,plain,
% 1.00/1.19 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2577,plain,
% 1.00/1.19 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp15) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp15))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp15) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(2578,plain,
% 1.00/1.19 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp15) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[2577])).
% 1.00/1.19 tff(2579,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.00/1.19 tff(2580,plain,
% 1.00/1.19 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2579, 2578])).
% 1.00/1.19 tff(2581,plain,
% 1.00/1.19 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2580, 2576])).
% 1.00/1.19 tff(2582,plain,(
% 1.00/1.19 ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.00/1.19 inference(skolemize,[status(sab)],[2581])).
% 1.00/1.19 tff(2583,plain,
% 1.00/1.19 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2582, 2575])).
% 1.00/1.19 tff(2584,plain,
% 1.00/1.19 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2585,plain,
% 1.00/1.19 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2586,plain,
% 1.00/1.19 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[2585])).
% 1.00/1.19 tff(2587,plain,
% 1.00/1.19 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[2586, 2584])).
% 1.00/1.19 tff(2588,plain,
% 1.00/1.19 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(2589,plain,
% 1.00/1.19 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2588, 2587])).
% 1.00/1.19 tff(2590,plain,
% 1.00/1.19 (hskp15 | hskp10),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2589, 117, 2398, 2396, 2397, 2583])).
% 1.00/1.19 tff(2591,plain,
% 1.00/1.19 (hskp10),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2590, 2573])).
% 1.00/1.19 tff(2592,plain,
% 1.00/1.19 (~c3_1(a140)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1751, 2591])).
% 1.00/1.19 tff(2593,plain,
% 1.00/1.19 (~c2_1(a140)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1757, 2591])).
% 1.00/1.19 tff(2594,plain,
% 1.00/1.19 (hskp24),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2425, 2573, 2401])).
% 1.00/1.19 tff(2595,plain,
% 1.00/1.19 (~c2_1(a182)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1229, 2594])).
% 1.00/1.19 tff(2596,plain,
% 1.00/1.19 (~c0_1(a182)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1242, 2594])).
% 1.00/1.19 tff(2597,plain,
% 1.00/1.19 (c0_1(a140)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1765, 2591])).
% 1.00/1.19 tff(2598,plain,
% 1.00/1.19 (c1_1(a182)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2435, 117, 2284, 2597, 2596, 2595, 2274, 2273, 2593, 2592, 21])).
% 1.00/1.19 tff(2599,plain,
% 1.00/1.19 ((~c0_1(a131)) | c1_1(a131)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1417, 117, 1920, 2284, 2274, 2273, 92, 1082])).
% 1.00/1.19 tff(2600,plain,
% 1.00/1.19 (~c0_1(a131)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2599, 126])).
% 1.00/1.19 tff(2601,plain,
% 1.00/1.19 (c0_1(a131) | c1_1(a131) | (~c3_1(a155))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[396, 117, 2284, 2274, 2273, 92, 382])).
% 1.00/1.19 tff(2602,plain,
% 1.00/1.19 (~c3_1(a155)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2601, 2600, 126])).
% 1.00/1.19 tff(2603,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2604,plain,
% 1.00/1.19 ((hskp0 | (~ndr1_0) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2605,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[2604])).
% 1.00/1.19 tff(2606,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[2605, 2603])).
% 1.00/1.19 tff(2607,plain,
% 1.00/1.19 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(2608,plain,
% 1.00/1.19 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 1.00/1.19 tff(2609,plain,
% 1.00/1.19 (hskp0 | c0_1(a131) | c1_1(a131) | c3_1(a155)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2608, 117, 2284, 2273, 92, 1962])).
% 1.00/1.19 tff(2610,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2609, 2602, 2600, 11, 126])).
% 1.00/1.19 tff(2611,plain,(c1_1(a131) | hskp0 | c2_1(a131) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(2612,plain,
% 1.00/1.19 (hskp13),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2611, 126, 11, 92])).
% 1.00/1.19 tff(2613,plain,
% 1.00/1.19 (~c1_1(a143)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[725, 2612])).
% 1.00/1.19 tff(2614,plain,
% 1.00/1.19 (~hskp6),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[80, 2538])).
% 1.00/1.19 tff(2615,plain,
% 1.00/1.19 (hskp21 | hskp6),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1444, 117, 2511, 2510, 2509, 1072])).
% 1.00/1.19 tff(2616,plain,
% 1.00/1.19 (hskp21),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2615, 2614])).
% 1.00/1.19 tff(2617,plain,
% 1.00/1.19 (~c1_1(a170)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1450, 2616])).
% 1.00/1.19 tff(2618,plain,
% 1.00/1.19 (c2_1(a143)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[773, 2612])).
% 1.00/1.19 tff(2619,plain,
% 1.00/1.19 (c2_1(a170)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1459, 2616])).
% 1.00/1.19 tff(2620,plain,
% 1.00/1.19 (c0_1(a170)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1467, 2616])).
% 1.00/1.19 tff(2621,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2622,plain,
% 1.00/1.19 (((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a143) | c0_1(a143) | (~c2_1(a143))) <=> (c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2623,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a143) | c0_1(a143) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[2622])).
% 1.00/1.19 tff(2624,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a143) | c0_1(a143) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[2623, 2621])).
% 1.00/1.19 tff(2625,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a143) | c0_1(a143) | (~c2_1(a143)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(2626,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2625, 2624])).
% 1.00/1.19 tff(2627,plain,
% 1.00/1.19 (c0_1(a143)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2626, 117, 2546, 2469, 2461, 2620, 2619, 2618, 2617, 2613, 10])).
% 1.00/1.19 tff(2628,plain,
% 1.00/1.19 (~c3_1(a182)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1223, 2594])).
% 1.00/1.19 tff(2629,plain,
% 1.00/1.19 (c3_1(a143)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[765, 2612])).
% 1.00/1.19 tff(2630,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2631,plain,
% 1.00/1.19 ((hskp8 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a182) | c0_1(a182) | c3_1(a182)) <=> (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2632,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[2631])).
% 1.00/1.19 tff(2633,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[2632, 2630])).
% 1.00/1.19 tff(2634,plain,
% 1.00/1.19 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a182) | c0_1(a182) | c3_1(a182))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(2635,plain,
% 1.00/1.19 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 1.00/1.19 tff(2636,plain,
% 1.00/1.19 (hskp8),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2635, 117, 2618, 2629, 2596, 2595, 2628, 2487, 2627])).
% 1.00/1.19 tff(2637,plain,
% 1.00/1.19 (~c3_1(a134)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1525, 2636])).
% 1.00/1.19 tff(2638,plain,
% 1.00/1.19 (~c0_1(a134)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1531, 2636])).
% 1.00/1.19 tff(2639,plain,
% 1.00/1.19 (c2_1(a134)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1539, 2636])).
% 1.00/1.19 tff(2640,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2504, 117, 2639, 2398, 2595, 2628, 2638, 2637, 2397, 1398, 2400, 2598])).
% 1.00/1.19 tff(2641,plain,(c1_1(a131) | c2_1(a131) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(2642,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2641, 2530, 2529, 11])).
% 1.00/1.19 tff(2643,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(2644,plain,
% 1.00/1.19 (~c1_1(a123)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[190, 2643])).
% 1.00/1.19 tff(2645,plain,
% 1.00/1.19 (~c0_1(a123)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[221, 2643])).
% 1.00/1.19 tff(2646,plain,
% 1.00/1.19 (c2_1(a123)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[198, 2643])).
% 1.00/1.19 tff(2647,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2648,plain,
% 1.00/1.19 (((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a142) | (~c2_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123))) <=> (c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2649,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a142) | (~c2_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[2648])).
% 1.00/1.19 tff(2650,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a142) | (~c2_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[2649, 2647])).
% 1.00/1.19 tff(2651,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a142) | (~c2_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(2652,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 1.00/1.19 tff(2653,plain,
% 1.00/1.19 (~c2_1(a142)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[2652, 117, 2546, 2469, 2461, 2511, 2646, 2509, 2645, 2644, 10])).
% 1.00/1.19 tff(2654,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2655,plain,
% 1.00/1.19 (((~ndr1_0) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142))) <=> (c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(2656,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[2655])).
% 1.00/1.19 tff(2657,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[2656, 2654])).
% 1.00/1.19 tff(2658,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(2659,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 1.00/1.20 tff(2660,plain,
% 1.00/1.20 ($false),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[2659, 117, 2511, 2510, 1862, 2509, 1854, 1200, 2401, 2653])).
% 1.00/1.20 % SZS output end Proof
% 1.03/1.20 % E exiting
%------------------------------------------------------------------------------