%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN458-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:11 AM UTC 2025
% Result : Unsatisfiable 0.62s 0.81s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN458-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 12:35:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.62/0.81 % SZS status Unsatisfiable
% 0.62/0.81 % SZS output start Proof
% 0.62/0.81 tff(c0_1_type, type, (
% 0.62/0.81 c0_1: $i > $o)).
% 0.62/0.81 tff(a1089_type, type, (
% 0.62/0.81 a1089: $i)).
% 0.62/0.81 tff(c1_1_type, type, (
% 0.62/0.81 c1_1: $i > $o)).
% 0.62/0.81 tff(c2_1_type, type, (
% 0.62/0.81 c2_1: $i > $o)).
% 0.62/0.81 tff(c3_1_type, type, (
% 0.62/0.81 c3_1: $i > $o)).
% 0.62/0.81 tff(ndr1_0_type, type, (
% 0.62/0.81 ndr1_0: $o)).
% 0.62/0.81 tff(hskp5_type, type, (
% 0.62/0.81 hskp5: $o)).
% 0.62/0.81 tff(a1080_type, type, (
% 0.62/0.81 a1080: $i)).
% 0.62/0.81 tff(hskp0_type, type, (
% 0.62/0.81 hskp0: $o)).
% 0.62/0.81 tff(a1085_type, type, (
% 0.62/0.81 a1085: $i)).
% 0.62/0.81 tff(hskp3_type, type, (
% 0.62/0.81 hskp3: $o)).
% 0.62/0.81 tff(a1120_type, type, (
% 0.62/0.81 a1120: $i)).
% 0.62/0.81 tff(hskp21_type, type, (
% 0.62/0.81 hskp21: $o)).
% 0.62/0.81 tff(hskp9_type, type, (
% 0.62/0.81 hskp9: $o)).
% 0.62/0.81 tff(a1082_type, type, (
% 0.62/0.81 a1082: $i)).
% 0.62/0.81 tff(hskp2_type, type, (
% 0.62/0.81 hskp2: $o)).
% 0.62/0.81 tff(a1146_type, type, (
% 0.62/0.81 a1146: $i)).
% 0.62/0.81 tff(hskp26_type, type, (
% 0.62/0.81 hskp26: $o)).
% 0.62/0.81 tff(a1113_type, type, (
% 0.62/0.81 a1113: $i)).
% 0.62/0.81 tff(hskp19_type, type, (
% 0.62/0.81 hskp19: $o)).
% 0.62/0.81 tff(a1092_type, type, (
% 0.62/0.81 a1092: $i)).
% 0.62/0.81 tff(a1109_type, type, (
% 0.62/0.81 a1109: $i)).
% 0.62/0.81 tff(hskp30_type, type, (
% 0.62/0.81 hskp30: $o)).
% 0.62/0.81 tff(a1097_type, type, (
% 0.62/0.81 a1097: $i)).
% 0.62/0.81 tff(hskp14_type, type, (
% 0.62/0.81 hskp14: $o)).
% 0.62/0.81 tff(a1103_type, type, (
% 0.62/0.81 a1103: $i)).
% 0.62/0.81 tff(hskp18_type, type, (
% 0.62/0.81 hskp18: $o)).
% 0.62/0.81 tff(hskp13_type, type, (
% 0.62/0.81 hskp13: $o)).
% 0.62/0.81 tff(hskp27_type, type, (
% 0.62/0.81 hskp27: $o)).
% 0.62/0.81 tff(hskp20_type, type, (
% 0.62/0.81 hskp20: $o)).
% 0.62/0.81 tff(a1098_type, type, (
% 0.62/0.81 a1098: $i)).
% 0.62/0.81 tff(hskp15_type, type, (
% 0.62/0.81 hskp15: $o)).
% 0.62/0.81 tff(hskp28_type, type, (
% 0.62/0.81 hskp28: $o)).
% 0.62/0.81 tff(hskp1_type, type, (
% 0.62/0.81 hskp1: $o)).
% 0.62/0.81 tff(a1081_type, type, (
% 0.62/0.81 a1081: $i)).
% 0.62/0.81 tff(hskp11_type, type, (
% 0.62/0.81 hskp11: $o)).
% 0.62/0.81 tff(a1091_type, type, (
% 0.62/0.81 a1091: $i)).
% 0.62/0.81 tff(a1095_type, type, (
% 0.62/0.81 a1095: $i)).
% 0.62/0.81 tff(a1083_type, type, (
% 0.62/0.81 a1083: $i)).
% 0.62/0.81 tff(a1090_type, type, (
% 0.62/0.81 a1090: $i)).
% 0.62/0.81 tff(hskp10_type, type, (
% 0.62/0.81 hskp10: $o)).
% 0.62/0.81 tff(a1088_type, type, (
% 0.62/0.81 a1088: $i)).
% 0.62/0.81 tff(hskp8_type, type, (
% 0.62/0.81 hskp8: $o)).
% 0.62/0.81 tff(a1084_type, type, (
% 0.62/0.81 a1084: $i)).
% 0.62/0.81 tff(hskp4_type, type, (
% 0.62/0.81 hskp4: $o)).
% 0.62/0.81 tff(a1122_type, type, (
% 0.62/0.81 a1122: $i)).
% 0.62/0.81 tff(hskp23_type, type, (
% 0.62/0.81 hskp23: $o)).
% 0.62/0.81 tff(a1102_type, type, (
% 0.62/0.81 a1102: $i)).
% 0.62/0.81 tff(hskp17_type, type, (
% 0.62/0.81 hskp17: $o)).
% 0.62/0.81 tff(a1100_type, type, (
% 0.62/0.81 a1100: $i)).
% 0.62/0.81 tff(hskp16_type, type, (
% 0.62/0.81 hskp16: $o)).
% 0.62/0.81 tff(a1148_type, type, (
% 0.62/0.81 a1148: $i)).
% 0.62/0.81 tff(hskp31_type, type, (
% 0.62/0.81 hskp31: $o)).
% 0.62/0.81 tff(a1121_type, type, (
% 0.62/0.81 a1121: $i)).
% 0.62/0.81 tff(hskp22_type, type, (
% 0.62/0.81 hskp22: $o)).
% 0.62/0.81 tff(1,plain,
% 0.62/0.81 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(2,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[1])).
% 0.62/0.81 tff(3,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(4,plain,
% 0.62/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(5,plain,
% 0.62/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[4])).
% 0.62/0.81 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.62/0.81 tff(7,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.62/0.81 tff(8,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.62/0.81 tff(9,plain,(
% 0.62/0.81 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[8])).
% 0.62/0.81 tff(10,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.62/0.81 tff(11,assumption,(~c1_1(a1085)), introduced(assumption)).
% 0.62/0.81 tff(12,assumption,(~c0_1(a1085)), introduced(assumption)).
% 0.62/0.81 tff(13,plain,
% 0.62/0.81 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(14,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[13])).
% 0.62/0.81 tff(15,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(16,plain,
% 0.62/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(17,plain,
% 0.62/0.81 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[16])).
% 0.62/0.81 tff(18,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.62/0.81 tff(19,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.62/0.81 tff(20,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.62/0.81 tff(21,plain,(
% 0.62/0.81 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[20])).
% 0.62/0.81 tff(22,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.62/0.81 tff(23,assumption,(hskp0), introduced(assumption)).
% 0.62/0.81 tff(24,plain,
% 0.62/0.81 (((~hskp0) | (~c2_1(a1080))) <=> ((~hskp0) | (~c2_1(a1080)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(25,plain,
% 0.62/0.81 (((~c2_1(a1080)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1080)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(26,axiom,((~c2_1(a1080)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.62/0.81 tff(27,plain,
% 0.62/0.81 ((~hskp0) | (~c2_1(a1080))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.62/0.81 tff(28,plain,
% 0.62/0.81 ((~hskp0) | (~c2_1(a1080))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.62/0.81 tff(29,plain,
% 0.62/0.81 (~c2_1(a1080)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[28, 23])).
% 0.62/0.81 tff(30,plain,
% 0.62/0.81 (((~hskp0) | (~c0_1(a1080))) <=> ((~hskp0) | (~c0_1(a1080)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(31,plain,
% 0.62/0.81 (((~c0_1(a1080)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1080)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(32,axiom,((~c0_1(a1080)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.62/0.81 tff(33,plain,
% 0.62/0.81 ((~hskp0) | (~c0_1(a1080))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.62/0.81 tff(34,plain,
% 0.62/0.81 ((~hskp0) | (~c0_1(a1080))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.62/0.81 tff(35,plain,
% 0.62/0.81 (~c0_1(a1080)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[34, 23])).
% 0.62/0.81 tff(36,plain,
% 0.62/0.81 (((~hskp0) | c1_1(a1080)) <=> ((~hskp0) | c1_1(a1080))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(37,axiom,((~hskp0) | c1_1(a1080)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.62/0.81 tff(38,plain,
% 0.62/0.81 ((~hskp0) | c1_1(a1080)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.62/0.81 tff(39,plain,
% 0.62/0.81 ((~hskp0) | c1_1(a1080)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.62/0.81 tff(40,plain,
% 0.62/0.81 ((~hskp0) | c1_1(a1080)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.62/0.81 tff(41,plain,
% 0.62/0.81 ((~hskp0) | c1_1(a1080)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.62/0.81 tff(42,plain,
% 0.62/0.81 ((~hskp0) | c1_1(a1080)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[41, 36])).
% 0.62/0.81 tff(43,plain,
% 0.62/0.81 (c1_1(a1080)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[42, 23])).
% 0.62/0.81 tff(44,plain,
% 0.62/0.81 (^[U: $i] : refl((hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(45,plain,
% 0.62/0.81 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[44])).
% 0.62/0.81 tff(46,plain,
% 0.62/0.81 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(47,plain,
% 0.62/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(48,plain,
% 0.62/0.81 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[47])).
% 0.62/0.81 tff(49,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.62/0.81 tff(50,plain,
% 0.62/0.81 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.62/0.81 tff(51,plain,
% 0.62/0.81 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.62/0.81 tff(52,plain,(
% 0.62/0.81 ![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[51])).
% 0.62/0.81 tff(53,plain,
% 0.62/0.81 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.62/0.81 tff(54,assumption,(~hskp9), introduced(assumption)).
% 0.62/0.81 tff(55,plain,
% 0.62/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(56,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[55])).
% 0.62/0.81 tff(57,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(58,plain,
% 0.62/0.81 (^[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))) | (~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))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(59,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[58])).
% 0.62/0.81 tff(60,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.62/0.81 tff(61,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.62/0.81 tff(62,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.62/0.81 tff(63,plain,(
% 0.62/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[62])).
% 0.62/0.81 tff(64,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.62/0.81 tff(65,assumption,(~hskp2), introduced(assumption)).
% 0.62/0.81 tff(66,assumption,(~c2_1(a1080)), introduced(assumption)).
% 0.62/0.81 tff(67,plain,
% 0.62/0.81 (^[U: $i] : refl((hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(68,plain,
% 0.62/0.81 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[67])).
% 0.62/0.81 tff(69,plain,
% 0.62/0.81 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(70,plain,
% 0.62/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(71,plain,
% 0.62/0.82 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[70])).
% 0.62/0.82 tff(72,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.62/0.82 tff(73,plain,
% 0.62/0.82 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.62/0.82 tff(74,plain,
% 0.62/0.82 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.62/0.82 tff(75,plain,(
% 0.62/0.82 ![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[74])).
% 0.62/0.82 tff(76,plain,
% 0.62/0.82 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.62/0.82 tff(77,plain,
% 0.62/0.82 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(78,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[77])).
% 0.62/0.82 tff(79,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(80,plain,
% 0.62/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(81,plain,
% 0.62/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[80])).
% 0.62/0.82 tff(82,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.62/0.82 tff(83,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.62/0.82 tff(84,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.62/0.82 tff(85,plain,(
% 0.62/0.82 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[84])).
% 0.62/0.82 tff(86,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.62/0.82 tff(87,assumption,(~c0_1(a1080)), introduced(assumption)).
% 0.62/0.82 tff(88,assumption,(~c2_1(a1085)), introduced(assumption)).
% 0.62/0.82 tff(89,assumption,(c0_1(a1097)), introduced(assumption)).
% 0.62/0.82 tff(90,plain,
% 0.62/0.82 (^[U: $i] : refl((hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(91,plain,
% 0.62/0.82 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[90])).
% 0.62/0.82 tff(92,plain,
% 0.62/0.82 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(93,plain,
% 0.62/0.82 (^[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)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(94,plain,
% 0.62/0.82 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[93])).
% 0.62/0.82 tff(95,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.62/0.82 tff(96,plain,
% 0.62/0.82 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.62/0.82 tff(97,plain,
% 0.62/0.82 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.62/0.82 tff(98,plain,(
% 0.62/0.82 ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[97])).
% 0.62/0.82 tff(99,plain,
% 0.62/0.82 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.62/0.82 tff(100,plain,
% 0.62/0.82 (((~hskp5) | c2_1(a1085)) <=> ((~hskp5) | c2_1(a1085))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(101,axiom,((~hskp5) | c2_1(a1085)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.62/0.82 tff(102,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a1085)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.62/0.82 tff(103,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a1085)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[102, 100])).
% 0.62/0.82 tff(104,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a1085)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[103, 100])).
% 0.62/0.82 tff(105,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a1085)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.62/0.82 tff(106,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a1085)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[105, 100])).
% 0.62/0.82 tff(107,plain,
% 0.62/0.82 (~hskp5),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[106, 88])).
% 0.62/0.82 tff(108,plain,
% 0.62/0.82 ((hskp0 | hskp5) <=> (hskp0 | hskp5)),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(109,axiom,(hskp0 | hskp5), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.62/0.82 tff(110,plain,
% 0.62/0.82 (hskp0 | hskp5),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.62/0.82 tff(111,plain,
% 0.62/0.82 (hskp0),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.62/0.82 tff(112,plain,
% 0.62/0.82 (~c2_1(a1080)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[28, 111])).
% 0.62/0.82 tff(113,plain,
% 0.62/0.82 (~c0_1(a1080)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[34, 111])).
% 0.62/0.82 tff(114,plain,
% 0.62/0.82 (c1_1(a1080)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[42, 111])).
% 0.62/0.82 tff(115,assumption,(~hskp5), introduced(assumption)).
% 0.62/0.82 tff(116,plain,
% 0.62/0.82 (hskp0),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[110, 115])).
% 0.62/0.82 tff(117,plain,
% 0.62/0.82 (~c2_1(a1080)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[28, 116])).
% 0.62/0.82 tff(118,plain,
% 0.62/0.82 (~c0_1(a1080)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[34, 116])).
% 0.62/0.82 tff(119,assumption,(hskp18), introduced(assumption)).
% 0.62/0.82 tff(120,plain,
% 0.62/0.82 (((~hskp18) | (~c1_1(a1103))) <=> ((~hskp18) | (~c1_1(a1103)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(121,plain,
% 0.62/0.82 (((~c1_1(a1103)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a1103)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(122,axiom,((~c1_1(a1103)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.62/0.82 tff(123,plain,
% 0.62/0.82 ((~hskp18) | (~c1_1(a1103))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.62/0.82 tff(124,plain,
% 0.62/0.82 ((~hskp18) | (~c1_1(a1103))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[123, 120])).
% 0.62/0.82 tff(125,plain,
% 0.62/0.82 (~c1_1(a1103)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[124, 119])).
% 0.62/0.82 tff(126,plain,
% 0.62/0.82 (c1_1(a1080)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[42, 116])).
% 0.62/0.82 tff(127,plain,
% 0.62/0.82 (((~hskp18) | c3_1(a1103)) <=> ((~hskp18) | c3_1(a1103))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(128,axiom,((~hskp18) | c3_1(a1103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.62/0.82 tff(129,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.62/0.82 tff(130,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[129, 127])).
% 0.62/0.82 tff(131,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.62/0.82 tff(132,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.62/0.82 tff(133,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.62/0.82 tff(134,plain,
% 0.62/0.82 (c3_1(a1103)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[133, 119])).
% 0.62/0.82 tff(135,plain,
% 0.62/0.82 (((~hskp18) | c0_1(a1103)) <=> ((~hskp18) | c0_1(a1103))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(136,axiom,((~hskp18) | c0_1(a1103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.62/0.82 tff(137,plain,
% 0.62/0.82 ((~hskp18) | c0_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.62/0.82 tff(138,plain,
% 0.62/0.82 ((~hskp18) | c0_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[137, 135])).
% 0.62/0.82 tff(139,plain,
% 0.62/0.82 ((~hskp18) | c0_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[138, 135])).
% 0.62/0.82 tff(140,plain,
% 0.62/0.82 ((~hskp18) | c0_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.62/0.82 tff(141,plain,
% 0.62/0.82 ((~hskp18) | c0_1(a1103)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[140, 135])).
% 0.62/0.82 tff(142,plain,
% 0.62/0.82 (c0_1(a1103)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[141, 119])).
% 0.62/0.82 tff(143,assumption,(~ndr1_0), introduced(assumption)).
% 0.62/0.82 tff(144,plain,
% 0.62/0.82 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(145,plain,
% 0.62/0.82 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(146,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 0.62/0.82 tff(147,plain,
% 0.62/0.82 (ndr1_0 | (~hskp13)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.62/0.82 tff(148,plain,
% 0.62/0.82 (ndr1_0 | (~hskp13)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.62/0.82 tff(149,plain,
% 0.62/0.82 (~hskp13),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[148, 143])).
% 0.62/0.82 tff(150,plain,
% 0.62/0.82 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(151,plain,
% 0.62/0.82 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(152,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.62/0.82 tff(153,plain,
% 0.62/0.82 (ndr1_0 | (~hskp27)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.62/0.82 tff(154,plain,
% 0.62/0.82 (ndr1_0 | (~hskp27)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[153, 150])).
% 0.62/0.82 tff(155,plain,
% 0.62/0.82 (~hskp27),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[154, 143])).
% 0.62/0.82 tff(156,plain,
% 0.62/0.82 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(157,plain,
% 0.62/0.82 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(158,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 0.62/0.82 tff(159,plain,
% 0.62/0.82 (ndr1_0 | (~hskp20)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.62/0.82 tff(160,plain,
% 0.62/0.82 (ndr1_0 | (~hskp20)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[159, 156])).
% 0.62/0.82 tff(161,plain,
% 0.62/0.82 (~hskp20),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[160, 143])).
% 0.62/0.82 tff(162,plain,
% 0.62/0.82 ((hskp27 | hskp20 | hskp13) <=> (hskp27 | hskp20 | hskp13)),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(163,plain,
% 0.62/0.82 (((hskp20 | hskp27) | hskp13) <=> (hskp27 | hskp20 | hskp13)),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(164,axiom,((hskp20 | hskp27) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.62/0.82 tff(165,plain,
% 0.62/0.82 (hskp27 | hskp20 | hskp13),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.62/0.82 tff(166,plain,
% 0.62/0.82 (hskp27 | hskp20 | hskp13),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[165, 162])).
% 0.62/0.82 tff(167,plain,
% 0.62/0.82 (hskp27 | hskp20 | hskp13),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.62/0.82 tff(168,plain,
% 0.62/0.82 (hskp27 | hskp20 | hskp13),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[167, 162])).
% 0.62/0.82 tff(169,plain,
% 0.62/0.82 (hskp27 | hskp20 | hskp13),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[168, 162])).
% 0.62/0.82 tff(170,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[169, 161, 155, 149])).
% 0.62/0.82 tff(171,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(172,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(173,plain,
% 0.62/0.82 ((hskp5 | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)) | (~c0_1(a1103)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(174,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)) | (~c0_1(a1103)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[173])).
% 0.62/0.82 tff(175,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)) | (~c0_1(a1103)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[174, 172])).
% 0.62/0.82 tff(176,plain,
% 0.62/0.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)) | (~c0_1(a1103)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(177,plain,
% 0.62/0.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.62/0.82 tff(178,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[177, 115, 171, 142, 134, 126, 125, 118, 117, 10])).
% 0.62/0.82 tff(179,plain,((~hskp18) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(180,plain,
% 0.62/0.82 (~hskp18),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[179, 107])).
% 0.62/0.82 tff(181,plain,
% 0.62/0.82 (^[U: $i] : refl((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(182,plain,
% 0.62/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[181])).
% 0.62/0.82 tff(183,plain,
% 0.62/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(184,plain,
% 0.62/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(185,plain,
% 0.62/0.82 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[184])).
% 0.62/0.82 tff(186,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.62/0.82 tff(187,plain,
% 0.62/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.62/0.82 tff(188,plain,
% 0.62/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.62/0.82 tff(189,plain,(
% 0.62/0.82 ![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[188])).
% 0.62/0.82 tff(190,plain,
% 0.62/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.62/0.82 tff(191,assumption,(c1_1(a1080)), introduced(assumption)).
% 0.62/0.82 tff(192,assumption,(ndr1_0), introduced(assumption)).
% 0.62/0.82 tff(193,assumption,(~hskp14), introduced(assumption)).
% 0.62/0.82 tff(194,plain,
% 0.62/0.82 (^[U: $i] : refl((hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(195,plain,
% 0.62/0.82 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[194])).
% 0.62/0.82 tff(196,plain,
% 0.62/0.82 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(197,plain,
% 0.62/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(198,plain,
% 0.62/0.82 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[197])).
% 0.62/0.82 tff(199,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.62/0.82 tff(200,plain,
% 0.62/0.82 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.62/0.82 tff(201,plain,
% 0.62/0.82 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.62/0.82 tff(202,plain,(
% 0.62/0.82 ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[201])).
% 0.62/0.82 tff(203,plain,
% 0.62/0.82 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.62/0.82 tff(204,plain,
% 0.62/0.82 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(205,plain,
% 0.62/0.82 ((hskp15 | hskp14 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(206,plain,
% 0.62/0.82 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[205])).
% 0.62/0.82 tff(207,plain,
% 0.62/0.82 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[206, 204])).
% 0.62/0.82 tff(208,plain,
% 0.62/0.82 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(209,plain,
% 0.62/0.82 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.62/0.82 tff(210,plain,
% 0.62/0.82 (hskp15 | hskp14 | c0_1(a1080) | (~ndr1_0) | (~c1_1(a1080))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[209, 66, 203])).
% 0.62/0.82 tff(211,plain,
% 0.62/0.82 (hskp15),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[210, 193, 192, 191, 87])).
% 0.62/0.82 tff(212,plain,
% 0.62/0.82 (((~hskp15) | (~c1_1(a1098))) <=> ((~hskp15) | (~c1_1(a1098)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(213,plain,
% 0.62/0.82 (((~c1_1(a1098)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a1098)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(214,axiom,((~c1_1(a1098)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.62/0.82 tff(215,plain,
% 0.62/0.82 ((~hskp15) | (~c1_1(a1098))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.62/0.82 tff(216,plain,
% 0.62/0.82 ((~hskp15) | (~c1_1(a1098))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[215, 212])).
% 0.62/0.82 tff(217,plain,
% 0.62/0.82 (~c1_1(a1098)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[216, 211])).
% 0.62/0.82 tff(218,plain,
% 0.62/0.82 (((~hskp15) | c2_1(a1098)) <=> ((~hskp15) | c2_1(a1098))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(219,axiom,((~hskp15) | c2_1(a1098)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.62/0.82 tff(220,plain,
% 0.62/0.82 ((~hskp15) | c2_1(a1098)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.62/0.82 tff(221,plain,
% 0.62/0.82 ((~hskp15) | c2_1(a1098)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[220, 218])).
% 0.62/0.82 tff(222,plain,
% 0.62/0.82 ((~hskp15) | c2_1(a1098)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[221, 218])).
% 0.62/0.82 tff(223,plain,
% 0.62/0.82 ((~hskp15) | c2_1(a1098)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.62/0.82 tff(224,plain,
% 0.62/0.82 ((~hskp15) | c2_1(a1098)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[223, 218])).
% 0.62/0.82 tff(225,plain,
% 0.62/0.82 (c2_1(a1098)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[224, 211])).
% 0.62/0.82 tff(226,plain,
% 0.62/0.82 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(227,plain,
% 0.62/0.82 ((hskp14 | (~ndr1_0) | c1_1(a1098) | (~c2_1(a1098)) | (~c0_1(a1098))) <=> (hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(228,plain,
% 0.62/0.82 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1098) | (~c2_1(a1098)) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[227])).
% 0.62/0.82 tff(229,plain,
% 0.62/0.82 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1098) | (~c2_1(a1098)) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[228, 226])).
% 0.62/0.82 tff(230,plain,
% 0.62/0.82 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1098) | (~c2_1(a1098)) | (~c0_1(a1098)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(231,plain,
% 0.62/0.82 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.62/0.82 tff(232,plain,
% 0.62/0.82 (~c0_1(a1098)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[231, 192, 193, 225, 217, 190])).
% 0.62/0.82 tff(233,plain,
% 0.62/0.82 (^[U: $i] : refl((hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(234,plain,
% 0.62/0.82 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[233])).
% 0.62/0.82 tff(235,plain,
% 0.62/0.82 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(236,plain,
% 0.62/0.82 (^[U: $i] : 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)) | hskp18) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(237,plain,
% 0.62/0.82 (![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp18) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[236])).
% 0.62/0.82 tff(238,axiom,(![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.62/0.82 tff(239,plain,
% 0.62/0.82 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.62/0.82 tff(240,plain,
% 0.62/0.82 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[239, 235])).
% 0.62/0.82 tff(241,plain,(
% 0.62/0.82 ![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[240])).
% 0.62/0.82 tff(242,plain,
% 0.62/0.82 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[241, 234])).
% 0.62/0.82 tff(243,plain,
% 0.62/0.82 (((~hskp15) | (~c3_1(a1098))) <=> ((~hskp15) | (~c3_1(a1098)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(244,plain,
% 0.62/0.82 (((~c3_1(a1098)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1098)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(245,axiom,((~c3_1(a1098)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.62/0.82 tff(246,plain,
% 0.62/0.82 ((~hskp15) | (~c3_1(a1098))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.62/0.82 tff(247,plain,
% 0.62/0.82 ((~hskp15) | (~c3_1(a1098))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[246, 243])).
% 0.62/0.82 tff(248,plain,
% 0.62/0.82 (~c3_1(a1098)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[247, 211])).
% 0.62/0.82 tff(249,assumption,(~hskp18), introduced(assumption)).
% 0.62/0.82 tff(250,plain,
% 0.62/0.82 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(251,plain,
% 0.62/0.82 ((hskp18 | (~ndr1_0) | c0_1(a1098) | c3_1(a1098) | (~c2_1(a1098))) <=> (hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(252,plain,
% 0.62/0.82 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1098) | c3_1(a1098) | (~c2_1(a1098)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[251])).
% 0.62/0.82 tff(253,plain,
% 0.62/0.82 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1098) | c3_1(a1098) | (~c2_1(a1098)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[252, 250])).
% 0.62/0.82 tff(254,plain,
% 0.62/0.82 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1098) | c3_1(a1098) | (~c2_1(a1098)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(255,plain,
% 0.62/0.82 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.62/0.82 tff(256,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[255, 192, 249, 225, 248, 242, 232])).
% 0.62/0.82 tff(257,plain,(hskp14 | (~ndr1_0) | hskp18 | (~c1_1(a1080)) | c0_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(258,plain,
% 0.62/0.82 (hskp14 | hskp18 | (~c1_1(a1080)) | c0_1(a1080) | c2_1(a1080)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[257, 171])).
% 0.62/0.82 tff(259,plain,
% 0.62/0.82 (hskp14),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[258, 180, 114, 113, 112])).
% 0.62/0.82 tff(260,plain,
% 0.62/0.82 (((~hskp14) | (~c2_1(a1097))) <=> ((~hskp14) | (~c2_1(a1097)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(261,plain,
% 0.62/0.82 (((~c2_1(a1097)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1097)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(262,axiom,((~c2_1(a1097)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.62/0.82 tff(263,plain,
% 0.62/0.82 ((~hskp14) | (~c2_1(a1097))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.62/0.82 tff(264,plain,
% 0.62/0.82 ((~hskp14) | (~c2_1(a1097))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[263, 260])).
% 0.62/0.82 tff(265,plain,
% 0.62/0.82 (~c2_1(a1097)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[264, 259])).
% 0.62/0.82 tff(266,plain,
% 0.62/0.82 (((~hskp14) | c1_1(a1097)) <=> ((~hskp14) | c1_1(a1097))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(267,axiom,((~hskp14) | c1_1(a1097)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.62/0.83 tff(268,plain,
% 0.62/0.83 ((~hskp14) | c1_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.62/0.83 tff(269,plain,
% 0.62/0.83 ((~hskp14) | c1_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[268, 266])).
% 0.62/0.83 tff(270,plain,
% 0.62/0.83 ((~hskp14) | c1_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[269, 266])).
% 0.62/0.83 tff(271,plain,
% 0.62/0.83 ((~hskp14) | c1_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.62/0.83 tff(272,plain,
% 0.62/0.83 ((~hskp14) | c1_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[271, 266])).
% 0.62/0.83 tff(273,plain,
% 0.62/0.83 (c1_1(a1097)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[272, 259])).
% 0.62/0.83 tff(274,plain,
% 0.62/0.83 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(275,plain,
% 0.62/0.83 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097))) <=> (hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(276,plain,
% 0.62/0.83 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[275])).
% 0.62/0.83 tff(277,plain,
% 0.62/0.83 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[276, 274])).
% 0.62/0.83 tff(278,plain,
% 0.62/0.83 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(279,plain,
% 0.62/0.83 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.62/0.83 tff(280,plain,
% 0.62/0.83 (hskp30 | (~c0_1(a1097))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[279, 171, 54, 273, 265, 99])).
% 0.62/0.83 tff(281,plain,
% 0.62/0.83 (hskp30),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[280, 89])).
% 0.62/0.83 tff(282,plain,
% 0.62/0.83 (((~hskp30) | c1_1(a1109)) <=> ((~hskp30) | c1_1(a1109))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(283,axiom,((~hskp30) | c1_1(a1109)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.62/0.83 tff(284,plain,
% 0.62/0.83 ((~hskp30) | c1_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.62/0.83 tff(285,plain,
% 0.62/0.83 ((~hskp30) | c1_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[284, 282])).
% 0.62/0.83 tff(286,plain,
% 0.62/0.83 ((~hskp30) | c1_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[285, 282])).
% 0.62/0.83 tff(287,plain,
% 0.62/0.83 ((~hskp30) | c1_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.62/0.83 tff(288,plain,
% 0.62/0.83 ((~hskp30) | c1_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[287, 282])).
% 0.62/0.83 tff(289,plain,
% 0.62/0.83 (c1_1(a1109)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[288, 281])).
% 0.62/0.83 tff(290,plain,
% 0.62/0.83 (^[U: $i] : refl((hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(291,plain,
% 0.62/0.83 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[290])).
% 0.62/0.83 tff(292,plain,
% 0.62/0.83 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(293,plain,
% 0.62/0.83 (^[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)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp9) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp9))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp9) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(294,plain,
% 0.62/0.83 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp9) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[293])).
% 0.62/0.83 tff(295,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.62/0.83 tff(296,plain,
% 0.62/0.83 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.62/0.83 tff(297,plain,
% 0.62/0.83 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[296, 292])).
% 0.62/0.83 tff(298,plain,(
% 0.62/0.83 ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[297])).
% 0.62/0.83 tff(299,plain,
% 0.62/0.83 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[298, 291])).
% 0.62/0.83 tff(300,plain,
% 0.62/0.83 (((~hskp14) | c3_1(a1097)) <=> ((~hskp14) | c3_1(a1097))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(301,axiom,((~hskp14) | c3_1(a1097)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.62/0.83 tff(302,plain,
% 0.62/0.83 ((~hskp14) | c3_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.62/0.83 tff(303,plain,
% 0.62/0.83 ((~hskp14) | c3_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[302, 300])).
% 0.62/0.83 tff(304,plain,
% 0.62/0.83 ((~hskp14) | c3_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[303, 300])).
% 0.62/0.83 tff(305,plain,
% 0.62/0.83 ((~hskp14) | c3_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[304, 300])).
% 0.62/0.83 tff(306,plain,
% 0.62/0.83 ((~hskp14) | c3_1(a1097)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[305, 300])).
% 0.62/0.83 tff(307,plain,
% 0.62/0.83 (c3_1(a1097)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[306, 259])).
% 0.62/0.83 tff(308,plain,
% 0.62/0.83 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(309,plain,
% 0.62/0.83 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c0_1(a1097))) <=> (hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(310,plain,
% 0.62/0.83 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c0_1(a1097)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[309])).
% 0.62/0.83 tff(311,plain,
% 0.62/0.83 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c0_1(a1097)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[310, 308])).
% 0.62/0.83 tff(312,plain,
% 0.62/0.83 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c0_1(a1097)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(313,plain,
% 0.62/0.83 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.62/0.83 tff(314,plain,
% 0.62/0.83 (hskp28 | (~c0_1(a1097))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[313, 171, 54, 307, 265, 299])).
% 0.62/0.83 tff(315,plain,
% 0.62/0.83 (hskp28),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[314, 89])).
% 0.62/0.83 tff(316,plain,
% 0.62/0.83 (((~hskp30) | c0_1(a1109)) <=> ((~hskp30) | c0_1(a1109))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(317,axiom,((~hskp30) | c0_1(a1109)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.62/0.83 tff(318,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.62/0.83 tff(319,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[318, 316])).
% 0.62/0.83 tff(320,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[319, 316])).
% 0.62/0.83 tff(321,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[320, 316])).
% 0.62/0.83 tff(322,plain,
% 0.62/0.83 ((~hskp30) | c0_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[321, 316])).
% 0.62/0.83 tff(323,plain,
% 0.62/0.83 (c0_1(a1109)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[322, 281])).
% 0.62/0.83 tff(324,plain,
% 0.62/0.83 (((~hskp30) | c3_1(a1109)) <=> ((~hskp30) | c3_1(a1109))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(325,axiom,((~hskp30) | c3_1(a1109)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.62/0.83 tff(326,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.62/0.83 tff(327,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[326, 324])).
% 0.62/0.83 tff(328,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[327, 324])).
% 0.62/0.83 tff(329,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.62/0.83 tff(330,plain,
% 0.62/0.83 ((~hskp30) | c3_1(a1109)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[329, 324])).
% 0.62/0.83 tff(331,plain,
% 0.62/0.83 (c3_1(a1109)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[330, 281])).
% 0.62/0.83 tff(332,plain,
% 0.62/0.83 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(333,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | 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)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[332])).
% 0.62/0.83 tff(334,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | 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)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(335,plain,
% 0.62/0.83 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(336,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[335])).
% 0.62/0.83 tff(337,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.62/0.83 tff(338,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.62/0.83 tff(339,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[338, 334])).
% 0.62/0.83 tff(340,plain,(
% 0.62/0.83 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(skolemize,[status(sab)],[339])).
% 0.62/0.83 tff(341,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[340, 333])).
% 0.62/0.83 tff(342,assumption,(hskp28), introduced(assumption)).
% 0.62/0.83 tff(343,plain,
% 0.62/0.83 (((~hskp28) | c3_1(a1092)) <=> ((~hskp28) | c3_1(a1092))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(344,axiom,((~hskp28) | c3_1(a1092)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.62/0.83 tff(345,plain,
% 0.62/0.83 ((~hskp28) | c3_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.62/0.83 tff(346,plain,
% 0.62/0.83 ((~hskp28) | c3_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[345, 343])).
% 0.62/0.83 tff(347,plain,
% 0.62/0.83 ((~hskp28) | c3_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[346, 343])).
% 0.62/0.83 tff(348,plain,
% 0.62/0.83 ((~hskp28) | c3_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[347, 343])).
% 0.62/0.83 tff(349,plain,
% 0.62/0.83 ((~hskp28) | c3_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[348, 343])).
% 0.62/0.83 tff(350,plain,
% 0.62/0.83 (c3_1(a1092)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[349, 342])).
% 0.62/0.83 tff(351,plain,
% 0.62/0.83 (((~hskp28) | c2_1(a1092)) <=> ((~hskp28) | c2_1(a1092))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(352,axiom,((~hskp28) | c2_1(a1092)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.62/0.83 tff(353,plain,
% 0.62/0.83 ((~hskp28) | c2_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.62/0.83 tff(354,plain,
% 0.62/0.83 ((~hskp28) | c2_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[353, 351])).
% 0.62/0.83 tff(355,plain,
% 0.62/0.83 ((~hskp28) | c2_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[354, 351])).
% 0.62/0.83 tff(356,plain,
% 0.62/0.83 ((~hskp28) | c2_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[355, 351])).
% 0.62/0.83 tff(357,plain,
% 0.62/0.83 ((~hskp28) | c2_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[356, 351])).
% 0.62/0.83 tff(358,plain,
% 0.62/0.83 (c2_1(a1092)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[357, 342])).
% 0.62/0.83 tff(359,plain,
% 0.62/0.83 (((~hskp28) | c0_1(a1092)) <=> ((~hskp28) | c0_1(a1092))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(360,axiom,((~hskp28) | c0_1(a1092)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.62/0.83 tff(361,plain,
% 0.62/0.83 ((~hskp28) | c0_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.62/0.83 tff(362,plain,
% 0.62/0.83 ((~hskp28) | c0_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[361, 359])).
% 0.62/0.83 tff(363,plain,
% 0.62/0.83 ((~hskp28) | c0_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[362, 359])).
% 0.62/0.83 tff(364,plain,
% 0.62/0.83 ((~hskp28) | c0_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[363, 359])).
% 0.62/0.83 tff(365,plain,
% 0.62/0.83 ((~hskp28) | c0_1(a1092)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[364, 359])).
% 0.62/0.83 tff(366,plain,
% 0.62/0.83 (c0_1(a1092)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[365, 342])).
% 0.62/0.83 tff(367,assumption,(c3_1(a1109)), introduced(assumption)).
% 0.62/0.83 tff(368,assumption,(c1_1(a1109)), introduced(assumption)).
% 0.62/0.83 tff(369,assumption,(c0_1(a1109)), introduced(assumption)).
% 0.62/0.83 tff(370,plain,
% 0.62/0.83 ((ndr1_0 | (~hskp0)) <=> (ndr1_0 | (~hskp0))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(371,plain,
% 0.62/0.83 (((~hskp0) | ndr1_0) <=> (ndr1_0 | (~hskp0))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(372,axiom,((~hskp0) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.62/0.83 tff(373,plain,
% 0.62/0.83 (ndr1_0 | (~hskp0)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.62/0.83 tff(374,plain,
% 0.62/0.83 (ndr1_0 | (~hskp0)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[373, 370])).
% 0.62/0.83 tff(375,plain,
% 0.62/0.83 (ndr1_0),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[374, 111])).
% 0.62/0.83 tff(376,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(377,plain,
% 0.62/0.83 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085)) <=> (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(378,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[377])).
% 0.62/0.83 tff(379,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[378, 376])).
% 0.62/0.83 tff(380,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(381,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.62/0.83 tff(382,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[381, 375, 369, 368, 367, 366, 358, 350, 88, 12, 11, 341])).
% 0.62/0.83 tff(383,plain,((~hskp28) | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(384,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[383, 331, 323, 12, 88, 315, 289, 11])).
% 0.62/0.83 tff(385,plain,((~c0_1(a1097)) | c0_1(a1085) | c2_1(a1085) | c1_1(a1085) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(386,plain,
% 0.62/0.83 (~c0_1(a1097)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[385, 88, 12, 11, 54])).
% 0.62/0.83 tff(387,plain,
% 0.62/0.83 (^[U: $i] : refl((hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(388,plain,
% 0.62/0.83 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[387])).
% 0.62/0.83 tff(389,plain,
% 0.62/0.83 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(390,plain,
% 0.62/0.83 (^[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)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp2) <=> ((hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp2))), rewrite(((hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(391,plain,
% 0.62/0.83 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp2) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[390])).
% 0.62/0.83 tff(392,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.62/0.83 tff(393,plain,
% 0.62/0.83 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.62/0.83 tff(394,plain,
% 0.62/0.83 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[393, 389])).
% 0.62/0.83 tff(395,plain,(
% 0.62/0.83 ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[394])).
% 0.62/0.83 tff(396,plain,
% 0.62/0.83 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[395, 388])).
% 0.62/0.83 tff(397,plain,
% 0.62/0.83 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(398,plain,
% 0.62/0.83 ((hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097))) <=> (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(399,plain,
% 0.62/0.83 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[398])).
% 0.62/0.83 tff(400,plain,
% 0.62/0.83 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[399, 397])).
% 0.62/0.83 tff(401,plain,
% 0.62/0.83 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(402,plain,
% 0.62/0.83 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.62/0.83 tff(403,plain,
% 0.62/0.83 (hskp2 | c0_1(a1097)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[402, 171, 54, 273, 307, 396])).
% 0.62/0.83 tff(404,plain,
% 0.62/0.83 (hskp2),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[403, 386])).
% 0.62/0.83 tff(405,plain,
% 0.62/0.83 (((~hskp2) | (~c3_1(a1082))) <=> ((~hskp2) | (~c3_1(a1082)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(406,plain,
% 0.62/0.83 (((~c3_1(a1082)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a1082)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(407,axiom,((~c3_1(a1082)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.62/0.83 tff(408,plain,
% 0.62/0.83 ((~hskp2) | (~c3_1(a1082))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.62/0.83 tff(409,plain,
% 0.62/0.83 ((~hskp2) | (~c3_1(a1082))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[408, 405])).
% 0.62/0.83 tff(410,plain,
% 0.62/0.83 (~c3_1(a1082)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[409, 404])).
% 0.62/0.83 tff(411,assumption,(~hskp1), introduced(assumption)).
% 0.62/0.83 tff(412,assumption,(~c3_1(a1085)), introduced(assumption)).
% 0.62/0.83 tff(413,plain,
% 0.62/0.83 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(414,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_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) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[413])).
% 0.62/0.83 tff(415,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_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) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(416,plain,
% 0.62/0.83 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(417,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[416])).
% 0.62/0.83 tff(418,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.62/0.83 tff(419,plain,
% 0.62/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.62/0.84 tff(420,plain,
% 0.62/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[419, 415])).
% 0.62/0.84 tff(421,plain,(
% 0.62/0.84 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.84 inference(skolemize,[status(sab)],[420])).
% 0.62/0.84 tff(422,plain,
% 0.62/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[421, 414])).
% 0.62/0.84 tff(423,plain,
% 0.62/0.84 (hskp14),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[257, 375, 249, 191, 87, 66])).
% 0.62/0.84 tff(424,assumption,(~c3_1(a1080)), introduced(assumption)).
% 0.62/0.84 tff(425,plain,
% 0.62/0.84 (^[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)) | c1_1(W) | 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)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(426,plain,
% 0.62/0.84 (![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)) | c1_1(W) | 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)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[425])).
% 0.62/0.84 tff(427,plain,
% 0.62/0.84 (![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)) | c1_1(W) | 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)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(428,plain,
% 0.62/0.84 (^[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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_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)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_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))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_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)) | c1_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)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_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)) | c1_1(W) | c0_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)) | c1_1(W) | 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)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_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)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(429,plain,
% 0.62/0.84 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[428])).
% 0.62/0.84 tff(430,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.62/0.84 tff(431,plain,
% 0.62/0.84 (![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)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.62/0.84 tff(432,plain,
% 0.62/0.84 (![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)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[431, 427])).
% 0.62/0.84 tff(433,plain,(
% 0.62/0.84 ![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)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.62/0.84 inference(skolemize,[status(sab)],[432])).
% 0.62/0.84 tff(434,plain,
% 0.62/0.84 (![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)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[433, 426])).
% 0.62/0.84 tff(435,assumption,(hskp14), introduced(assumption)).
% 0.62/0.84 tff(436,plain,
% 0.62/0.84 (~c2_1(a1097)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[264, 435])).
% 0.62/0.84 tff(437,plain,
% 0.62/0.84 (c3_1(a1097)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[306, 435])).
% 0.62/0.84 tff(438,plain,
% 0.62/0.84 (c1_1(a1097)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[272, 435])).
% 0.62/0.84 tff(439,plain,
% 0.62/0.84 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(440,plain,
% 0.62/0.84 (((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085)) <=> (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(441,plain,
% 0.62/0.84 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[440])).
% 0.62/0.84 tff(442,plain,
% 0.62/0.84 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[441, 439])).
% 0.62/0.84 tff(443,plain,
% 0.62/0.84 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(444,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.62/0.84 tff(445,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[444, 192, 438, 437, 191, 436, 12, 11, 66, 434, 424, 412])).
% 0.62/0.84 tff(446,plain,((~hskp14) | (~ndr1_0) | (~c1_1(a1080)) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | c3_1(a1080) | c3_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(447,plain,
% 0.62/0.84 (c3_1(a1080)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[446, 412, 191, 12, 11, 66, 375, 423])).
% 0.62/0.84 tff(448,plain,
% 0.62/0.84 (^[U: $i] : refl((hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(449,plain,
% 0.62/0.84 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[448])).
% 0.62/0.84 tff(450,plain,
% 0.62/0.84 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(451,plain,
% 0.62/0.84 (^[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)) | hskp30) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp30))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) | hskp18) <=> ((hskp30 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp30 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) | hskp18) <=> (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(452,plain,
% 0.62/0.84 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) | hskp18) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[451])).
% 0.62/0.84 tff(453,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.62/0.84 tff(454,plain,
% 0.62/0.84 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.62/0.84 tff(455,plain,
% 0.62/0.84 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[454, 450])).
% 0.62/0.84 tff(456,plain,(
% 0.62/0.84 ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.84 inference(skolemize,[status(sab)],[455])).
% 0.62/0.84 tff(457,plain,
% 0.62/0.84 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[456, 449])).
% 0.62/0.84 tff(458,plain,
% 0.62/0.84 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(459,plain,
% 0.62/0.84 ((hskp30 | hskp18 | (~ndr1_0) | c0_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080))) <=> (hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(460,plain,
% 0.62/0.84 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[459])).
% 0.62/0.84 tff(461,plain,
% 0.62/0.84 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[460, 458])).
% 0.62/0.84 tff(462,plain,
% 0.62/0.84 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(463,plain,
% 0.62/0.84 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.62/0.84 tff(464,plain,
% 0.62/0.84 (hskp30 | hskp18 | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[463, 87, 457])).
% 0.62/0.84 tff(465,plain,
% 0.62/0.84 (hskp30),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[464, 447, 249, 191, 375])).
% 0.62/0.84 tff(466,plain,
% 0.62/0.84 (c3_1(a1109)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[330, 465])).
% 0.62/0.84 tff(467,plain,
% 0.62/0.84 (c1_1(a1109)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[288, 465])).
% 0.62/0.84 tff(468,plain,
% 0.62/0.84 (c0_1(a1109)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[322, 465])).
% 0.62/0.84 tff(469,assumption,(c2_1(a1109)), introduced(assumption)).
% 0.62/0.84 tff(470,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(471,plain,
% 0.62/0.84 (((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085)) <=> (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(472,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[471])).
% 0.62/0.84 tff(473,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[472, 470])).
% 0.62/0.84 tff(474,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(475,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.62/0.84 tff(476,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[475, 375, 369, 368, 367, 88, 12, 11, 341, 469])).
% 0.62/0.84 tff(477,plain,((~c2_1(a1109)) | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(478,plain,
% 0.62/0.84 (~c2_1(a1109)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[477, 468, 467, 466, 88, 12, 11])).
% 0.62/0.84 tff(479,plain,
% 0.62/0.84 (~hskp28),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[383, 468, 467, 466, 88, 12, 11])).
% 0.62/0.84 tff(480,plain,
% 0.62/0.84 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(481,plain,
% 0.62/0.84 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a1109) | (~c3_1(a1109)) | (~c0_1(a1109))) <=> (hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(482,plain,
% 0.62/0.84 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1109) | (~c3_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109)))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[481])).
% 0.62/0.84 tff(483,plain,
% 0.62/0.84 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1109) | (~c3_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109))),
% 0.62/0.84 inference(transitivity,[status(thm)],[482, 480])).
% 0.62/0.84 tff(484,plain,
% 0.62/0.84 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1109) | (~c3_1(a1109)) | (~c0_1(a1109)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(485,plain,
% 0.62/0.84 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.62/0.84 tff(486,plain,
% 0.62/0.84 (hskp28 | hskp9 | c2_1(a1109)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[485, 375, 468, 466, 299])).
% 0.62/0.84 tff(487,plain,
% 0.62/0.84 (hskp9),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[486, 479, 478])).
% 0.62/0.84 tff(488,plain,
% 0.62/0.84 (((~hskp9) | (~c1_1(a1089))) <=> ((~hskp9) | (~c1_1(a1089)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(489,plain,
% 0.62/0.84 (((~c1_1(a1089)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1089)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(490,axiom,((~c1_1(a1089)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.62/0.84 tff(491,plain,
% 0.62/0.84 ((~hskp9) | (~c1_1(a1089))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.62/0.84 tff(492,plain,
% 0.62/0.84 ((~hskp9) | (~c1_1(a1089))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[491, 488])).
% 0.62/0.84 tff(493,plain,
% 0.62/0.84 (~c1_1(a1089)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[492, 487])).
% 0.62/0.84 tff(494,plain,
% 0.62/0.84 (((~hskp9) | c3_1(a1089)) <=> ((~hskp9) | c3_1(a1089))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(495,axiom,((~hskp9) | c3_1(a1089)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.62/0.84 tff(496,plain,
% 0.62/0.84 ((~hskp9) | c3_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.62/0.84 tff(497,plain,
% 0.62/0.84 ((~hskp9) | c3_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[496, 494])).
% 0.62/0.84 tff(498,plain,
% 0.62/0.84 ((~hskp9) | c3_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[497, 494])).
% 0.62/0.84 tff(499,plain,
% 0.62/0.84 ((~hskp9) | c3_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[498, 494])).
% 0.62/0.84 tff(500,plain,
% 0.62/0.84 ((~hskp9) | c3_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[499, 494])).
% 0.62/0.84 tff(501,plain,
% 0.62/0.84 (c3_1(a1089)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[500, 487])).
% 0.62/0.84 tff(502,plain,
% 0.62/0.84 (((~hskp9) | c2_1(a1089)) <=> ((~hskp9) | c2_1(a1089))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(503,axiom,((~hskp9) | c2_1(a1089)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.62/0.84 tff(504,plain,
% 0.62/0.84 ((~hskp9) | c2_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.62/0.84 tff(505,plain,
% 0.62/0.84 ((~hskp9) | c2_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[504, 502])).
% 0.62/0.84 tff(506,plain,
% 0.62/0.84 ((~hskp9) | c2_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[505, 502])).
% 0.62/0.84 tff(507,plain,
% 0.62/0.84 ((~hskp9) | c2_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[506, 502])).
% 0.62/0.84 tff(508,plain,
% 0.62/0.84 ((~hskp9) | c2_1(a1089)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[507, 502])).
% 0.62/0.84 tff(509,plain,
% 0.62/0.84 (c2_1(a1089)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[508, 487])).
% 0.62/0.84 tff(510,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(511,plain,
% 0.62/0.84 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1085) | c0_1(a1085) | c3_1(a1085) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085)) <=> (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(512,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1085) | c0_1(a1085) | c3_1(a1085) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[511])).
% 0.62/0.84 tff(513,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1085) | c0_1(a1085) | c3_1(a1085) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[512, 510])).
% 0.62/0.84 tff(514,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1085) | c0_1(a1085) | c3_1(a1085) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(515,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.62/0.84 tff(516,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[515, 375, 509, 501, 88, 493, 12, 11, 422, 412])).
% 0.62/0.84 tff(517,plain,(c3_1(a1085) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | hskp18 | (~c1_1(a1080)) | c0_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(518,plain,
% 0.62/0.84 (c3_1(a1085)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[517, 180, 12, 11, 112, 114, 113, 88])).
% 0.62/0.84 tff(519,plain,
% 0.62/0.84 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(520,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[519])).
% 0.62/0.84 tff(521,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(522,plain,
% 0.62/0.84 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~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(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(523,plain,
% 0.62/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[522])).
% 0.62/0.85 tff(524,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.62/0.85 tff(525,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.62/0.85 tff(526,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[525, 521])).
% 0.62/0.85 tff(527,plain,(
% 0.62/0.85 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(skolemize,[status(sab)],[526])).
% 0.62/0.85 tff(528,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[527, 520])).
% 0.62/0.85 tff(529,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(530,plain,
% 0.62/0.85 ((hskp1 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)) | c2_1(a1085) | c1_1(a1085) | (~c3_1(a1085))) <=> (hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(531,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)) | c2_1(a1085) | c1_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[530])).
% 0.62/0.85 tff(532,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)) | c2_1(a1085) | c1_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[531, 529])).
% 0.62/0.85 tff(533,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)) | c2_1(a1085) | c1_1(a1085) | (~c3_1(a1085)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(534,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.62/0.85 tff(535,plain,
% 0.62/0.85 (hskp1 | (~c0_1(a1097))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[534, 171, 273, 88, 265, 11, 528, 518])).
% 0.62/0.85 tff(536,plain,
% 0.62/0.85 (~c0_1(a1097)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[535, 411])).
% 0.62/0.85 tff(537,plain,
% 0.62/0.85 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(538,plain,
% 0.62/0.85 ((hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097))) <=> (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(539,plain,
% 0.62/0.85 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[538])).
% 0.62/0.85 tff(540,plain,
% 0.62/0.85 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[539, 537])).
% 0.62/0.85 tff(541,plain,
% 0.62/0.85 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(542,plain,
% 0.62/0.85 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.62/0.85 tff(543,plain,
% 0.62/0.85 (hskp30 | c0_1(a1097)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[542, 171, 180, 273, 307, 457])).
% 0.62/0.85 tff(544,plain,
% 0.62/0.85 (hskp30),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[543, 536])).
% 0.62/0.85 tff(545,plain,
% 0.62/0.85 (c1_1(a1109)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[288, 544])).
% 0.62/0.85 tff(546,plain,
% 0.62/0.85 (^[U: $i] : refl((hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(547,plain,
% 0.62/0.85 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[546])).
% 0.62/0.85 tff(548,plain,
% 0.62/0.85 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(549,plain,
% 0.62/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) | hskp1) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp1))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp1) <=> (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) | hskp1) <=> (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(550,plain,
% 0.62/0.85 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) | hskp1) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[549])).
% 0.62/0.85 tff(551,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.62/0.85 tff(552,plain,
% 0.62/0.85 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.62/0.85 tff(553,plain,
% 0.62/0.85 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[552, 548])).
% 0.62/0.85 tff(554,plain,(
% 0.62/0.85 ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.62/0.85 inference(skolemize,[status(sab)],[553])).
% 0.62/0.85 tff(555,plain,
% 0.62/0.85 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[554, 547])).
% 0.62/0.85 tff(556,plain,
% 0.62/0.85 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(557,plain,
% 0.62/0.85 ((hskp28 | hskp1 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085))) <=> (hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(558,plain,
% 0.69/0.85 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[557])).
% 0.69/0.85 tff(559,plain,
% 0.69/0.85 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[558, 556])).
% 0.69/0.85 tff(560,plain,
% 0.69/0.85 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(561,plain,
% 0.69/0.85 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.69/0.85 tff(562,plain,
% 0.69/0.85 (hskp28 | hskp1 | c0_1(a1085) | (~c3_1(a1085))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[561, 171, 11, 555])).
% 0.69/0.85 tff(563,plain,
% 0.69/0.85 (hskp28),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[562, 411, 12, 518])).
% 0.69/0.85 tff(564,plain,
% 0.69/0.85 (c0_1(a1109)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[322, 544])).
% 0.69/0.85 tff(565,plain,
% 0.69/0.85 (c3_1(a1109)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[330, 544])).
% 0.69/0.85 tff(566,plain,
% 0.69/0.85 ($false),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[383, 565, 564, 12, 88, 563, 545, 11])).
% 0.69/0.85 tff(567,plain,(hskp1 | c0_1(a1085) | c2_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.85 tff(568,plain,
% 0.69/0.85 (hskp1),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[567, 88, 12, 11])).
% 0.69/0.85 tff(569,plain,
% 0.69/0.85 (((~hskp2) | (~c0_1(a1082))) <=> ((~hskp2) | (~c0_1(a1082)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(570,plain,
% 0.69/0.85 (((~c0_1(a1082)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1082)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(571,axiom,((~c0_1(a1082)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.69/0.85 tff(572,plain,
% 0.69/0.85 ((~hskp2) | (~c0_1(a1082))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.69/0.85 tff(573,plain,
% 0.69/0.85 ((~hskp2) | (~c0_1(a1082))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[572, 569])).
% 0.69/0.85 tff(574,plain,
% 0.69/0.85 (~c0_1(a1082)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[573, 404])).
% 0.69/0.85 tff(575,plain,
% 0.69/0.85 (((~hskp2) | (~c2_1(a1082))) <=> ((~hskp2) | (~c2_1(a1082)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(576,plain,
% 0.69/0.85 (((~c2_1(a1082)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1082)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(577,axiom,((~c2_1(a1082)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.69/0.85 tff(578,plain,
% 0.69/0.85 ((~hskp2) | (~c2_1(a1082))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.69/0.85 tff(579,plain,
% 0.69/0.85 ((~hskp2) | (~c2_1(a1082))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[578, 575])).
% 0.69/0.85 tff(580,plain,
% 0.69/0.85 (~c2_1(a1082)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[579, 404])).
% 0.69/0.85 tff(581,assumption,(~c2_1(a1082)), introduced(assumption)).
% 0.69/0.85 tff(582,assumption,(~c3_1(a1082)), introduced(assumption)).
% 0.69/0.85 tff(583,assumption,(~c0_1(a1082)), introduced(assumption)).
% 0.69/0.85 tff(584,assumption,(hskp1), introduced(assumption)).
% 0.69/0.85 tff(585,plain,
% 0.69/0.85 (((~hskp1) | (~c0_1(a1081))) <=> ((~hskp1) | (~c0_1(a1081)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(586,plain,
% 0.69/0.85 (((~c0_1(a1081)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1081)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(587,axiom,((~c0_1(a1081)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.69/0.85 tff(588,plain,
% 0.69/0.85 ((~hskp1) | (~c0_1(a1081))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.69/0.85 tff(589,plain,
% 0.69/0.85 ((~hskp1) | (~c0_1(a1081))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[588, 585])).
% 0.69/0.85 tff(590,plain,
% 0.69/0.85 (~c0_1(a1081)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[589, 584])).
% 0.69/0.85 tff(591,plain,
% 0.69/0.85 (((~hskp1) | (~c1_1(a1081))) <=> ((~hskp1) | (~c1_1(a1081)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(592,plain,
% 0.69/0.85 (((~c1_1(a1081)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1081)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(593,axiom,((~c1_1(a1081)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.69/0.85 tff(594,plain,
% 0.69/0.85 ((~hskp1) | (~c1_1(a1081))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.69/0.85 tff(595,plain,
% 0.69/0.85 ((~hskp1) | (~c1_1(a1081))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[594, 591])).
% 0.69/0.85 tff(596,plain,
% 0.69/0.85 (~c1_1(a1081)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[595, 584])).
% 0.69/0.85 tff(597,assumption,(~c1_1(a1081)), introduced(assumption)).
% 0.69/0.85 tff(598,assumption,(~c0_1(a1081)), introduced(assumption)).
% 0.69/0.85 tff(599,plain,
% 0.69/0.85 (ndr1_0),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[374, 116])).
% 0.69/0.85 tff(600,assumption,(~hskp30), introduced(assumption)).
% 0.69/0.85 tff(601,plain,
% 0.69/0.85 (~c3_1(a1080)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[464, 600, 249, 191, 599])).
% 0.69/0.85 tff(602,plain,
% 0.69/0.85 (hskp14),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[257, 599, 249, 191, 87, 66])).
% 0.69/0.85 tff(603,plain,
% 0.69/0.85 (~c2_1(a1097)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[264, 602])).
% 0.69/0.85 tff(604,plain,
% 0.69/0.85 (c3_1(a1097)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[306, 602])).
% 0.69/0.85 tff(605,plain,
% 0.69/0.85 (c1_1(a1097)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[272, 602])).
% 0.69/0.85 tff(606,plain,
% 0.69/0.85 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(607,plain,
% 0.69/0.85 (((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081)) <=> (c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(608,plain,
% 0.69/0.85 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[607])).
% 0.69/0.85 tff(609,plain,
% 0.69/0.85 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[608, 606])).
% 0.69/0.85 tff(610,plain,
% 0.69/0.85 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(611,plain,
% 0.69/0.85 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.69/0.85 tff(612,plain,
% 0.69/0.85 (c3_1(a1081) | c3_1(a1080)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[611, 599, 605, 604, 191, 603, 598, 597, 66, 434])).
% 0.69/0.85 tff(613,plain,
% 0.69/0.85 (c3_1(a1081)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[612, 601])).
% 0.69/0.85 tff(614,plain,
% 0.69/0.85 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(615,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[614])).
% 0.69/0.85 tff(616,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(617,plain,
% 0.69/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(618,plain,
% 0.69/0.85 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[617])).
% 0.69/0.85 tff(619,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.69/0.85 tff(620,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.69/0.85 tff(621,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[620, 616])).
% 0.69/0.85 tff(622,plain,(
% 0.69/0.85 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[621])).
% 0.69/0.85 tff(623,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[622, 615])).
% 0.69/0.85 tff(624,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(625,plain,
% 0.69/0.85 ((hskp5 | (~ndr1_0) | c1_1(a1081) | (~c2_1(a1081)) | (~c3_1(a1081)) | c1_1(a1081) | c0_1(a1081) | (~c2_1(a1081))) <=> (hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(626,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1081) | (~c2_1(a1081)) | (~c3_1(a1081)) | c1_1(a1081) | c0_1(a1081) | (~c2_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[625])).
% 0.69/0.85 tff(627,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1081) | (~c2_1(a1081)) | (~c3_1(a1081)) | c1_1(a1081) | c0_1(a1081) | (~c2_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[626, 624])).
% 0.69/0.85 tff(628,plain,
% 0.69/0.85 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1081) | (~c2_1(a1081)) | (~c3_1(a1081)) | c1_1(a1081) | c0_1(a1081) | (~c2_1(a1081)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(629,plain,
% 0.69/0.85 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.69/0.85 tff(630,plain,
% 0.69/0.85 (hskp5 | c0_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[629, 597, 623])).
% 0.69/0.85 tff(631,plain,
% 0.69/0.85 (~c2_1(a1081)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[630, 613, 115, 598, 599])).
% 0.69/0.85 tff(632,plain,
% 0.69/0.85 (hskp30 | c0_1(a1097)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[542, 599, 249, 605, 604, 457])).
% 0.69/0.86 tff(633,plain,
% 0.69/0.86 (c0_1(a1097)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[632, 600])).
% 0.69/0.86 tff(634,plain,
% 0.69/0.86 (hskp30 | hskp9 | (~c0_1(a1097))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[279, 599, 605, 603, 99])).
% 0.69/0.86 tff(635,plain,
% 0.69/0.86 (hskp9),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[634, 633, 600])).
% 0.69/0.86 tff(636,plain,
% 0.69/0.86 (~c1_1(a1089)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[492, 635])).
% 0.69/0.86 tff(637,plain,
% 0.69/0.86 (c3_1(a1089)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[500, 635])).
% 0.69/0.86 tff(638,plain,
% 0.69/0.86 (c2_1(a1089)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[508, 635])).
% 0.69/0.86 tff(639,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(640,plain,
% 0.69/0.86 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1081) | c1_1(a1081) | c0_1(a1081)) <=> (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(641,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1081) | c1_1(a1081) | c0_1(a1081))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[640])).
% 0.69/0.86 tff(642,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1081) | c1_1(a1081) | c0_1(a1081))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[641, 639])).
% 0.69/0.86 tff(643,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1081) | c1_1(a1081) | c0_1(a1081))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(644,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.69/0.86 tff(645,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[644, 599, 638, 637, 636, 583, 581, 582, 598, 597, 422, 631])).
% 0.69/0.86 tff(646,plain,(hskp30 | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | hskp5 | (~c1_1(a1080)) | c2_1(a1080) | hskp18 | c0_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(647,plain,
% 0.69/0.86 (hskp30),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[646, 126, 581, 582, 598, 597, 583, 115, 66, 249, 87])).
% 0.69/0.86 tff(648,plain,
% 0.69/0.86 (c3_1(a1109)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[330, 647])).
% 0.69/0.86 tff(649,plain,
% 0.69/0.86 (c1_1(a1109)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[288, 647])).
% 0.69/0.86 tff(650,plain,
% 0.69/0.86 (c0_1(a1109)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[322, 647])).
% 0.69/0.86 tff(651,assumption,(hskp11), introduced(assumption)).
% 0.69/0.86 tff(652,plain,
% 0.69/0.86 (((~hskp11) | (~c3_1(a1091))) <=> ((~hskp11) | (~c3_1(a1091)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(653,plain,
% 0.69/0.86 (((~c3_1(a1091)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a1091)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(654,axiom,((~c3_1(a1091)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.69/0.86 tff(655,plain,
% 0.69/0.86 ((~hskp11) | (~c3_1(a1091))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.69/0.86 tff(656,plain,
% 0.69/0.86 ((~hskp11) | (~c3_1(a1091))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[655, 652])).
% 0.69/0.86 tff(657,plain,
% 0.69/0.86 (~c3_1(a1091)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[656, 651])).
% 0.69/0.86 tff(658,plain,
% 0.69/0.86 (((~hskp11) | (~c0_1(a1091))) <=> ((~hskp11) | (~c0_1(a1091)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(659,plain,
% 0.69/0.86 (((~c0_1(a1091)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a1091)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(660,axiom,((~c0_1(a1091)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.69/0.86 tff(661,plain,
% 0.69/0.86 ((~hskp11) | (~c0_1(a1091))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[660, 659])).
% 0.69/0.86 tff(662,plain,
% 0.69/0.86 ((~hskp11) | (~c0_1(a1091))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[661, 658])).
% 0.69/0.86 tff(663,plain,
% 0.69/0.86 (~c0_1(a1091)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[662, 651])).
% 0.69/0.86 tff(664,plain,
% 0.69/0.86 (((~hskp11) | c2_1(a1091)) <=> ((~hskp11) | c2_1(a1091))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(665,axiom,((~hskp11) | c2_1(a1091)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.69/0.86 tff(666,plain,
% 0.69/0.86 ((~hskp11) | c2_1(a1091)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.69/0.86 tff(667,plain,
% 0.69/0.86 ((~hskp11) | c2_1(a1091)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[666, 664])).
% 0.69/0.86 tff(668,plain,
% 0.69/0.86 ((~hskp11) | c2_1(a1091)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[667, 664])).
% 0.69/0.86 tff(669,plain,
% 0.69/0.86 ((~hskp11) | c2_1(a1091)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[668, 664])).
% 0.69/0.86 tff(670,plain,
% 0.69/0.86 ((~hskp11) | c2_1(a1091)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[669, 664])).
% 0.69/0.86 tff(671,plain,
% 0.69/0.86 (c2_1(a1091)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[670, 651])).
% 0.69/0.86 tff(672,plain,
% 0.69/0.86 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(673,plain,
% 0.69/0.86 ((hskp18 | (~ndr1_0) | c0_1(a1091) | c3_1(a1091) | (~c2_1(a1091))) <=> (hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(674,plain,
% 0.69/0.86 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1091) | c3_1(a1091) | (~c2_1(a1091)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[673])).
% 0.69/0.86 tff(675,plain,
% 0.69/0.86 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1091) | c3_1(a1091) | (~c2_1(a1091)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[674, 672])).
% 0.69/0.86 tff(676,plain,
% 0.69/0.86 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1091) | c3_1(a1091) | (~c2_1(a1091)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(677,plain,
% 0.69/0.86 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.69/0.86 tff(678,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[677, 192, 249, 671, 663, 657, 242])).
% 0.69/0.86 tff(679,plain,((~hskp11) | (~ndr1_0) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(680,plain,
% 0.69/0.86 (~hskp11),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[679, 599, 249])).
% 0.69/0.86 tff(681,plain,
% 0.69/0.86 (hskp14),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[257, 599, 249, 126, 87, 66])).
% 0.69/0.86 tff(682,plain,
% 0.69/0.86 (~c2_1(a1097)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[264, 681])).
% 0.69/0.86 tff(683,plain,
% 0.69/0.86 (c3_1(a1097)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[306, 681])).
% 0.69/0.86 tff(684,plain,
% 0.69/0.86 (c1_1(a1097)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[272, 681])).
% 0.69/0.86 tff(685,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(686,plain,
% 0.69/0.86 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(687,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[686])).
% 0.69/0.86 tff(688,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[687, 685])).
% 0.69/0.86 tff(689,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(690,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.69/0.86 tff(691,plain,
% 0.69/0.86 (c1_1(a1082)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[690, 192, 369, 368, 367, 366, 358, 350, 583, 581, 341])).
% 0.69/0.86 tff(692,plain,
% 0.69/0.86 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(693,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[692])).
% 0.69/0.86 tff(694,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(695,plain,
% 0.69/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(696,plain,
% 0.69/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[695])).
% 0.69/0.86 tff(697,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.69/0.86 tff(698,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.69/0.86 tff(699,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[698, 694])).
% 0.69/0.86 tff(700,plain,(
% 0.69/0.86 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[699])).
% 0.69/0.86 tff(701,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[700, 693])).
% 0.69/0.86 tff(702,assumption,(~hskp11), introduced(assumption)).
% 0.69/0.86 tff(703,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(704,plain,
% 0.69/0.86 ((hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1081) | c0_1(a1081) | (~c3_1(a1081))) <=> (hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(705,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1081) | c0_1(a1081) | (~c3_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[704])).
% 0.69/0.86 tff(706,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1081) | c0_1(a1081) | (~c3_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[705, 703])).
% 0.69/0.86 tff(707,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1081) | c0_1(a1081) | (~c3_1(a1081)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(708,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.69/0.86 tff(709,plain,
% 0.69/0.86 (~c3_1(a1081)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[708, 192, 702, 366, 358, 350, 598, 597, 701])).
% 0.69/0.86 tff(710,assumption,(~c2_1(a1097)), introduced(assumption)).
% 0.69/0.86 tff(711,assumption,(c3_1(a1097)), introduced(assumption)).
% 0.69/0.86 tff(712,assumption,(c1_1(a1097)), introduced(assumption)).
% 0.69/0.86 tff(713,plain,
% 0.69/0.86 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(714,plain,
% 0.69/0.86 (((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1082) | c3_1(a1082) | (~c1_1(a1082)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081)) <=> (c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(715,plain,
% 0.69/0.86 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1082) | c3_1(a1082) | (~c1_1(a1082)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[714])).
% 0.69/0.86 tff(716,plain,
% 0.69/0.86 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1082) | c3_1(a1082) | (~c1_1(a1082)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[715, 713])).
% 0.69/0.86 tff(717,plain,
% 0.69/0.86 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1082) | c3_1(a1082) | (~c1_1(a1082)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(718,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.69/0.86 tff(719,plain,
% 0.69/0.86 (c3_1(a1081) | (~c1_1(a1082))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[718, 192, 712, 711, 710, 581, 582, 598, 597, 434])).
% 0.69/0.86 tff(720,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[719, 709, 691])).
% 0.69/0.86 tff(721,plain,((~hskp28) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | hskp11 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | c0_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(722,plain,
% 0.69/0.86 (~hskp28),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[721, 599, 684, 683, 682, 581, 582, 598, 597, 680, 650, 649, 648, 583])).
% 0.69/0.86 tff(723,assumption,(~hskp28), introduced(assumption)).
% 0.69/0.86 tff(724,plain,
% 0.69/0.86 (hskp28 | hskp9 | c2_1(a1109)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[485, 599, 369, 367, 299])).
% 0.69/0.86 tff(725,plain,
% 0.69/0.86 (c2_1(a1109)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[724, 723, 54])).
% 0.69/0.86 tff(726,plain,
% 0.69/0.86 (^[U: $i] : refl((hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(727,plain,
% 0.69/0.86 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[726])).
% 0.69/0.86 tff(728,plain,
% 0.69/0.86 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(729,plain,
% 0.69/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) | hskp13) <=> ((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) | hskp13) <=> (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(730,plain,
% 0.69/0.86 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) | hskp13) <=> ![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[729])).
% 0.69/0.86 tff(731,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.69/0.86 tff(732,plain,
% 0.69/0.86 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.69/0.86 tff(733,plain,
% 0.69/0.86 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[732, 728])).
% 0.69/0.86 tff(734,plain,(
% 0.69/0.86 ![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[733])).
% 0.69/0.86 tff(735,plain,
% 0.69/0.86 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[734, 727])).
% 0.69/0.86 tff(736,plain,
% 0.69/0.86 (((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))) <=> ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(737,plain,
% 0.69/0.86 ((hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109))) <=> (hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(738,plain,
% 0.69/0.86 (((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[737])).
% 0.69/0.86 tff(739,plain,
% 0.69/0.86 (((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[738, 736])).
% 0.69/0.86 tff(740,plain,
% 0.69/0.86 ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(741,plain,
% 0.71/0.86 ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.71/0.86 tff(742,plain,
% 0.71/0.86 (hskp13 | (~c2_1(a1109))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[741, 115, 599, 369, 368, 735])).
% 0.71/0.86 tff(743,plain,
% 0.71/0.86 (hskp13),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[742, 725])).
% 0.71/0.86 tff(744,plain,
% 0.71/0.86 (((~hskp13) | (~c2_1(a1095))) <=> ((~hskp13) | (~c2_1(a1095)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(745,plain,
% 0.71/0.86 (((~c2_1(a1095)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1095)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(746,axiom,((~c2_1(a1095)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.71/0.86 tff(747,plain,
% 0.71/0.86 ((~hskp13) | (~c2_1(a1095))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.71/0.86 tff(748,plain,
% 0.71/0.86 ((~hskp13) | (~c2_1(a1095))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[747, 744])).
% 0.71/0.86 tff(749,plain,
% 0.71/0.86 (~c2_1(a1095)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[748, 743])).
% 0.71/0.86 tff(750,plain,
% 0.71/0.86 (((~hskp13) | (~c1_1(a1095))) <=> ((~hskp13) | (~c1_1(a1095)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(751,plain,
% 0.71/0.86 (((~c1_1(a1095)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1095)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(752,axiom,((~c1_1(a1095)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.71/0.86 tff(753,plain,
% 0.71/0.86 ((~hskp13) | (~c1_1(a1095))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.71/0.86 tff(754,plain,
% 0.71/0.86 ((~hskp13) | (~c1_1(a1095))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[753, 750])).
% 0.71/0.86 tff(755,plain,
% 0.71/0.86 (~c1_1(a1095)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[754, 743])).
% 0.71/0.86 tff(756,plain,
% 0.71/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(757,plain,
% 0.71/0.86 (((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1095) | c1_1(a1095) | c0_1(a1095)) <=> (c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(758,plain,
% 0.71/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1095) | c1_1(a1095) | c0_1(a1095))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[757])).
% 0.71/0.86 tff(759,plain,
% 0.71/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1095) | c1_1(a1095) | c0_1(a1095))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[758, 756])).
% 0.71/0.87 tff(760,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1095) | c1_1(a1095) | c0_1(a1095))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(761,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.71/0.87 tff(762,plain,
% 0.71/0.87 (c0_1(a1095)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[761, 599, 369, 368, 367, 755, 749, 341, 725])).
% 0.71/0.87 tff(763,plain,
% 0.71/0.87 (((~hskp13) | c3_1(a1095)) <=> ((~hskp13) | c3_1(a1095))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(764,axiom,((~hskp13) | c3_1(a1095)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.71/0.87 tff(765,plain,
% 0.71/0.87 ((~hskp13) | c3_1(a1095)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[764, 763])).
% 0.71/0.87 tff(766,plain,
% 0.71/0.87 ((~hskp13) | c3_1(a1095)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[765, 763])).
% 0.71/0.87 tff(767,plain,
% 0.71/0.87 ((~hskp13) | c3_1(a1095)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[766, 763])).
% 0.71/0.87 tff(768,plain,
% 0.71/0.87 ((~hskp13) | c3_1(a1095)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[767, 763])).
% 0.71/0.87 tff(769,plain,
% 0.71/0.87 ((~hskp13) | c3_1(a1095)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[768, 763])).
% 0.71/0.87 tff(770,plain,
% 0.71/0.87 (c3_1(a1095)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[769, 743])).
% 0.71/0.87 tff(771,plain,
% 0.71/0.87 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(772,plain,
% 0.71/0.87 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095))) <=> (hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(773,plain,
% 0.71/0.87 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[772])).
% 0.71/0.87 tff(774,plain,
% 0.71/0.87 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[773, 771])).
% 0.71/0.87 tff(775,plain,
% 0.71/0.87 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(776,plain,
% 0.71/0.87 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.71/0.87 tff(777,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[776, 599, 723, 54, 770, 749, 299, 762])).
% 0.71/0.87 tff(778,plain,(hskp28 | hskp9 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(779,plain,
% 0.71/0.87 (hskp9),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[778, 722, 650, 649, 648, 115])).
% 0.71/0.87 tff(780,plain,
% 0.71/0.87 (~c1_1(a1089)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[492, 779])).
% 0.71/0.87 tff(781,plain,
% 0.71/0.87 (c3_1(a1089)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[500, 779])).
% 0.71/0.87 tff(782,plain,
% 0.71/0.87 (c2_1(a1089)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[508, 779])).
% 0.71/0.87 tff(783,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(784,plain,
% 0.71/0.87 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(785,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[784])).
% 0.71/0.87 tff(786,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[785, 783])).
% 0.71/0.87 tff(787,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(788,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.71/0.87 tff(789,plain,
% 0.71/0.87 (c1_1(a1082)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[788, 599, 782, 781, 780, 583, 581, 582, 422])).
% 0.71/0.87 tff(790,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(791,plain,
% 0.71/0.87 ((hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082))) <=> (hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(792,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[791])).
% 0.71/0.87 tff(793,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[792, 790])).
% 0.71/0.87 tff(794,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(795,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.71/0.87 tff(796,plain,
% 0.71/0.87 (~c0_1(a1089)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[795, 115, 599, 781, 780, 583, 581, 10, 789])).
% 0.71/0.87 tff(797,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(798,plain,
% 0.71/0.87 ((hskp5 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089))) <=> (hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(799,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[798])).
% 0.71/0.87 tff(800,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[799, 797])).
% 0.71/0.87 tff(801,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(802,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.71/0.87 tff(803,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[802, 115, 599, 782, 781, 780, 623, 796])).
% 0.71/0.87 tff(804,plain,(hskp5 | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | hskp18 | c2_1(a1080) | c0_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(805,plain,
% 0.71/0.87 (hskp5),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[804, 249, 581, 582, 598, 597, 583, 66, 87])).
% 0.71/0.87 tff(806,plain,
% 0.71/0.87 (((~hskp5) | (~c1_1(a1085))) <=> ((~hskp5) | (~c1_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(807,plain,
% 0.71/0.87 (((~c1_1(a1085)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(808,axiom,((~c1_1(a1085)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.71/0.87 tff(809,plain,
% 0.71/0.87 ((~hskp5) | (~c1_1(a1085))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.71/0.87 tff(810,plain,
% 0.71/0.87 ((~hskp5) | (~c1_1(a1085))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[809, 806])).
% 0.71/0.87 tff(811,plain,
% 0.71/0.87 (~c1_1(a1085)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[810, 805])).
% 0.71/0.87 tff(812,plain,
% 0.71/0.87 (((~hskp5) | (~c0_1(a1085))) <=> ((~hskp5) | (~c0_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(813,plain,
% 0.71/0.87 (((~c0_1(a1085)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(814,axiom,((~c0_1(a1085)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.71/0.87 tff(815,plain,
% 0.71/0.87 ((~hskp5) | (~c0_1(a1085))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[814, 813])).
% 0.71/0.87 tff(816,plain,
% 0.71/0.87 ((~hskp5) | (~c0_1(a1085))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[815, 812])).
% 0.71/0.87 tff(817,plain,
% 0.71/0.87 (~c0_1(a1085)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[816, 805])).
% 0.71/0.87 tff(818,plain,
% 0.71/0.87 (c2_1(a1085)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[106, 805])).
% 0.71/0.87 tff(819,plain,
% 0.71/0.87 ((ndr1_0 | (~hskp5)) <=> (ndr1_0 | (~hskp5))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(820,plain,
% 0.71/0.87 (((~hskp5) | ndr1_0) <=> (ndr1_0 | (~hskp5))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(821,axiom,((~hskp5) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 0.71/0.87 tff(822,plain,
% 0.71/0.87 (ndr1_0 | (~hskp5)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.71/0.87 tff(823,plain,
% 0.71/0.87 (ndr1_0 | (~hskp5)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[822, 819])).
% 0.71/0.87 tff(824,plain,
% 0.71/0.87 (ndr1_0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[823, 805])).
% 0.71/0.87 tff(825,plain,
% 0.71/0.87 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(826,plain,
% 0.71/0.87 ((hskp18 | (~ndr1_0) | c0_1(a1085) | c3_1(a1085) | (~c2_1(a1085))) <=> (hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(827,plain,
% 0.71/0.87 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1085) | c3_1(a1085) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[826])).
% 0.71/0.87 tff(828,plain,
% 0.71/0.87 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1085) | c3_1(a1085) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 0.71/0.87 inference(transitivity,[status(thm)],[827, 825])).
% 0.71/0.87 tff(829,plain,
% 0.71/0.87 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1085) | c3_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(830,plain,
% 0.71/0.87 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[829, 828])).
% 0.71/0.87 tff(831,plain,
% 0.71/0.87 (c3_1(a1085)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[830, 824, 249, 818, 817, 242])).
% 0.71/0.87 tff(832,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(833,plain,
% 0.71/0.87 (((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(834,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[833])).
% 0.71/0.87 tff(835,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[834, 832])).
% 0.71/0.87 tff(836,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(837,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.71/0.87 tff(838,plain,
% 0.71/0.87 (c1_1(a1082)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[837, 824, 818, 811, 583, 581, 582, 422, 831])).
% 0.71/0.87 tff(839,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(840,plain,
% 0.71/0.87 ((hskp3 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(841,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[840])).
% 0.71/0.87 tff(842,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[841, 839])).
% 0.71/0.87 tff(843,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(844,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.71/0.87 tff(845,plain,
% 0.71/0.87 (hskp3),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[844, 824, 818, 817, 811, 583, 581, 22, 838])).
% 0.71/0.87 tff(846,plain,
% 0.71/0.87 (((~hskp3) | (~c2_1(a1083))) <=> ((~hskp3) | (~c2_1(a1083)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(847,plain,
% 0.71/0.87 (((~c2_1(a1083)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1083)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(848,axiom,((~c2_1(a1083)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.71/0.87 tff(849,plain,
% 0.71/0.87 ((~hskp3) | (~c2_1(a1083))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[848, 847])).
% 0.71/0.87 tff(850,plain,
% 0.71/0.87 ((~hskp3) | (~c2_1(a1083))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[849, 846])).
% 0.71/0.87 tff(851,plain,
% 0.71/0.87 (~c2_1(a1083)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[850, 845])).
% 0.71/0.87 tff(852,plain,
% 0.71/0.87 (((~hskp3) | (~c3_1(a1083))) <=> ((~hskp3) | (~c3_1(a1083)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(853,plain,
% 0.71/0.87 (((~c3_1(a1083)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1083)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(854,axiom,((~c3_1(a1083)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.71/0.87 tff(855,plain,
% 0.71/0.87 ((~hskp3) | (~c3_1(a1083))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.71/0.87 tff(856,plain,
% 0.71/0.87 ((~hskp3) | (~c3_1(a1083))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[855, 852])).
% 0.71/0.87 tff(857,plain,
% 0.71/0.87 (~c3_1(a1083)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[856, 845])).
% 0.71/0.87 tff(858,assumption,(~c1_1(a1080)), introduced(assumption)).
% 0.71/0.87 tff(859,plain,
% 0.71/0.87 (~hskp0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[42, 858])).
% 0.71/0.87 tff(860,plain,
% 0.71/0.87 (hskp5),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[110, 859])).
% 0.71/0.87 tff(861,plain,
% 0.71/0.87 (ndr1_0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[823, 860])).
% 0.71/0.87 tff(862,plain,
% 0.71/0.87 (c2_1(a1085)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[106, 860])).
% 0.71/0.87 tff(863,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(864,plain,
% 0.71/0.87 (((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080)) <=> (c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(865,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[864])).
% 0.71/0.87 tff(866,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[865, 863])).
% 0.71/0.87 tff(867,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(868,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[867, 866])).
% 0.71/0.87 tff(869,plain,
% 0.71/0.87 (c1_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[868, 11, 583, 581, 582, 87, 66, 422])).
% 0.71/0.87 tff(870,plain,
% 0.71/0.87 (~c3_1(a1085)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[869, 862, 858, 861])).
% 0.71/0.87 tff(871,plain,
% 0.71/0.87 ((~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[830, 249, 12, 242])).
% 0.71/0.87 tff(872,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[871, 870, 862, 861])).
% 0.71/0.87 tff(873,plain,(c1_1(a1080) | hskp18 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(874,plain,
% 0.71/0.87 (c1_1(a1080)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[873, 12, 249, 11, 583, 581, 582, 87, 66])).
% 0.71/0.87 tff(875,plain,
% 0.71/0.87 ((ndr1_0 | (~hskp30)) <=> (ndr1_0 | (~hskp30))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(876,plain,
% 0.71/0.87 (((~hskp30) | ndr1_0) <=> (ndr1_0 | (~hskp30))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(877,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.71/0.87 tff(878,plain,
% 0.71/0.87 (ndr1_0 | (~hskp30)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.71/0.87 tff(879,plain,
% 0.71/0.87 (ndr1_0 | (~hskp30)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[878, 875])).
% 0.71/0.87 tff(880,plain,
% 0.71/0.87 (~hskp30),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[879, 143])).
% 0.71/0.87 tff(881,plain,
% 0.71/0.87 (~hskp5),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[823, 143])).
% 0.71/0.87 tff(882,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[646, 881, 880, 581, 582, 598, 597, 583, 191, 66, 249, 87])).
% 0.71/0.87 tff(883,plain,(ndr1_0 | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | (~c1_1(a1080)) | c2_1(a1080) | hskp18 | c0_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(884,plain,
% 0.71/0.87 (ndr1_0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[883, 874, 582, 598, 597, 583, 581, 66, 249, 87])).
% 0.71/0.87 tff(885,plain,
% 0.71/0.87 (hskp30),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[646, 107, 581, 582, 598, 597, 583, 874, 66, 249, 87])).
% 0.71/0.87 tff(886,plain,
% 0.71/0.87 (c0_1(a1109)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[322, 885])).
% 0.71/0.87 tff(887,plain,
% 0.71/0.87 (c1_1(a1109)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[288, 885])).
% 0.71/0.87 tff(888,plain,
% 0.71/0.88 (c3_1(a1109)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[330, 885])).
% 0.71/0.88 tff(889,plain,
% 0.71/0.88 (~c2_1(a1109)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[477, 888, 887, 886, 88, 12, 11])).
% 0.71/0.88 tff(890,plain,
% 0.71/0.88 (~hskp28),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[383, 886, 887, 888, 88, 12, 11])).
% 0.71/0.88 tff(891,plain,
% 0.71/0.88 (hskp9),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[485, 375, 890, 886, 888, 299, 889])).
% 0.71/0.88 tff(892,plain,
% 0.71/0.88 (~c1_1(a1089)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[492, 891])).
% 0.71/0.88 tff(893,plain,
% 0.71/0.88 (c3_1(a1089)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[500, 891])).
% 0.71/0.88 tff(894,plain,
% 0.71/0.88 (c2_1(a1089)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[508, 891])).
% 0.71/0.88 tff(895,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(896,plain,
% 0.71/0.88 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085)) <=> (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(897,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[896])).
% 0.71/0.88 tff(898,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[897, 895])).
% 0.71/0.88 tff(899,plain,
% 0.71/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(900,plain,
% 0.71/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.71/0.88 tff(901,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[900, 375, 894, 893, 88, 892, 12, 11, 583, 581, 582, 422])).
% 0.71/0.88 tff(902,plain,(c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | hskp18 | c0_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(903,plain,
% 0.71/0.88 (c2_1(a1085)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[902, 12, 11, 583, 581, 582, 598, 597, 66, 249, 87])).
% 0.71/0.88 tff(904,plain,
% 0.71/0.88 (c3_1(a1085)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[871, 884, 903])).
% 0.71/0.88 tff(905,plain,
% 0.71/0.88 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(906,plain,
% 0.71/0.88 ((hskp19 | (~ndr1_0) | c0_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085))) <=> (hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(907,plain,
% 0.71/0.88 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[906])).
% 0.71/0.88 tff(908,plain,
% 0.71/0.88 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[907, 905])).
% 0.71/0.88 tff(909,plain,
% 0.71/0.88 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(910,plain,
% 0.71/0.88 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[909, 908])).
% 0.71/0.88 tff(911,plain,
% 0.71/0.88 (hskp19 | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[910, 12, 76])).
% 0.71/0.88 tff(912,plain,
% 0.71/0.88 (hskp19),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[911, 904, 903, 884])).
% 0.71/0.88 tff(913,plain,
% 0.71/0.88 (((~hskp19) | (~c2_1(a1113))) <=> ((~hskp19) | (~c2_1(a1113)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(914,plain,
% 0.71/0.88 (((~c2_1(a1113)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1113)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(915,axiom,((~c2_1(a1113)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.71/0.88 tff(916,plain,
% 0.71/0.88 ((~hskp19) | (~c2_1(a1113))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[915, 914])).
% 0.71/0.88 tff(917,plain,
% 0.71/0.88 ((~hskp19) | (~c2_1(a1113))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[916, 913])).
% 0.71/0.88 tff(918,plain,
% 0.71/0.88 (~c2_1(a1113)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[917, 912])).
% 0.71/0.88 tff(919,plain,
% 0.71/0.88 (((~hskp19) | c1_1(a1113)) <=> ((~hskp19) | c1_1(a1113))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(920,axiom,((~hskp19) | c1_1(a1113)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.71/0.88 tff(921,plain,
% 0.71/0.88 ((~hskp19) | c1_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.71/0.88 tff(922,plain,
% 0.71/0.88 ((~hskp19) | c1_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[921, 919])).
% 0.71/0.88 tff(923,plain,
% 0.71/0.88 ((~hskp19) | c1_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[922, 919])).
% 0.71/0.88 tff(924,plain,
% 0.71/0.88 ((~hskp19) | c1_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[923, 919])).
% 0.71/0.88 tff(925,plain,
% 0.71/0.88 ((~hskp19) | c1_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[924, 919])).
% 0.71/0.88 tff(926,plain,
% 0.71/0.88 (c1_1(a1113)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[925, 912])).
% 0.71/0.88 tff(927,plain,
% 0.71/0.88 (((~hskp19) | c0_1(a1113)) <=> ((~hskp19) | c0_1(a1113))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(928,axiom,((~hskp19) | c0_1(a1113)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.71/0.88 tff(929,plain,
% 0.71/0.88 ((~hskp19) | c0_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[928, 927])).
% 0.71/0.88 tff(930,plain,
% 0.71/0.88 ((~hskp19) | c0_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[929, 927])).
% 0.71/0.88 tff(931,plain,
% 0.71/0.88 ((~hskp19) | c0_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[930, 927])).
% 0.71/0.88 tff(932,plain,
% 0.71/0.88 ((~hskp19) | c0_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[931, 927])).
% 0.71/0.88 tff(933,plain,
% 0.71/0.88 ((~hskp19) | c0_1(a1113)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[932, 927])).
% 0.71/0.88 tff(934,plain,
% 0.71/0.88 (c0_1(a1113)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[933, 912])).
% 0.71/0.88 tff(935,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(936,plain,
% 0.71/0.88 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1113) | c3_1(a1113) | (~c0_1(a1113)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(937,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1113) | c3_1(a1113) | (~c0_1(a1113)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[936])).
% 0.71/0.88 tff(938,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1113) | c3_1(a1113) | (~c0_1(a1113)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[937, 935])).
% 0.71/0.88 tff(939,plain,
% 0.71/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1113) | c3_1(a1113) | (~c0_1(a1113)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(940,plain,
% 0.71/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.71/0.88 tff(941,plain,
% 0.71/0.88 (c3_1(a1113)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[940, 884, 934, 926, 903, 918, 12, 11, 64])).
% 0.71/0.88 tff(942,assumption,(~c3_1(a1083)), introduced(assumption)).
% 0.71/0.88 tff(943,assumption,(~c2_1(a1083)), introduced(assumption)).
% 0.71/0.88 tff(944,plain,
% 0.71/0.88 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(945,plain,
% 0.71/0.88 ((hskp21 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085))) <=> (hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(946,plain,
% 0.71/0.88 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[945])).
% 0.71/0.88 tff(947,plain,
% 0.71/0.88 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[946, 944])).
% 0.71/0.88 tff(948,plain,
% 0.71/0.88 ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(949,plain,
% 0.71/0.88 ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.71/0.88 tff(950,plain,
% 0.71/0.88 (hskp21 | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[949, 11, 53])).
% 0.71/0.88 tff(951,plain,
% 0.71/0.88 (hskp21),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[950, 904, 903, 884])).
% 0.71/0.88 tff(952,plain,
% 0.71/0.88 (((~hskp21) | (~c3_1(a1120))) <=> ((~hskp21) | (~c3_1(a1120)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(953,plain,
% 0.71/0.88 (((~c3_1(a1120)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a1120)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(954,axiom,((~c3_1(a1120)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.71/0.88 tff(955,plain,
% 0.71/0.88 ((~hskp21) | (~c3_1(a1120))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.71/0.88 tff(956,plain,
% 0.71/0.88 ((~hskp21) | (~c3_1(a1120))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[955, 952])).
% 0.71/0.88 tff(957,plain,
% 0.71/0.88 (~c3_1(a1120)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[956, 951])).
% 0.71/0.88 tff(958,plain,
% 0.71/0.88 (((~hskp21) | c2_1(a1120)) <=> ((~hskp21) | c2_1(a1120))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(959,axiom,((~hskp21) | c2_1(a1120)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.71/0.88 tff(960,plain,
% 0.71/0.88 ((~hskp21) | c2_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.71/0.88 tff(961,plain,
% 0.71/0.88 ((~hskp21) | c2_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[960, 958])).
% 0.71/0.88 tff(962,plain,
% 0.71/0.88 ((~hskp21) | c2_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[961, 958])).
% 0.71/0.88 tff(963,plain,
% 0.71/0.88 ((~hskp21) | c2_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[962, 958])).
% 0.71/0.88 tff(964,plain,
% 0.71/0.88 ((~hskp21) | c2_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[963, 958])).
% 0.71/0.88 tff(965,plain,
% 0.71/0.88 (c2_1(a1120)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[964, 951])).
% 0.71/0.88 tff(966,plain,
% 0.71/0.88 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(967,plain,
% 0.71/0.88 ((hskp18 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120))) <=> (hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(968,plain,
% 0.71/0.88 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[967])).
% 0.71/0.88 tff(969,plain,
% 0.71/0.88 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[968, 966])).
% 0.71/0.88 tff(970,plain,
% 0.71/0.88 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(971,plain,
% 0.71/0.88 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.71/0.88 tff(972,plain,
% 0.71/0.88 (c0_1(a1120)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[971, 884, 249, 965, 957, 242])).
% 0.71/0.88 tff(973,plain,
% 0.71/0.88 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(974,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[973])).
% 0.71/0.88 tff(975,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(976,plain,
% 0.71/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(977,plain,
% 0.71/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[976])).
% 0.71/0.88 tff(978,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.71/0.88 tff(979,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[978, 977])).
% 0.71/0.88 tff(980,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[979, 975])).
% 0.71/0.88 tff(981,plain,(
% 0.71/0.88 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[980])).
% 0.71/0.88 tff(982,plain,
% 0.71/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[981, 974])).
% 0.71/0.88 tff(983,plain,
% 0.71/0.88 (((~hskp21) | c1_1(a1120)) <=> ((~hskp21) | c1_1(a1120))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(984,axiom,((~hskp21) | c1_1(a1120)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.71/0.88 tff(985,plain,
% 0.71/0.88 ((~hskp21) | c1_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[984, 983])).
% 0.71/0.88 tff(986,plain,
% 0.71/0.88 ((~hskp21) | c1_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[985, 983])).
% 0.71/0.88 tff(987,plain,
% 0.71/0.88 ((~hskp21) | c1_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[986, 983])).
% 0.71/0.88 tff(988,plain,
% 0.71/0.88 ((~hskp21) | c1_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[987, 983])).
% 0.71/0.88 tff(989,plain,
% 0.71/0.88 ((~hskp21) | c1_1(a1120)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[988, 983])).
% 0.71/0.88 tff(990,plain,
% 0.71/0.88 (c1_1(a1120)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[989, 951])).
% 0.71/0.88 tff(991,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(992,plain,
% 0.71/0.88 ((hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085))) <=> (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(993,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[992])).
% 0.71/0.88 tff(994,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[993, 991])).
% 0.71/0.88 tff(995,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(996,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.71/0.88 tff(997,plain,
% 0.71/0.88 (hskp10),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[996, 884, 990, 965, 12, 11, 982, 904, 972])).
% 0.71/0.88 tff(998,plain,
% 0.71/0.88 (((~hskp10) | (~c3_1(a1090))) <=> ((~hskp10) | (~c3_1(a1090)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(999,plain,
% 0.71/0.88 (((~c3_1(a1090)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a1090)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1000,axiom,((~c3_1(a1090)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.71/0.88 tff(1001,plain,
% 0.71/0.88 ((~hskp10) | (~c3_1(a1090))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.71/0.88 tff(1002,plain,
% 0.71/0.88 ((~hskp10) | (~c3_1(a1090))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1001, 998])).
% 0.71/0.88 tff(1003,plain,
% 0.71/0.88 (~c3_1(a1090)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1002, 997])).
% 0.71/0.88 tff(1004,plain,
% 0.71/0.88 (((~hskp10) | (~c1_1(a1090))) <=> ((~hskp10) | (~c1_1(a1090)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1005,plain,
% 0.71/0.88 (((~c1_1(a1090)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1090)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1006,axiom,((~c1_1(a1090)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.71/0.88 tff(1007,plain,
% 0.71/0.88 ((~hskp10) | (~c1_1(a1090))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.71/0.88 tff(1008,plain,
% 0.71/0.88 ((~hskp10) | (~c1_1(a1090))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1007, 1004])).
% 0.71/0.88 tff(1009,plain,
% 0.71/0.88 (~c1_1(a1090)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1008, 997])).
% 0.71/0.88 tff(1010,plain,
% 0.71/0.88 (((~hskp10) | (~c0_1(a1090))) <=> ((~hskp10) | (~c0_1(a1090)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1011,plain,
% 0.71/0.88 (((~c0_1(a1090)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a1090)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1012,axiom,((~c0_1(a1090)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.71/0.88 tff(1013,plain,
% 0.71/0.88 ((~hskp10) | (~c0_1(a1090))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 0.71/0.88 tff(1014,plain,
% 0.71/0.88 ((~hskp10) | (~c0_1(a1090))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1013, 1010])).
% 0.71/0.88 tff(1015,plain,
% 0.71/0.88 (~c0_1(a1090)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1014, 997])).
% 0.71/0.88 tff(1016,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1017,plain,
% 0.71/0.88 ((hskp3 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1018,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1017])).
% 0.71/0.88 tff(1019,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1018, 1016])).
% 0.71/0.88 tff(1020,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1021,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.71/0.88 tff(1022,plain,
% 0.71/0.88 (hskp3 | c0_1(a1085) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1021, 11, 87, 66, 22])).
% 0.71/0.88 tff(1023,plain,
% 0.71/0.88 (hskp3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1022, 884, 874, 903, 12])).
% 0.71/0.88 tff(1024,plain,
% 0.71/0.88 (((~hskp3) | c1_1(a1083)) <=> ((~hskp3) | c1_1(a1083))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1025,axiom,((~hskp3) | c1_1(a1083)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.71/0.88 tff(1026,plain,
% 0.71/0.88 ((~hskp3) | c1_1(a1083)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 0.71/0.88 tff(1027,plain,
% 0.71/0.88 ((~hskp3) | c1_1(a1083)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1026, 1024])).
% 0.71/0.88 tff(1028,plain,
% 0.71/0.88 ((~hskp3) | c1_1(a1083)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1027, 1024])).
% 0.71/0.88 tff(1029,plain,
% 0.71/0.88 ((~hskp3) | c1_1(a1083)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1028, 1024])).
% 0.71/0.88 tff(1030,plain,
% 0.71/0.88 ((~hskp3) | c1_1(a1083)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1029, 1024])).
% 0.71/0.88 tff(1031,plain,
% 0.71/0.88 (c1_1(a1083)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1030, 1023])).
% 0.71/0.88 tff(1032,plain,
% 0.71/0.88 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1033,plain,
% 0.71/0.88 (((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090)) <=> (c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1034,plain,
% 0.71/0.88 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1033])).
% 0.71/0.88 tff(1035,plain,
% 0.71/0.88 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1034, 1032])).
% 0.71/0.89 tff(1036,plain,
% 0.71/0.89 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1037,plain,
% 0.71/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 0.71/0.89 tff(1038,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1037, 884, 926, 1031, 918, 1015, 1009, 1003, 943, 942, 434, 941])).
% 0.71/0.89 tff(1039,plain,(c0_1(a1085) | c2_1(a1083) | c3_1(a1083) | c1_1(a1085) | hskp18 | c0_1(a1080) | c2_1(a1080) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1040,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1039, 857, 851, 817, 811, 249, 87, 66, 582, 598, 597, 583, 581])).
% 0.71/0.89 tff(1041,plain,(hskp18 | c0_1(a1080) | c2_1(a1080) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1042,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1041, 596, 590, 66, 249, 583, 582, 87, 581])).
% 0.71/0.89 tff(1043,plain,((~hskp1) | c2_1(a1080) | hskp18 | c0_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1044,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1043, 580, 574, 180, 568, 112, 113, 410])).
% 0.71/0.89 tff(1045,plain,(c2_1(a1085) | hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1046,plain,
% 0.71/0.89 (c2_1(a1085)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1045, 54, 12, 11])).
% 0.71/0.89 tff(1047,plain,
% 0.71/0.89 ((~hskp11) | hskp18),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[679, 171])).
% 0.71/0.89 tff(1048,plain,
% 0.71/0.89 (~hskp11),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1047, 249])).
% 0.71/0.89 tff(1049,plain,
% 0.71/0.89 (hskp18 | (~c2_1(a1085)) | c3_1(a1085)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[830, 171, 12, 242])).
% 0.71/0.89 tff(1050,plain,
% 0.71/0.89 (c3_1(a1085)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1049, 249, 1046])).
% 0.71/0.89 tff(1051,plain,
% 0.71/0.89 (^[U: $i] : refl((hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1052,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1051])).
% 0.71/0.89 tff(1053,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1054,plain,
% 0.71/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) | hskp11) <=> ((hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp11))), rewrite(((hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) | hskp11) <=> (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1055,plain,
% 0.71/0.89 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) | hskp11) <=> ![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1054])).
% 0.71/0.89 tff(1056,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.71/0.89 tff(1057,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.71/0.89 tff(1058,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1057, 1053])).
% 0.71/0.89 tff(1059,plain,(
% 0.71/0.89 ![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[1058])).
% 0.71/0.89 tff(1060,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1059, 1052])).
% 0.71/0.89 tff(1061,plain,
% 0.71/0.89 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1062,plain,
% 0.71/0.89 ((hskp11 | hskp9 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085))) <=> (hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1063,plain,
% 0.71/0.89 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1062])).
% 0.71/0.89 tff(1064,plain,
% 0.71/0.89 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1063, 1061])).
% 0.71/0.89 tff(1065,plain,
% 0.71/0.89 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1066,plain,
% 0.71/0.89 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 0.71/0.89 tff(1067,plain,
% 0.71/0.89 (hskp11 | hskp9 | (~c2_1(a1085)) | (~c3_1(a1085))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1066, 171, 11, 1060])).
% 0.71/0.89 tff(1068,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1067, 1050, 1048, 54, 1046])).
% 0.71/0.89 tff(1069,plain,(hskp18 | hskp9 | c1_1(a1085) | c0_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1070,plain,
% 0.71/0.89 (hskp18),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1069, 54, 11, 12])).
% 0.71/0.89 tff(1071,plain,
% 0.71/0.89 (c0_1(a1103)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[141, 1070])).
% 0.71/0.89 tff(1072,plain,
% 0.71/0.89 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1073,plain,
% 0.71/0.89 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1072])).
% 0.71/0.89 tff(1074,plain,
% 0.71/0.89 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1075,plain,
% 0.71/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1076,plain,
% 0.71/0.89 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1075])).
% 0.71/0.89 tff(1077,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.71/0.89 tff(1078,plain,
% 0.71/0.89 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.71/0.89 tff(1079,plain,
% 0.71/0.89 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1078, 1074])).
% 0.71/0.89 tff(1080,plain,(
% 0.71/0.89 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[1079])).
% 0.71/0.89 tff(1081,plain,
% 0.71/0.89 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1080, 1073])).
% 0.71/0.89 tff(1082,plain,
% 0.71/0.89 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1083,plain,
% 0.71/0.89 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1084,plain,
% 0.71/0.89 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1083])).
% 0.71/0.89 tff(1085,plain,
% 0.71/0.89 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1084, 1082])).
% 0.71/0.89 tff(1086,plain,
% 0.71/0.89 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1087,plain,
% 0.71/0.89 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.71/0.89 tff(1088,plain,
% 0.71/0.89 (hskp9 | hskp8 | c0_1(a1085) | (~c2_1(a1085))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1087, 171, 11, 1081])).
% 0.71/0.89 tff(1089,plain,
% 0.71/0.89 (hskp8),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1088, 1046, 54, 12])).
% 0.71/0.89 tff(1090,plain,
% 0.71/0.89 (((~hskp8) | (~c2_1(a1088))) <=> ((~hskp8) | (~c2_1(a1088)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1091,plain,
% 0.71/0.89 (((~c2_1(a1088)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a1088)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1092,axiom,((~c2_1(a1088)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.71/0.89 tff(1093,plain,
% 0.71/0.89 ((~hskp8) | (~c2_1(a1088))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.71/0.89 tff(1094,plain,
% 0.71/0.89 ((~hskp8) | (~c2_1(a1088))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1093, 1090])).
% 0.71/0.89 tff(1095,plain,
% 0.71/0.89 (~c2_1(a1088)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1094, 1089])).
% 0.71/0.89 tff(1096,plain,
% 0.71/0.89 (((~hskp8) | c3_1(a1088)) <=> ((~hskp8) | c3_1(a1088))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1097,axiom,((~hskp8) | c3_1(a1088)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.71/0.89 tff(1098,plain,
% 0.71/0.89 ((~hskp8) | c3_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 0.71/0.89 tff(1099,plain,
% 0.71/0.89 ((~hskp8) | c3_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1098, 1096])).
% 0.71/0.89 tff(1100,plain,
% 0.71/0.89 ((~hskp8) | c3_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1099, 1096])).
% 0.71/0.89 tff(1101,plain,
% 0.71/0.89 ((~hskp8) | c3_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1100, 1096])).
% 0.71/0.89 tff(1102,plain,
% 0.71/0.89 ((~hskp8) | c3_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1101, 1096])).
% 0.71/0.89 tff(1103,plain,
% 0.71/0.89 (c3_1(a1088)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1102, 1089])).
% 0.71/0.89 tff(1104,plain,
% 0.71/0.89 (((~hskp8) | c0_1(a1088)) <=> ((~hskp8) | c0_1(a1088))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1105,axiom,((~hskp8) | c0_1(a1088)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.71/0.89 tff(1106,plain,
% 0.71/0.89 ((~hskp8) | c0_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 0.71/0.89 tff(1107,plain,
% 0.71/0.89 ((~hskp8) | c0_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1106, 1104])).
% 0.71/0.89 tff(1108,plain,
% 0.71/0.89 ((~hskp8) | c0_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1107, 1104])).
% 0.71/0.89 tff(1109,plain,
% 0.71/0.89 ((~hskp8) | c0_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1108, 1104])).
% 0.71/0.89 tff(1110,plain,
% 0.71/0.89 ((~hskp8) | c0_1(a1088)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1109, 1104])).
% 0.71/0.89 tff(1111,plain,
% 0.71/0.89 (c0_1(a1088)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1110, 1089])).
% 0.71/0.89 tff(1112,plain,
% 0.71/0.89 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1113,plain,
% 0.71/0.89 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088))) <=> (hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1114,plain,
% 0.71/0.89 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1113])).
% 0.71/0.89 tff(1115,plain,
% 0.71/0.89 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1114, 1112])).
% 0.71/0.89 tff(1116,plain,
% 0.71/0.89 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1117,plain,
% 0.71/0.89 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 0.71/0.89 tff(1118,plain,
% 0.71/0.89 (hskp28),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1117, 171, 54, 1111, 1103, 1095, 299])).
% 0.71/0.89 tff(1119,plain,
% 0.71/0.89 (c2_1(a1092)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[357, 1118])).
% 0.71/0.89 tff(1120,plain,
% 0.71/0.89 (c0_1(a1092)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[365, 1118])).
% 0.71/0.89 tff(1121,plain,
% 0.71/0.89 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1122,plain,
% 0.71/0.89 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1123,plain,
% 0.71/0.89 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.71/0.89 tff(1124,plain,
% 0.71/0.89 (hskp14 | c1_1(a1092)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1123, 171, 1120, 1119, 190])).
% 0.71/0.89 tff(1125,plain,
% 0.71/0.89 (c1_1(a1092)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1124, 193])).
% 0.71/0.89 tff(1126,plain,
% 0.71/0.89 (c3_1(a1092)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[349, 1118])).
% 0.71/0.89 tff(1127,plain,
% 0.71/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1128,plain,
% 0.71/0.89 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080)) <=> (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1129,plain,
% 0.71/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1128])).
% 0.71/0.89 tff(1130,plain,
% 0.71/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1129, 1127])).
% 0.71/0.89 tff(1131,plain,
% 0.71/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1132,plain,
% 0.71/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.71/0.89 tff(1133,plain,
% 0.71/0.89 (c1_1(a1080) | c0_1(a1080) | (~c1_1(a1092))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1132, 171, 1120, 1119, 1126, 66, 341])).
% 0.71/0.89 tff(1134,plain,
% 0.71/0.89 (c1_1(a1080)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1133, 1125, 87])).
% 0.71/0.89 tff(1135,plain,
% 0.71/0.89 (hskp3 | c0_1(a1080) | (~c1_1(a1080))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1021, 171, 1046, 12, 11, 66, 22])).
% 0.71/0.89 tff(1136,plain,
% 0.71/0.89 (hskp3),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1135, 1134, 87])).
% 0.71/0.89 tff(1137,plain,
% 0.71/0.89 (~c3_1(a1083)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[856, 1136])).
% 0.71/0.89 tff(1138,plain,
% 0.71/0.89 (~c2_1(a1083)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[850, 1136])).
% 0.71/0.89 tff(1139,plain,
% 0.71/0.89 (~c1_1(a1103)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[124, 1070])).
% 0.71/0.89 tff(1140,plain,
% 0.71/0.89 (c1_1(a1083)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1030, 1136])).
% 0.71/0.89 tff(1141,plain,
% 0.71/0.89 (c3_1(a1103)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[133, 1070])).
% 0.71/0.89 tff(1142,plain,
% 0.71/0.89 (hskp15 | hskp14 | c0_1(a1080) | (~c1_1(a1080))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[209, 171, 66, 203])).
% 0.71/0.89 tff(1143,plain,
% 0.71/0.89 (hskp15),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1142, 1134, 193, 87])).
% 0.71/0.89 tff(1144,plain,
% 0.71/0.89 (~c1_1(a1098)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[216, 1143])).
% 0.71/0.89 tff(1145,plain,
% 0.71/0.89 (c2_1(a1098)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[224, 1143])).
% 0.71/0.89 tff(1146,plain,
% 0.71/0.89 (~c0_1(a1098)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[231, 171, 193, 1145, 1144, 190])).
% 0.71/0.89 tff(1147,plain,
% 0.71/0.89 (~c3_1(a1098)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[247, 1143])).
% 0.71/0.89 tff(1148,plain,
% 0.71/0.89 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1149,plain,
% 0.71/0.89 (((~ndr1_0) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098)) <=> (c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1150,plain,
% 0.71/0.89 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098)))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1149])).
% 0.71/0.89 tff(1151,plain,
% 0.71/0.89 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1150, 1148])).
% 0.71/0.89 tff(1152,plain,
% 0.71/0.89 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1153,plain,
% 0.71/0.89 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 0.71/0.89 tff(1154,plain,
% 0.71/0.89 ((~c3_1(a1080)) | c0_1(a1098)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1153, 171, 1140, 1134, 1144, 1147, 1138, 1137, 66, 434])).
% 0.71/0.89 tff(1155,plain,
% 0.71/0.89 (~c3_1(a1080)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1154, 1146])).
% 0.71/0.89 tff(1156,plain,
% 0.71/0.89 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1157,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1156])).
% 0.71/0.89 tff(1158,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1159,plain,
% 0.71/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1160,plain,
% 0.71/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1159])).
% 0.71/0.89 tff(1161,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.71/0.89 tff(1162,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 0.71/0.89 tff(1163,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1162, 1158])).
% 0.71/0.89 tff(1164,plain,(
% 0.71/0.89 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[1163])).
% 0.71/0.89 tff(1165,plain,
% 0.71/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1164, 1157])).
% 0.71/0.89 tff(1166,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1167,plain,
% 0.71/0.89 ((hskp4 | (~ndr1_0) | c0_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1168,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1167])).
% 0.71/0.90 tff(1169,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1168, 1166])).
% 0.71/0.90 tff(1170,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1171,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 0.71/0.90 tff(1172,plain,
% 0.71/0.90 (hskp4 | c3_1(a1080) | (~c1_1(a1080))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1171, 171, 1046, 12, 11, 87, 1165])).
% 0.71/0.90 tff(1173,plain,
% 0.71/0.90 (hskp4),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1172, 1155, 1134])).
% 0.71/0.90 tff(1174,plain,
% 0.71/0.90 (((~hskp4) | c0_1(a1084)) <=> ((~hskp4) | c0_1(a1084))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1175,axiom,((~hskp4) | c0_1(a1084)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.71/0.90 tff(1176,plain,
% 0.71/0.90 ((~hskp4) | c0_1(a1084)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 0.71/0.90 tff(1177,plain,
% 0.71/0.90 ((~hskp4) | c0_1(a1084)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1176, 1174])).
% 0.71/0.90 tff(1178,plain,
% 0.71/0.90 ((~hskp4) | c0_1(a1084)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1177, 1174])).
% 0.71/0.90 tff(1179,plain,
% 0.71/0.90 ((~hskp4) | c0_1(a1084)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1178, 1174])).
% 0.71/0.90 tff(1180,plain,
% 0.71/0.90 ((~hskp4) | c0_1(a1084)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1179, 1174])).
% 0.71/0.90 tff(1181,plain,
% 0.71/0.90 (c0_1(a1084)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1180, 1173])).
% 0.71/0.90 tff(1182,plain,
% 0.71/0.90 (((~hskp4) | (~c1_1(a1084))) <=> ((~hskp4) | (~c1_1(a1084)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1183,plain,
% 0.71/0.90 (((~c1_1(a1084)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a1084)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1184,axiom,((~c1_1(a1084)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.71/0.90 tff(1185,plain,
% 0.71/0.90 ((~hskp4) | (~c1_1(a1084))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 0.71/0.90 tff(1186,plain,
% 0.71/0.90 ((~hskp4) | (~c1_1(a1084))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1185, 1182])).
% 0.71/0.90 tff(1187,plain,
% 0.71/0.90 (~c1_1(a1084)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1186, 1173])).
% 0.71/0.90 tff(1188,plain,
% 0.71/0.90 (((~hskp4) | (~c3_1(a1084))) <=> ((~hskp4) | (~c3_1(a1084)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1189,plain,
% 0.71/0.90 (((~c3_1(a1084)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1084)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1190,axiom,((~c3_1(a1084)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.71/0.90 tff(1191,plain,
% 0.71/0.90 ((~hskp4) | (~c3_1(a1084))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.71/0.90 tff(1192,plain,
% 0.71/0.90 ((~hskp4) | (~c3_1(a1084))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1191, 1188])).
% 0.71/0.90 tff(1193,plain,
% 0.71/0.90 (~c3_1(a1084)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1192, 1173])).
% 0.71/0.90 tff(1194,assumption,(c0_1(a1084)), introduced(assumption)).
% 0.71/0.90 tff(1195,assumption,(~c1_1(a1103)), introduced(assumption)).
% 0.71/0.90 tff(1196,assumption,(c0_1(a1103)), introduced(assumption)).
% 0.71/0.90 tff(1197,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1198,plain,
% 0.71/0.90 ((hskp14 | (~ndr1_0) | c1_1(a1103) | (~c2_1(a1103)) | (~c0_1(a1103))) <=> (hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1199,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1103) | (~c2_1(a1103)) | (~c0_1(a1103)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1198])).
% 0.71/0.90 tff(1200,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1103) | (~c2_1(a1103)) | (~c0_1(a1103)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1199, 1197])).
% 0.71/0.90 tff(1201,plain,
% 0.71/0.90 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1103) | (~c2_1(a1103)) | (~c0_1(a1103)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1202,plain,
% 0.71/0.90 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 0.71/0.90 tff(1203,plain,
% 0.71/0.90 (hskp14 | (~c2_1(a1103))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1202, 192, 1196, 1195, 190])).
% 0.71/0.90 tff(1204,plain,
% 0.71/0.90 (~c2_1(a1103)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1203, 193])).
% 0.71/0.90 tff(1205,plain,
% 0.71/0.90 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(1206,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[1205])).
% 0.71/0.90 tff(1207,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1208,plain,
% 0.71/0.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(1209,plain,
% 0.71/0.90 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[1208])).
% 0.71/0.90 tff(1210,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.71/0.90 tff(1211,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 0.71/0.90 tff(1212,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1211, 1207])).
% 0.71/0.90 tff(1213,plain,(
% 0.71/0.90 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.71/0.90 inference(skolemize,[status(sab)],[1212])).
% 0.71/0.90 tff(1214,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1213, 1206])).
% 0.71/0.90 tff(1215,assumption,(c1_1(a1083)), introduced(assumption)).
% 0.71/0.90 tff(1216,assumption,(c3_1(a1103)), introduced(assumption)).
% 0.71/0.90 tff(1217,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1218,plain,
% 0.71/0.90 ((hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103))) <=> (hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1219,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1218])).
% 0.71/0.90 tff(1220,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1219, 1217])).
% 0.71/0.90 tff(1221,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1222,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 0.71/0.90 tff(1223,plain,
% 0.71/0.90 (hskp23),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1222, 192, 1216, 1215, 1195, 943, 942, 1214, 1204])).
% 0.71/0.90 tff(1224,plain,
% 0.71/0.90 (((~hskp23) | c2_1(a1122)) <=> ((~hskp23) | c2_1(a1122))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1225,axiom,((~hskp23) | c2_1(a1122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.71/0.90 tff(1226,plain,
% 0.71/0.90 ((~hskp23) | c2_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 0.71/0.90 tff(1227,plain,
% 0.71/0.90 ((~hskp23) | c2_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1226, 1224])).
% 0.71/0.90 tff(1228,plain,
% 0.71/0.90 ((~hskp23) | c2_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1227, 1224])).
% 0.71/0.90 tff(1229,plain,
% 0.71/0.90 ((~hskp23) | c2_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1228, 1224])).
% 0.71/0.90 tff(1230,plain,
% 0.71/0.90 ((~hskp23) | c2_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1229, 1224])).
% 0.71/0.90 tff(1231,plain,
% 0.71/0.90 (c2_1(a1122)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1230, 1223])).
% 0.71/0.90 tff(1232,assumption,(~c3_1(a1084)), introduced(assumption)).
% 0.71/0.90 tff(1233,assumption,(~c1_1(a1084)), introduced(assumption)).
% 0.71/0.90 tff(1234,plain,
% 0.71/0.90 (((~hskp23) | c0_1(a1122)) <=> ((~hskp23) | c0_1(a1122))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1235,axiom,((~hskp23) | c0_1(a1122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.71/0.90 tff(1236,plain,
% 0.71/0.90 ((~hskp23) | c0_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 0.71/0.90 tff(1237,plain,
% 0.71/0.90 ((~hskp23) | c0_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1236, 1234])).
% 0.71/0.90 tff(1238,plain,
% 0.71/0.90 ((~hskp23) | c0_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1237, 1234])).
% 0.71/0.90 tff(1239,plain,
% 0.71/0.90 ((~hskp23) | c0_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1238, 1234])).
% 0.71/0.90 tff(1240,plain,
% 0.71/0.90 ((~hskp23) | c0_1(a1122)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1239, 1234])).
% 0.71/0.90 tff(1241,plain,
% 0.71/0.90 (c0_1(a1122)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1240, 1223])).
% 0.71/0.90 tff(1242,plain,
% 0.71/0.90 (((~hskp23) | (~c3_1(a1122))) <=> ((~hskp23) | (~c3_1(a1122)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1243,plain,
% 0.71/0.90 (((~c3_1(a1122)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1122)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1244,axiom,((~c3_1(a1122)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.71/0.90 tff(1245,plain,
% 0.71/0.90 ((~hskp23) | (~c3_1(a1122))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 0.71/0.90 tff(1246,plain,
% 0.71/0.90 ((~hskp23) | (~c3_1(a1122))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1245, 1242])).
% 0.71/0.90 tff(1247,plain,
% 0.71/0.90 (~c3_1(a1122)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1246, 1223])).
% 0.71/0.90 tff(1248,assumption,(c2_1(a1122)), introduced(assumption)).
% 0.71/0.90 tff(1249,assumption,(c0_1(a1122)), introduced(assumption)).
% 0.71/0.90 tff(1250,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1251,plain,
% 0.71/0.90 ((hskp14 | (~ndr1_0) | c1_1(a1122) | (~c2_1(a1122)) | (~c0_1(a1122))) <=> (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1252,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c2_1(a1122)) | (~c0_1(a1122)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1251])).
% 0.71/0.90 tff(1253,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c2_1(a1122)) | (~c0_1(a1122)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1252, 1250])).
% 0.71/0.90 tff(1254,plain,
% 0.71/0.90 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c2_1(a1122)) | (~c0_1(a1122)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1255,plain,
% 0.71/0.90 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 0.71/0.90 tff(1256,plain,
% 0.71/0.90 (hskp14 | c1_1(a1122)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1255, 192, 1249, 1248, 190])).
% 0.71/0.90 tff(1257,plain,
% 0.71/0.90 (c1_1(a1122)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1256, 193])).
% 0.71/0.90 tff(1258,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1259,plain,
% 0.71/0.90 ((hskp14 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084))) <=> (hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1260,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1259])).
% 0.71/0.90 tff(1261,plain,
% 0.71/0.90 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1260, 1258])).
% 0.71/0.90 tff(1262,plain,
% 0.71/0.90 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1263,plain,
% 0.71/0.90 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.71/0.90 tff(1264,plain,
% 0.71/0.90 (hskp14 | (~c2_1(a1084))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1263, 192, 1194, 1233, 190])).
% 0.71/0.90 tff(1265,plain,
% 0.71/0.90 (~c2_1(a1084)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1264, 193])).
% 0.71/0.90 tff(1266,plain,
% 0.71/0.90 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(1267,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[1266])).
% 0.71/0.90 tff(1268,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1269,plain,
% 0.71/0.90 (^[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)) | 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))) | (~ndr1_0)) | c3_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))) | (~ndr1_0)) | c3_1(U)) | 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))) | (~ndr1_0)) | c3_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)) | c3_1(U)) | c1_1(V)) | 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) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | 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)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(1270,plain,
% 0.71/0.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | 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) | c1_1(V) | c3_1(V))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[1269])).
% 0.71/0.90 tff(1271,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.71/0.90 tff(1272,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 0.71/0.90 tff(1273,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1272, 1268])).
% 0.71/0.90 tff(1274,plain,(
% 0.71/0.90 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.71/0.90 inference(skolemize,[status(sab)],[1273])).
% 0.71/0.90 tff(1275,plain,
% 0.71/0.90 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1274, 1267])).
% 0.71/0.90 tff(1276,assumption,(~c3_1(a1122)), introduced(assumption)).
% 0.71/0.90 tff(1277,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1278,plain,
% 0.71/0.90 ((hskp9 | (~ndr1_0) | c3_1(a1122) | (~c1_1(a1122)) | (~c0_1(a1122)) | c2_1(a1084) | c1_1(a1084) | c3_1(a1084)) <=> (hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1279,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a1122) | (~c1_1(a1122)) | (~c0_1(a1122)) | c2_1(a1084) | c1_1(a1084) | c3_1(a1084))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1278])).
% 0.71/0.90 tff(1280,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a1122) | (~c1_1(a1122)) | (~c0_1(a1122)) | c2_1(a1084) | c1_1(a1084) | c3_1(a1084))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1279, 1277])).
% 0.71/0.90 tff(1281,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a1122) | (~c1_1(a1122)) | (~c0_1(a1122)) | c2_1(a1084) | c1_1(a1084) | c3_1(a1084))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1282,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.71/0.90 tff(1283,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1282, 192, 54, 1249, 1276, 1233, 1232, 1275, 1265, 1257])).
% 0.71/0.90 tff(1284,plain,(hskp14 | (~ndr1_0) | hskp9 | (~c0_1(a1122)) | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1122)) | (~c0_1(a1084))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1285,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1284, 1247, 1241, 54, 192, 193, 1233, 1232, 1231, 1194])).
% 0.71/0.90 tff(1286,plain,(hskp14 | hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | (~c3_1(a1103)) | (~c1_1(a1083)) | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1103))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1287,plain,
% 0.71/0.90 (hskp14 | hskp9 | c1_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | (~c3_1(a1103)) | (~c1_1(a1083)) | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1103))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1286, 171])).
% 0.71/0.90 tff(1288,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1287, 1193, 1187, 54, 193, 1181, 1141, 1140, 1139, 1138, 1137, 1071])).
% 0.71/0.90 tff(1289,plain,(hskp14 | hskp9 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1290,plain,
% 0.71/0.90 (hskp14),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1289, 87, 12, 11, 54, 66])).
% 0.71/0.90 tff(1291,plain,
% 0.71/0.90 (~c2_1(a1097)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[264, 1290])).
% 0.71/0.90 tff(1292,plain,
% 0.71/0.90 (c3_1(a1097)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[306, 1290])).
% 0.71/0.90 tff(1293,plain,
% 0.71/0.90 (c1_1(a1097)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[272, 1290])).
% 0.71/0.90 tff(1294,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1295,plain,
% 0.71/0.90 ((hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097))) <=> (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1296,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1295])).
% 0.71/0.90 tff(1297,plain,
% 0.71/0.90 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1296, 1294])).
% 0.71/0.90 tff(1298,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1299,plain,
% 0.71/0.90 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 0.71/0.90 tff(1300,plain,
% 0.71/0.90 (hskp26),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1299, 171, 1120, 1119, 1126, 1293, 1292, 1291, 86])).
% 0.71/0.90 tff(1301,plain,
% 0.71/0.90 (((~hskp26) | (~c0_1(a1146))) <=> ((~hskp26) | (~c0_1(a1146)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1302,plain,
% 0.71/0.90 (((~c0_1(a1146)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1146)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1303,axiom,((~c0_1(a1146)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.71/0.90 tff(1304,plain,
% 0.71/0.90 ((~hskp26) | (~c0_1(a1146))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 0.71/0.90 tff(1305,plain,
% 0.71/0.90 ((~hskp26) | (~c0_1(a1146))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1304, 1301])).
% 0.71/0.90 tff(1306,plain,
% 0.71/0.90 (~c0_1(a1146)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1305, 1300])).
% 0.71/0.90 tff(1307,plain,
% 0.71/0.90 (((~hskp26) | c3_1(a1146)) <=> ((~hskp26) | c3_1(a1146))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1308,axiom,((~hskp26) | c3_1(a1146)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.71/0.90 tff(1309,plain,
% 0.71/0.90 ((~hskp26) | c3_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 0.71/0.90 tff(1310,plain,
% 0.71/0.90 ((~hskp26) | c3_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1309, 1307])).
% 0.71/0.90 tff(1311,plain,
% 0.71/0.90 ((~hskp26) | c3_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1310, 1307])).
% 0.71/0.90 tff(1312,plain,
% 0.71/0.90 ((~hskp26) | c3_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1311, 1307])).
% 0.71/0.90 tff(1313,plain,
% 0.71/0.90 ((~hskp26) | c3_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1312, 1307])).
% 0.71/0.90 tff(1314,plain,
% 0.71/0.90 (c3_1(a1146)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1313, 1300])).
% 0.71/0.90 tff(1315,plain,
% 0.71/0.90 (((~hskp26) | c2_1(a1146)) <=> ((~hskp26) | c2_1(a1146))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1316,axiom,((~hskp26) | c2_1(a1146)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.71/0.90 tff(1317,plain,
% 0.71/0.90 ((~hskp26) | c2_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 0.71/0.90 tff(1318,plain,
% 0.71/0.90 ((~hskp26) | c2_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1317, 1315])).
% 0.71/0.90 tff(1319,plain,
% 0.71/0.90 ((~hskp26) | c2_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1318, 1315])).
% 0.71/0.90 tff(1320,plain,
% 0.71/0.90 ((~hskp26) | c2_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1319, 1315])).
% 0.71/0.90 tff(1321,plain,
% 0.71/0.90 ((~hskp26) | c2_1(a1146)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1320, 1315])).
% 0.71/0.90 tff(1322,plain,
% 0.71/0.90 (c2_1(a1146)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1321, 1300])).
% 0.71/0.90 tff(1323,plain,
% 0.71/0.90 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1324,plain,
% 0.71/0.90 ((hskp19 | (~ndr1_0) | c0_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146))) <=> (hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1325,plain,
% 0.71/0.90 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1324])).
% 0.71/0.90 tff(1326,plain,
% 0.71/0.90 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1325, 1323])).
% 0.71/0.90 tff(1327,plain,
% 0.71/0.90 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1328,plain,
% 0.71/0.90 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 0.71/0.90 tff(1329,plain,
% 0.71/0.90 (hskp19),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1328, 171, 1322, 1314, 1306, 76])).
% 0.71/0.90 tff(1330,plain,
% 0.71/0.90 (~c2_1(a1113)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[917, 1329])).
% 0.71/0.90 tff(1331,plain,
% 0.71/0.90 (c1_1(a1113)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[925, 1329])).
% 0.71/0.90 tff(1332,plain,
% 0.71/0.90 (c0_1(a1113)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[933, 1329])).
% 0.71/0.90 tff(1333,plain,
% 0.71/0.90 (c3_1(a1113)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[940, 171, 1332, 1331, 1046, 1330, 12, 11, 64])).
% 0.71/0.90 tff(1334,plain,
% 0.71/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1335,plain,
% 0.71/0.90 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1113)) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080)) <=> (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1336,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1113)) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1335])).
% 0.71/0.91 tff(1337,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1113)) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1336, 1334])).
% 0.71/0.91 tff(1338,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1113)) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1339,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 0.71/0.91 tff(1340,plain,
% 0.71/0.91 (c1_1(a1080)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1339, 171, 1120, 1119, 1126, 1332, 1331, 87, 66, 341, 1333])).
% 0.71/0.91 tff(1341,plain,
% 0.71/0.91 (hskp3),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1135, 1340, 87])).
% 0.71/0.91 tff(1342,plain,
% 0.71/0.91 (~c3_1(a1083)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[856, 1341])).
% 0.71/0.91 tff(1343,plain,
% 0.71/0.91 (~c2_1(a1083)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[850, 1341])).
% 0.71/0.91 tff(1344,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1345,plain,
% 0.71/0.91 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1346,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1345])).
% 0.71/0.91 tff(1347,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1346, 1344])).
% 0.71/0.91 tff(1348,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1349,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 0.71/0.91 tff(1350,plain,
% 0.71/0.91 (~c0_1(a1083)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1349, 171, 1332, 1331, 1046, 1330, 12, 11, 1343, 1342, 64])).
% 0.71/0.91 tff(1351,plain,
% 0.71/0.91 (c1_1(a1083)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1030, 1341])).
% 0.71/0.91 tff(1352,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1353,plain,
% 0.71/0.91 ((hskp4 | (~ndr1_0) | c0_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1354,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1353])).
% 0.71/0.91 tff(1355,plain,
% 0.71/0.91 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1354, 1352])).
% 0.71/0.91 tff(1356,plain,
% 0.71/0.91 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1357,plain,
% 0.71/0.91 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 0.71/0.91 tff(1358,plain,
% 0.71/0.91 (hskp4),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1357, 171, 1046, 1351, 12, 11, 1342, 1165, 1350])).
% 0.71/0.91 tff(1359,plain,
% 0.71/0.91 (c0_1(a1084)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1180, 1358])).
% 0.71/0.91 tff(1360,plain,
% 0.71/0.91 (~c3_1(a1084)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1192, 1358])).
% 0.71/0.91 tff(1361,assumption,(~c2_1(a1084)), introduced(assumption)).
% 0.71/0.91 tff(1362,assumption,(~c2_1(a1113)), introduced(assumption)).
% 0.71/0.91 tff(1363,assumption,(c2_1(a1085)), introduced(assumption)).
% 0.71/0.91 tff(1364,assumption,(c1_1(a1113)), introduced(assumption)).
% 0.71/0.91 tff(1365,assumption,(c0_1(a1113)), introduced(assumption)).
% 0.71/0.91 tff(1366,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1367,plain,
% 0.71/0.91 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1368,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1367])).
% 0.71/0.91 tff(1369,plain,
% 0.71/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1368, 1366])).
% 0.71/0.91 tff(1370,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1371,plain,
% 0.71/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 0.71/0.91 tff(1372,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1371, 192, 1365, 1364, 1363, 1194, 1362, 12, 11, 1232, 64, 1361])).
% 0.71/0.91 tff(1373,plain,(c2_1(a1084) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c2_1(a1085)) | (~c0_1(a1084)) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(1374,plain,
% 0.71/0.91 (c2_1(a1084) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c2_1(a1085)) | (~c0_1(a1084)) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1373, 171])).
% 0.71/0.91 tff(1375,plain,
% 0.71/0.91 (c2_1(a1084)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1374, 1360, 1332, 1331, 1046, 1359, 1330, 12, 11])).
% 0.71/0.91 tff(1376,plain,
% 0.71/0.91 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(1377,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[1376])).
% 0.71/0.91 tff(1378,plain,
% 0.71/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1379,plain,
% 0.71/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.75/0.91 inference(bind,[status(th)],[])).
% 0.75/0.91 tff(1380,plain,
% 0.75/0.91 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.75/0.91 inference(quant_intro,[status(thm)],[1379])).
% 0.75/0.91 tff(1381,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.75/0.91 tff(1382,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 0.75/0.91 tff(1383,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1382, 1378])).
% 0.75/0.91 tff(1384,plain,(
% 0.75/0.91 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.75/0.91 inference(skolemize,[status(sab)],[1383])).
% 0.75/0.91 tff(1385,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1384, 1377])).
% 0.75/0.91 tff(1386,plain,
% 0.75/0.91 (~c1_1(a1084)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1186, 1358])).
% 0.75/0.91 tff(1387,plain,
% 0.75/0.91 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1388,plain,
% 0.75/0.91 (((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085)) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1389,plain,
% 0.75/0.91 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1388])).
% 0.75/0.91 tff(1390,plain,
% 0.75/0.91 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.75/0.91 inference(transitivity,[status(thm)],[1389, 1387])).
% 0.75/0.91 tff(1391,plain,
% 0.75/0.91 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1392,plain,
% 0.75/0.91 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.75/0.91 tff(1393,plain,
% 0.75/0.91 (c3_1(a1085)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1392, 171, 1331, 1351, 1330, 12, 11, 1343, 1342, 434, 1333])).
% 0.75/0.91 tff(1394,plain,
% 0.75/0.91 (hskp11),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1067, 1393, 54, 1046])).
% 0.75/0.91 tff(1395,plain,
% 0.75/0.91 (~c0_1(a1091)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[662, 1394])).
% 0.75/0.91 tff(1396,plain,
% 0.75/0.91 (c2_1(a1091)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[670, 1394])).
% 0.75/0.91 tff(1397,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1398,plain,
% 0.75/0.91 ((hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1084)) | c0_1(a1091) | (~c2_1(a1091)) | (~c1_1(a1091))) <=> (hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1399,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1084)) | c0_1(a1091) | (~c2_1(a1091)) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1398])).
% 0.75/0.91 tff(1400,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1084)) | c0_1(a1091) | (~c2_1(a1091)) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091)))),
% 0.75/0.91 inference(transitivity,[status(thm)],[1399, 1397])).
% 0.75/0.91 tff(1401,plain,
% 0.75/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1084)) | c0_1(a1091) | (~c2_1(a1091)) | (~c1_1(a1091)))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1402,plain,
% 0.75/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 0.75/0.91 tff(1403,plain,
% 0.75/0.91 (~c1_1(a1091)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1402, 171, 54, 1396, 1395, 1386, 1360, 1385, 1375])).
% 0.75/0.91 tff(1404,plain,
% 0.75/0.91 (~c3_1(a1091)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[656, 1394])).
% 0.75/0.91 tff(1405,plain,
% 0.75/0.91 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1406,plain,
% 0.75/0.91 (((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1091) | c0_1(a1091) | c3_1(a1091)) <=> (c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1407,plain,
% 0.75/0.91 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1091) | c0_1(a1091) | c3_1(a1091))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1406])).
% 0.75/0.91 tff(1408,plain,
% 0.75/0.91 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1091) | c0_1(a1091) | c3_1(a1091))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.75/0.91 inference(transitivity,[status(thm)],[1407, 1405])).
% 0.75/0.91 tff(1409,plain,
% 0.75/0.91 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1091) | c0_1(a1091) | c3_1(a1091))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1410,plain,
% 0.75/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 0.75/0.91 tff(1411,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1410, 171, 1331, 1351, 1330, 1395, 1404, 1343, 1342, 434, 1403, 1333])).
% 0.75/0.91 tff(1412,plain,(c0_1(a1080) | hskp9 | c0_1(a1085) | c1_1(a1085) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(1413,plain,
% 0.75/0.91 (c0_1(a1080)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1412, 66, 12, 11, 54])).
% 0.75/0.91 tff(1414,plain,
% 0.75/0.91 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) <=> (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)))),
% 0.75/0.91 inference(bind,[status(th)],[])).
% 0.75/0.91 tff(1415,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.75/0.91 inference(quant_intro,[status(thm)],[1414])).
% 0.75/0.91 tff(1416,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1417,plain,
% 0.75/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) | hskp17))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))))),
% 0.75/0.91 inference(bind,[status(th)],[])).
% 0.75/0.91 tff(1418,plain,
% 0.75/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.75/0.91 inference(quant_intro,[status(thm)],[1417])).
% 0.75/0.91 tff(1419,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.75/0.91 tff(1420,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 0.75/0.91 tff(1421,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1420, 1416])).
% 0.75/0.91 tff(1422,plain,(
% 0.75/0.91 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.75/0.91 inference(skolemize,[status(sab)],[1421])).
% 0.75/0.91 tff(1423,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1422, 1415])).
% 0.75/0.91 tff(1424,plain,
% 0.75/0.91 (~hskp0),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[34, 1413])).
% 0.75/0.91 tff(1425,assumption,(c1_1(a1092)), introduced(assumption)).
% 0.75/0.92 tff(1426,plain,
% 0.75/0.92 (^[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))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1427,plain,
% 0.75/0.92 (![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)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1426])).
% 0.75/0.92 tff(1428,plain,
% 0.75/0.92 (![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)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1429,plain,
% 0.75/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp2) <=> ((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp2) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1430,plain,
% 0.75/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp2) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1429])).
% 0.75/0.92 tff(1431,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.75/0.92 tff(1432,plain,
% 0.75/0.92 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 0.75/0.92 tff(1433,plain,
% 0.75/0.92 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1432, 1428])).
% 0.75/0.92 tff(1434,plain,(
% 0.75/0.92 ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(skolemize,[status(sab)],[1433])).
% 0.75/0.92 tff(1435,plain,
% 0.75/0.92 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1434, 1427])).
% 0.75/0.92 tff(1436,plain,
% 0.75/0.92 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1437,plain,
% 0.75/0.92 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1438,plain,
% 0.75/0.92 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.75/0.92 tff(1439,plain,
% 0.75/0.92 (hskp19 | hskp2 | (~c1_1(a1092))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1438, 171, 1120, 1126, 1435])).
% 0.75/0.92 tff(1440,plain,
% 0.75/0.92 (hskp19),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1439, 65, 1425])).
% 0.75/0.92 tff(1441,plain,
% 0.75/0.92 (~c2_1(a1113)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[917, 1440])).
% 0.75/0.92 tff(1442,plain,
% 0.75/0.92 (c1_1(a1113)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[925, 1440])).
% 0.75/0.92 tff(1443,plain,
% 0.75/0.92 (c0_1(a1113)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[933, 1440])).
% 0.75/0.92 tff(1444,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1445,plain,
% 0.75/0.92 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1446,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1445])).
% 0.75/0.92 tff(1447,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1446, 1444])).
% 0.75/0.92 tff(1448,plain,
% 0.75/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1449,plain,
% 0.75/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 0.75/0.92 tff(1450,plain,
% 0.75/0.92 (c3_1(a1080)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1449, 171, 1443, 1442, 1046, 1441, 12, 11, 1413, 66, 64])).
% 0.75/0.92 tff(1451,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1452,plain,
% 0.75/0.92 ((hskp1 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080))) <=> (hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1453,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1452])).
% 0.75/0.92 tff(1454,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1453, 1451])).
% 0.75/0.92 tff(1455,plain,
% 0.75/0.92 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1456,plain,
% 0.75/0.92 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 0.75/0.92 tff(1457,plain,
% 0.75/0.92 (hskp1),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1456, 171, 1443, 1442, 858, 1441, 66, 528, 1450])).
% 0.75/0.92 tff(1458,plain,
% 0.75/0.92 (~c1_1(a1081)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[595, 1457])).
% 0.75/0.92 tff(1459,plain,
% 0.75/0.92 (~c0_1(a1081)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[589, 1457])).
% 0.75/0.92 tff(1460,plain,
% 0.75/0.92 (((~hskp1) | c3_1(a1081)) <=> ((~hskp1) | c3_1(a1081))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1461,axiom,((~hskp1) | c3_1(a1081)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.75/0.92 tff(1462,plain,
% 0.75/0.92 ((~hskp1) | c3_1(a1081)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 0.75/0.92 tff(1463,plain,
% 0.75/0.92 ((~hskp1) | c3_1(a1081)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1462, 1460])).
% 0.75/0.92 tff(1464,plain,
% 0.75/0.92 ((~hskp1) | c3_1(a1081)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1463, 1460])).
% 0.75/0.92 tff(1465,plain,
% 0.75/0.92 ((~hskp1) | c3_1(a1081)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1464, 1460])).
% 0.75/0.92 tff(1466,plain,
% 0.75/0.92 ((~hskp1) | c3_1(a1081)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1465, 1460])).
% 0.75/0.92 tff(1467,plain,
% 0.75/0.92 (c3_1(a1081)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1466, 1457])).
% 0.75/0.92 tff(1468,plain,
% 0.75/0.92 (hskp11),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[708, 171, 1120, 1119, 1126, 1467, 1459, 1458, 701])).
% 0.75/0.92 tff(1469,plain,
% 0.75/0.92 (~c3_1(a1091)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[656, 1468])).
% 0.75/0.92 tff(1470,plain,
% 0.75/0.92 (~c0_1(a1091)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[662, 1468])).
% 0.75/0.92 tff(1471,plain,
% 0.75/0.92 (c2_1(a1091)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[670, 1468])).
% 0.75/0.92 tff(1472,plain,
% 0.75/0.92 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1473,plain,
% 0.75/0.92 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113))) <=> (hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1474,plain,
% 0.75/0.92 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1473])).
% 0.75/0.92 tff(1475,plain,
% 0.75/0.92 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1474, 1472])).
% 0.75/0.92 tff(1476,plain,
% 0.75/0.92 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1477,plain,
% 0.75/0.92 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 0.75/0.92 tff(1478,plain,
% 0.75/0.92 (hskp30),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1477, 171, 54, 1443, 1442, 1441, 99])).
% 0.75/0.92 tff(1479,plain,
% 0.75/0.92 (c3_1(a1109)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[330, 1478])).
% 0.75/0.92 tff(1480,plain,
% 0.75/0.92 (c1_1(a1109)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[288, 1478])).
% 0.75/0.92 tff(1481,plain,
% 0.75/0.92 (c0_1(a1109)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[322, 1478])).
% 0.75/0.92 tff(1482,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1483,plain,
% 0.75/0.92 ((hskp17 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c0_1(a1091) | (~c2_1(a1091)) | c3_1(a1091)) <=> (hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1484,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c0_1(a1091) | (~c2_1(a1091)) | c3_1(a1091))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1483])).
% 0.75/0.92 tff(1485,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c0_1(a1091) | (~c2_1(a1091)) | c3_1(a1091))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1484, 1482])).
% 0.75/0.92 tff(1486,plain,
% 0.75/0.92 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c0_1(a1091) | (~c2_1(a1091)) | c3_1(a1091))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1487,plain,
% 0.75/0.92 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 0.75/0.92 tff(1488,plain,
% 0.75/0.92 (hskp17),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1487, 171, 1481, 1480, 1479, 1471, 1470, 1469, 1423])).
% 0.75/0.92 tff(1489,plain,
% 0.75/0.92 (((~hskp17) | (~c0_1(a1102))) <=> ((~hskp17) | (~c0_1(a1102)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1490,plain,
% 0.75/0.92 (((~c0_1(a1102)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1102)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1491,axiom,((~c0_1(a1102)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.75/0.92 tff(1492,plain,
% 0.75/0.92 ((~hskp17) | (~c0_1(a1102))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 0.75/0.92 tff(1493,plain,
% 0.75/0.92 ((~hskp17) | (~c0_1(a1102))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1492, 1489])).
% 0.75/0.92 tff(1494,plain,
% 0.75/0.92 (~c0_1(a1102)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1493, 1488])).
% 0.75/0.92 tff(1495,plain,
% 0.75/0.92 (((~hskp17) | c3_1(a1102)) <=> ((~hskp17) | c3_1(a1102))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1496,axiom,((~hskp17) | c3_1(a1102)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.75/0.92 tff(1497,plain,
% 0.75/0.92 ((~hskp17) | c3_1(a1102)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 0.75/0.92 tff(1498,plain,
% 0.75/0.92 ((~hskp17) | c3_1(a1102)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1497, 1495])).
% 0.75/0.92 tff(1499,plain,
% 0.75/0.92 ((~hskp17) | c3_1(a1102)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1498, 1495])).
% 0.75/0.92 tff(1500,plain,
% 0.75/0.92 ((~hskp17) | c3_1(a1102)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1499, 1495])).
% 0.75/0.92 tff(1501,plain,
% 0.75/0.92 ((~hskp17) | c3_1(a1102)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1500, 1495])).
% 0.75/0.92 tff(1502,plain,
% 0.75/0.92 (c3_1(a1102)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1501, 1488])).
% 0.75/0.92 tff(1503,plain,
% 0.75/0.92 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1504,plain,
% 0.75/0.92 ((hskp9 | hskp2 | (~ndr1_0) | c0_1(a1102) | (~c3_1(a1102)) | (~c1_1(a1102))) <=> (hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1505,plain,
% 0.75/0.92 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1102) | (~c3_1(a1102)) | (~c1_1(a1102)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1504])).
% 0.75/0.92 tff(1506,plain,
% 0.75/0.92 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1102) | (~c3_1(a1102)) | (~c1_1(a1102)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1505, 1503])).
% 0.75/0.92 tff(1507,plain,
% 0.75/0.92 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1102) | (~c3_1(a1102)) | (~c1_1(a1102)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1508,plain,
% 0.75/0.92 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1507, 1506])).
% 0.75/0.92 tff(1509,plain,
% 0.75/0.92 (~c1_1(a1102)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1508, 171, 54, 65, 1502, 1494, 396])).
% 0.75/0.92 tff(1510,plain,
% 0.75/0.92 (((~hskp17) | (~c2_1(a1102))) <=> ((~hskp17) | (~c2_1(a1102)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1511,plain,
% 0.75/0.92 (((~c2_1(a1102)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1102)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1512,axiom,((~c2_1(a1102)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.75/0.92 tff(1513,plain,
% 0.75/0.92 ((~hskp17) | (~c2_1(a1102))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 0.75/0.92 tff(1514,plain,
% 0.75/0.92 ((~hskp17) | (~c2_1(a1102))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1513, 1510])).
% 0.75/0.92 tff(1515,plain,
% 0.75/0.92 (~c2_1(a1102)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1514, 1488])).
% 0.75/0.92 tff(1516,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1517,plain,
% 0.75/0.92 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1102) | c1_1(a1102) | c0_1(a1102)) <=> (c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1518,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1102) | c1_1(a1102) | c0_1(a1102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1517])).
% 0.75/0.92 tff(1519,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1102) | c1_1(a1102) | c0_1(a1102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1518, 1516])).
% 0.75/0.92 tff(1520,plain,
% 0.75/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1102) | c1_1(a1102) | c0_1(a1102))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1521,plain,
% 0.75/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 0.75/0.92 tff(1522,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1521, 171, 1481, 1480, 1479, 1120, 1119, 1126, 1494, 1515, 341, 1509])).
% 0.75/0.92 tff(1523,plain,(hskp2 | hskp9 | c1_1(a1080) | c2_1(a1080) | c0_1(a1085) | c1_1(a1085) | (~c1_1(a1092))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(1524,plain,
% 0.75/0.92 (hskp2),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1523, 1125, 858, 66, 12, 11, 54])).
% 0.75/0.92 tff(1525,plain,
% 0.75/0.92 (~c0_1(a1082)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[573, 1524])).
% 0.75/0.92 tff(1526,plain,
% 0.75/0.92 (~c2_1(a1082)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[579, 1524])).
% 0.75/0.92 tff(1527,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1528,plain,
% 0.75/0.92 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1529,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1528])).
% 0.75/0.92 tff(1530,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1529, 1527])).
% 0.75/0.92 tff(1531,plain,
% 0.75/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1532,plain,
% 0.75/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 0.75/0.92 tff(1533,plain,
% 0.75/0.92 (c0_1(a1082) | c1_1(a1082)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1532, 171, 1120, 1119, 1126, 581, 341, 1125])).
% 0.75/0.92 tff(1534,plain,
% 0.75/0.92 (c1_1(a1082)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1533, 583])).
% 0.75/0.92 tff(1535,plain,
% 0.75/0.92 (hskp3 | c0_1(a1082) | (~c1_1(a1082))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[844, 171, 1046, 12, 11, 581, 22])).
% 0.75/0.92 tff(1536,plain,
% 0.75/0.92 (hskp3),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1535, 583, 1534])).
% 0.75/0.92 tff(1537,plain,
% 0.75/0.92 (~c3_1(a1083)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[856, 1536])).
% 0.75/0.92 tff(1538,plain,
% 0.75/0.92 (~c2_1(a1083)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[850, 1536])).
% 0.75/0.92 tff(1539,plain,
% 0.75/0.92 (c1_1(a1083)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1030, 1536])).
% 0.75/0.92 tff(1540,plain,
% 0.75/0.92 (^[U: $i] : refl((hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1541,plain,
% 0.75/0.92 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1540])).
% 0.75/0.92 tff(1542,plain,
% 0.75/0.92 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1543,plain,
% 0.75/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp16) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp16) <=> (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp16) <=> (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.75/0.93 inference(bind,[status(th)],[])).
% 0.75/0.93 tff(1544,plain,
% 0.75/0.93 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp16) <=> ![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.75/0.93 inference(quant_intro,[status(thm)],[1543])).
% 0.75/0.93 tff(1545,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.75/0.93 tff(1546,plain,
% 0.75/0.93 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.75/0.93 tff(1547,plain,
% 0.75/0.93 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1546, 1542])).
% 0.75/0.93 tff(1548,plain,(
% 0.75/0.93 ![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.75/0.93 inference(skolemize,[status(sab)],[1547])).
% 0.75/0.93 tff(1549,plain,
% 0.75/0.93 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1548, 1541])).
% 0.75/0.93 tff(1550,assumption,(~hskp0), introduced(assumption)).
% 0.75/0.93 tff(1551,plain,
% 0.75/0.93 (((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)))) <=> ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1552,plain,
% 0.75/0.93 ((hskp0 | hskp16 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082))) <=> (hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1553,plain,
% 0.75/0.93 (((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1552])).
% 0.75/0.93 tff(1554,plain,
% 0.75/0.93 (((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1553, 1551])).
% 0.75/0.93 tff(1555,plain,
% 0.75/0.93 ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1556,plain,
% 0.75/0.93 ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 0.75/0.93 tff(1557,plain,
% 0.75/0.93 (hskp16 | c0_1(a1082) | (~c1_1(a1082))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1556, 1550, 171, 581, 1549])).
% 0.75/0.93 tff(1558,plain,
% 0.75/0.93 (hskp16),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1557, 583, 1534])).
% 0.75/0.93 tff(1559,plain,
% 0.75/0.93 (((~hskp16) | (~c3_1(a1100))) <=> ((~hskp16) | (~c3_1(a1100)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1560,plain,
% 0.75/0.93 (((~c3_1(a1100)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a1100)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1561,axiom,((~c3_1(a1100)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.75/0.93 tff(1562,plain,
% 0.75/0.93 ((~hskp16) | (~c3_1(a1100))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 0.75/0.93 tff(1563,plain,
% 0.75/0.93 ((~hskp16) | (~c3_1(a1100))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1562, 1559])).
% 0.75/0.93 tff(1564,plain,
% 0.75/0.93 (~c3_1(a1100)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1563, 1558])).
% 0.75/0.93 tff(1565,plain,
% 0.75/0.93 (((~hskp16) | (~c0_1(a1100))) <=> ((~hskp16) | (~c0_1(a1100)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1566,plain,
% 0.75/0.93 (((~c0_1(a1100)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1100)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1567,axiom,((~c0_1(a1100)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.75/0.93 tff(1568,plain,
% 0.75/0.93 ((~hskp16) | (~c0_1(a1100))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 0.75/0.93 tff(1569,plain,
% 0.75/0.93 ((~hskp16) | (~c0_1(a1100))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1568, 1565])).
% 0.75/0.93 tff(1570,plain,
% 0.75/0.93 (~c0_1(a1100)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1569, 1558])).
% 0.75/0.93 tff(1571,plain,
% 0.75/0.93 (((~hskp16) | c1_1(a1100)) <=> ((~hskp16) | c1_1(a1100))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1572,axiom,((~hskp16) | c1_1(a1100)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.75/0.93 tff(1573,plain,
% 0.75/0.93 ((~hskp16) | c1_1(a1100)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 0.75/0.93 tff(1574,plain,
% 0.75/0.93 ((~hskp16) | c1_1(a1100)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1573, 1571])).
% 0.75/0.93 tff(1575,plain,
% 0.75/0.93 ((~hskp16) | c1_1(a1100)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1574, 1571])).
% 0.75/0.93 tff(1576,plain,
% 0.75/0.93 ((~hskp16) | c1_1(a1100)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1575, 1571])).
% 0.75/0.93 tff(1577,plain,
% 0.75/0.93 ((~hskp16) | c1_1(a1100)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1576, 1571])).
% 0.75/0.93 tff(1578,plain,
% 0.75/0.93 (c1_1(a1100)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1577, 1558])).
% 0.75/0.93 tff(1579,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1580,plain,
% 0.75/0.93 ((hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1581,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1580])).
% 0.75/0.93 tff(1582,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1581, 1579])).
% 0.75/0.93 tff(1583,plain,
% 0.75/0.93 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1584,plain,
% 0.75/0.93 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 0.75/0.93 tff(1585,plain,
% 0.75/0.93 (hskp4),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1584, 171, 1578, 1046, 1570, 1564, 12, 11, 1165])).
% 0.75/0.93 tff(1586,plain,
% 0.75/0.93 (c0_1(a1084)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1180, 1585])).
% 0.75/0.93 tff(1587,plain,
% 0.75/0.93 (~c1_1(a1084)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1186, 1585])).
% 0.75/0.93 tff(1588,plain,
% 0.75/0.93 (~c3_1(a1084)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1192, 1585])).
% 0.75/0.93 tff(1589,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1287, 1588, 1587, 54, 193, 1586, 1141, 1539, 1139, 1538, 1537, 1071])).
% 0.75/0.93 tff(1590,plain,(c0_1(a1082) | hskp9 | hskp14 | c0_1(a1085) | c1_1(a1085) | hskp0 | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(1591,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1590, 1526, 1525, 193, 12, 11, 1424, 54])).
% 0.75/0.93 tff(1592,plain,(hskp14 | c0_1(a1085) | c1_1(a1085) | hskp9 | c1_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(1593,plain,
% 0.75/0.93 (hskp14),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1592, 858, 11, 54, 12, 66])).
% 0.75/0.93 tff(1594,plain,
% 0.75/0.93 (~c2_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[264, 1593])).
% 0.75/0.93 tff(1595,plain,
% 0.75/0.93 (c3_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[306, 1593])).
% 0.75/0.93 tff(1596,plain,
% 0.75/0.93 (c1_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[272, 1593])).
% 0.75/0.93 tff(1597,plain,
% 0.75/0.93 (hskp26),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1299, 171, 1120, 1119, 1126, 1596, 1595, 1594, 86])).
% 0.75/0.93 tff(1598,plain,
% 0.75/0.93 (~c0_1(a1146)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1305, 1597])).
% 0.75/0.93 tff(1599,plain,
% 0.75/0.93 (c3_1(a1146)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1313, 1597])).
% 0.75/0.93 tff(1600,plain,
% 0.75/0.93 (c2_1(a1146)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1321, 1597])).
% 0.75/0.93 tff(1601,plain,
% 0.75/0.93 (hskp19),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1328, 171, 1600, 1599, 1598, 76])).
% 0.75/0.93 tff(1602,plain,
% 0.75/0.93 (~c2_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[917, 1601])).
% 0.75/0.93 tff(1603,plain,
% 0.75/0.93 (c1_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[925, 1601])).
% 0.75/0.93 tff(1604,plain,
% 0.75/0.93 (c0_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[933, 1601])).
% 0.75/0.93 tff(1605,plain,
% 0.75/0.93 (c3_1(a1080)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1449, 171, 1604, 1603, 1046, 1602, 12, 11, 1413, 66, 64])).
% 0.75/0.93 tff(1606,plain,
% 0.75/0.93 (hskp1),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1456, 171, 1604, 1603, 858, 1602, 66, 528, 1605])).
% 0.75/0.93 tff(1607,plain,
% 0.75/0.93 (~c1_1(a1081)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[595, 1606])).
% 0.75/0.93 tff(1608,plain,
% 0.75/0.93 (~c0_1(a1081)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[589, 1606])).
% 0.75/0.93 tff(1609,plain,
% 0.75/0.93 (c3_1(a1081)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1466, 1606])).
% 0.75/0.93 tff(1610,plain,
% 0.75/0.93 (hskp11),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[708, 171, 1120, 1119, 1126, 1609, 1608, 1607, 701])).
% 0.75/0.93 tff(1611,plain,
% 0.75/0.93 (~c3_1(a1091)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[656, 1610])).
% 0.75/0.93 tff(1612,plain,
% 0.75/0.93 (~c0_1(a1091)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[662, 1610])).
% 0.75/0.93 tff(1613,plain,
% 0.75/0.93 (c2_1(a1091)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[670, 1610])).
% 0.75/0.93 tff(1614,plain,
% 0.75/0.93 (hskp30),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1477, 171, 54, 1604, 1603, 1602, 99])).
% 0.75/0.93 tff(1615,plain,
% 0.75/0.93 (c3_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[330, 1614])).
% 0.75/0.93 tff(1616,plain,
% 0.75/0.93 (c1_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[288, 1614])).
% 0.75/0.93 tff(1617,plain,
% 0.75/0.93 (c0_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[322, 1614])).
% 0.75/0.93 tff(1618,plain,
% 0.75/0.93 (hskp17),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1487, 171, 1617, 1616, 1615, 1613, 1612, 1611, 1423])).
% 0.75/0.93 tff(1619,plain,
% 0.75/0.93 (~c2_1(a1102)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1514, 1618])).
% 0.75/0.93 tff(1620,plain,
% 0.75/0.93 (~c0_1(a1102)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1493, 1618])).
% 0.75/0.93 tff(1621,plain,
% 0.75/0.93 (c1_1(a1102)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1521, 171, 1617, 1616, 1615, 1120, 1119, 1126, 1620, 1619, 341])).
% 0.75/0.93 tff(1622,plain,
% 0.75/0.93 (c3_1(a1102)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1501, 1618])).
% 0.75/0.93 tff(1623,plain,
% 0.75/0.93 (hskp2 | (~c1_1(a1102))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1508, 171, 54, 1622, 1620, 396])).
% 0.75/0.93 tff(1624,plain,
% 0.75/0.93 (hskp2),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1623, 1621])).
% 0.75/0.93 tff(1625,plain,
% 0.75/0.93 (~c0_1(a1082)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[573, 1624])).
% 0.75/0.93 tff(1626,plain,
% 0.75/0.93 (~c3_1(a1082)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[409, 1624])).
% 0.75/0.93 tff(1627,plain,
% 0.75/0.93 (~c2_1(a1082)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[579, 1624])).
% 0.75/0.93 tff(1628,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1629,plain,
% 0.75/0.93 ((hskp3 | (~ndr1_0) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1630,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1629])).
% 0.75/0.93 tff(1631,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1630, 1628])).
% 0.75/0.93 tff(1632,plain,
% 0.75/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1633,plain,
% 0.75/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1632, 1631])).
% 0.75/0.93 tff(1634,plain,
% 0.75/0.93 (hskp3),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1633, 171, 1046, 1620, 1619, 12, 11, 22, 1621])).
% 0.75/0.93 tff(1635,plain,
% 0.75/0.93 (~c2_1(a1083)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[850, 1634])).
% 0.75/0.93 tff(1636,plain,
% 0.75/0.93 (c1_1(a1083)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1030, 1634])).
% 0.75/0.93 tff(1637,plain,
% 0.75/0.93 (~c3_1(a1083)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[856, 1634])).
% 0.75/0.93 tff(1638,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1639,plain,
% 0.75/0.93 (((~ndr1_0) | c2_1(a1083) | (~c1_1(a1083)) | (~c0_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1640,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1083) | (~c1_1(a1083)) | (~c0_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1639])).
% 0.75/0.93 tff(1641,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1083) | (~c1_1(a1083)) | (~c0_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1640, 1638])).
% 0.75/0.93 tff(1642,plain,
% 0.75/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1083) | (~c1_1(a1083)) | (~c0_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1643,plain,
% 0.75/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.75/0.93 tff(1644,plain,
% 0.75/0.93 (~c0_1(a1083)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1643, 192, 1363, 1215, 12, 11, 943, 942, 64])).
% 0.75/0.93 tff(1645,plain,
% 0.75/0.93 (hskp4),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1357, 192, 1363, 1215, 12, 11, 942, 1165, 1644])).
% 0.75/0.93 tff(1646,plain,
% 0.75/0.93 (c0_1(a1084)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1180, 1645])).
% 0.75/0.93 tff(1647,plain,
% 0.75/0.93 (~c3_1(a1084)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1192, 1645])).
% 0.75/0.93 tff(1648,plain,
% 0.75/0.93 (~c1_1(a1084)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1186, 1645])).
% 0.75/0.93 tff(1649,plain,
% 0.75/0.93 (hskp14),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1286, 54, 192, 1648, 1647, 1646, 1216, 1215, 1195, 943, 942, 1196])).
% 0.75/0.93 tff(1650,plain,
% 0.75/0.93 (~c2_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[264, 1649])).
% 0.75/0.93 tff(1651,plain,
% 0.75/0.93 (c3_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[306, 1649])).
% 0.75/0.93 tff(1652,plain,
% 0.75/0.93 (c1_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[272, 1649])).
% 0.75/0.93 tff(1653,plain,
% 0.75/0.93 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1654,plain,
% 0.75/0.93 (((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085)) <=> (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1655,plain,
% 0.75/0.93 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1654])).
% 0.75/0.93 tff(1656,plain,
% 0.75/0.93 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1655, 1653])).
% 0.75/0.93 tff(1657,plain,
% 0.75/0.93 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1658,plain,
% 0.75/0.93 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 0.75/0.93 tff(1659,plain,
% 0.75/0.93 (c3_1(a1085)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1658, 192, 1652, 1651, 1215, 1650, 12, 11, 943, 942, 434])).
% 0.75/0.93 tff(1660,plain,
% 0.75/0.93 (hskp19 | (~c3_1(a1085))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[910, 192, 1363, 12, 76])).
% 0.75/0.93 tff(1661,plain,
% 0.75/0.93 (hskp19),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1660, 1659])).
% 0.75/0.93 tff(1662,plain,
% 0.75/0.93 (~c2_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[917, 1661])).
% 0.75/0.93 tff(1663,plain,
% 0.75/0.93 (c1_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[925, 1661])).
% 0.75/0.93 tff(1664,plain,
% 0.75/0.93 (c0_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[933, 1661])).
% 0.75/0.93 tff(1665,plain,
% 0.75/0.93 (c3_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[940, 192, 1664, 1663, 1363, 1662, 12, 11, 64])).
% 0.75/0.93 tff(1666,plain,
% 0.75/0.93 (c2_1(a1084)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1373, 1664, 192, 1663, 1363, 1646, 1662, 12, 11, 1647])).
% 0.75/0.93 tff(1667,plain,
% 0.75/0.93 (hskp9 | hskp8),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1087, 192, 1363, 12, 11, 1081])).
% 0.75/0.93 tff(1668,plain,
% 0.75/0.93 (hskp8),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1667, 54])).
% 0.75/0.93 tff(1669,plain,
% 0.75/0.93 (~c2_1(a1088)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1094, 1668])).
% 0.75/0.93 tff(1670,plain,
% 0.75/0.93 (c0_1(a1088)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1110, 1668])).
% 0.75/0.93 tff(1671,plain,
% 0.75/0.93 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1672,plain,
% 0.75/0.93 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c0_1(a1088))) <=> (hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1673,plain,
% 0.75/0.93 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c0_1(a1088)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1672])).
% 0.75/0.93 tff(1674,plain,
% 0.75/0.93 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c0_1(a1088)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1673, 1671])).
% 0.75/0.93 tff(1675,plain,
% 0.75/0.93 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c0_1(a1088)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1676,plain,
% 0.75/0.93 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 0.75/0.93 tff(1677,plain,
% 0.75/0.93 (hskp30 | (~c1_1(a1088))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1676, 192, 54, 1670, 1669, 99])).
% 0.75/0.93 tff(1678,plain,
% 0.75/0.93 (~c1_1(a1088)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1677, 600])).
% 0.75/0.93 tff(1679,plain,
% 0.75/0.93 (c3_1(a1088)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1102, 1668])).
% 0.75/0.93 tff(1680,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1681,plain,
% 0.75/0.93 ((hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1088) | c1_1(a1088) | (~c3_1(a1088))) <=> (hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1682,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1088) | c1_1(a1088) | (~c3_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1681])).
% 0.75/0.93 tff(1683,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1088) | c1_1(a1088) | (~c3_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1682, 1680])).
% 0.75/0.93 tff(1684,plain,
% 0.75/0.93 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1088) | c1_1(a1088) | (~c3_1(a1088)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1685,plain,
% 0.75/0.93 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 0.75/0.93 tff(1686,plain,
% 0.75/0.93 (hskp23 | c1_1(a1088)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1685, 192, 1679, 1215, 1669, 943, 942, 1214])).
% 0.75/0.93 tff(1687,plain,
% 0.75/0.93 (hskp23),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1686, 1678])).
% 0.75/0.93 tff(1688,plain,
% 0.75/0.93 (c2_1(a1122)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1230, 1687])).
% 0.75/0.93 tff(1689,plain,
% 0.75/0.93 (~c3_1(a1122)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1246, 1687])).
% 0.75/0.93 tff(1690,plain,
% 0.75/0.93 (c0_1(a1122)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1240, 1687])).
% 0.75/0.93 tff(1691,plain,
% 0.75/0.93 (hskp14),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1284, 1690, 54, 192, 1689, 1648, 1647, 1688, 1646])).
% 0.75/0.93 tff(1692,plain,
% 0.75/0.93 (~c2_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[264, 1691])).
% 0.75/0.93 tff(1693,plain,
% 0.75/0.93 (c3_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[306, 1691])).
% 0.75/0.93 tff(1694,plain,
% 0.75/0.93 (c1_1(a1097)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[272, 1691])).
% 0.75/0.93 tff(1695,plain,
% 0.75/0.93 (c3_1(a1085)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1658, 192, 1694, 1693, 1215, 1692, 12, 11, 943, 942, 434])).
% 0.75/0.93 tff(1696,plain,
% 0.75/0.93 (hskp19),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1660, 1695])).
% 0.75/0.93 tff(1697,plain,
% 0.75/0.93 (~c2_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[917, 1696])).
% 0.75/0.93 tff(1698,plain,
% 0.75/0.93 (c1_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[925, 1696])).
% 0.75/0.93 tff(1699,plain,
% 0.75/0.93 (c0_1(a1113)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[933, 1696])).
% 0.75/0.93 tff(1700,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1477, 192, 600, 54, 1699, 1698, 1697, 99])).
% 0.75/0.93 tff(1701,plain,(hskp30 | (~ndr1_0) | hskp9 | (~c2_1(a1085)) | c0_1(a1085) | (~c1_1(a1083)) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(1702,plain,
% 0.75/0.93 (hskp30),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1701, 54, 192, 1363, 12, 1215, 11, 943, 942])).
% 0.75/0.93 tff(1703,plain,
% 0.75/0.93 (c3_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[330, 1702])).
% 0.75/0.93 tff(1704,plain,
% 0.75/0.93 (c1_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[288, 1702])).
% 0.75/0.93 tff(1705,plain,
% 0.75/0.93 (c0_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[322, 1702])).
% 0.75/0.93 tff(1706,plain,
% 0.75/0.93 (hskp28),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1117, 192, 54, 1670, 1679, 1669, 299])).
% 0.75/0.93 tff(1707,plain,
% 0.75/0.93 (hskp11),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[721, 1650, 192, 1706, 1705, 581, 582, 598, 597, 1651, 1652, 1704, 1703, 583])).
% 0.75/0.93 tff(1708,plain,
% 0.75/0.93 (~c0_1(a1091)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[662, 1707])).
% 0.75/0.93 tff(1709,plain,
% 0.75/0.93 (c2_1(a1091)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[670, 1707])).
% 0.75/0.93 tff(1710,plain,
% 0.75/0.93 ((~c2_1(a1084)) | (~c1_1(a1091))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1402, 192, 54, 1709, 1708, 1648, 1647, 1385])).
% 0.75/0.93 tff(1711,plain,
% 0.75/0.93 (~c1_1(a1091)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1710, 1666])).
% 0.75/0.93 tff(1712,plain,
% 0.75/0.93 (~c3_1(a1091)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[656, 1707])).
% 0.75/0.93 tff(1713,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1410, 192, 1663, 1215, 1662, 1708, 1712, 943, 942, 434, 1711, 1665])).
% 0.75/0.93 tff(1714,plain,(hskp9 | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c2_1(a1085)) | c0_1(a1085) | c1_1(a1085) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | (~c3_1(a1103)) | c1_1(a1103) | (~c0_1(a1103))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(1715,plain,
% 0.75/0.93 (hskp9 | (~c1_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c2_1(a1085)) | c0_1(a1085) | c1_1(a1085) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | (~c3_1(a1103)) | c1_1(a1103) | (~c0_1(a1103))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1714, 171])).
% 0.75/0.93 tff(1716,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1715, 1637, 1636, 54, 1608, 1046, 12, 11, 1607, 1635, 1627, 1626, 1625, 1141, 1139, 1071])).
% 0.75/0.93 tff(1717,plain,(c1_1(a1080) | hskp9 | c0_1(a1085) | c1_1(a1085) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(1718,plain,
% 0.75/0.93 (c1_1(a1080)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1717, 66, 12, 11, 54])).
% 0.75/0.93 tff(1719,plain,
% 0.75/0.93 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1720,plain,
% 0.75/0.93 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080))) <=> (hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1721,plain,
% 0.75/0.93 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1720])).
% 0.75/0.93 tff(1722,plain,
% 0.75/0.93 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1721, 1719])).
% 0.75/0.93 tff(1723,plain,
% 0.75/0.93 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1724,plain,
% 0.75/0.93 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 0.75/0.93 tff(1725,plain,
% 0.75/0.93 (hskp30 | (~c0_1(a1080)) | (~c1_1(a1080))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1724, 171, 54, 66, 99])).
% 0.75/0.93 tff(1726,plain,
% 0.75/0.93 (hskp30),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1725, 1718, 1413])).
% 0.75/0.93 tff(1727,plain,
% 0.75/0.93 (c3_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[330, 1726])).
% 0.75/0.93 tff(1728,plain,
% 0.75/0.93 (c1_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[288, 1726])).
% 0.75/0.93 tff(1729,plain,
% 0.75/0.93 (c0_1(a1109)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[322, 1726])).
% 0.75/0.93 tff(1730,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1731,plain,
% 0.75/0.94 (((~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1732,plain,
% 0.75/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[1731])).
% 0.75/0.94 tff(1733,plain,
% 0.75/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 0.75/0.94 inference(transitivity,[status(thm)],[1732, 1730])).
% 0.75/0.94 tff(1734,plain,
% 0.75/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(1735,plain,
% 0.75/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 0.75/0.94 tff(1736,plain,
% 0.75/0.94 ((~c0_1(a1080)) | c3_1(a1080) | (~c1_1(a1080))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1735, 171, 1046, 12, 11, 66, 64])).
% 0.75/0.94 tff(1737,plain,
% 0.75/0.94 (c3_1(a1080)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1736, 1718, 1413])).
% 0.75/0.94 tff(1738,plain,
% 0.75/0.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1739,plain,
% 0.75/0.94 ((hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080))) <=> (hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1740,plain,
% 0.75/0.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[1739])).
% 0.75/0.94 tff(1741,plain,
% 0.75/0.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.94 inference(transitivity,[status(thm)],[1740, 1738])).
% 0.75/0.94 tff(1742,plain,
% 0.75/0.94 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(1743,plain,
% 0.75/0.94 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 0.75/0.94 tff(1744,plain,
% 0.75/0.94 (hskp26 | (~c3_1(a1080)) | (~c1_1(a1080))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1743, 171, 1120, 1119, 1126, 66, 86])).
% 0.75/0.94 tff(1745,plain,
% 0.75/0.94 (hskp26),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1744, 1737, 1718])).
% 0.75/0.94 tff(1746,plain,
% 0.75/0.94 (~c0_1(a1146)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1305, 1745])).
% 0.75/0.94 tff(1747,plain,
% 0.75/0.94 (c3_1(a1146)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1313, 1745])).
% 0.75/0.94 tff(1748,plain,
% 0.75/0.94 (c2_1(a1146)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1321, 1745])).
% 0.75/0.94 tff(1749,plain,
% 0.75/0.94 (hskp19),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1328, 171, 1748, 1747, 1746, 76])).
% 0.75/0.94 tff(1750,plain,
% 0.75/0.94 (c1_1(a1113)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[925, 1749])).
% 0.75/0.94 tff(1751,plain,
% 0.75/0.94 (c0_1(a1113)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[933, 1749])).
% 0.75/0.94 tff(1752,plain,
% 0.75/0.94 (~c2_1(a1113)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[917, 1749])).
% 0.75/0.94 tff(1753,assumption,(~c0_1(a1146)), introduced(assumption)).
% 0.75/0.94 tff(1754,assumption,(c3_1(a1146)), introduced(assumption)).
% 0.75/0.94 tff(1755,plain,
% 0.75/0.94 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1756,plain,
% 0.75/0.94 ((hskp9 | hskp2 | (~ndr1_0) | c0_1(a1146) | (~c3_1(a1146)) | (~c1_1(a1146))) <=> (hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1757,plain,
% 0.75/0.94 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1146) | (~c3_1(a1146)) | (~c1_1(a1146)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[1756])).
% 0.75/0.94 tff(1758,plain,
% 0.75/0.94 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1146) | (~c3_1(a1146)) | (~c1_1(a1146)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146)))),
% 0.75/0.94 inference(transitivity,[status(thm)],[1757, 1755])).
% 0.75/0.94 tff(1759,plain,
% 0.75/0.94 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1146) | (~c3_1(a1146)) | (~c1_1(a1146)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(1760,plain,
% 0.75/0.94 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 0.75/0.94 tff(1761,plain,
% 0.75/0.94 (hskp2 | (~c1_1(a1146))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1760, 171, 54, 1754, 1753, 396])).
% 0.75/0.94 tff(1762,plain,
% 0.75/0.94 (~c1_1(a1146)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1761, 65])).
% 0.75/0.94 tff(1763,assumption,(c2_1(a1146)), introduced(assumption)).
% 0.75/0.94 tff(1764,plain,
% 0.75/0.94 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1765,plain,
% 0.75/0.94 ((hskp11 | hskp9 | (~ndr1_0) | c1_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146))) <=> (hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1766,plain,
% 0.75/0.94 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[1765])).
% 0.75/0.94 tff(1767,plain,
% 0.75/0.94 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146)))),
% 0.75/0.94 inference(transitivity,[status(thm)],[1766, 1764])).
% 0.75/0.94 tff(1768,plain,
% 0.75/0.94 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(1769,plain,
% 0.75/0.94 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 0.75/0.94 tff(1770,plain,
% 0.75/0.94 (hskp11 | c1_1(a1146)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1769, 171, 54, 1763, 1754, 1060])).
% 0.75/0.94 tff(1771,plain,
% 0.75/0.94 (hskp11),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1770, 1762])).
% 0.75/0.94 tff(1772,plain,
% 0.75/0.94 (~c3_1(a1091)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[656, 1771])).
% 0.75/0.94 tff(1773,plain,
% 0.75/0.94 (~c0_1(a1091)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[662, 1771])).
% 0.75/0.94 tff(1774,plain,
% 0.75/0.94 (c2_1(a1091)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[670, 1771])).
% 0.75/0.94 tff(1775,plain,
% 0.75/0.94 (hskp17),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1487, 171, 369, 368, 367, 1774, 1773, 1772, 1423])).
% 0.75/0.94 tff(1776,plain,
% 0.75/0.94 (~c0_1(a1102)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1493, 1775])).
% 0.75/0.94 tff(1777,plain,
% 0.75/0.94 (c3_1(a1102)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1501, 1775])).
% 0.75/0.94 tff(1778,plain,
% 0.75/0.94 (~c1_1(a1102)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1508, 171, 54, 65, 1777, 1776, 396])).
% 0.75/0.94 tff(1779,plain,
% 0.75/0.94 (~c2_1(a1102)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1514, 1775])).
% 0.75/0.94 tff(1780,assumption,(c3_1(a1092)), introduced(assumption)).
% 0.75/0.94 tff(1781,assumption,(c2_1(a1092)), introduced(assumption)).
% 0.75/0.94 tff(1782,assumption,(c0_1(a1092)), introduced(assumption)).
% 0.75/0.94 tff(1783,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1521, 171, 369, 368, 367, 1782, 1781, 1780, 1776, 1779, 341, 1778])).
% 0.75/0.94 tff(1784,plain,(hskp2 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1092)) | (~c2_1(a1092)) | (~c3_1(a1092)) | hskp9 | (~c2_1(a1146)) | (~c3_1(a1146)) | c0_1(a1146)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(1785,plain,
% 0.75/0.94 (hskp2),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1784, 1729, 1728, 1727, 1120, 1119, 1126, 54, 1748, 1747, 1746])).
% 0.75/0.94 tff(1786,plain,
% 0.75/0.94 (~c0_1(a1082)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[573, 1785])).
% 0.75/0.94 tff(1787,plain,
% 0.75/0.94 (~c2_1(a1082)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[579, 1785])).
% 0.75/0.94 tff(1788,plain,
% 0.75/0.94 (c3_1(a1113)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[940, 171, 1365, 1364, 1046, 1362, 12, 11, 64])).
% 0.75/0.94 tff(1789,plain,
% 0.75/0.94 (c0_1(a1082) | c1_1(a1082)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[690, 171, 369, 368, 367, 1120, 1119, 1126, 581, 341])).
% 0.75/0.94 tff(1790,plain,
% 0.75/0.94 (c1_1(a1082)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1789, 583])).
% 0.75/0.94 tff(1791,plain,
% 0.75/0.94 (hskp16),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1557, 583, 1790])).
% 0.75/0.94 tff(1792,plain,
% 0.75/0.94 (~c3_1(a1100)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1563, 1791])).
% 0.75/0.94 tff(1793,plain,
% 0.75/0.94 (~c0_1(a1100)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1569, 1791])).
% 0.75/0.94 tff(1794,plain,
% 0.75/0.94 (c1_1(a1100)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1577, 1791])).
% 0.75/0.94 tff(1795,plain,
% 0.75/0.94 (hskp4),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1584, 171, 1794, 1046, 1793, 1792, 12, 11, 1165])).
% 0.75/0.94 tff(1796,plain,
% 0.75/0.94 (c0_1(a1084)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1180, 1795])).
% 0.75/0.94 tff(1797,plain,
% 0.75/0.94 (~c3_1(a1084)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1192, 1795])).
% 0.75/0.94 tff(1798,plain,
% 0.75/0.94 (c2_1(a1084)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1374, 1797, 1365, 1364, 1046, 1796, 1362, 12, 11])).
% 0.75/0.94 tff(1799,plain,
% 0.75/0.94 (~c1_1(a1084)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1186, 1795])).
% 0.75/0.94 tff(1800,plain,
% 0.75/0.94 (hskp3),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1535, 583, 1790])).
% 0.75/0.94 tff(1801,plain,
% 0.75/0.94 (~c3_1(a1083)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[856, 1800])).
% 0.75/0.94 tff(1802,plain,
% 0.75/0.94 (~c2_1(a1083)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[850, 1800])).
% 0.75/0.94 tff(1803,plain,
% 0.75/0.94 (c1_1(a1083)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1030, 1800])).
% 0.75/0.94 tff(1804,plain,
% 0.75/0.94 (c3_1(a1085)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1392, 171, 1364, 1803, 1362, 12, 11, 1802, 1801, 434, 1788])).
% 0.75/0.94 tff(1805,plain,
% 0.75/0.94 (hskp11),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1067, 1804, 54, 1046])).
% 0.75/0.94 tff(1806,plain,
% 0.75/0.94 (~c0_1(a1091)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[662, 1805])).
% 0.75/0.94 tff(1807,plain,
% 0.75/0.94 (c2_1(a1091)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[670, 1805])).
% 0.75/0.94 tff(1808,plain,
% 0.75/0.94 (~c1_1(a1091)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1402, 171, 54, 1807, 1806, 1799, 1797, 1385, 1798])).
% 0.75/0.94 tff(1809,plain,
% 0.75/0.94 (~c3_1(a1091)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[656, 1805])).
% 0.75/0.94 tff(1810,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1410, 171, 1364, 1803, 1362, 1806, 1809, 1802, 1801, 434, 1808, 1788])).
% 0.75/0.94 tff(1811,plain,(c0_1(a1082) | (~c1_1(a1113)) | c2_1(a1113) | hskp9 | (~c0_1(a1113)) | c0_1(a1085) | c1_1(a1085) | hskp0 | c2_1(a1082) | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(1812,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1811, 1787, 1786, 1752, 54, 1751, 12, 11, 1424, 1750, 1729, 1728, 1727])).
% 0.75/0.94 tff(1813,plain,(c2_1(a1080) | hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(1814,plain,
% 0.75/0.94 (c2_1(a1080)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1813, 54, 12, 11])).
% 0.75/0.94 tff(1815,plain,
% 0.75/0.94 (~hskp0),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[28, 1814])).
% 0.75/0.94 tff(1816,plain,
% 0.75/0.94 (^[U: $i] : refl((hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.75/0.94 inference(bind,[status(th)],[])).
% 0.75/0.94 tff(1817,plain,
% 0.75/0.94 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.75/0.94 inference(quant_intro,[status(thm)],[1816])).
% 0.75/0.94 tff(1818,plain,
% 0.75/0.94 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1819,plain,
% 0.75/0.94 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp2) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp2) <=> (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.75/0.94 inference(bind,[status(th)],[])).
% 0.75/0.94 tff(1820,plain,
% 0.75/0.94 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp2) <=> ![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.75/0.94 inference(quant_intro,[status(thm)],[1819])).
% 0.75/0.94 tff(1821,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.75/0.94 tff(1822,plain,
% 0.75/0.94 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 0.75/0.94 tff(1823,plain,
% 0.75/0.94 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1822, 1818])).
% 0.75/0.94 tff(1824,plain,(
% 0.75/0.94 ![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.75/0.94 inference(skolemize,[status(sab)],[1823])).
% 0.75/0.94 tff(1825,plain,
% 0.75/0.94 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1824, 1817])).
% 0.75/0.94 tff(1826,plain,
% 0.75/0.94 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1827,plain,
% 0.75/0.94 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(1828,plain,
% 0.75/0.94 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 0.75/0.94 tff(1829,plain,
% 0.75/0.94 (hskp0 | hskp2 | c1_1(a1092)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1828, 171, 1120, 1119, 1825])).
% 0.75/0.94 tff(1830,plain,
% 0.75/0.94 (c1_1(a1092)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1829, 65, 1815])).
% 0.75/0.94 tff(1831,plain,
% 0.75/0.94 (hskp19),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1439, 1830, 65])).
% 0.75/0.94 tff(1832,plain,
% 0.75/0.94 (~c2_1(a1113)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[917, 1831])).
% 0.75/0.94 tff(1833,plain,
% 0.75/0.94 (c1_1(a1113)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[925, 1831])).
% 0.75/0.94 tff(1834,plain,
% 0.75/0.94 (c0_1(a1113)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[933, 1831])).
% 0.75/0.94 tff(1835,plain,
% 0.75/0.94 (c3_1(a1113)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[940, 171, 1834, 1833, 1046, 1832, 12, 11, 64])).
% 0.75/0.94 tff(1836,plain,
% 0.75/0.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1837,plain,
% 0.75/0.94 ((hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113))) <=> (hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(1838,plain,
% 0.75/0.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[1837])).
% 0.75/0.94 tff(1839,plain,
% 0.75/0.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.75/0.94 inference(transitivity,[status(thm)],[1838, 1836])).
% 0.75/0.94 tff(1840,plain,
% 0.75/0.94 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(1841,plain,
% 0.75/0.94 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 0.75/0.94 tff(1842,plain,
% 0.75/0.94 (hskp26),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1841, 171, 1120, 1119, 1126, 1833, 1832, 86, 1835])).
% 0.75/0.94 tff(1843,plain,
% 0.75/0.94 (~c0_1(a1146)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1305, 1842])).
% 0.75/0.94 tff(1844,plain,
% 0.75/0.94 (c3_1(a1146)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1313, 1842])).
% 0.75/0.94 tff(1845,plain,
% 0.75/0.94 (c2_1(a1146)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1321, 1842])).
% 0.75/0.94 tff(1846,plain,
% 0.75/0.94 (hskp30),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1477, 171, 54, 1834, 1833, 1832, 99])).
% 0.75/0.94 tff(1847,plain,
% 0.75/0.94 (c3_1(a1109)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[330, 1846])).
% 0.75/0.94 tff(1848,plain,
% 0.75/0.94 (c0_1(a1109)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[322, 1846])).
% 0.75/0.94 tff(1849,plain,
% 0.75/0.94 (c1_1(a1109)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[288, 1846])).
% 0.75/0.94 tff(1850,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1784, 1849, 1848, 65, 1847, 1120, 1119, 1126, 54, 1845, 1844, 1843])).
% 0.75/0.94 tff(1851,plain,(hskp2 | hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(1852,plain,
% 0.75/0.94 (hskp2),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1851, 54, 12, 11])).
% 0.75/0.94 tff(1853,plain,
% 0.75/0.94 (~c0_1(a1082)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[573, 1852])).
% 0.75/0.94 tff(1854,plain,
% 0.75/0.94 (~c2_1(a1082)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[579, 1852])).
% 0.75/0.94 tff(1855,plain,
% 0.75/0.94 (hskp14),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1590, 583, 581, 12, 11, 1815, 54])).
% 0.75/0.94 tff(1856,plain,
% 0.75/0.94 (~c2_1(a1097)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[264, 1855])).
% 0.75/0.94 tff(1857,plain,
% 0.75/0.94 (c3_1(a1097)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[306, 1855])).
% 0.75/0.94 tff(1858,plain,
% 0.75/0.94 (c1_1(a1097)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[272, 1855])).
% 0.75/0.94 tff(1859,plain,
% 0.75/0.94 (hskp26),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1299, 171, 1120, 1119, 1126, 1858, 1857, 1856, 86])).
% 0.78/0.94 tff(1860,plain,
% 0.78/0.94 (~c0_1(a1146)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1305, 1859])).
% 0.78/0.94 tff(1861,plain,
% 0.78/0.94 (c3_1(a1146)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1313, 1859])).
% 0.78/0.94 tff(1862,plain,
% 0.78/0.94 (c2_1(a1146)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1321, 1859])).
% 0.78/0.94 tff(1863,plain,
% 0.78/0.94 (hskp19),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1328, 171, 1862, 1861, 1860, 76])).
% 0.78/0.94 tff(1864,plain,
% 0.78/0.94 (~c2_1(a1113)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[917, 1863])).
% 0.78/0.94 tff(1865,plain,
% 0.78/0.94 (c1_1(a1113)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[925, 1863])).
% 0.78/0.94 tff(1866,plain,
% 0.78/0.94 (c0_1(a1113)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[933, 1863])).
% 0.78/0.94 tff(1867,plain,
% 0.78/0.94 (hskp30),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1477, 171, 54, 1866, 1865, 1864, 99])).
% 0.78/0.94 tff(1868,plain,
% 0.78/0.94 (c3_1(a1109)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[330, 1867])).
% 0.78/0.94 tff(1869,plain,
% 0.78/0.94 (c0_1(a1109)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[322, 1867])).
% 0.78/0.94 tff(1870,plain,
% 0.78/0.94 (c1_1(a1109)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[288, 1867])).
% 0.78/0.94 tff(1871,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1811, 1870, 1869, 581, 54, 583, 12, 11, 1815, 1865, 1866, 1864, 1868])).
% 0.78/0.94 tff(1872,plain,(c0_1(a1082) | c2_1(a1082) | hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1873,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1872, 1854, 1853, 54, 12, 11])).
% 0.78/0.94 tff(1874,plain,(hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1875,plain,
% 0.78/0.94 (hskp9),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1874, 12, 11])).
% 0.78/0.94 tff(1876,plain,
% 0.78/0.94 (~c1_1(a1089)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[492, 1875])).
% 0.78/0.94 tff(1877,plain,
% 0.78/0.94 (c3_1(a1089)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[500, 1875])).
% 0.78/0.94 tff(1878,plain,
% 0.78/0.94 (c2_1(a1089)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[508, 1875])).
% 0.78/0.94 tff(1879,plain,
% 0.78/0.94 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1880,plain,
% 0.78/0.94 ((hskp21 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089))) <=> (hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1881,plain,
% 0.78/0.94 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1880])).
% 0.78/0.94 tff(1882,plain,
% 0.78/0.94 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1881, 1879])).
% 0.78/0.94 tff(1883,plain,
% 0.78/0.94 ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1884,plain,
% 0.78/0.94 ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 0.78/0.94 tff(1885,plain,
% 0.78/0.94 (hskp21),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1884, 171, 1878, 1877, 1876, 53])).
% 0.78/0.94 tff(1886,plain,
% 0.78/0.94 (c1_1(a1120)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[989, 1885])).
% 0.78/0.94 tff(1887,plain,
% 0.78/0.94 (~c3_1(a1120)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[956, 1885])).
% 0.78/0.94 tff(1888,plain,
% 0.78/0.94 (c2_1(a1120)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[964, 1885])).
% 0.78/0.94 tff(1889,plain,
% 0.78/0.94 (~hskp18),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[179, 115])).
% 0.78/0.94 tff(1890,plain,
% 0.78/0.94 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(1891,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[1890])).
% 0.78/0.94 tff(1892,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1893,plain,
% 0.78/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(1894,plain,
% 0.78/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[1893])).
% 0.78/0.94 tff(1895,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.78/0.94 tff(1896,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 0.78/0.94 tff(1897,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1896, 1892])).
% 0.78/0.94 tff(1898,plain,(
% 0.78/0.94 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(skolemize,[status(sab)],[1897])).
% 0.78/0.94 tff(1899,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1898, 1891])).
% 0.78/0.94 tff(1900,assumption,(~c3_1(a1120)), introduced(assumption)).
% 0.78/0.94 tff(1901,assumption,(c2_1(a1120)), introduced(assumption)).
% 0.78/0.94 tff(1902,assumption,(c1_1(a1120)), introduced(assumption)).
% 0.78/0.94 tff(1903,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1904,plain,
% 0.78/0.94 ((hskp5 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c0_1(a1120)) | c3_1(a1120) | (~c1_1(a1120)) | (~c0_1(a1120))) <=> (hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1905,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c0_1(a1120)) | c3_1(a1120) | (~c1_1(a1120)) | (~c0_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1904])).
% 0.78/0.94 tff(1906,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c0_1(a1120)) | c3_1(a1120) | (~c1_1(a1120)) | (~c0_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1905, 1903])).
% 0.78/0.94 tff(1907,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c0_1(a1120)) | c3_1(a1120) | (~c1_1(a1120)) | (~c0_1(a1120)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1908,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 0.78/0.94 tff(1909,plain,
% 0.78/0.94 (hskp5 | (~c0_1(a1120))),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1908, 171, 1902, 1901, 1900, 1899])).
% 0.78/0.94 tff(1910,plain,
% 0.78/0.94 (~c0_1(a1120)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1909, 115])).
% 0.78/0.94 tff(1911,plain,
% 0.78/0.94 (hskp18 | c0_1(a1120)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[971, 171, 1901, 1900, 242])).
% 0.78/0.94 tff(1912,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1911, 1910, 1889])).
% 0.78/0.94 tff(1913,plain,(hskp5 | (~c2_1(a1120)) | c3_1(a1120) | (~c1_1(a1120))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1914,plain,
% 0.78/0.94 (hskp5),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1913, 1888, 1887, 1886])).
% 0.78/0.94 tff(1915,plain,
% 0.78/0.94 (c2_1(a1085)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[106, 1914])).
% 0.78/0.95 tff(1916,assumption,(~hskp19), introduced(assumption)).
% 0.78/0.95 tff(1917,assumption,(c3_1(a1089)), introduced(assumption)).
% 0.78/0.95 tff(1918,assumption,(c2_1(a1089)), introduced(assumption)).
% 0.78/0.95 tff(1919,plain,
% 0.78/0.95 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1920,plain,
% 0.78/0.95 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1921,plain,
% 0.78/0.95 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 0.78/0.95 tff(1922,plain,
% 0.78/0.95 (hskp19 | c0_1(a1089)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1921, 171, 1918, 1917, 76])).
% 0.78/0.95 tff(1923,plain,
% 0.78/0.95 (c0_1(a1089)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1922, 1916])).
% 0.78/0.95 tff(1924,assumption,(~c1_1(a1089)), introduced(assumption)).
% 0.78/0.95 tff(1925,plain,
% 0.78/0.95 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1926,plain,
% 0.78/0.95 ((hskp14 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089))) <=> (hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1927,plain,
% 0.78/0.95 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1926])).
% 0.78/0.95 tff(1928,plain,
% 0.78/0.95 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1927, 1925])).
% 0.78/0.95 tff(1929,plain,
% 0.78/0.95 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1930,plain,
% 0.78/0.95 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1929, 1928])).
% 0.78/0.95 tff(1931,plain,
% 0.78/0.95 (hskp14 | (~c0_1(a1089))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1930, 171, 1918, 1924, 190])).
% 0.78/0.95 tff(1932,plain,
% 0.78/0.95 (hskp14),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1931, 1923])).
% 0.78/0.95 tff(1933,plain,
% 0.78/0.95 (~c2_1(a1097)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[264, 1932])).
% 0.78/0.95 tff(1934,plain,
% 0.78/0.95 (c3_1(a1097)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[306, 1932])).
% 0.78/0.95 tff(1935,plain,
% 0.78/0.95 (c1_1(a1097)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[272, 1932])).
% 0.78/0.95 tff(1936,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1937,plain,
% 0.78/0.95 ((hskp26 | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097))) <=> (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1938,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1937])).
% 0.78/0.95 tff(1939,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1938, 1936])).
% 0.78/0.95 tff(1940,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1941,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 0.78/0.95 tff(1942,plain,
% 0.78/0.95 (hskp26),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1941, 171, 1935, 1934, 1918, 1917, 1933, 86, 1923])).
% 0.78/0.95 tff(1943,plain,
% 0.78/0.95 (~c0_1(a1146)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1305, 1942])).
% 0.78/0.95 tff(1944,plain,
% 0.78/0.95 (c3_1(a1146)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1313, 1942])).
% 0.78/0.95 tff(1945,plain,
% 0.78/0.95 (c2_1(a1146)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1321, 1942])).
% 0.78/0.95 tff(1946,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1328, 171, 1916, 1945, 1944, 1943, 76])).
% 0.78/0.95 tff(1947,plain,(hskp19 | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1948,plain,
% 0.78/0.95 (hskp19),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1947, 1878, 1877, 1876])).
% 0.78/0.95 tff(1949,plain,
% 0.78/0.95 (~c2_1(a1113)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[917, 1948])).
% 0.78/0.95 tff(1950,plain,
% 0.78/0.95 (c1_1(a1113)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[925, 1948])).
% 0.78/0.95 tff(1951,plain,
% 0.78/0.95 (c0_1(a1113)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[933, 1948])).
% 0.78/0.95 tff(1952,plain,
% 0.78/0.95 (c3_1(a1113)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[940, 171, 1951, 1950, 1915, 1949, 12, 11, 64])).
% 0.78/0.95 tff(1953,assumption,(hskp3), introduced(assumption)).
% 0.78/0.95 tff(1954,plain,
% 0.78/0.95 (~c3_1(a1083)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[856, 1953])).
% 0.78/0.95 tff(1955,plain,
% 0.78/0.95 (~c2_1(a1083)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[850, 1953])).
% 0.78/0.95 tff(1956,plain,
% 0.78/0.95 (c1_1(a1083)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1030, 1953])).
% 0.78/0.95 tff(1957,plain,
% 0.78/0.95 (c3_1(a1085)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1392, 171, 1950, 1956, 1949, 12, 11, 1955, 1954, 434, 1952])).
% 0.78/0.95 tff(1958,plain,
% 0.78/0.95 (~c0_1(a1083)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1349, 171, 1951, 1950, 1915, 1949, 12, 11, 1955, 1954, 64])).
% 0.78/0.95 tff(1959,plain,
% 0.78/0.95 (hskp4),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1357, 171, 1915, 1956, 12, 11, 1954, 1165, 1958])).
% 0.78/0.95 tff(1960,plain,
% 0.78/0.95 (~c3_1(a1084)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1192, 1959])).
% 0.78/0.95 tff(1961,plain,
% 0.78/0.95 (c0_1(a1084)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1180, 1959])).
% 0.78/0.95 tff(1962,plain,
% 0.78/0.95 (c2_1(a1084)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1374, 1961, 1951, 1950, 1915, 1960, 1949, 12, 11])).
% 0.78/0.95 tff(1963,plain,
% 0.78/0.95 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1964,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1963])).
% 0.78/0.95 tff(1965,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1966,plain,
% 0.78/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp31) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1967,plain,
% 0.78/0.95 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1966])).
% 0.78/0.95 tff(1968,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.78/0.95 tff(1969,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 0.78/0.95 tff(1970,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1969, 1965])).
% 0.78/0.95 tff(1971,plain,(
% 0.78/0.95 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.95 inference(skolemize,[status(sab)],[1970])).
% 0.78/0.95 tff(1972,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1971, 1964])).
% 0.78/0.95 tff(1973,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1974,plain,
% 0.78/0.95 ((hskp31 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c2_1(a1084)) | c3_1(a1084) | (~c0_1(a1084))) <=> (hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1975,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c2_1(a1084)) | c3_1(a1084) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1974])).
% 0.78/0.95 tff(1976,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c2_1(a1084)) | c3_1(a1084) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1975, 1973])).
% 0.78/0.95 tff(1977,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c2_1(a1084)) | c3_1(a1084) | (~c0_1(a1084)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1978,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 0.78/0.95 tff(1979,plain,
% 0.78/0.95 (hskp31),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1978, 171, 1886, 1888, 1961, 1887, 1960, 1972, 1962])).
% 0.78/0.95 tff(1980,plain,
% 0.78/0.95 (((~hskp31) | c2_1(a1148)) <=> ((~hskp31) | c2_1(a1148))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1981,axiom,((~hskp31) | c2_1(a1148)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.78/0.95 tff(1982,plain,
% 0.78/0.95 ((~hskp31) | c2_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.78/0.95 tff(1983,plain,
% 0.78/0.95 ((~hskp31) | c2_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1982, 1980])).
% 0.78/0.95 tff(1984,plain,
% 0.78/0.95 ((~hskp31) | c2_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1983, 1980])).
% 0.78/0.95 tff(1985,plain,
% 0.78/0.95 ((~hskp31) | c2_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1984, 1980])).
% 0.78/0.95 tff(1986,plain,
% 0.78/0.95 ((~hskp31) | c2_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1985, 1980])).
% 0.78/0.95 tff(1987,plain,
% 0.78/0.95 (c2_1(a1148)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1986, 1979])).
% 0.78/0.95 tff(1988,plain,
% 0.78/0.95 (((~hskp31) | c1_1(a1148)) <=> ((~hskp31) | c1_1(a1148))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1989,axiom,((~hskp31) | c1_1(a1148)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.78/0.95 tff(1990,plain,
% 0.78/0.95 ((~hskp31) | c1_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 0.78/0.95 tff(1991,plain,
% 0.78/0.95 ((~hskp31) | c1_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1990, 1988])).
% 0.78/0.95 tff(1992,plain,
% 0.78/0.95 ((~hskp31) | c1_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1991, 1988])).
% 0.78/0.95 tff(1993,plain,
% 0.78/0.95 ((~hskp31) | c1_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1992, 1988])).
% 0.78/0.95 tff(1994,plain,
% 0.78/0.95 ((~hskp31) | c1_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1993, 1988])).
% 0.78/0.95 tff(1995,plain,
% 0.78/0.95 (c1_1(a1148)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1994, 1979])).
% 0.78/0.95 tff(1996,plain,
% 0.78/0.95 (((~hskp31) | c0_1(a1148)) <=> ((~hskp31) | c0_1(a1148))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1997,axiom,((~hskp31) | c0_1(a1148)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.78/0.95 tff(1998,plain,
% 0.78/0.95 ((~hskp31) | c0_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 0.78/0.95 tff(1999,plain,
% 0.78/0.95 ((~hskp31) | c0_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1998, 1996])).
% 0.78/0.95 tff(2000,plain,
% 0.78/0.95 ((~hskp31) | c0_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1999, 1996])).
% 0.78/0.95 tff(2001,plain,
% 0.78/0.95 ((~hskp31) | c0_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[2000, 1996])).
% 0.78/0.95 tff(2002,plain,
% 0.78/0.95 ((~hskp31) | c0_1(a1148)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[2001, 1996])).
% 0.78/0.95 tff(2003,plain,
% 0.78/0.95 (c0_1(a1148)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[2002, 1979])).
% 0.78/0.95 tff(2004,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2005,plain,
% 0.78/0.95 ((hskp10 | (~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085))) <=> (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2006,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[2005])).
% 0.78/0.95 tff(2007,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[2006, 2004])).
% 0.78/0.95 tff(2008,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(2009,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 0.78/0.95 tff(2010,plain,
% 0.78/0.95 (hskp10),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[2009, 171, 2003, 1995, 1987, 12, 11, 982, 1957])).
% 0.78/0.95 tff(2011,plain,
% 0.78/0.95 (~c3_1(a1090)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1002, 2010])).
% 0.78/0.95 tff(2012,plain,
% 0.78/0.95 (~c1_1(a1090)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1008, 2010])).
% 0.78/0.95 tff(2013,plain,
% 0.78/0.95 (~c0_1(a1090)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1014, 2010])).
% 0.78/0.95 tff(2014,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1037, 171, 1950, 1956, 1949, 2013, 2012, 2011, 1955, 1954, 434, 1952])).
% 0.78/0.95 tff(2015,plain,((~hskp3) | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(2016,plain,
% 0.78/0.95 (~hskp3),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[2015, 12, 11])).
% 0.78/0.95 tff(2017,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1021, 171, 2016, 1915, 43, 12, 11, 35, 29, 22])).
% 0.78/0.95 tff(2018,plain,((~hskp0) | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(2019,plain,
% 0.78/0.95 (~hskp0),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[2018, 12, 11])).
% 0.78/0.95 tff(2020,plain,
% 0.78/0.95 (^[U: $i] : refl((hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(2021,plain,
% 0.78/0.95 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[2020])).
% 0.78/0.95 tff(2022,plain,
% 0.78/0.95 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2023,plain,
% 0.78/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp16) <=> ((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp16) <=> (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(2024,plain,
% 0.78/0.95 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp16) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[2023])).
% 0.78/0.95 tff(2025,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.78/0.95 tff(2026,plain,
% 0.78/0.95 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 0.78/0.95 tff(2027,plain,
% 0.78/0.95 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[2026, 2022])).
% 0.78/0.95 tff(2028,plain,(
% 0.78/0.95 ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.95 inference(skolemize,[status(sab)],[2027])).
% 0.78/0.95 tff(2029,plain,
% 0.78/0.95 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[2028, 2021])).
% 0.78/0.95 tff(2030,plain,
% 0.78/0.95 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2031,plain,
% 0.78/0.95 ((hskp0 | hskp2 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089))) <=> (hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2032,plain,
% 0.78/0.95 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[2031])).
% 0.78/0.95 tff(2033,plain,
% 0.78/0.95 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[2032, 2030])).
% 0.78/0.95 tff(2034,plain,
% 0.78/0.95 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(2035,plain,
% 0.78/0.95 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[2034, 2033])).
% 0.78/0.95 tff(2036,plain,
% 0.78/0.95 (hskp0 | hskp2 | (~c0_1(a1089))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[2035, 171, 1878, 1876, 1825])).
% 0.78/0.95 tff(2037,plain,
% 0.78/0.95 (~c0_1(a1089)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[2036, 65, 2019])).
% 0.78/0.95 tff(2038,assumption,(hskp4), introduced(assumption)).
% 0.78/0.95 tff(2039,plain,
% 0.78/0.95 (c0_1(a1084)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1180, 2038])).
% 0.78/0.95 tff(2040,plain,
% 0.78/0.95 (~c3_1(a1084)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1192, 2038])).
% 0.78/0.95 tff(2041,plain,
% 0.78/0.95 (c2_1(a1084)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1374, 2040, 1951, 1950, 1915, 2039, 1949, 12, 11])).
% 0.78/0.95 tff(2042,plain,
% 0.78/0.95 (~c1_1(a1084)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1186, 2038])).
% 0.78/0.95 tff(2043,plain,
% 0.78/0.95 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2044,plain,
% 0.78/0.95 ((hskp0 | hskp2 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084))) <=> (hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2045,plain,
% 0.78/0.95 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[2044])).
% 0.78/0.95 tff(2046,plain,
% 0.78/0.95 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[2045, 2043])).
% 0.78/0.95 tff(2047,plain,
% 0.78/0.95 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(2048,plain,
% 0.78/0.95 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 0.78/0.95 tff(2049,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[2048, 1550, 171, 65, 2039, 2042, 1825, 2041])).
% 0.78/0.95 tff(2050,plain,((~hskp4) | hskp0 | hskp2 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(2051,plain,
% 0.78/0.95 (~hskp4),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[2050, 65, 2019, 12, 11])).
% 0.78/0.95 tff(2052,assumption,(~c0_1(a1089)), introduced(assumption)).
% 0.78/0.95 tff(2053,assumption,(hskp16), introduced(assumption)).
% 0.78/0.95 tff(2054,plain,
% 0.78/0.95 (~c3_1(a1100)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1563, 2053])).
% 0.78/0.95 tff(2055,plain,
% 0.78/0.95 (~c0_1(a1100)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1569, 2053])).
% 0.78/0.95 tff(2056,plain,
% 0.78/0.95 (c1_1(a1100)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1577, 2053])).
% 0.78/0.95 tff(2057,assumption,(~hskp4), introduced(assumption)).
% 0.78/0.95 tff(2058,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2059,plain,
% 0.78/0.95 ((hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089))) <=> (hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(2060,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[2059])).
% 0.78/0.95 tff(2061,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[2060, 2058])).
% 0.78/0.95 tff(2062,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(2063,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 0.78/0.96 tff(2064,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2063, 171, 2057, 2056, 1918, 2055, 2054, 1924, 1165, 2052])).
% 0.78/0.96 tff(2065,plain,((~hskp16) | hskp4 | (~c2_1(a1089)) | c1_1(a1089) | c0_1(a1089)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(2066,plain,
% 0.78/0.96 (~hskp16),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2065, 2051, 1878, 1876, 2037])).
% 0.78/0.96 tff(2067,plain,
% 0.78/0.96 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2068,plain,
% 0.78/0.96 ((hskp16 | hskp4 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120))) <=> (hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2069,plain,
% 0.78/0.96 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[2068])).
% 0.78/0.96 tff(2070,plain,
% 0.78/0.96 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[2069, 2067])).
% 0.78/0.96 tff(2071,plain,
% 0.78/0.96 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(2072,plain,
% 0.78/0.96 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 0.78/0.96 tff(2073,plain,
% 0.78/0.96 (hskp16 | hskp4 | c0_1(a1120)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2072, 171, 1888, 1887, 2029])).
% 0.78/0.96 tff(2074,plain,
% 0.78/0.96 (c0_1(a1120)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2073, 2066, 2051])).
% 0.78/0.96 tff(2075,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2076,plain,
% 0.78/0.96 ((hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1089) | c0_1(a1089) | (~c3_1(a1089))) <=> (hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2077,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1089) | c0_1(a1089) | (~c3_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[2076])).
% 0.78/0.96 tff(2078,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1089) | c0_1(a1089) | (~c3_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[2077, 2075])).
% 0.78/0.96 tff(2079,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1089) | c0_1(a1089) | (~c3_1(a1089)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(2080,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2079, 2078])).
% 0.78/0.96 tff(2081,plain,
% 0.78/0.96 (hskp10 | c0_1(a1089) | (~c0_1(a1120))),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2080, 171, 1886, 1888, 1877, 1876, 982])).
% 0.78/0.96 tff(2082,plain,
% 0.78/0.96 (hskp10),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2081, 2074, 2037])).
% 0.78/0.96 tff(2083,plain,
% 0.78/0.96 (~c3_1(a1090)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1002, 2082])).
% 0.78/0.96 tff(2084,plain,
% 0.78/0.96 (~c0_1(a1090)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1014, 2082])).
% 0.78/0.96 tff(2085,plain,
% 0.78/0.96 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2086,plain,
% 0.78/0.96 ((hskp16 | hskp4 | (~ndr1_0) | c0_1(a1090) | c3_1(a1090) | (~c2_1(a1090))) <=> (hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2087,plain,
% 0.78/0.96 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1090) | c3_1(a1090) | (~c2_1(a1090)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[2086])).
% 0.78/0.96 tff(2088,plain,
% 0.78/0.96 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1090) | c3_1(a1090) | (~c2_1(a1090)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[2087, 2085])).
% 0.78/0.96 tff(2089,plain,
% 0.78/0.96 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1090) | c3_1(a1090) | (~c2_1(a1090)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(2090,plain,
% 0.78/0.96 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 0.78/0.96 tff(2091,plain,
% 0.78/0.96 (~c2_1(a1090)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2090, 171, 2066, 2051, 2084, 2083, 2029])).
% 0.78/0.96 tff(2092,plain,
% 0.78/0.96 (~c1_1(a1090)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1008, 2082])).
% 0.78/0.96 tff(2093,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2094,plain,
% 0.78/0.96 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090) | c0_1(a1090) | c3_1(a1090) | c2_1(a1090) | c1_1(a1090) | c0_1(a1090)) <=> (c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2095,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090) | c0_1(a1090) | c3_1(a1090) | c2_1(a1090) | c1_1(a1090) | c0_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090)))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[2094])).
% 0.78/0.96 tff(2096,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090) | c0_1(a1090) | c3_1(a1090) | c2_1(a1090) | c1_1(a1090) | c0_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090))),
% 0.78/0.96 inference(transitivity,[status(thm)],[2095, 2093])).
% 0.78/0.96 tff(2097,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090) | c0_1(a1090) | c3_1(a1090) | c2_1(a1090) | c1_1(a1090) | c0_1(a1090))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(2098,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2097, 2096])).
% 0.78/0.96 tff(2099,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2098, 171, 1878, 1877, 2084, 2092, 2083, 1876, 422, 2091])).
% 0.78/0.96 tff(2100,plain,(hskp2 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(2101,plain,
% 0.78/0.96 (hskp2),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2100, 12, 11])).
% 0.78/0.96 tff(2102,plain,
% 0.78/0.96 (~c0_1(a1082)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[573, 2101])).
% 0.78/0.96 tff(2103,plain,
% 0.78/0.96 (~c2_1(a1082)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[579, 2101])).
% 0.78/0.96 tff(2104,plain,
% 0.78/0.96 (^[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)) | c1_1(W) | 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)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(2105,plain,
% 0.78/0.96 (![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)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[2104])).
% 0.78/0.96 tff(2106,plain,
% 0.78/0.96 (![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)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2107,plain,
% 0.78/0.96 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_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)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_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)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | 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)) | (~c2_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)) | (~c2_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) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | 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) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_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) | (~c2_1(W))) | c1_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) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(2108,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[2107])).
% 0.78/0.96 tff(2109,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.78/0.96 tff(2110,plain,
% 0.78/0.96 (![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 0.78/0.96 tff(2111,plain,
% 0.78/0.96 (![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2110, 2106])).
% 0.78/0.96 tff(2112,plain,(
% 0.78/0.96 ![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[2111])).
% 0.78/0.96 tff(2113,plain,
% 0.78/0.96 (![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2112, 2105])).
% 0.78/0.96 tff(2114,assumption,(~c1_1(a1082)), introduced(assumption)).
% 0.78/0.96 tff(2115,plain,
% 0.78/0.96 (c0_1(a1082) | c3_1(a1082) | c1_1(a1082)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[788, 171, 1918, 1917, 1924, 581, 422])).
% 0.78/0.96 tff(2116,plain,
% 0.78/0.96 (c3_1(a1082)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2115, 2114, 583])).
% 0.78/0.96 tff(2117,plain,
% 0.78/0.96 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(2118,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[2117])).
% 0.78/0.96 tff(2119,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2120,plain,
% 0.78/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_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) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(2121,plain,
% 0.78/0.96 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[2120])).
% 0.78/0.96 tff(2122,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.78/0.96 tff(2123,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 0.78/0.96 tff(2124,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2123, 2119])).
% 0.78/0.96 tff(2125,plain,(
% 0.78/0.96 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.96 inference(skolemize,[status(sab)],[2124])).
% 0.78/0.96 tff(2126,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2125, 2118])).
% 0.78/0.96 tff(2127,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2128,plain,
% 0.78/0.96 ((hskp0 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c3_1(a1082)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2129,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c3_1(a1082)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082)))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[2128])).
% 0.78/0.96 tff(2130,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c3_1(a1082)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082))),
% 0.78/0.96 inference(transitivity,[status(thm)],[2129, 2127])).
% 0.78/0.96 tff(2131,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c3_1(a1082)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(2132,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 0.78/0.96 tff(2133,plain,
% 0.78/0.96 (hskp0 | c0_1(a1082) | (~c3_1(a1082)) | c1_1(a1082)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2132, 171, 581, 2126])).
% 0.78/0.96 tff(2134,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2133, 2116, 2114, 583, 1550])).
% 0.78/0.96 tff(2135,plain,(c1_1(a1082) | c0_1(a1082) | hskp0 | c2_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(2136,plain,
% 0.78/0.96 (c1_1(a1082)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2135, 1550, 583, 581, 1878, 1877, 1876])).
% 0.78/0.96 tff(2137,plain,
% 0.78/0.96 (hskp0 | hskp16 | c0_1(a1082) | (~c1_1(a1082))),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1556, 171, 581, 1549])).
% 0.78/0.96 tff(2138,plain,
% 0.78/0.96 (hskp16),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2137, 2136, 583, 1550])).
% 0.78/0.96 tff(2139,plain,
% 0.78/0.96 (~c0_1(a1100)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1569, 2138])).
% 0.78/0.96 tff(2140,plain,
% 0.78/0.96 (c1_1(a1100)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1577, 2138])).
% 0.78/0.96 tff(2141,plain,
% 0.78/0.96 (~c3_1(a1100)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1563, 2138])).
% 0.78/0.96 tff(2142,plain,
% 0.78/0.96 (hskp4),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1584, 171, 2140, 1915, 2139, 2141, 12, 11, 1165])).
% 0.78/0.96 tff(2143,plain,
% 0.78/0.96 (~c3_1(a1084)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1192, 2142])).
% 0.78/0.96 tff(2144,plain,
% 0.78/0.96 (c0_1(a1084)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1180, 2142])).
% 0.78/0.96 tff(2145,plain,
% 0.78/0.96 (c2_1(a1084)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1374, 2144, 1951, 1950, 1915, 2143, 1949, 12, 11])).
% 0.78/0.96 tff(2146,plain,
% 0.78/0.96 (hskp31),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1978, 171, 1886, 1888, 2144, 1887, 2143, 1972, 2145])).
% 0.78/0.96 tff(2147,plain,
% 0.78/0.96 (c2_1(a1148)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1986, 2146])).
% 0.78/0.96 tff(2148,plain,
% 0.78/0.96 (c1_1(a1148)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1994, 2146])).
% 0.78/0.96 tff(2149,plain,
% 0.78/0.96 (c0_1(a1148)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2002, 2146])).
% 0.78/0.96 tff(2150,plain,
% 0.78/0.96 (((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2151,plain,
% 0.78/0.96 (((~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c0_1(a1100) | (~c2_1(a1100)) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2152,plain,
% 0.78/0.96 (((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c0_1(a1100) | (~c2_1(a1100)) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[2151])).
% 0.78/0.96 tff(2153,plain,
% 0.78/0.96 (((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c0_1(a1100) | (~c2_1(a1100)) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[2152, 2150])).
% 0.78/0.96 tff(2154,plain,
% 0.78/0.96 ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c0_1(a1100) | (~c2_1(a1100)) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(2155,plain,
% 0.78/0.96 ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 0.78/0.96 tff(2156,plain,
% 0.78/0.96 (~c2_1(a1100)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2155, 171, 2149, 2148, 2147, 2140, 1915, 2139, 12, 11, 2113])).
% 0.78/0.96 tff(2157,plain,
% 0.78/0.96 (hskp3 | c0_1(a1082) | (~c1_1(a1082))),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[844, 171, 1915, 12, 11, 581, 22])).
% 0.78/0.96 tff(2158,plain,
% 0.78/0.96 (hskp3),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2157, 2136, 583])).
% 0.78/0.96 tff(2159,plain,
% 0.78/0.96 (~c3_1(a1083)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[856, 2158])).
% 0.78/0.96 tff(2160,plain,
% 0.78/0.96 (~c2_1(a1083)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[850, 2158])).
% 0.78/0.96 tff(2161,plain,
% 0.78/0.96 (c1_1(a1083)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1030, 2158])).
% 0.78/0.96 tff(2162,plain,
% 0.78/0.96 (c3_1(a1085)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1392, 171, 1950, 2161, 1949, 12, 11, 2160, 2159, 434, 1952])).
% 0.78/0.96 tff(2163,plain,
% 0.78/0.96 (hskp10),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2009, 171, 2149, 2148, 2147, 12, 11, 982, 2162])).
% 0.78/0.96 tff(2164,plain,
% 0.78/0.96 (~c3_1(a1090)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1002, 2163])).
% 0.78/0.96 tff(2165,plain,
% 0.78/0.96 (~c1_1(a1090)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1008, 2163])).
% 0.78/0.96 tff(2166,plain,
% 0.78/0.96 (~c0_1(a1090)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1014, 2163])).
% 0.78/0.96 tff(2167,plain,
% 0.78/0.96 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2168,plain,
% 0.78/0.96 (((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090)) <=> (c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2169,plain,
% 0.78/0.96 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2168])).
% 0.78/0.97 tff(2170,plain,
% 0.78/0.97 (((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2169, 2167])).
% 0.78/0.97 tff(2171,plain,
% 0.78/0.97 ((~![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)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2172,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2171, 2170])).
% 0.78/0.97 tff(2173,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2172, 171, 1950, 2140, 1949, 2141, 2166, 2165, 2164, 434, 1952, 2156])).
% 0.78/0.97 tff(2174,plain,(hskp0 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(2175,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2174, 2103, 2102, 11, 12, 2019])).
% 0.78/0.97 tff(2176,plain,(c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(2177,plain,
% 0.78/0.97 (c0_1(a1085)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2176, 11])).
% 0.78/0.97 tff(2178,plain,
% 0.78/0.97 (~hskp5),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[816, 2177])).
% 0.78/0.97 tff(2179,plain,
% 0.78/0.97 (hskp0),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[110, 2178])).
% 0.78/0.97 tff(2180,plain,
% 0.78/0.97 (~c2_1(a1080)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[28, 2179])).
% 0.78/0.97 tff(2181,plain,
% 0.78/0.97 (~c0_1(a1080)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[34, 2179])).
% 0.78/0.97 tff(2182,plain,
% 0.78/0.97 (c1_1(a1080)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[42, 2179])).
% 0.78/0.97 tff(2183,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2184,plain,
% 0.78/0.97 ((hskp5 | (~ndr1_0) | c1_1(a1085) | (~c3_1(a1085)) | (~c0_1(a1085)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2185,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1085) | (~c3_1(a1085)) | (~c0_1(a1085)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2184])).
% 0.78/0.97 tff(2186,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1085) | (~c3_1(a1085)) | (~c0_1(a1085)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2185, 2183])).
% 0.78/0.97 tff(2187,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1085) | (~c3_1(a1085)) | (~c0_1(a1085)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2188,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 0.78/0.97 tff(2189,plain,
% 0.78/0.97 (~c3_1(a1085)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2188, 2178, 171, 2182, 2177, 11, 2181, 2180, 10])).
% 0.78/0.97 tff(2190,assumption,(c0_1(a1085)), introduced(assumption)).
% 0.78/0.97 tff(2191,plain,
% 0.78/0.97 (^[U: $i] : refl((hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(2192,plain,
% 0.78/0.97 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[2191])).
% 0.78/0.97 tff(2193,plain,
% 0.78/0.97 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2194,plain,
% 0.78/0.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp5) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp5) <=> (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(2195,plain,
% 0.78/0.97 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp5) <=> ![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[2194])).
% 0.78/0.97 tff(2196,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.78/0.97 tff(2197,plain,
% 0.78/0.97 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 0.78/0.97 tff(2198,plain,
% 0.78/0.97 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2197, 2193])).
% 0.78/0.97 tff(2199,plain,(
% 0.78/0.97 ![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[2198])).
% 0.78/0.97 tff(2200,plain,
% 0.78/0.97 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2199, 2192])).
% 0.78/0.97 tff(2201,plain,
% 0.78/0.97 (~hskp5),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[816, 2190])).
% 0.78/0.97 tff(2202,plain,
% 0.78/0.97 (((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085))) <=> ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2203,plain,
% 0.78/0.97 ((hskp5 | hskp22 | (~ndr1_0) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085))) <=> (hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2204,plain,
% 0.78/0.97 (((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | (~ndr1_0) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)))) <=> ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085)))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2203])).
% 0.78/0.97 tff(2205,plain,
% 0.78/0.97 (((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | (~ndr1_0) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)))) <=> ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2204, 2202])).
% 0.78/0.97 tff(2206,plain,
% 0.78/0.97 ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | (~ndr1_0) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2207,plain,
% 0.78/0.97 ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 0.78/0.97 tff(2208,plain,
% 0.78/0.97 (hskp22 | c2_1(a1085) | c3_1(a1085)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2207, 2201, 171, 2190, 2200])).
% 0.78/0.97 tff(2209,plain,
% 0.78/0.97 (hskp22),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2208, 88, 412])).
% 0.78/0.97 tff(2210,plain,
% 0.78/0.97 (((~hskp22) | (~c0_1(a1121))) <=> ((~hskp22) | (~c0_1(a1121)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2211,plain,
% 0.78/0.97 (((~c0_1(a1121)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a1121)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2212,axiom,((~c0_1(a1121)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.78/0.97 tff(2213,plain,
% 0.78/0.97 ((~hskp22) | (~c0_1(a1121))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 0.78/0.97 tff(2214,plain,
% 0.78/0.97 ((~hskp22) | (~c0_1(a1121))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2213, 2210])).
% 0.78/0.97 tff(2215,plain,
% 0.78/0.97 (~c0_1(a1121)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2214, 2209])).
% 0.78/0.97 tff(2216,plain,
% 0.78/0.97 (((~hskp22) | c3_1(a1121)) <=> ((~hskp22) | c3_1(a1121))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2217,axiom,((~hskp22) | c3_1(a1121)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.78/0.97 tff(2218,plain,
% 0.78/0.97 ((~hskp22) | c3_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 0.78/0.97 tff(2219,plain,
% 0.78/0.97 ((~hskp22) | c3_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2218, 2216])).
% 0.78/0.97 tff(2220,plain,
% 0.78/0.97 ((~hskp22) | c3_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2219, 2216])).
% 0.78/0.97 tff(2221,plain,
% 0.78/0.97 ((~hskp22) | c3_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2220, 2216])).
% 0.78/0.97 tff(2222,plain,
% 0.78/0.97 ((~hskp22) | c3_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2221, 2216])).
% 0.78/0.97 tff(2223,plain,
% 0.78/0.97 (c3_1(a1121)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2222, 2209])).
% 0.78/0.97 tff(2224,plain,
% 0.78/0.97 (((~hskp22) | c1_1(a1121)) <=> ((~hskp22) | c1_1(a1121))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2225,axiom,((~hskp22) | c1_1(a1121)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.78/0.97 tff(2226,plain,
% 0.78/0.97 ((~hskp22) | c1_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 0.78/0.97 tff(2227,plain,
% 0.78/0.97 ((~hskp22) | c1_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2226, 2224])).
% 0.78/0.97 tff(2228,plain,
% 0.78/0.97 ((~hskp22) | c1_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2227, 2224])).
% 0.78/0.97 tff(2229,plain,
% 0.78/0.97 ((~hskp22) | c1_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2228, 2224])).
% 0.78/0.97 tff(2230,plain,
% 0.78/0.97 ((~hskp22) | c1_1(a1121)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2229, 2224])).
% 0.78/0.97 tff(2231,plain,
% 0.78/0.97 (c1_1(a1121)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2230, 2209])).
% 0.78/0.97 tff(2232,assumption,(~c0_1(a1121)), introduced(assumption)).
% 0.78/0.97 tff(2233,assumption,(c3_1(a1121)), introduced(assumption)).
% 0.78/0.97 tff(2234,assumption,(c1_1(a1121)), introduced(assumption)).
% 0.78/0.97 tff(2235,plain,
% 0.78/0.97 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2236,plain,
% 0.78/0.97 ((hskp30 | hskp18 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121))) <=> (hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2237,plain,
% 0.78/0.97 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2236])).
% 0.78/0.97 tff(2238,plain,
% 0.78/0.97 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2237, 2235])).
% 0.78/0.97 tff(2239,plain,
% 0.78/0.97 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2240,plain,
% 0.78/0.97 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 0.78/0.97 tff(2241,plain,
% 0.78/0.97 (hskp30),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2240, 171, 1889, 2234, 2233, 2232, 457])).
% 0.78/0.97 tff(2242,plain,
% 0.78/0.97 (c3_1(a1109)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[330, 2241])).
% 0.78/0.97 tff(2243,plain,
% 0.78/0.97 (c0_1(a1109)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[322, 2241])).
% 0.78/0.97 tff(2244,plain,
% 0.78/0.97 (c1_1(a1109)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[288, 2241])).
% 0.78/0.97 tff(2245,plain,
% 0.78/0.97 (hskp28),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[778, 54, 2244, 2243, 2242, 115])).
% 0.78/0.97 tff(2246,plain,
% 0.78/0.97 (c3_1(a1092)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[349, 2245])).
% 0.78/0.97 tff(2247,plain,
% 0.78/0.97 (c2_1(a1092)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[357, 2245])).
% 0.78/0.97 tff(2248,plain,
% 0.78/0.97 (~hskp11),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1047, 1889])).
% 0.78/0.97 tff(2249,plain,
% 0.78/0.97 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2250,plain,
% 0.78/0.97 ((hskp11 | hskp9 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c3_1(a1092))) <=> (hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2251,plain,
% 0.78/0.97 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c3_1(a1092)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2250])).
% 0.78/0.97 tff(2252,plain,
% 0.78/0.97 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c3_1(a1092)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2251, 2249])).
% 0.78/0.97 tff(2253,plain,
% 0.78/0.97 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c3_1(a1092)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2254,plain,
% 0.78/0.97 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 0.78/0.97 tff(2255,plain,
% 0.78/0.97 (c1_1(a1092)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2254, 171, 2248, 54, 2247, 2246, 1060])).
% 0.78/0.97 tff(2256,plain,
% 0.78/0.97 (c0_1(a1092)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[365, 2245])).
% 0.78/0.97 tff(2257,plain,
% 0.78/0.97 (((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))) <=> ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2258,plain,
% 0.78/0.97 ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2259,plain,
% 0.78/0.97 ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 0.78/0.97 tff(2260,plain,
% 0.78/0.97 (hskp13 | (~c1_1(a1092))),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2259, 115, 171, 2256, 2247, 735])).
% 0.78/0.97 tff(2261,plain,
% 0.78/0.97 (hskp13),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2260, 2255])).
% 0.78/0.97 tff(2262,plain,
% 0.78/0.97 (~c1_1(a1095)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[754, 2261])).
% 0.78/0.97 tff(2263,plain,
% 0.78/0.97 (c3_1(a1095)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[769, 2261])).
% 0.78/0.97 tff(2264,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2265,plain,
% 0.78/0.97 ((hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1095) | c0_1(a1095) | (~c3_1(a1095))) <=> (hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2266,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1095) | c0_1(a1095) | (~c3_1(a1095)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2265])).
% 0.78/0.97 tff(2267,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1095) | c0_1(a1095) | (~c3_1(a1095)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2266, 2264])).
% 0.78/0.97 tff(2268,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1095) | c0_1(a1095) | (~c3_1(a1095)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2269,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 0.78/0.97 tff(2270,plain,
% 0.78/0.97 (c0_1(a1095)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2269, 171, 2248, 2256, 2247, 2246, 2263, 2262, 701])).
% 0.78/0.97 tff(2271,plain,
% 0.78/0.97 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2272,plain,
% 0.78/0.97 ((hskp9 | hskp2 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121))) <=> (hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2273,plain,
% 0.78/0.97 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2272])).
% 0.78/0.97 tff(2274,plain,
% 0.78/0.97 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2273, 2271])).
% 0.78/0.97 tff(2275,plain,
% 0.78/0.97 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2276,plain,
% 0.78/0.97 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 0.78/0.97 tff(2277,plain,
% 0.78/0.97 (hskp9 | hskp2),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2276, 171, 2234, 2233, 2232, 396])).
% 0.78/0.97 tff(2278,plain,
% 0.78/0.97 (hskp2),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2277, 54])).
% 0.78/0.97 tff(2279,plain,
% 0.78/0.97 (~c2_1(a1082)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[579, 2278])).
% 0.78/0.97 tff(2280,plain,
% 0.78/0.97 (~c0_1(a1082)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[573, 2278])).
% 0.78/0.97 tff(2281,plain,
% 0.78/0.97 (c1_1(a1082)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[690, 171, 2243, 2244, 2242, 2256, 2247, 2246, 2280, 2279, 341])).
% 0.78/0.97 tff(2282,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2283,plain,
% 0.78/0.97 ((hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082))) <=> (hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2284,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2283])).
% 0.78/0.97 tff(2285,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2284, 2282])).
% 0.78/0.97 tff(2286,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2287,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 0.78/0.97 tff(2288,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2287, 115, 171, 2263, 2262, 2280, 2279, 10, 2281, 2270])).
% 0.78/0.97 tff(2289,plain,(hskp9 | hskp5 | (~c1_1(a1121)) | (~c3_1(a1121)) | c0_1(a1121)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(2290,plain,
% 0.78/0.97 (hskp9),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2289, 2231, 2201, 2223, 2215])).
% 0.78/0.97 tff(2291,plain,
% 0.78/0.97 (~c1_1(a1089)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[492, 2290])).
% 0.78/0.97 tff(2292,plain,
% 0.78/0.97 (~hskp18),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[179, 2201])).
% 0.78/0.97 tff(2293,plain,
% 0.78/0.97 (hskp30),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2240, 171, 2292, 2231, 2223, 2215, 457])).
% 0.78/0.97 tff(2294,plain,
% 0.78/0.97 (c3_1(a1109)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[330, 2293])).
% 0.78/0.97 tff(2295,plain,
% 0.78/0.97 (c1_1(a1109)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[288, 2293])).
% 0.78/0.97 tff(2296,plain,
% 0.78/0.97 (c0_1(a1109)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[322, 2293])).
% 0.78/0.97 tff(2297,assumption,(hskp9), introduced(assumption)).
% 0.78/0.97 tff(2298,plain,
% 0.78/0.97 (~c1_1(a1089)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[492, 2297])).
% 0.78/0.97 tff(2299,plain,
% 0.78/0.97 (c2_1(a1089)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[508, 2297])).
% 0.78/0.97 tff(2300,plain,
% 0.78/0.97 (c3_1(a1089)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[500, 2297])).
% 0.78/0.97 tff(2301,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1947, 2300, 2299, 1916, 2298])).
% 0.78/0.97 tff(2302,plain,((~hskp9) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(2303,plain,
% 0.78/0.97 (~hskp9),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2302, 1916])).
% 0.78/0.97 tff(2304,plain,
% 0.78/0.97 (hskp28),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[778, 2303, 368, 369, 367, 115])).
% 0.78/0.97 tff(2305,plain,
% 0.78/0.97 (c3_1(a1092)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[349, 2304])).
% 0.78/0.97 tff(2306,plain,
% 0.78/0.98 (c2_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[357, 2304])).
% 0.78/0.98 tff(2307,plain,
% 0.78/0.98 (c1_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2254, 171, 2248, 2303, 2306, 2305, 1060])).
% 0.78/0.98 tff(2308,plain,
% 0.78/0.98 (c0_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[365, 2304])).
% 0.78/0.98 tff(2309,plain,
% 0.78/0.98 (hskp13 | (~c1_1(a1092))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2259, 115, 171, 2308, 2306, 735])).
% 0.78/0.98 tff(2310,plain,
% 0.78/0.98 (hskp13),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2309, 2307])).
% 0.78/0.98 tff(2311,plain,
% 0.78/0.98 (~c1_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[754, 2310])).
% 0.78/0.98 tff(2312,plain,
% 0.78/0.98 (c3_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[769, 2310])).
% 0.78/0.98 tff(2313,plain,
% 0.78/0.98 (c0_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2269, 171, 2248, 2308, 2306, 2305, 2312, 2311, 701])).
% 0.78/0.98 tff(2314,plain,
% 0.78/0.98 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2315,plain,
% 0.78/0.98 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2316,plain,
% 0.78/0.98 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2315, 2314])).
% 0.78/0.98 tff(2317,plain,
% 0.78/0.98 (hskp19 | hskp2),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2316, 171, 369, 368, 367, 1435])).
% 0.78/0.98 tff(2318,plain,
% 0.78/0.98 (hskp2),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2317, 1916])).
% 0.78/0.98 tff(2319,plain,
% 0.78/0.98 (~c2_1(a1082)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[579, 2318])).
% 0.78/0.98 tff(2320,plain,
% 0.78/0.98 (~c0_1(a1082)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[573, 2318])).
% 0.78/0.98 tff(2321,plain,
% 0.78/0.98 (c1_1(a1082)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[690, 171, 369, 368, 367, 2308, 2306, 2305, 2320, 2319, 341])).
% 0.78/0.98 tff(2322,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2287, 115, 171, 2312, 2311, 2320, 2319, 10, 2321, 2313])).
% 0.78/0.98 tff(2323,plain,(hskp19 | hskp5 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2324,plain,
% 0.78/0.98 (hskp19),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2323, 2296, 2201, 2295, 2294])).
% 0.78/0.98 tff(2325,plain,
% 0.78/0.98 (~c2_1(a1113)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[917, 2324])).
% 0.78/0.98 tff(2326,plain,
% 0.78/0.98 (c2_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[508, 2290])).
% 0.78/0.98 tff(2327,plain,
% 0.78/0.98 (c1_1(a1113)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[925, 2324])).
% 0.78/0.98 tff(2328,plain,
% 0.78/0.98 (c0_1(a1113)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[933, 2324])).
% 0.78/0.98 tff(2329,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2330,plain,
% 0.78/0.98 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089))) <=> (c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2331,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2330])).
% 0.78/0.98 tff(2332,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2331, 2329])).
% 0.78/0.98 tff(2333,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2334,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 0.78/0.98 tff(2335,plain,
% 0.78/0.98 (c0_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2334, 171, 2328, 2327, 2326, 88, 2325, 2291, 2190, 64, 412])).
% 0.78/0.98 tff(2336,plain,
% 0.78/0.98 (hskp0),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[110, 2201])).
% 0.78/0.98 tff(2337,plain,
% 0.78/0.98 (~c2_1(a1080)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[28, 2336])).
% 0.78/0.98 tff(2338,plain,
% 0.78/0.98 (~c0_1(a1080)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[34, 2336])).
% 0.78/0.98 tff(2339,plain,
% 0.78/0.98 (c1_1(a1080)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[42, 2336])).
% 0.78/0.98 tff(2340,plain,
% 0.78/0.98 (c3_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[500, 2290])).
% 0.78/0.98 tff(2341,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2342,plain,
% 0.78/0.98 ((hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2343,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2342])).
% 0.78/0.98 tff(2344,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2343, 2341])).
% 0.78/0.98 tff(2345,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2346,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 0.78/0.98 tff(2347,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2346, 2201, 171, 2340, 2339, 2291, 2338, 2337, 10, 2335])).
% 0.78/0.98 tff(2348,plain,(c2_1(a1085) | (~c0_1(a1085)) | c3_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2349,plain,
% 0.78/0.98 (c2_1(a1085)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2348, 2177, 2189])).
% 0.78/0.98 tff(2350,plain,
% 0.78/0.98 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(2351,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[2350])).
% 0.78/0.98 tff(2352,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2353,plain,
% 0.78/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(2354,plain,
% 0.78/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[2353])).
% 0.78/0.98 tff(2355,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.78/0.98 tff(2356,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2355, 2354])).
% 0.78/0.98 tff(2357,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2356, 2352])).
% 0.78/0.98 tff(2358,plain,(
% 0.78/0.98 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.78/0.98 inference(skolemize,[status(sab)],[2357])).
% 0.78/0.98 tff(2359,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2358, 2351])).
% 0.78/0.98 tff(2360,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2361,plain,
% 0.78/0.98 ((hskp17 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c0_1(a1085)) | c1_1(a1085) | (~c2_1(a1085)) | c3_1(a1085)) <=> (hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2362,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c0_1(a1085)) | c1_1(a1085) | (~c2_1(a1085)) | c3_1(a1085))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2361])).
% 0.78/0.98 tff(2363,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c0_1(a1085)) | c1_1(a1085) | (~c2_1(a1085)) | c3_1(a1085))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2362, 2360])).
% 0.78/0.98 tff(2364,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c0_1(a1085)) | c1_1(a1085) | (~c2_1(a1085)) | c3_1(a1085))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2365,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 0.78/0.98 tff(2366,plain,
% 0.78/0.98 (hskp17 | (~c0_1(a1085)) | (~c2_1(a1085)) | c3_1(a1085)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2365, 171, 11, 2359])).
% 0.78/0.98 tff(2367,plain,
% 0.78/0.98 (hskp17),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2366, 2349, 2177, 2189])).
% 0.78/0.98 tff(2368,plain,
% 0.78/0.98 (~c2_1(a1102)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1514, 2367])).
% 0.78/0.98 tff(2369,plain,
% 0.78/0.98 (~c0_1(a1102)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1493, 2367])).
% 0.78/0.98 tff(2370,plain,
% 0.78/0.98 (hskp14),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[258, 1889, 126, 118, 117])).
% 0.78/0.98 tff(2371,plain,
% 0.78/0.98 (~c2_1(a1097)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[264, 2370])).
% 0.78/0.98 tff(2372,plain,
% 0.78/0.98 (c3_1(a1097)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[306, 2370])).
% 0.78/0.98 tff(2373,plain,
% 0.78/0.98 (c1_1(a1097)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[272, 2370])).
% 0.78/0.98 tff(2374,plain,
% 0.78/0.98 (hskp30 | hskp9 | (~c0_1(a1097))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[279, 171, 712, 710, 99])).
% 0.78/0.98 tff(2375,plain,
% 0.78/0.98 (~c0_1(a1097)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2374, 600, 54])).
% 0.78/0.98 tff(2376,plain,
% 0.78/0.98 (hskp30 | c0_1(a1097)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[542, 171, 249, 712, 711, 457])).
% 0.78/0.98 tff(2377,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2376, 2375, 600])).
% 0.78/0.98 tff(2378,plain,(hskp30 | hskp18 | (~c1_1(a1097)) | (~c3_1(a1097)) | hskp9 | c2_1(a1097)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2379,plain,
% 0.78/0.98 (hskp30),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2378, 54, 2373, 2372, 1889, 2371])).
% 0.78/0.98 tff(2380,plain,
% 0.78/0.98 (c3_1(a1109)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[330, 2379])).
% 0.78/0.98 tff(2381,plain,
% 0.78/0.98 (c0_1(a1109)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[322, 2379])).
% 0.78/0.98 tff(2382,plain,
% 0.78/0.98 (c1_1(a1109)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[288, 2379])).
% 0.78/0.98 tff(2383,plain,
% 0.78/0.98 (hskp28),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[778, 2382, 54, 2381, 2380, 115])).
% 0.78/0.98 tff(2384,plain,
% 0.78/0.98 (c3_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[349, 2383])).
% 0.78/0.98 tff(2385,plain,
% 0.78/0.98 (c2_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[357, 2383])).
% 0.78/0.98 tff(2386,plain,
% 0.78/0.98 (c1_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2254, 171, 2248, 54, 2385, 2384, 1060])).
% 0.78/0.98 tff(2387,plain,
% 0.78/0.98 (c0_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[365, 2383])).
% 0.78/0.98 tff(2388,plain,
% 0.78/0.98 (hskp13 | (~c1_1(a1092))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2259, 115, 171, 2387, 2385, 735])).
% 0.78/0.98 tff(2389,plain,
% 0.78/0.98 (hskp13),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2388, 2386])).
% 0.78/0.98 tff(2390,plain,
% 0.78/0.98 (~c1_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[754, 2389])).
% 0.78/0.98 tff(2391,plain,
% 0.78/0.98 (c3_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[769, 2389])).
% 0.78/0.98 tff(2392,plain,
% 0.78/0.98 (c0_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2269, 171, 2248, 2387, 2385, 2384, 2391, 2390, 701])).
% 0.78/0.98 tff(2393,assumption,(~c2_1(a1102)), introduced(assumption)).
% 0.78/0.98 tff(2394,assumption,(~c0_1(a1102)), introduced(assumption)).
% 0.78/0.98 tff(2395,plain,
% 0.78/0.98 (c1_1(a1102)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1521, 171, 2381, 2382, 2380, 2387, 2385, 2384, 2394, 2393, 341])).
% 0.78/0.98 tff(2396,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2397,plain,
% 0.78/0.98 ((hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102))) <=> (hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2398,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2397])).
% 0.78/0.98 tff(2399,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2398, 2396])).
% 0.78/0.98 tff(2400,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2401,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 0.78/0.98 tff(2402,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2401, 115, 171, 2391, 2394, 2393, 2390, 10, 2395, 2392])).
% 0.78/0.98 tff(2403,plain,(hskp9 | hskp5 | c0_1(a1102) | c2_1(a1102)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2404,plain,
% 0.78/0.98 (hskp9),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2403, 2178, 2369, 2368])).
% 0.78/0.98 tff(2405,plain,
% 0.78/0.98 (~c1_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[492, 2404])).
% 0.78/0.98 tff(2406,plain,
% 0.78/0.98 (c3_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[500, 2404])).
% 0.78/0.98 tff(2407,plain,
% 0.78/0.98 (~c0_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2346, 2178, 171, 2406, 2182, 2405, 2181, 2180, 10])).
% 0.78/0.98 tff(2408,plain,
% 0.78/0.98 (c2_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[508, 2404])).
% 0.78/0.98 tff(2409,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[802, 2178, 171, 2408, 2406, 2405, 623, 2407])).
% 0.78/0.98 tff(2410,plain,(c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2411,plain,
% 0.78/0.98 (~hskp5),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[810, 2410])).
% 0.78/0.98 tff(2412,plain,
% 0.78/0.98 (hskp0),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[110, 2411])).
% 0.78/0.98 tff(2413,plain,
% 0.78/0.98 (~c2_1(a1080)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[28, 2412])).
% 0.78/0.98 tff(2414,plain,
% 0.78/0.98 (~c0_1(a1080)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[34, 2412])).
% 0.78/0.98 tff(2415,plain,
% 0.78/0.98 (c1_1(a1080)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[42, 2412])).
% 0.78/0.98 tff(2416,plain,
% 0.78/0.98 (~hskp18),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[179, 2411])).
% 0.78/0.98 tff(2417,plain,
% 0.78/0.98 (hskp14),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[258, 2416, 2415, 2414, 2413])).
% 0.78/0.98 tff(2418,plain,
% 0.78/0.98 (~c2_1(a1097)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[264, 2417])).
% 0.78/0.98 tff(2419,plain,
% 0.78/0.98 (c3_1(a1097)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[306, 2417])).
% 0.78/0.98 tff(2420,plain,
% 0.78/0.98 (c1_1(a1097)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[272, 2417])).
% 0.78/0.98 tff(2421,plain,
% 0.78/0.98 (hskp30 | hskp9),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2378, 2420, 2419, 2416, 2418])).
% 0.78/0.98 tff(2422,plain,
% 0.78/0.98 (hskp30),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2421, 54])).
% 0.78/0.98 tff(2423,plain,
% 0.78/0.98 (c3_1(a1109)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[330, 2422])).
% 0.78/0.98 tff(2424,plain,
% 0.78/0.98 (c0_1(a1109)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[322, 2422])).
% 0.78/0.98 tff(2425,plain,
% 0.78/0.98 (c1_1(a1109)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[288, 2422])).
% 0.78/0.98 tff(2426,plain,
% 0.78/0.98 (hskp28 | hskp9 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[778, 2411])).
% 0.78/0.98 tff(2427,plain,
% 0.78/0.98 (hskp28),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2426, 2425, 54, 2424, 2423])).
% 0.78/0.98 tff(2428,plain,
% 0.78/0.98 (c3_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[349, 2427])).
% 0.78/0.98 tff(2429,plain,
% 0.78/0.98 (c2_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[357, 2427])).
% 0.78/0.98 tff(2430,plain,
% 0.78/0.98 (~hskp11),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1047, 2416])).
% 0.78/0.98 tff(2431,plain,
% 0.78/0.98 (c1_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2254, 171, 2430, 54, 2429, 2428, 1060])).
% 0.78/0.98 tff(2432,plain,
% 0.78/0.98 (c0_1(a1092)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[365, 2427])).
% 0.78/0.98 tff(2433,plain,
% 0.78/0.98 (hskp13 | (~c1_1(a1092))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2259, 2411, 171, 2432, 2429, 735])).
% 0.78/0.98 tff(2434,plain,
% 0.78/0.98 (hskp13),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2433, 2431])).
% 0.78/0.98 tff(2435,plain,
% 0.78/0.98 (~c1_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[754, 2434])).
% 0.78/0.98 tff(2436,plain,
% 0.78/0.98 (c3_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[769, 2434])).
% 0.78/0.98 tff(2437,plain,
% 0.78/0.98 (c0_1(a1095)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2269, 171, 2430, 2432, 2429, 2428, 2436, 2435, 701])).
% 0.78/0.98 tff(2438,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2439,plain,
% 0.78/0.98 ((hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2440,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2439])).
% 0.78/0.98 tff(2441,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2440, 2438])).
% 0.78/0.98 tff(2442,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2443,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 0.78/0.98 tff(2444,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2443, 2411, 171, 2436, 2415, 2435, 2414, 2413, 10, 2437])).
% 0.78/0.98 tff(2445,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2446,plain,
% 0.78/0.98 (~c1_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[492, 2445])).
% 0.78/0.98 tff(2447,plain,
% 0.78/0.98 (c3_1(a1089)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[500, 2445])).
% 0.78/0.99 tff(2448,plain,
% 0.78/0.99 (~c0_1(a1089)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2346, 2411, 171, 2447, 2415, 2446, 2414, 2413, 10])).
% 0.78/0.99 tff(2449,plain,
% 0.78/0.99 (c2_1(a1089)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[508, 2445])).
% 0.78/0.99 tff(2450,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[802, 2411, 171, 2449, 2447, 2446, 623, 2448])).
% 0.78/0.99 % SZS output end Proof
% 0.78/0.99 % E exiting
%------------------------------------------------------------------------------