%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN476-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:39:16 AM UTC 2025
% Result : Unsatisfiable 0.92s 1.09s
% Output : Proof 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN476-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:36:05 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.92/1.09 % SZS status Unsatisfiable
% 0.92/1.09 % SZS output start Proof
% 0.92/1.09 tff(c1_1_type, type, (
% 0.92/1.09 c1_1: $i > $o)).
% 0.92/1.09 tff(a1100_type, type, (
% 0.92/1.09 a1100: $i)).
% 0.92/1.09 tff(c3_1_type, type, (
% 0.92/1.09 c3_1: $i > $o)).
% 0.92/1.09 tff(c0_1_type, type, (
% 0.92/1.09 c0_1: $i > $o)).
% 0.92/1.09 tff(c2_1_type, type, (
% 0.92/1.09 c2_1: $i > $o)).
% 0.92/1.09 tff(ndr1_0_type, type, (
% 0.92/1.09 ndr1_0: $o)).
% 0.92/1.09 tff(hskp5_type, type, (
% 0.92/1.09 hskp5: $o)).
% 0.92/1.09 tff(hskp2_type, type, (
% 0.92/1.09 hskp2: $o)).
% 0.92/1.09 tff(a1105_type, type, (
% 0.92/1.09 a1105: $i)).
% 0.92/1.09 tff(a1136_type, type, (
% 0.92/1.09 a1136: $i)).
% 0.92/1.09 tff(hskp30_type, type, (
% 0.92/1.09 hskp30: $o)).
% 0.92/1.09 tff(hskp0_type, type, (
% 0.92/1.09 hskp0: $o)).
% 0.92/1.09 tff(a1098_type, type, (
% 0.92/1.09 a1098: $i)).
% 0.92/1.09 tff(a1103_type, type, (
% 0.92/1.09 a1103: $i)).
% 0.92/1.09 tff(hskp21_type, type, (
% 0.92/1.09 hskp21: $o)).
% 0.92/1.09 tff(a1147_type, type, (
% 0.92/1.09 a1147: $i)).
% 0.92/1.09 tff(hskp23_type, type, (
% 0.92/1.09 hskp23: $o)).
% 0.92/1.09 tff(a1102_type, type, (
% 0.92/1.09 a1102: $i)).
% 0.92/1.09 tff(hskp4_type, type, (
% 0.92/1.09 hskp4: $o)).
% 0.92/1.09 tff(hskp7_type, type, (
% 0.92/1.09 hskp7: $o)).
% 0.92/1.09 tff(a1099_type, type, (
% 0.92/1.09 a1099: $i)).
% 0.92/1.09 tff(hskp1_type, type, (
% 0.92/1.09 hskp1: $o)).
% 0.92/1.09 tff(a1116_type, type, (
% 0.92/1.09 a1116: $i)).
% 0.92/1.09 tff(hskp29_type, type, (
% 0.92/1.09 hskp29: $o)).
% 0.92/1.09 tff(hskp13_type, type, (
% 0.92/1.09 hskp13: $o)).
% 0.92/1.09 tff(hskp27_type, type, (
% 0.92/1.09 hskp27: $o)).
% 0.92/1.09 tff(hskp16_type, type, (
% 0.92/1.09 hskp16: $o)).
% 0.92/1.09 tff(a1118_type, type, (
% 0.92/1.09 a1118: $i)).
% 0.92/1.09 tff(hskp14_type, type, (
% 0.92/1.09 hskp14: $o)).
% 0.92/1.09 tff(a1130_type, type, (
% 0.92/1.09 a1130: $i)).
% 0.92/1.09 tff(hskp20_type, type, (
% 0.92/1.09 hskp20: $o)).
% 0.92/1.09 tff(a1108_type, type, (
% 0.92/1.09 a1108: $i)).
% 0.92/1.09 tff(hskp9_type, type, (
% 0.92/1.09 hskp9: $o)).
% 0.92/1.09 tff(a1119_type, type, (
% 0.92/1.09 a1119: $i)).
% 0.92/1.09 tff(hskp15_type, type, (
% 0.92/1.09 hskp15: $o)).
% 0.92/1.09 tff(a1111_type, type, (
% 0.92/1.09 a1111: $i)).
% 0.92/1.09 tff(hskp28_type, type, (
% 0.92/1.09 hskp28: $o)).
% 0.92/1.09 tff(a1104_type, type, (
% 0.92/1.09 a1104: $i)).
% 0.92/1.09 tff(hskp6_type, type, (
% 0.92/1.09 hskp6: $o)).
% 0.92/1.09 tff(a1115_type, type, (
% 0.92/1.09 a1115: $i)).
% 0.92/1.09 tff(a1127_type, type, (
% 0.92/1.09 a1127: $i)).
% 0.92/1.09 tff(hskp19_type, type, (
% 0.92/1.09 hskp19: $o)).
% 0.92/1.09 tff(a1149_type, type, (
% 0.92/1.09 a1149: $i)).
% 0.92/1.09 tff(hskp24_type, type, (
% 0.92/1.09 hskp24: $o)).
% 0.92/1.09 tff(a1131_type, type, (
% 0.92/1.09 a1131: $i)).
% 0.92/1.09 tff(a1101_type, type, (
% 0.92/1.09 a1101: $i)).
% 0.92/1.09 tff(hskp3_type, type, (
% 0.92/1.09 hskp3: $o)).
% 0.92/1.09 tff(hskp8_type, type, (
% 0.92/1.09 hskp8: $o)).
% 0.92/1.09 tff(a1107_type, type, (
% 0.92/1.09 a1107: $i)).
% 0.92/1.10 tff(a1113_type, type, (
% 0.92/1.10 a1113: $i)).
% 0.92/1.10 tff(hskp11_type, type, (
% 0.92/1.10 hskp11: $o)).
% 0.92/1.10 tff(a1121_type, type, (
% 0.92/1.10 a1121: $i)).
% 0.92/1.10 tff(a1110_type, type, (
% 0.92/1.10 a1110: $i)).
% 0.92/1.10 tff(hskp10_type, type, (
% 0.92/1.10 hskp10: $o)).
% 0.92/1.10 tff(a1145_type, type, (
% 0.92/1.10 a1145: $i)).
% 0.92/1.10 tff(hskp22_type, type, (
% 0.92/1.10 hskp22: $o)).
% 0.92/1.10 tff(a1125_type, type, (
% 0.92/1.10 a1125: $i)).
% 0.92/1.10 tff(hskp18_type, type, (
% 0.92/1.10 hskp18: $o)).
% 0.92/1.10 tff(a1180_type, type, (
% 0.92/1.10 a1180: $i)).
% 0.92/1.10 tff(hskp26_type, type, (
% 0.92/1.10 hskp26: $o)).
% 0.92/1.10 tff(hskp12_type, type, (
% 0.92/1.10 hskp12: $o)).
% 0.92/1.10 tff(a1114_type, type, (
% 0.92/1.10 a1114: $i)).
% 0.92/1.10 tff(a1124_type, type, (
% 0.92/1.10 a1124: $i)).
% 0.92/1.10 tff(hskp17_type, type, (
% 0.92/1.10 hskp17: $o)).
% 0.92/1.10 tff(1,plain,
% 0.92/1.10 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(2,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[1])).
% 0.92/1.10 tff(3,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(4,plain,
% 0.92/1.10 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(5,plain,
% 0.92/1.10 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[4])).
% 0.92/1.10 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.92/1.10 tff(7,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.92/1.10 tff(8,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.92/1.10 tff(9,plain,(
% 0.92/1.10 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.10 inference(skolemize,[status(sab)],[8])).
% 0.92/1.10 tff(10,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.92/1.10 tff(11,assumption,(hskp0), introduced(assumption)).
% 0.92/1.10 tff(12,plain,
% 0.92/1.10 (((~hskp0) | (~c1_1(a1098))) <=> ((~hskp0) | (~c1_1(a1098)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(13,plain,
% 0.92/1.10 (((~c1_1(a1098)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1098)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(14,axiom,((~c1_1(a1098)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.92/1.10 tff(15,plain,
% 0.92/1.10 ((~hskp0) | (~c1_1(a1098))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.92/1.10 tff(16,plain,
% 0.92/1.10 ((~hskp0) | (~c1_1(a1098))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.92/1.10 tff(17,plain,
% 0.92/1.10 (~c1_1(a1098)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.92/1.10 tff(18,plain,
% 0.92/1.10 (((~hskp0) | (~c2_1(a1098))) <=> ((~hskp0) | (~c2_1(a1098)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(19,plain,
% 0.92/1.10 (((~c2_1(a1098)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1098)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(20,axiom,((~c2_1(a1098)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.92/1.10 tff(21,plain,
% 0.92/1.10 ((~hskp0) | (~c2_1(a1098))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.92/1.10 tff(22,plain,
% 0.92/1.10 ((~hskp0) | (~c2_1(a1098))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.92/1.10 tff(23,plain,
% 0.92/1.10 (~c2_1(a1098)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[22, 11])).
% 0.92/1.10 tff(24,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(25,plain,
% 0.92/1.10 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[24])).
% 0.92/1.10 tff(26,plain,
% 0.92/1.10 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(27,plain,
% 0.92/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp21))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp0) <=> ((hskp21 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp0))), rewrite(((hskp21 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp0) <=> (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp0) <=> (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(28,plain,
% 0.92/1.10 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp0) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[27])).
% 0.92/1.10 tff(29,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.92/1.10 tff(30,plain,
% 0.92/1.10 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.92/1.10 tff(31,plain,
% 0.92/1.10 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.92/1.10 tff(32,plain,(
% 0.92/1.10 ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[31])).
% 0.92/1.10 tff(33,plain,
% 0.92/1.10 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.92/1.10 tff(34,assumption,(~c1_1(a1098)), introduced(assumption)).
% 0.92/1.10 tff(35,assumption,(~c2_1(a1098)), introduced(assumption)).
% 0.92/1.10 tff(36,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(37,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[36])).
% 0.92/1.10 tff(38,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(39,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(40,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[39])).
% 0.92/1.10 tff(41,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 0.92/1.10 tff(42,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.92/1.10 tff(43,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.92/1.10 tff(44,plain,(
% 0.92/1.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[43])).
% 0.92/1.10 tff(45,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.92/1.10 tff(46,assumption,(~c0_1(a1136)), introduced(assumption)).
% 0.92/1.10 tff(47,assumption,(~c3_1(a1098)), introduced(assumption)).
% 0.92/1.10 tff(48,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(49,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[48])).
% 0.92/1.10 tff(50,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(51,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(52,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[51])).
% 0.92/1.10 tff(53,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 0.92/1.10 tff(54,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.92/1.10 tff(55,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.92/1.10 tff(56,plain,(
% 0.92/1.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[55])).
% 0.92/1.10 tff(57,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.92/1.10 tff(58,plain,
% 0.92/1.10 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(59,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[58])).
% 0.92/1.10 tff(60,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(61,plain,
% 0.92/1.10 (^[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) | c3_1(U) | 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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(62,plain,
% 0.92/1.10 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[61])).
% 0.92/1.10 tff(63,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.92/1.10 tff(64,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.92/1.10 tff(65,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.92/1.10 tff(66,plain,(
% 0.92/1.10 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[65])).
% 0.92/1.10 tff(67,plain,
% 0.92/1.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.92/1.10 tff(68,assumption,(~hskp7), introduced(assumption)).
% 0.92/1.10 tff(69,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(70,plain,
% 0.92/1.10 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[69])).
% 0.92/1.10 tff(71,plain,
% 0.92/1.10 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(72,plain,
% 0.92/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp5) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp5))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp5) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp5) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(73,plain,
% 0.92/1.10 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp5) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[72])).
% 0.92/1.10 tff(74,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.92/1.10 tff(75,plain,
% 0.92/1.10 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.92/1.10 tff(76,plain,
% 0.92/1.10 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.92/1.10 tff(77,plain,(
% 0.92/1.10 ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.92/1.10 inference(skolemize,[status(sab)],[76])).
% 0.92/1.10 tff(78,plain,
% 0.92/1.10 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.92/1.10 tff(79,assumption,(~ndr1_0), introduced(assumption)).
% 0.92/1.10 tff(80,plain,
% 0.92/1.10 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(81,plain,
% 0.92/1.10 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(82,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 0.92/1.10 tff(83,plain,
% 0.92/1.10 (ndr1_0 | (~hskp13)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.92/1.10 tff(84,plain,
% 0.92/1.10 (ndr1_0 | (~hskp13)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.92/1.10 tff(85,plain,
% 0.92/1.10 (~hskp13),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[84, 79])).
% 0.92/1.10 tff(86,plain,
% 0.92/1.10 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(87,plain,
% 0.92/1.10 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(88,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.92/1.10 tff(89,plain,
% 0.92/1.10 (ndr1_0 | (~hskp27)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.92/1.10 tff(90,plain,
% 0.92/1.10 (ndr1_0 | (~hskp27)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.92/1.10 tff(91,plain,
% 0.92/1.10 (~hskp27),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[90, 79])).
% 0.92/1.10 tff(92,plain,
% 0.92/1.10 ((ndr1_0 | (~hskp16)) <=> (ndr1_0 | (~hskp16))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(93,plain,
% 0.92/1.10 (((~hskp16) | ndr1_0) <=> (ndr1_0 | (~hskp16))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(94,axiom,((~hskp16) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 0.92/1.10 tff(95,plain,
% 0.92/1.10 (ndr1_0 | (~hskp16)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.92/1.10 tff(96,plain,
% 0.92/1.10 (ndr1_0 | (~hskp16)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[95, 92])).
% 0.92/1.10 tff(97,plain,
% 0.92/1.10 (~hskp16),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[96, 79])).
% 0.92/1.10 tff(98,plain,
% 0.92/1.10 ((hskp27 | hskp16 | hskp13) <=> (hskp27 | hskp16 | hskp13)),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(99,plain,
% 0.92/1.10 (((hskp16 | hskp13) | hskp27) <=> (hskp27 | hskp16 | hskp13)),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(100,plain,
% 0.92/1.10 ((hskp16 | hskp13) <=> (hskp16 | hskp13)),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(101,plain,
% 0.92/1.10 (((hskp16 | hskp13) | hskp27) <=> ((hskp16 | hskp13) | hskp27)),
% 0.92/1.10 inference(monotonicity,[status(thm)],[100])).
% 0.92/1.10 tff(102,plain,
% 0.92/1.10 (((hskp16 | hskp13) | hskp27) <=> (hskp27 | hskp16 | hskp13)),
% 0.92/1.10 inference(transitivity,[status(thm)],[101, 99])).
% 0.92/1.10 tff(103,axiom,((hskp16 | hskp13) | hskp27), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.92/1.10 tff(104,plain,
% 0.92/1.10 (hskp27 | hskp16 | hskp13),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.92/1.10 tff(105,plain,
% 0.92/1.10 (hskp27 | hskp16 | hskp13),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[104, 98])).
% 0.92/1.10 tff(106,plain,
% 0.92/1.10 (hskp27 | hskp16 | hskp13),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.92/1.10 tff(107,plain,
% 0.92/1.10 (hskp27 | hskp16 | hskp13),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[106, 98])).
% 0.92/1.10 tff(108,plain,
% 0.92/1.10 (hskp27 | hskp16 | hskp13),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[107, 98])).
% 0.92/1.10 tff(109,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[108, 97, 91, 85])).
% 0.92/1.10 tff(110,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(111,plain,
% 0.92/1.10 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(112,plain,
% 0.92/1.10 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098)) <=> (hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(113,plain,
% 0.92/1.10 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[112])).
% 0.92/1.10 tff(114,plain,
% 0.92/1.10 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 0.92/1.10 inference(transitivity,[status(thm)],[113, 111])).
% 0.92/1.10 tff(115,plain,
% 0.92/1.10 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(116,plain,
% 0.92/1.10 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.92/1.10 tff(117,plain,
% 0.92/1.10 (hskp7 | hskp5 | c2_1(a1098) | c3_1(a1098)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[116, 110, 34, 78])).
% 0.92/1.10 tff(118,plain,
% 0.92/1.10 (hskp5),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[117, 68, 35, 47])).
% 0.92/1.10 tff(119,plain,
% 0.92/1.10 (((~hskp5) | (~c2_1(a1103))) <=> ((~hskp5) | (~c2_1(a1103)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(120,plain,
% 0.92/1.10 (((~c2_1(a1103)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1103)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(121,axiom,((~c2_1(a1103)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.92/1.10 tff(122,plain,
% 0.92/1.10 ((~hskp5) | (~c2_1(a1103))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.92/1.10 tff(123,plain,
% 0.92/1.10 ((~hskp5) | (~c2_1(a1103))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[122, 119])).
% 0.92/1.10 tff(124,plain,
% 0.92/1.10 (~c2_1(a1103)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[123, 118])).
% 0.92/1.10 tff(125,plain,
% 0.92/1.10 (((~hskp5) | (~c0_1(a1103))) <=> ((~hskp5) | (~c0_1(a1103)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(126,plain,
% 0.92/1.10 (((~c0_1(a1103)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1103)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(127,axiom,((~c0_1(a1103)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.92/1.10 tff(128,plain,
% 0.92/1.10 ((~hskp5) | (~c0_1(a1103))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.92/1.10 tff(129,plain,
% 0.92/1.10 ((~hskp5) | (~c0_1(a1103))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[128, 125])).
% 0.92/1.10 tff(130,plain,
% 0.92/1.10 (~c0_1(a1103)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[129, 118])).
% 0.92/1.10 tff(131,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(132,plain,
% 0.92/1.10 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[131])).
% 0.92/1.10 tff(133,plain,
% 0.92/1.10 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(134,plain,
% 0.92/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp14) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp14))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp14) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp14) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(135,plain,
% 0.92/1.11 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp14) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[134])).
% 0.92/1.11 tff(136,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.92/1.11 tff(137,plain,
% 0.92/1.11 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.92/1.11 tff(138,plain,
% 0.92/1.11 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.92/1.11 tff(139,plain,(
% 0.92/1.11 ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[138])).
% 0.92/1.11 tff(140,plain,
% 0.92/1.11 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.92/1.11 tff(141,plain,
% 0.92/1.11 (((~hskp5) | c3_1(a1103)) <=> ((~hskp5) | c3_1(a1103))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(142,axiom,((~hskp5) | c3_1(a1103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.92/1.11 tff(143,plain,
% 0.92/1.11 ((~hskp5) | c3_1(a1103)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.92/1.11 tff(144,plain,
% 0.92/1.11 ((~hskp5) | c3_1(a1103)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[143, 141])).
% 0.92/1.11 tff(145,plain,
% 0.92/1.11 ((~hskp5) | c3_1(a1103)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[144, 141])).
% 0.92/1.11 tff(146,plain,
% 0.92/1.11 ((~hskp5) | c3_1(a1103)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.92/1.11 tff(147,plain,
% 0.92/1.11 ((~hskp5) | c3_1(a1103)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[146, 141])).
% 0.92/1.11 tff(148,plain,
% 0.92/1.11 (c3_1(a1103)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[147, 118])).
% 0.92/1.11 tff(149,plain,
% 0.92/1.11 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(150,plain,
% 0.92/1.11 ((hskp14 | hskp7 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103))) <=> (hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(151,plain,
% 0.92/1.11 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[150])).
% 0.92/1.11 tff(152,plain,
% 0.92/1.11 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[151, 149])).
% 0.92/1.11 tff(153,plain,
% 0.92/1.11 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(154,plain,
% 0.92/1.11 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.92/1.11 tff(155,plain,
% 0.92/1.11 (hskp14),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[154, 110, 68, 148, 130, 124, 140])).
% 0.92/1.11 tff(156,plain,
% 0.92/1.11 (((~hskp14) | (~c3_1(a1118))) <=> ((~hskp14) | (~c3_1(a1118)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(157,plain,
% 0.92/1.11 (((~c3_1(a1118)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a1118)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(158,axiom,((~c3_1(a1118)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.92/1.11 tff(159,plain,
% 0.92/1.11 ((~hskp14) | (~c3_1(a1118))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.92/1.11 tff(160,plain,
% 0.92/1.11 ((~hskp14) | (~c3_1(a1118))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[159, 156])).
% 0.92/1.11 tff(161,plain,
% 0.92/1.11 (~c3_1(a1118)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[160, 155])).
% 0.92/1.11 tff(162,plain,
% 0.92/1.11 (((~hskp14) | (~c2_1(a1118))) <=> ((~hskp14) | (~c2_1(a1118)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(163,plain,
% 0.92/1.11 (((~c2_1(a1118)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1118)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(164,axiom,((~c2_1(a1118)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.92/1.11 tff(165,plain,
% 0.92/1.11 ((~hskp14) | (~c2_1(a1118))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.92/1.11 tff(166,plain,
% 0.92/1.11 ((~hskp14) | (~c2_1(a1118))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[165, 162])).
% 0.92/1.11 tff(167,plain,
% 0.92/1.11 (~c2_1(a1118)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[166, 155])).
% 0.92/1.11 tff(168,plain,
% 0.92/1.11 (((~hskp14) | c1_1(a1118)) <=> ((~hskp14) | c1_1(a1118))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(169,axiom,((~hskp14) | c1_1(a1118)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.92/1.11 tff(170,plain,
% 0.92/1.11 ((~hskp14) | c1_1(a1118)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.92/1.11 tff(171,plain,
% 0.92/1.11 ((~hskp14) | c1_1(a1118)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[170, 168])).
% 0.92/1.11 tff(172,plain,
% 0.92/1.11 ((~hskp14) | c1_1(a1118)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[171, 168])).
% 0.92/1.11 tff(173,plain,
% 0.92/1.11 ((~hskp14) | c1_1(a1118)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.92/1.11 tff(174,plain,
% 0.92/1.11 ((~hskp14) | c1_1(a1118)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[173, 168])).
% 0.92/1.11 tff(175,plain,
% 0.92/1.11 (c1_1(a1118)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[174, 155])).
% 0.92/1.11 tff(176,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(177,plain,
% 0.92/1.11 ((hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103))) <=> (hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(178,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[177])).
% 0.92/1.11 tff(179,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[178, 176])).
% 0.92/1.11 tff(180,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(181,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.92/1.11 tff(182,plain,
% 0.92/1.11 (hskp29),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[181, 110, 175, 148, 167, 161, 130, 124, 67])).
% 0.92/1.11 tff(183,plain,
% 0.92/1.11 (((~hskp29) | c3_1(a1116)) <=> ((~hskp29) | c3_1(a1116))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(184,axiom,((~hskp29) | c3_1(a1116)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.92/1.11 tff(185,plain,
% 0.92/1.11 ((~hskp29) | c3_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.92/1.11 tff(186,plain,
% 0.92/1.11 ((~hskp29) | c3_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[185, 183])).
% 0.92/1.11 tff(187,plain,
% 0.92/1.11 ((~hskp29) | c3_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[186, 183])).
% 0.92/1.11 tff(188,plain,
% 0.92/1.11 ((~hskp29) | c3_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.92/1.11 tff(189,plain,
% 0.92/1.11 ((~hskp29) | c3_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[188, 183])).
% 0.92/1.11 tff(190,plain,
% 0.92/1.11 (c3_1(a1116)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[189, 182])).
% 0.92/1.11 tff(191,plain,
% 0.92/1.11 (((~hskp29) | c2_1(a1116)) <=> ((~hskp29) | c2_1(a1116))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(192,axiom,((~hskp29) | c2_1(a1116)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.92/1.11 tff(193,plain,
% 0.92/1.11 ((~hskp29) | c2_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.92/1.11 tff(194,plain,
% 0.92/1.11 ((~hskp29) | c2_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[193, 191])).
% 0.92/1.11 tff(195,plain,
% 0.92/1.11 ((~hskp29) | c2_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[194, 191])).
% 0.92/1.11 tff(196,plain,
% 0.92/1.11 ((~hskp29) | c2_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.92/1.11 tff(197,plain,
% 0.92/1.11 ((~hskp29) | c2_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[196, 191])).
% 0.92/1.11 tff(198,plain,
% 0.92/1.11 (c2_1(a1116)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[197, 182])).
% 0.92/1.11 tff(199,plain,
% 0.92/1.11 (((~hskp29) | c0_1(a1116)) <=> ((~hskp29) | c0_1(a1116))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(200,axiom,((~hskp29) | c0_1(a1116)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.92/1.11 tff(201,plain,
% 0.92/1.11 ((~hskp29) | c0_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.92/1.11 tff(202,plain,
% 0.92/1.11 ((~hskp29) | c0_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[201, 199])).
% 0.92/1.11 tff(203,plain,
% 0.92/1.11 ((~hskp29) | c0_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[202, 199])).
% 0.92/1.11 tff(204,plain,
% 0.92/1.11 ((~hskp29) | c0_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.92/1.11 tff(205,plain,
% 0.92/1.11 ((~hskp29) | c0_1(a1116)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[204, 199])).
% 0.92/1.11 tff(206,plain,
% 0.92/1.11 (c0_1(a1116)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[205, 182])).
% 0.92/1.11 tff(207,assumption,(~c0_1(a1103)), introduced(assumption)).
% 0.92/1.11 tff(208,assumption,(~c3_1(a1118)), introduced(assumption)).
% 0.92/1.11 tff(209,assumption,(c0_1(a1118)), introduced(assumption)).
% 0.92/1.11 tff(210,assumption,(c1_1(a1118)), introduced(assumption)).
% 0.92/1.11 tff(211,assumption,(~c2_1(a1103)), introduced(assumption)).
% 0.92/1.11 tff(212,assumption,(~c2_1(a1118)), introduced(assumption)).
% 0.92/1.11 tff(213,assumption,(c3_1(a1103)), introduced(assumption)).
% 0.92/1.11 tff(214,plain,
% 0.92/1.11 (hskp29),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[181, 110, 210, 213, 212, 208, 207, 211, 67])).
% 0.92/1.11 tff(215,plain,
% 0.92/1.11 (c0_1(a1116)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[205, 214])).
% 0.92/1.11 tff(216,plain,
% 0.92/1.11 (c3_1(a1116)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[189, 214])).
% 0.92/1.11 tff(217,plain,
% 0.92/1.11 (c2_1(a1116)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[197, 214])).
% 0.92/1.11 tff(218,assumption,(~c1_1(a1103)), introduced(assumption)).
% 0.92/1.11 tff(219,plain,
% 0.92/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(220,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[219])).
% 0.92/1.11 tff(221,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(222,plain,
% 0.92/1.11 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_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(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(223,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[222])).
% 0.92/1.11 tff(224,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(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 0.92/1.11 tff(225,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.92/1.11 tff(226,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.92/1.11 tff(227,plain,(
% 0.92/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[226])).
% 0.92/1.11 tff(228,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.92/1.11 tff(229,assumption,(c3_1(a1116)), introduced(assumption)).
% 0.92/1.11 tff(230,assumption,(c2_1(a1116)), introduced(assumption)).
% 0.92/1.11 tff(231,assumption,(c0_1(a1116)), introduced(assumption)).
% 0.92/1.11 tff(232,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(233,plain,
% 0.92/1.11 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103))) <=> (c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(234,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[233])).
% 0.92/1.11 tff(235,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[234, 232])).
% 0.92/1.11 tff(236,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(237,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.92/1.11 tff(238,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[237, 110, 231, 230, 229, 210, 213, 212, 211, 228, 218, 209])).
% 0.92/1.11 tff(239,plain,(c1_1(a1103) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c1_1(a1118)) | (~c3_1(a1103)) | c2_1(a1118) | c2_1(a1103) | (~c0_1(a1118))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(240,plain,
% 0.92/1.11 (c1_1(a1103)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[239, 209, 217, 216, 210, 213, 212, 211, 215])).
% 0.92/1.11 tff(241,plain,
% 0.92/1.11 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(242,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[241])).
% 0.92/1.11 tff(243,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(244,plain,
% 0.92/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(245,plain,
% 0.92/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[244])).
% 0.92/1.11 tff(246,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.92/1.11 tff(247,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.92/1.11 tff(248,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.92/1.11 tff(249,plain,(
% 0.92/1.11 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[248])).
% 0.92/1.11 tff(250,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.92/1.11 tff(251,plain,
% 0.92/1.11 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(252,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[251])).
% 0.92/1.11 tff(253,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(254,plain,
% 0.92/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_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)) | hskp2) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_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)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(255,plain,
% 0.92/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[254])).
% 0.92/1.12 tff(256,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)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.92/1.12 tff(257,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.92/1.12 tff(258,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[257, 253])).
% 0.92/1.12 tff(259,plain,(
% 0.92/1.12 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(skolemize,[status(sab)],[258])).
% 0.92/1.12 tff(260,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[259, 252])).
% 0.92/1.12 tff(261,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(262,plain,
% 0.92/1.12 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103))) <=> (hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(263,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[262])).
% 0.92/1.12 tff(264,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[263, 261])).
% 0.92/1.12 tff(265,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(266,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.92/1.12 tff(267,plain,
% 0.92/1.12 (hskp2 | (~c1_1(a1103))),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[266, 110, 215, 217, 216, 213, 211, 260])).
% 0.92/1.12 tff(268,plain,
% 0.92/1.12 (hskp2),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[267, 240])).
% 0.92/1.12 tff(269,plain,
% 0.92/1.12 (((~hskp2) | (~c3_1(a1100))) <=> ((~hskp2) | (~c3_1(a1100)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(270,plain,
% 0.92/1.12 (((~c3_1(a1100)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a1100)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(271,axiom,((~c3_1(a1100)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.92/1.12 tff(272,plain,
% 0.92/1.12 ((~hskp2) | (~c3_1(a1100))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.92/1.12 tff(273,plain,
% 0.92/1.12 ((~hskp2) | (~c3_1(a1100))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[272, 269])).
% 0.92/1.12 tff(274,plain,
% 0.92/1.12 (~c3_1(a1100)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[273, 268])).
% 0.92/1.12 tff(275,plain,
% 0.92/1.12 (((~hskp2) | c2_1(a1100)) <=> ((~hskp2) | c2_1(a1100))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(276,axiom,((~hskp2) | c2_1(a1100)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.92/1.12 tff(277,plain,
% 0.92/1.12 ((~hskp2) | c2_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.92/1.12 tff(278,plain,
% 0.92/1.12 ((~hskp2) | c2_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[277, 275])).
% 0.92/1.12 tff(279,plain,
% 0.92/1.12 ((~hskp2) | c2_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[278, 275])).
% 0.92/1.12 tff(280,plain,
% 0.92/1.12 ((~hskp2) | c2_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.92/1.12 tff(281,plain,
% 0.92/1.12 ((~hskp2) | c2_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[280, 275])).
% 0.92/1.12 tff(282,plain,
% 0.92/1.12 (c2_1(a1100)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[281, 268])).
% 0.92/1.12 tff(283,plain,
% 0.92/1.12 (((~hskp2) | c0_1(a1100)) <=> ((~hskp2) | c0_1(a1100))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(284,axiom,((~hskp2) | c0_1(a1100)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.92/1.12 tff(285,plain,
% 0.92/1.12 ((~hskp2) | c0_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.92/1.12 tff(286,plain,
% 0.92/1.12 ((~hskp2) | c0_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[285, 283])).
% 0.92/1.12 tff(287,plain,
% 0.92/1.12 ((~hskp2) | c0_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[286, 283])).
% 0.92/1.12 tff(288,plain,
% 0.92/1.12 ((~hskp2) | c0_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.92/1.12 tff(289,plain,
% 0.92/1.12 ((~hskp2) | c0_1(a1100)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[288, 283])).
% 0.92/1.12 tff(290,plain,
% 0.92/1.12 (c0_1(a1100)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[289, 268])).
% 0.92/1.12 tff(291,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(292,plain,
% 0.92/1.12 ((hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103))) <=> (hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(293,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[292])).
% 0.92/1.12 tff(294,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[293, 291])).
% 0.92/1.12 tff(295,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(296,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.92/1.12 tff(297,plain,
% 0.92/1.12 (hskp20),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[296, 110, 213, 290, 282, 207, 274, 250, 240])).
% 0.92/1.12 tff(298,plain,
% 0.92/1.12 (((~hskp20) | (~c0_1(a1130))) <=> ((~hskp20) | (~c0_1(a1130)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(299,plain,
% 0.92/1.12 (((~c0_1(a1130)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a1130)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(300,axiom,((~c0_1(a1130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.92/1.12 tff(301,plain,
% 0.92/1.12 ((~hskp20) | (~c0_1(a1130))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.92/1.12 tff(302,plain,
% 0.92/1.12 ((~hskp20) | (~c0_1(a1130))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[301, 298])).
% 0.92/1.12 tff(303,plain,
% 0.92/1.12 (~c0_1(a1130)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[302, 297])).
% 0.92/1.12 tff(304,plain,
% 0.92/1.12 (((~hskp20) | (~c3_1(a1130))) <=> ((~hskp20) | (~c3_1(a1130)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(305,plain,
% 0.92/1.12 (((~c3_1(a1130)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a1130)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(306,axiom,((~c3_1(a1130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.92/1.12 tff(307,plain,
% 0.92/1.12 ((~hskp20) | (~c3_1(a1130))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.92/1.12 tff(308,plain,
% 0.92/1.12 ((~hskp20) | (~c3_1(a1130))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[307, 304])).
% 0.92/1.12 tff(309,plain,
% 0.92/1.12 (~c3_1(a1130)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[308, 297])).
% 0.92/1.12 tff(310,assumption,(~c0_1(a1130)), introduced(assumption)).
% 0.92/1.12 tff(311,plain,
% 0.92/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(312,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[311])).
% 0.92/1.12 tff(313,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(314,plain,
% 0.92/1.12 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(315,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[314])).
% 0.92/1.12 tff(316,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.92/1.12 tff(317,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.92/1.12 tff(318,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[317, 313])).
% 0.92/1.12 tff(319,plain,(
% 0.92/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.12 inference(skolemize,[status(sab)],[318])).
% 0.92/1.12 tff(320,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[319, 312])).
% 0.92/1.12 tff(321,assumption,(~c3_1(a1130)), introduced(assumption)).
% 0.92/1.12 tff(322,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(323,plain,
% 0.92/1.12 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | c3_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(324,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | c3_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[323])).
% 0.92/1.12 tff(325,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | c3_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[324, 322])).
% 0.92/1.12 tff(326,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | c3_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(327,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.92/1.12 tff(328,plain,
% 0.92/1.12 (c0_1(a1130) | (~c0_1(a1118)) | (~c1_1(a1130))),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[327, 110, 215, 217, 216, 321, 212, 208, 320])).
% 0.92/1.12 tff(329,plain,
% 0.92/1.12 (~c1_1(a1130)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[328, 209, 310])).
% 0.92/1.12 tff(330,plain,
% 0.92/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(331,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[330])).
% 0.92/1.12 tff(332,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(333,plain,
% 0.92/1.12 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(334,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[333])).
% 0.92/1.12 tff(335,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.92/1.12 tff(336,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.92/1.12 tff(337,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[336, 332])).
% 0.92/1.12 tff(338,plain,(
% 0.92/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.12 inference(skolemize,[status(sab)],[337])).
% 0.92/1.12 tff(339,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[338, 331])).
% 0.92/1.12 tff(340,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(341,plain,
% 0.92/1.12 (((~ndr1_0) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130)) <=> (c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(342,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[341])).
% 0.92/1.12 tff(343,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130))),
% 0.92/1.12 inference(transitivity,[status(thm)],[342, 340])).
% 0.92/1.12 tff(344,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(345,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.92/1.12 tff(346,plain,
% 0.92/1.12 (c0_1(a1130) | (~c1_1(a1103)) | (~c0_1(a1118)) | c1_1(a1130)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[345, 110, 210, 213, 321, 208, 207, 339])).
% 0.92/1.12 tff(347,plain,
% 0.92/1.12 (~c1_1(a1103)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[346, 209, 310, 329])).
% 0.92/1.12 tff(348,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[237, 110, 215, 217, 216, 210, 213, 212, 211, 228, 347, 209])).
% 0.92/1.12 tff(349,plain,((~c0_1(a1118)) | (~c1_1(a1118)) | (~c3_1(a1103)) | c2_1(a1118) | c2_1(a1103) | c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(350,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[349, 309, 303, 213, 212, 211, 210, 209, 208, 207])).
% 0.92/1.12 tff(351,plain,((~c0_1(a1118)) | (~c3_1(a1103)) | c2_1(a1118) | c2_1(a1103) | (~c1_1(a1118)) | c3_1(a1118) | c0_1(a1103)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(352,plain,
% 0.92/1.12 (~c0_1(a1118)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[351, 148, 167, 124, 175, 161, 130])).
% 0.92/1.12 tff(353,assumption,(~hskp1), introduced(assumption)).
% 0.92/1.12 tff(354,assumption,(~c0_1(a1118)), introduced(assumption)).
% 0.92/1.12 tff(355,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(356,plain,
% 0.92/1.12 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(357,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[356])).
% 0.92/1.13 tff(358,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.13 inference(transitivity,[status(thm)],[357, 355])).
% 0.92/1.13 tff(359,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(360,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.92/1.13 tff(361,plain,
% 0.92/1.13 ((~c0_1(a1098)) | c0_1(a1118)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[360, 110, 231, 230, 229, 210, 208, 35, 47, 320])).
% 0.92/1.13 tff(362,plain,
% 0.92/1.13 (~c0_1(a1098)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[361, 354])).
% 0.92/1.13 tff(363,plain,
% 0.92/1.13 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(364,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[363])).
% 0.92/1.13 tff(365,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(366,plain,
% 0.92/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(367,plain,
% 0.92/1.13 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[366])).
% 0.92/1.13 tff(368,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.92/1.13 tff(369,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.92/1.13 tff(370,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[369, 365])).
% 0.92/1.13 tff(371,plain,(
% 0.92/1.13 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.13 inference(skolemize,[status(sab)],[370])).
% 0.92/1.13 tff(372,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[371, 364])).
% 0.92/1.13 tff(373,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(374,plain,
% 0.92/1.13 ((hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098)) <=> (hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(375,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[374])).
% 0.92/1.13 tff(376,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.13 inference(transitivity,[status(thm)],[375, 373])).
% 0.92/1.13 tff(377,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(378,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.92/1.13 tff(379,plain,
% 0.92/1.13 (hskp1 | c0_1(a1098) | c0_1(a1118)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[378, 110, 210, 208, 34, 47, 372])).
% 0.92/1.13 tff(380,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[379, 362, 354, 353])).
% 0.92/1.13 tff(381,plain,(c0_1(a1118) | hskp1 | (~c1_1(a1118)) | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(382,plain,
% 0.92/1.13 (hskp1),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[381, 352, 175, 161, 34, 47, 206, 198, 190, 35])).
% 0.92/1.13 tff(383,plain,
% 0.92/1.13 (((~hskp1) | (~c0_1(a1099))) <=> ((~hskp1) | (~c0_1(a1099)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(384,plain,
% 0.92/1.13 (((~c0_1(a1099)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1099)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(385,axiom,((~c0_1(a1099)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.92/1.13 tff(386,plain,
% 0.92/1.13 ((~hskp1) | (~c0_1(a1099))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.92/1.13 tff(387,plain,
% 0.92/1.13 ((~hskp1) | (~c0_1(a1099))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[386, 383])).
% 0.92/1.13 tff(388,plain,
% 0.92/1.13 (~c0_1(a1099)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[387, 382])).
% 0.92/1.13 tff(389,plain,
% 0.92/1.13 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(390,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[389])).
% 0.92/1.13 tff(391,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(392,plain,
% 0.92/1.13 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(393,plain,
% 0.92/1.13 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[392])).
% 0.92/1.13 tff(394,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.92/1.13 tff(395,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.92/1.13 tff(396,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[395, 391])).
% 0.92/1.13 tff(397,plain,(
% 0.92/1.13 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.13 inference(skolemize,[status(sab)],[396])).
% 0.92/1.13 tff(398,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[397, 390])).
% 0.92/1.13 tff(399,plain,
% 0.92/1.13 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(400,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[399])).
% 0.92/1.13 tff(401,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(402,plain,
% 0.92/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(403,plain,
% 0.92/1.13 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[402])).
% 0.92/1.13 tff(404,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.92/1.13 tff(405,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.92/1.13 tff(406,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[405, 401])).
% 0.92/1.13 tff(407,plain,(
% 0.92/1.13 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.13 inference(skolemize,[status(sab)],[406])).
% 0.92/1.13 tff(408,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[407, 400])).
% 0.92/1.13 tff(409,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(410,plain,
% 0.92/1.13 ((hskp15 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098)) <=> (hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(411,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[410])).
% 0.92/1.13 tff(412,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.13 inference(transitivity,[status(thm)],[411, 409])).
% 0.92/1.13 tff(413,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(414,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.92/1.13 tff(415,plain,
% 0.92/1.13 (hskp15 | c0_1(a1118)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[414, 110, 175, 161, 34, 35, 47, 408])).
% 0.92/1.13 tff(416,plain,
% 0.92/1.13 (hskp15),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[415, 352])).
% 0.92/1.13 tff(417,plain,
% 0.92/1.13 (((~hskp15) | (~c2_1(a1119))) <=> ((~hskp15) | (~c2_1(a1119)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(418,plain,
% 0.92/1.13 (((~c2_1(a1119)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a1119)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(419,axiom,((~c2_1(a1119)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.92/1.13 tff(420,plain,
% 0.92/1.13 ((~hskp15) | (~c2_1(a1119))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.92/1.13 tff(421,plain,
% 0.92/1.13 ((~hskp15) | (~c2_1(a1119))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[420, 417])).
% 0.92/1.13 tff(422,plain,
% 0.92/1.13 (~c2_1(a1119)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[421, 416])).
% 0.92/1.13 tff(423,plain,
% 0.92/1.13 (((~hskp15) | (~c0_1(a1119))) <=> ((~hskp15) | (~c0_1(a1119)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(424,plain,
% 0.92/1.13 (((~c0_1(a1119)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a1119)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(425,axiom,((~c0_1(a1119)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.92/1.13 tff(426,plain,
% 0.92/1.13 ((~hskp15) | (~c0_1(a1119))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.92/1.13 tff(427,plain,
% 0.92/1.13 ((~hskp15) | (~c0_1(a1119))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[426, 423])).
% 0.92/1.13 tff(428,plain,
% 0.92/1.13 (~c0_1(a1119)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[427, 416])).
% 0.92/1.13 tff(429,plain,
% 0.92/1.13 (((~hskp1) | c2_1(a1099)) <=> ((~hskp1) | c2_1(a1099))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(430,axiom,((~hskp1) | c2_1(a1099)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.92/1.13 tff(431,plain,
% 0.92/1.13 ((~hskp1) | c2_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.92/1.13 tff(432,plain,
% 0.92/1.13 ((~hskp1) | c2_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[431, 429])).
% 0.92/1.13 tff(433,plain,
% 0.92/1.13 ((~hskp1) | c2_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[432, 429])).
% 0.92/1.13 tff(434,plain,
% 0.92/1.13 ((~hskp1) | c2_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[433, 429])).
% 0.92/1.13 tff(435,plain,
% 0.92/1.13 ((~hskp1) | c2_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[434, 429])).
% 0.92/1.13 tff(436,plain,
% 0.92/1.13 (c2_1(a1099)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[435, 382])).
% 0.92/1.13 tff(437,plain,
% 0.92/1.13 (((~hskp1) | c1_1(a1099)) <=> ((~hskp1) | c1_1(a1099))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(438,axiom,((~hskp1) | c1_1(a1099)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.92/1.13 tff(439,plain,
% 0.92/1.13 ((~hskp1) | c1_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.92/1.13 tff(440,plain,
% 0.92/1.13 ((~hskp1) | c1_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[439, 437])).
% 0.92/1.13 tff(441,plain,
% 0.92/1.13 ((~hskp1) | c1_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[440, 437])).
% 0.92/1.13 tff(442,plain,
% 0.92/1.13 ((~hskp1) | c1_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[441, 437])).
% 0.92/1.13 tff(443,plain,
% 0.92/1.13 ((~hskp1) | c1_1(a1099)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[442, 437])).
% 0.92/1.13 tff(444,plain,
% 0.92/1.13 (c1_1(a1099)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[443, 382])).
% 0.92/1.13 tff(445,plain,
% 0.92/1.13 (((~hskp15) | c1_1(a1119)) <=> ((~hskp15) | c1_1(a1119))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(446,axiom,((~hskp15) | c1_1(a1119)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.92/1.13 tff(447,plain,
% 0.92/1.13 ((~hskp15) | c1_1(a1119)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.92/1.13 tff(448,plain,
% 0.92/1.13 ((~hskp15) | c1_1(a1119)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[447, 445])).
% 0.92/1.13 tff(449,plain,
% 0.92/1.13 ((~hskp15) | c1_1(a1119)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[448, 445])).
% 0.92/1.13 tff(450,plain,
% 0.92/1.13 ((~hskp15) | c1_1(a1119)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[449, 445])).
% 0.92/1.13 tff(451,plain,
% 0.92/1.13 ((~hskp15) | c1_1(a1119)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[450, 445])).
% 0.92/1.13 tff(452,plain,
% 0.92/1.13 (c1_1(a1119)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[451, 416])).
% 0.92/1.13 tff(453,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(454,plain,
% 0.92/1.13 ((hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1119) | c0_1(a1119) | (~c1_1(a1119))) <=> (hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(455,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1119) | c0_1(a1119) | (~c1_1(a1119)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[454])).
% 0.92/1.13 tff(456,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1119) | c0_1(a1119) | (~c1_1(a1119)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[455, 453])).
% 0.92/1.13 tff(457,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1119) | c0_1(a1119) | (~c1_1(a1119)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(458,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.92/1.13 tff(459,plain,
% 0.92/1.13 (hskp9),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[458, 110, 452, 444, 436, 428, 422, 388, 398])).
% 0.92/1.13 tff(460,plain,
% 0.92/1.13 (((~hskp9) | (~c3_1(a1108))) <=> ((~hskp9) | (~c3_1(a1108)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(461,plain,
% 0.92/1.13 (((~c3_1(a1108)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a1108)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(462,axiom,((~c3_1(a1108)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.92/1.13 tff(463,plain,
% 0.92/1.13 ((~hskp9) | (~c3_1(a1108))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.92/1.13 tff(464,plain,
% 0.92/1.13 ((~hskp9) | (~c3_1(a1108))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[463, 460])).
% 0.92/1.13 tff(465,plain,
% 0.92/1.13 (~c3_1(a1108)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[464, 459])).
% 0.92/1.13 tff(466,plain,
% 0.92/1.13 (((~hskp9) | (~c1_1(a1108))) <=> ((~hskp9) | (~c1_1(a1108)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(467,plain,
% 0.92/1.13 (((~c1_1(a1108)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1108)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(468,axiom,((~c1_1(a1108)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.92/1.13 tff(469,plain,
% 0.92/1.13 ((~hskp9) | (~c1_1(a1108))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.92/1.13 tff(470,plain,
% 0.92/1.13 ((~hskp9) | (~c1_1(a1108))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[469, 466])).
% 0.92/1.13 tff(471,plain,
% 0.92/1.13 (~c1_1(a1108)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[470, 459])).
% 0.92/1.13 tff(472,plain,
% 0.92/1.13 (((~hskp9) | c0_1(a1108)) <=> ((~hskp9) | c0_1(a1108))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(473,axiom,((~hskp9) | c0_1(a1108)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.92/1.13 tff(474,plain,
% 0.92/1.13 ((~hskp9) | c0_1(a1108)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.92/1.13 tff(475,plain,
% 0.92/1.13 ((~hskp9) | c0_1(a1108)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[474, 472])).
% 0.92/1.13 tff(476,plain,
% 0.92/1.13 ((~hskp9) | c0_1(a1108)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[475, 472])).
% 0.92/1.13 tff(477,plain,
% 0.92/1.13 ((~hskp9) | c0_1(a1108)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[476, 472])).
% 0.92/1.13 tff(478,plain,
% 0.92/1.13 ((~hskp9) | c0_1(a1108)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[477, 472])).
% 0.92/1.13 tff(479,plain,
% 0.92/1.13 (c0_1(a1108)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[478, 459])).
% 0.92/1.13 tff(480,plain,
% 0.92/1.13 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(481,plain,
% 0.92/1.13 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[480])).
% 0.92/1.13 tff(482,plain,
% 0.92/1.13 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(483,plain,
% 0.92/1.13 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(484,plain,
% 0.92/1.13 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[483])).
% 0.92/1.14 tff(485,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.92/1.14 tff(486,plain,
% 0.92/1.14 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.92/1.14 tff(487,plain,
% 0.92/1.14 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[486, 482])).
% 0.92/1.14 tff(488,plain,(
% 0.92/1.14 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.92/1.14 inference(skolemize,[status(sab)],[487])).
% 0.92/1.14 tff(489,plain,
% 0.92/1.14 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[488, 481])).
% 0.92/1.14 tff(490,plain,
% 0.92/1.14 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(491,plain,
% 0.92/1.14 ((hskp7 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118)) <=> (hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(492,plain,
% 0.92/1.14 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118)))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[491])).
% 0.92/1.14 tff(493,plain,
% 0.92/1.14 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 0.92/1.14 inference(transitivity,[status(thm)],[492, 490])).
% 0.92/1.14 tff(494,plain,
% 0.92/1.14 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(495,plain,
% 0.92/1.14 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.92/1.14 tff(496,plain,
% 0.92/1.14 (hskp6 | c0_1(a1118)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[495, 110, 68, 167, 161, 489])).
% 0.92/1.14 tff(497,plain,
% 0.92/1.14 (hskp6),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[496, 352])).
% 0.92/1.14 tff(498,plain,
% 0.92/1.14 (((~hskp6) | (~c2_1(a1104))) <=> ((~hskp6) | (~c2_1(a1104)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(499,plain,
% 0.92/1.14 (((~c2_1(a1104)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a1104)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(500,axiom,((~c2_1(a1104)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.92/1.14 tff(501,plain,
% 0.92/1.14 ((~hskp6) | (~c2_1(a1104))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.92/1.14 tff(502,plain,
% 0.92/1.14 ((~hskp6) | (~c2_1(a1104))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[501, 498])).
% 0.92/1.14 tff(503,plain,
% 0.92/1.14 (~c2_1(a1104)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[502, 497])).
% 0.92/1.14 tff(504,plain,
% 0.92/1.14 (((~hskp6) | c0_1(a1104)) <=> ((~hskp6) | c0_1(a1104))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(505,axiom,((~hskp6) | c0_1(a1104)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.92/1.14 tff(506,plain,
% 0.92/1.14 ((~hskp6) | c0_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.92/1.14 tff(507,plain,
% 0.92/1.14 ((~hskp6) | c0_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[506, 504])).
% 0.92/1.14 tff(508,plain,
% 0.92/1.14 ((~hskp6) | c0_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[507, 504])).
% 0.92/1.14 tff(509,plain,
% 0.92/1.14 ((~hskp6) | c0_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[508, 504])).
% 0.92/1.14 tff(510,plain,
% 0.92/1.14 ((~hskp6) | c0_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[509, 504])).
% 0.92/1.14 tff(511,plain,
% 0.92/1.14 (c0_1(a1104)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[510, 497])).
% 0.92/1.14 tff(512,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(513,plain,
% 0.92/1.14 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | c3_1(a1104) | (~c0_1(a1104)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(514,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | c3_1(a1104) | (~c0_1(a1104)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118)))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[513])).
% 0.92/1.14 tff(515,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | c3_1(a1104) | (~c0_1(a1104)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118))),
% 0.92/1.14 inference(transitivity,[status(thm)],[514, 512])).
% 0.92/1.14 tff(516,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | c3_1(a1104) | (~c0_1(a1104)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(517,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.92/1.14 tff(518,plain,
% 0.92/1.14 (c3_1(a1104)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[517, 110, 206, 198, 190, 175, 511, 161, 503, 320, 352])).
% 0.92/1.14 tff(519,plain,
% 0.92/1.14 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(520,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[519])).
% 0.92/1.14 tff(521,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(522,plain,
% 0.92/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(523,plain,
% 0.92/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[522])).
% 0.92/1.14 tff(524,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.92/1.14 tff(525,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.92/1.14 tff(526,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[525, 521])).
% 0.92/1.14 tff(527,plain,(
% 0.92/1.14 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(skolemize,[status(sab)],[526])).
% 0.92/1.14 tff(528,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[527, 520])).
% 0.92/1.14 tff(529,plain,
% 0.92/1.14 (((~hskp6) | c1_1(a1104)) <=> ((~hskp6) | c1_1(a1104))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(530,axiom,((~hskp6) | c1_1(a1104)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.92/1.14 tff(531,plain,
% 0.92/1.14 ((~hskp6) | c1_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.92/1.14 tff(532,plain,
% 0.92/1.14 ((~hskp6) | c1_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[531, 529])).
% 0.92/1.14 tff(533,plain,
% 0.92/1.14 ((~hskp6) | c1_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[532, 529])).
% 0.92/1.14 tff(534,plain,
% 0.92/1.14 ((~hskp6) | c1_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[533, 529])).
% 0.92/1.14 tff(535,plain,
% 0.92/1.14 ((~hskp6) | c1_1(a1104)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[534, 529])).
% 0.92/1.14 tff(536,plain,
% 0.92/1.14 (c1_1(a1104)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[535, 497])).
% 0.92/1.14 tff(537,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(538,plain,
% 0.92/1.14 ((hskp28 | (~ndr1_0) | (~c1_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1104)) | c2_1(a1104) | (~c3_1(a1104)) | (~c1_1(a1104))) <=> (hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(539,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1104)) | c2_1(a1104) | (~c3_1(a1104)) | (~c1_1(a1104)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[538])).
% 0.92/1.14 tff(540,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1104)) | c2_1(a1104) | (~c3_1(a1104)) | (~c1_1(a1104)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[539, 537])).
% 0.92/1.14 tff(541,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1104)) | c2_1(a1104) | (~c3_1(a1104)) | (~c1_1(a1104)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(542,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.92/1.14 tff(543,plain,
% 0.92/1.14 (hskp28 | (~c3_1(a1104))),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[542, 110, 511, 536, 503, 528])).
% 0.92/1.14 tff(544,plain,
% 0.92/1.14 (hskp28),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[543, 518])).
% 0.92/1.14 tff(545,plain,
% 0.92/1.14 (((~hskp28) | c2_1(a1111)) <=> ((~hskp28) | c2_1(a1111))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(546,axiom,((~hskp28) | c2_1(a1111)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.92/1.14 tff(547,plain,
% 0.92/1.14 ((~hskp28) | c2_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.92/1.14 tff(548,plain,
% 0.92/1.14 ((~hskp28) | c2_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[547, 545])).
% 0.92/1.14 tff(549,plain,
% 0.92/1.14 ((~hskp28) | c2_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[548, 545])).
% 0.92/1.14 tff(550,plain,
% 0.92/1.14 ((~hskp28) | c2_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[549, 545])).
% 0.92/1.14 tff(551,plain,
% 0.92/1.14 ((~hskp28) | c2_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[550, 545])).
% 0.92/1.14 tff(552,plain,
% 0.92/1.14 (c2_1(a1111)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[551, 544])).
% 0.92/1.14 tff(553,plain,
% 0.92/1.14 (((~hskp28) | c1_1(a1111)) <=> ((~hskp28) | c1_1(a1111))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(554,axiom,((~hskp28) | c1_1(a1111)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.92/1.14 tff(555,plain,
% 0.92/1.14 ((~hskp28) | c1_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.92/1.14 tff(556,plain,
% 0.92/1.14 ((~hskp28) | c1_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[555, 553])).
% 0.92/1.14 tff(557,plain,
% 0.92/1.14 ((~hskp28) | c1_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[556, 553])).
% 0.92/1.14 tff(558,plain,
% 0.92/1.14 ((~hskp28) | c1_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[557, 553])).
% 0.92/1.14 tff(559,plain,
% 0.92/1.14 ((~hskp28) | c1_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[558, 553])).
% 0.92/1.14 tff(560,plain,
% 0.92/1.14 (c1_1(a1111)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[559, 544])).
% 0.92/1.14 tff(561,plain,
% 0.92/1.14 (((~hskp28) | c0_1(a1111)) <=> ((~hskp28) | c0_1(a1111))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(562,axiom,((~hskp28) | c0_1(a1111)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.92/1.14 tff(563,plain,
% 0.92/1.14 ((~hskp28) | c0_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.92/1.14 tff(564,plain,
% 0.92/1.14 ((~hskp28) | c0_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[563, 561])).
% 0.92/1.14 tff(565,plain,
% 0.92/1.14 ((~hskp28) | c0_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[564, 561])).
% 0.92/1.14 tff(566,plain,
% 0.92/1.14 ((~hskp28) | c0_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[565, 561])).
% 0.92/1.14 tff(567,plain,
% 0.92/1.14 ((~hskp28) | c0_1(a1111)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[566, 561])).
% 0.92/1.14 tff(568,plain,
% 0.92/1.14 (c0_1(a1111)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[567, 544])).
% 0.92/1.14 tff(569,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(570,plain,
% 0.92/1.14 (((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099))) <=> (c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(571,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[570])).
% 0.92/1.14 tff(572,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[571, 569])).
% 0.92/1.14 tff(573,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(574,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.92/1.14 tff(575,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[574, 110, 568, 560, 552, 479, 444, 436, 471, 465, 388, 57])).
% 0.92/1.14 tff(576,plain,(hskp7 | c1_1(a1098) | c3_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(577,plain,
% 0.92/1.14 (hskp7),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[576, 47, 34, 35])).
% 0.92/1.14 tff(578,plain,
% 0.92/1.14 (((~hskp7) | (~c1_1(a1105))) <=> ((~hskp7) | (~c1_1(a1105)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(579,plain,
% 0.92/1.14 (((~c1_1(a1105)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1105)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(580,axiom,((~c1_1(a1105)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.92/1.14 tff(581,plain,
% 0.92/1.14 ((~hskp7) | (~c1_1(a1105))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.92/1.14 tff(582,plain,
% 0.92/1.14 ((~hskp7) | (~c1_1(a1105))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[581, 578])).
% 0.92/1.14 tff(583,plain,
% 0.92/1.14 (~c1_1(a1105)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[582, 577])).
% 0.92/1.14 tff(584,assumption,(ndr1_0), introduced(assumption)).
% 0.92/1.14 tff(585,assumption,(hskp7), introduced(assumption)).
% 0.92/1.14 tff(586,plain,
% 0.92/1.14 (((~hskp7) | c0_1(a1105)) <=> ((~hskp7) | c0_1(a1105))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(587,axiom,((~hskp7) | c0_1(a1105)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.92/1.14 tff(588,plain,
% 0.92/1.14 ((~hskp7) | c0_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.92/1.14 tff(589,plain,
% 0.92/1.14 ((~hskp7) | c0_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[588, 586])).
% 0.92/1.14 tff(590,plain,
% 0.92/1.14 ((~hskp7) | c0_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[589, 586])).
% 0.92/1.14 tff(591,plain,
% 0.92/1.14 ((~hskp7) | c0_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[590, 586])).
% 0.92/1.14 tff(592,plain,
% 0.92/1.14 ((~hskp7) | c0_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[591, 586])).
% 0.92/1.14 tff(593,plain,
% 0.92/1.14 (c0_1(a1105)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[592, 585])).
% 0.92/1.14 tff(594,plain,
% 0.92/1.14 (((~hskp7) | c3_1(a1105)) <=> ((~hskp7) | c3_1(a1105))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(595,axiom,((~hskp7) | c3_1(a1105)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.92/1.14 tff(596,plain,
% 0.92/1.14 ((~hskp7) | c3_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.92/1.14 tff(597,plain,
% 0.92/1.14 ((~hskp7) | c3_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[596, 594])).
% 0.92/1.14 tff(598,plain,
% 0.92/1.14 ((~hskp7) | c3_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[597, 594])).
% 0.92/1.14 tff(599,plain,
% 0.92/1.14 ((~hskp7) | c3_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[598, 594])).
% 0.92/1.14 tff(600,plain,
% 0.92/1.14 ((~hskp7) | c3_1(a1105)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[599, 594])).
% 0.92/1.14 tff(601,plain,
% 0.92/1.14 (c3_1(a1105)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[600, 585])).
% 0.92/1.14 tff(602,plain,
% 0.92/1.14 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(603,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[602])).
% 0.92/1.14 tff(604,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(605,plain,
% 0.92/1.14 (^[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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(606,plain,
% 0.92/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[605])).
% 0.92/1.14 tff(607,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.92/1.14 tff(608,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.92/1.14 tff(609,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[608, 604])).
% 0.92/1.14 tff(610,plain,(
% 0.92/1.14 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.14 inference(skolemize,[status(sab)],[609])).
% 0.92/1.14 tff(611,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[610, 603])).
% 0.92/1.14 tff(612,assumption,(~c1_1(a1105)), introduced(assumption)).
% 0.92/1.14 tff(613,assumption,(~hskp30), introduced(assumption)).
% 0.92/1.14 tff(614,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(615,plain,
% 0.92/1.14 ((hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098)) <=> (hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(616,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[615])).
% 0.92/1.14 tff(617,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[616, 614])).
% 0.92/1.14 tff(618,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(619,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.92/1.14 tff(620,plain,
% 0.92/1.14 ((~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[619, 613, 612, 34, 35, 47, 611])).
% 0.92/1.14 tff(621,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[620, 601, 593, 584])).
% 0.92/1.14 tff(622,plain,((~hskp7) | (~ndr1_0) | hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(623,plain,
% 0.92/1.14 (hskp30),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[622, 577, 110, 583, 34, 35, 47])).
% 0.92/1.14 tff(624,plain,
% 0.92/1.14 (((~hskp30) | c1_1(a1136)) <=> ((~hskp30) | c1_1(a1136))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(625,axiom,((~hskp30) | c1_1(a1136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.92/1.14 tff(626,plain,
% 0.92/1.14 ((~hskp30) | c1_1(a1136)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.92/1.14 tff(627,plain,
% 0.92/1.14 ((~hskp30) | c1_1(a1136)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[626, 624])).
% 0.92/1.14 tff(628,plain,
% 0.92/1.14 ((~hskp30) | c1_1(a1136)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[627, 624])).
% 0.92/1.14 tff(629,plain,
% 0.92/1.14 ((~hskp30) | c1_1(a1136)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[628, 624])).
% 0.92/1.14 tff(630,plain,
% 0.92/1.14 ((~hskp30) | c1_1(a1136)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[629, 624])).
% 0.92/1.14 tff(631,plain,
% 0.92/1.14 (c1_1(a1136)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[630, 623])).
% 0.92/1.14 tff(632,assumption,(~hskp14), introduced(assumption)).
% 0.92/1.15 tff(633,plain,
% 0.92/1.15 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(634,plain,
% 0.92/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[633])).
% 0.92/1.15 tff(635,plain,
% 0.92/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(636,plain,
% 0.92/1.15 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(637,plain,
% 0.92/1.15 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[636])).
% 0.92/1.15 tff(638,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.92/1.15 tff(639,plain,
% 0.92/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.92/1.15 tff(640,plain,
% 0.92/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[639, 635])).
% 0.92/1.15 tff(641,plain,(
% 0.92/1.15 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.15 inference(skolemize,[status(sab)],[640])).
% 0.92/1.15 tff(642,plain,
% 0.92/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[641, 634])).
% 0.92/1.15 tff(643,assumption,(~hskp20), introduced(assumption)).
% 0.92/1.15 tff(644,assumption,(~hskp19), introduced(assumption)).
% 0.92/1.15 tff(645,plain,
% 0.92/1.15 (^[U: $i] : refl((hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(646,plain,
% 0.92/1.15 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[645])).
% 0.92/1.15 tff(647,plain,
% 0.92/1.15 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(648,plain,
% 0.92/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp14) <=> ((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp14))), rewrite(((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp14) <=> (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(649,plain,
% 0.92/1.15 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp14) <=> ![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[648])).
% 0.92/1.15 tff(650,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.92/1.15 tff(651,plain,
% 0.92/1.15 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.92/1.15 tff(652,plain,
% 0.92/1.15 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[651, 647])).
% 0.92/1.15 tff(653,plain,(
% 0.92/1.15 ![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/1.15 inference(skolemize,[status(sab)],[652])).
% 0.92/1.15 tff(654,plain,
% 0.92/1.15 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[653, 646])).
% 0.92/1.15 tff(655,plain,
% 0.92/1.15 (c3_1(a1105)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[600, 577])).
% 0.92/1.15 tff(656,plain,
% 0.92/1.15 (c0_1(a1105)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[592, 577])).
% 0.92/1.15 tff(657,plain,
% 0.92/1.15 (((~hskp30) | c3_1(a1136)) <=> ((~hskp30) | c3_1(a1136))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(658,axiom,((~hskp30) | c3_1(a1136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.92/1.15 tff(659,plain,
% 0.92/1.15 ((~hskp30) | c3_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.92/1.15 tff(660,plain,
% 0.92/1.15 ((~hskp30) | c3_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[659, 657])).
% 0.92/1.15 tff(661,plain,
% 0.92/1.15 ((~hskp30) | c3_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[660, 657])).
% 0.92/1.15 tff(662,plain,
% 0.92/1.15 ((~hskp30) | c3_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[661, 657])).
% 0.92/1.15 tff(663,plain,
% 0.92/1.15 ((~hskp30) | c3_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[662, 657])).
% 0.92/1.15 tff(664,plain,
% 0.92/1.15 (c3_1(a1136)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[663, 623])).
% 0.92/1.15 tff(665,plain,
% 0.92/1.15 (((~hskp30) | c2_1(a1136)) <=> ((~hskp30) | c2_1(a1136))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(666,axiom,((~hskp30) | c2_1(a1136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.92/1.15 tff(667,plain,
% 0.92/1.15 ((~hskp30) | c2_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.92/1.15 tff(668,plain,
% 0.92/1.15 ((~hskp30) | c2_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[667, 665])).
% 0.92/1.15 tff(669,plain,
% 0.92/1.15 ((~hskp30) | c2_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[668, 665])).
% 0.92/1.15 tff(670,plain,
% 0.92/1.15 ((~hskp30) | c2_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[669, 665])).
% 0.92/1.15 tff(671,plain,
% 0.92/1.15 ((~hskp30) | c2_1(a1136)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[670, 665])).
% 0.92/1.15 tff(672,plain,
% 0.92/1.15 (c2_1(a1136)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[671, 623])).
% 0.92/1.15 tff(673,assumption,(c3_1(a1136)), introduced(assumption)).
% 0.92/1.15 tff(674,plain,
% 0.92/1.15 ((hskp23 | hskp14) <=> (hskp23 | hskp14)),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(675,axiom,(hskp23 | hskp14), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.92/1.15 tff(676,plain,
% 0.92/1.15 (hskp23 | hskp14),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.92/1.15 tff(677,plain,
% 0.92/1.15 (hskp23 | hskp14),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[676, 674])).
% 0.92/1.15 tff(678,plain,
% 0.92/1.15 (hskp23 | hskp14),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[677, 674])).
% 0.92/1.15 tff(679,plain,
% 0.92/1.15 (hskp23 | hskp14),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[678, 674])).
% 0.92/1.15 tff(680,plain,
% 0.92/1.15 (hskp23 | hskp14),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[679, 674])).
% 0.92/1.15 tff(681,plain,
% 0.92/1.15 (hskp23),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[680, 632])).
% 0.92/1.15 tff(682,plain,
% 0.92/1.15 (((~hskp23) | (~c3_1(a1147))) <=> ((~hskp23) | (~c3_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(683,plain,
% 0.92/1.15 (((~c3_1(a1147)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(684,axiom,((~c3_1(a1147)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.92/1.15 tff(685,plain,
% 0.92/1.15 ((~hskp23) | (~c3_1(a1147))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.92/1.15 tff(686,plain,
% 0.92/1.15 ((~hskp23) | (~c3_1(a1147))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[685, 682])).
% 0.92/1.15 tff(687,plain,
% 0.92/1.15 (~c3_1(a1147)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[686, 681])).
% 0.92/1.15 tff(688,plain,
% 0.92/1.15 (((~hskp23) | c0_1(a1147)) <=> ((~hskp23) | c0_1(a1147))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(689,axiom,((~hskp23) | c0_1(a1147)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.92/1.15 tff(690,plain,
% 0.92/1.15 ((~hskp23) | c0_1(a1147)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.92/1.15 tff(691,plain,
% 0.92/1.15 ((~hskp23) | c0_1(a1147)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[690, 688])).
% 0.92/1.15 tff(692,plain,
% 0.92/1.15 ((~hskp23) | c0_1(a1147)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[691, 688])).
% 0.92/1.15 tff(693,plain,
% 0.92/1.15 ((~hskp23) | c0_1(a1147)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[692, 688])).
% 0.92/1.15 tff(694,plain,
% 0.92/1.15 ((~hskp23) | c0_1(a1147)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[693, 688])).
% 0.92/1.15 tff(695,plain,
% 0.92/1.15 (c0_1(a1147)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[694, 681])).
% 0.92/1.15 tff(696,assumption,(c2_1(a1136)), introduced(assumption)).
% 0.92/1.15 tff(697,assumption,(c1_1(a1136)), introduced(assumption)).
% 0.92/1.15 tff(698,assumption,(~hskp29), introduced(assumption)).
% 0.92/1.15 tff(699,assumption,(~c3_1(a1147)), introduced(assumption)).
% 0.92/1.15 tff(700,assumption,(c0_1(a1147)), introduced(assumption)).
% 0.92/1.15 tff(701,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(702,plain,
% 0.92/1.15 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136))) <=> (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(703,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[702])).
% 0.92/1.15 tff(704,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[703, 701])).
% 0.92/1.15 tff(705,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(706,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.92/1.15 tff(707,plain,
% 0.92/1.15 (~c1_1(a1147)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[706, 110, 697, 696, 673, 700, 699, 45, 46])).
% 0.92/1.15 tff(708,plain,
% 0.92/1.15 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(709,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[708])).
% 0.92/1.15 tff(710,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(711,plain,
% 0.92/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(712,plain,
% 0.92/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[711])).
% 0.92/1.15 tff(713,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.92/1.15 tff(714,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.92/1.15 tff(715,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[714, 710])).
% 0.92/1.15 tff(716,plain,(
% 0.92/1.15 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.92/1.15 inference(skolemize,[status(sab)],[715])).
% 0.92/1.15 tff(717,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[716, 709])).
% 0.92/1.15 tff(718,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(719,plain,
% 0.92/1.15 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136))) <=> (hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(720,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[719])).
% 0.92/1.15 tff(721,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[720, 718])).
% 0.92/1.15 tff(722,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(723,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.92/1.15 tff(724,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[723, 110, 698, 697, 696, 700, 699, 717, 46, 707])).
% 0.92/1.15 tff(725,plain,(c0_1(a1136) | hskp29 | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1147)) | c3_1(a1147) | (~c3_1(a1136))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.15 tff(726,plain,
% 0.92/1.15 (c0_1(a1136)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[725, 698, 697, 696, 695, 687, 673])).
% 0.92/1.15 tff(727,plain,
% 0.92/1.15 (((~hskp23) | (~c2_1(a1147))) <=> ((~hskp23) | (~c2_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(728,plain,
% 0.92/1.15 (((~c2_1(a1147)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(729,axiom,((~c2_1(a1147)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.92/1.15 tff(730,plain,
% 0.92/1.15 ((~hskp23) | (~c2_1(a1147))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.92/1.15 tff(731,plain,
% 0.92/1.15 ((~hskp23) | (~c2_1(a1147))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[730, 727])).
% 0.92/1.15 tff(732,plain,
% 0.92/1.15 (~c2_1(a1147)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[731, 681])).
% 0.92/1.15 tff(733,assumption,(c0_1(a1136)), introduced(assumption)).
% 0.92/1.15 tff(734,assumption,(hskp21), introduced(assumption)).
% 0.92/1.15 tff(735,plain,
% 0.92/1.15 (((~hskp21) | (~c3_1(a1131))) <=> ((~hskp21) | (~c3_1(a1131)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(736,plain,
% 0.92/1.15 (((~c3_1(a1131)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a1131)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(737,axiom,((~c3_1(a1131)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.92/1.15 tff(738,plain,
% 0.92/1.15 ((~hskp21) | (~c3_1(a1131))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.92/1.15 tff(739,plain,
% 0.92/1.15 ((~hskp21) | (~c3_1(a1131))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[738, 735])).
% 0.92/1.15 tff(740,plain,
% 0.92/1.15 (~c3_1(a1131)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[739, 734])).
% 0.92/1.15 tff(741,plain,
% 0.92/1.15 (((~hskp21) | (~c0_1(a1131))) <=> ((~hskp21) | (~c0_1(a1131)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(742,plain,
% 0.92/1.15 (((~c0_1(a1131)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1131)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(743,axiom,((~c0_1(a1131)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.92/1.15 tff(744,plain,
% 0.92/1.15 ((~hskp21) | (~c0_1(a1131))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.92/1.15 tff(745,plain,
% 0.92/1.15 ((~hskp21) | (~c0_1(a1131))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[744, 741])).
% 0.92/1.15 tff(746,plain,
% 0.92/1.15 (~c0_1(a1131)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[745, 734])).
% 0.92/1.15 tff(747,assumption,(~c2_1(a1147)), introduced(assumption)).
% 0.92/1.15 tff(748,plain,
% 0.92/1.15 (((~hskp21) | c1_1(a1131)) <=> ((~hskp21) | c1_1(a1131))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(749,axiom,((~hskp21) | c1_1(a1131)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.92/1.15 tff(750,plain,
% 0.92/1.15 ((~hskp21) | c1_1(a1131)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.92/1.15 tff(751,plain,
% 0.92/1.15 ((~hskp21) | c1_1(a1131)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[750, 748])).
% 0.92/1.15 tff(752,plain,
% 0.92/1.15 ((~hskp21) | c1_1(a1131)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[751, 748])).
% 0.92/1.15 tff(753,plain,
% 0.92/1.15 ((~hskp21) | c1_1(a1131)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[752, 748])).
% 0.92/1.15 tff(754,plain,
% 0.92/1.15 ((~hskp21) | c1_1(a1131)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[753, 748])).
% 0.92/1.15 tff(755,plain,
% 0.92/1.15 (c1_1(a1131)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[754, 734])).
% 0.92/1.15 tff(756,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(757,plain,
% 0.92/1.15 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(758,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[757])).
% 0.92/1.15 tff(759,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[758, 756])).
% 0.92/1.15 tff(760,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(761,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.92/1.15 tff(762,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[761, 110, 696, 673, 700, 755, 747, 699, 746, 740, 320, 733])).
% 0.92/1.15 tff(763,plain,((~hskp21) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1136))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.15 tff(764,plain,
% 0.92/1.15 (~hskp21),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[763, 726, 673, 695, 732, 687, 696])).
% 0.92/1.15 tff(765,assumption,(~hskp6), introduced(assumption)).
% 0.92/1.15 tff(766,assumption,(~hskp21), introduced(assumption)).
% 0.92/1.15 tff(767,plain,
% 0.92/1.15 ((hskp24 | hskp21 | hskp6) <=> (hskp24 | hskp21 | hskp6)),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(768,plain,
% 0.92/1.15 (((hskp21 | hskp6) | hskp24) <=> (hskp24 | hskp21 | hskp6)),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(769,plain,
% 0.92/1.15 ((hskp6 | hskp21) <=> (hskp21 | hskp6)),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(770,plain,
% 0.92/1.15 (((hskp6 | hskp21) | hskp24) <=> ((hskp21 | hskp6) | hskp24)),
% 0.92/1.15 inference(monotonicity,[status(thm)],[769])).
% 0.92/1.15 tff(771,plain,
% 0.92/1.15 (((hskp6 | hskp21) | hskp24) <=> (hskp24 | hskp21 | hskp6)),
% 0.92/1.15 inference(transitivity,[status(thm)],[770, 768])).
% 0.92/1.15 tff(772,axiom,((hskp6 | hskp21) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.92/1.15 tff(773,plain,
% 0.92/1.15 (hskp24 | hskp21 | hskp6),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[772, 771])).
% 0.92/1.15 tff(774,plain,
% 0.92/1.15 (hskp24 | hskp21 | hskp6),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[773, 767])).
% 0.92/1.15 tff(775,plain,
% 0.92/1.15 (hskp24 | hskp21 | hskp6),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[774, 767])).
% 0.92/1.15 tff(776,plain,
% 0.92/1.15 (hskp24 | hskp21 | hskp6),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[775, 767])).
% 0.92/1.15 tff(777,plain,
% 0.92/1.15 (hskp24 | hskp21 | hskp6),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[776, 767])).
% 0.92/1.15 tff(778,plain,
% 0.92/1.15 (hskp24),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[777, 766, 765])).
% 0.92/1.15 tff(779,plain,
% 0.92/1.15 (((~hskp24) | (~c0_1(a1149))) <=> ((~hskp24) | (~c0_1(a1149)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(780,plain,
% 0.92/1.15 (((~c0_1(a1149)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a1149)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(781,axiom,((~c0_1(a1149)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.92/1.15 tff(782,plain,
% 0.92/1.15 ((~hskp24) | (~c0_1(a1149))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.92/1.15 tff(783,plain,
% 0.92/1.15 ((~hskp24) | (~c0_1(a1149))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[782, 779])).
% 0.92/1.15 tff(784,plain,
% 0.92/1.15 (~c0_1(a1149)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[783, 778])).
% 0.92/1.15 tff(785,plain,
% 0.92/1.15 (((~hskp24) | c3_1(a1149)) <=> ((~hskp24) | c3_1(a1149))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(786,axiom,((~hskp24) | c3_1(a1149)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.92/1.15 tff(787,plain,
% 0.92/1.15 ((~hskp24) | c3_1(a1149)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.92/1.15 tff(788,plain,
% 0.92/1.15 ((~hskp24) | c3_1(a1149)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[787, 785])).
% 0.92/1.15 tff(789,plain,
% 0.92/1.15 ((~hskp24) | c3_1(a1149)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[788, 785])).
% 0.92/1.16 tff(790,plain,
% 0.92/1.16 ((~hskp24) | c3_1(a1149)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[789, 785])).
% 0.92/1.16 tff(791,plain,
% 0.92/1.16 ((~hskp24) | c3_1(a1149)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[790, 785])).
% 0.92/1.16 tff(792,plain,
% 0.92/1.16 (c3_1(a1149)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[791, 778])).
% 0.92/1.16 tff(793,plain,
% 0.92/1.16 (((~hskp24) | c2_1(a1149)) <=> ((~hskp24) | c2_1(a1149))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(794,axiom,((~hskp24) | c2_1(a1149)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.92/1.16 tff(795,plain,
% 0.92/1.16 ((~hskp24) | c2_1(a1149)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.92/1.16 tff(796,plain,
% 0.92/1.16 ((~hskp24) | c2_1(a1149)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[795, 793])).
% 0.92/1.16 tff(797,plain,
% 0.92/1.16 ((~hskp24) | c2_1(a1149)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[796, 793])).
% 0.92/1.16 tff(798,plain,
% 0.92/1.16 ((~hskp24) | c2_1(a1149)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[797, 793])).
% 0.92/1.16 tff(799,plain,
% 0.92/1.16 ((~hskp24) | c2_1(a1149)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[798, 793])).
% 0.92/1.16 tff(800,plain,
% 0.92/1.16 (c2_1(a1149)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[799, 778])).
% 0.92/1.16 tff(801,plain,
% 0.92/1.16 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(802,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[801])).
% 0.92/1.16 tff(803,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(804,plain,
% 0.92/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(805,plain,
% 0.92/1.16 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[804])).
% 0.92/1.16 tff(806,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.92/1.16 tff(807,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[806, 805])).
% 0.92/1.16 tff(808,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[807, 803])).
% 0.92/1.16 tff(809,plain,(
% 0.92/1.16 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.16 inference(skolemize,[status(sab)],[808])).
% 0.92/1.16 tff(810,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[809, 802])).
% 0.92/1.16 tff(811,assumption,(hskp19), introduced(assumption)).
% 0.92/1.16 tff(812,plain,
% 0.92/1.16 (((~hskp19) | (~c2_1(a1127))) <=> ((~hskp19) | (~c2_1(a1127)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(813,plain,
% 0.92/1.16 (((~c2_1(a1127)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1127)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(814,axiom,((~c2_1(a1127)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.92/1.16 tff(815,plain,
% 0.92/1.16 ((~hskp19) | (~c2_1(a1127))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[814, 813])).
% 0.92/1.16 tff(816,plain,
% 0.92/1.16 ((~hskp19) | (~c2_1(a1127))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[815, 812])).
% 0.92/1.16 tff(817,plain,
% 0.92/1.16 (~c2_1(a1127)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[816, 811])).
% 0.92/1.16 tff(818,assumption,(~c0_1(a1149)), introduced(assumption)).
% 0.92/1.16 tff(819,plain,
% 0.92/1.16 (((~hskp19) | c3_1(a1127)) <=> ((~hskp19) | c3_1(a1127))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(820,axiom,((~hskp19) | c3_1(a1127)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.92/1.16 tff(821,plain,
% 0.92/1.16 ((~hskp19) | c3_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[820, 819])).
% 0.92/1.16 tff(822,plain,
% 0.92/1.16 ((~hskp19) | c3_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[821, 819])).
% 0.92/1.16 tff(823,plain,
% 0.92/1.16 ((~hskp19) | c3_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[822, 819])).
% 0.92/1.16 tff(824,plain,
% 0.92/1.16 ((~hskp19) | c3_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[823, 819])).
% 0.92/1.16 tff(825,plain,
% 0.92/1.16 ((~hskp19) | c3_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[824, 819])).
% 0.92/1.16 tff(826,plain,
% 0.92/1.16 (c3_1(a1127)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[825, 811])).
% 0.92/1.16 tff(827,plain,
% 0.92/1.16 (((~hskp19) | c1_1(a1127)) <=> ((~hskp19) | c1_1(a1127))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(828,axiom,((~hskp19) | c1_1(a1127)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.92/1.16 tff(829,plain,
% 0.92/1.16 ((~hskp19) | c1_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[828, 827])).
% 0.92/1.16 tff(830,plain,
% 0.92/1.16 ((~hskp19) | c1_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[829, 827])).
% 0.92/1.16 tff(831,plain,
% 0.92/1.16 ((~hskp19) | c1_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[830, 827])).
% 0.92/1.16 tff(832,plain,
% 0.92/1.16 ((~hskp19) | c1_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[831, 827])).
% 0.92/1.16 tff(833,plain,
% 0.92/1.16 ((~hskp19) | c1_1(a1127)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[832, 827])).
% 0.92/1.16 tff(834,plain,
% 0.92/1.16 (c1_1(a1127)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[833, 811])).
% 0.92/1.16 tff(835,assumption,(c3_1(a1149)), introduced(assumption)).
% 0.92/1.16 tff(836,assumption,(c2_1(a1149)), introduced(assumption)).
% 0.92/1.16 tff(837,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(838,plain,
% 0.92/1.16 ((hskp21 | (~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)) | c0_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149))) <=> (hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(839,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)) | c0_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[838])).
% 0.92/1.16 tff(840,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)) | c0_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[839, 837])).
% 0.92/1.16 tff(841,plain,
% 0.92/1.16 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)) | c0_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(842,plain,
% 0.92/1.16 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.92/1.16 tff(843,plain,
% 0.92/1.16 ($false),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[842, 110, 766, 836, 835, 834, 826, 818, 817, 810])).
% 0.92/1.16 tff(844,plain,((~hskp19) | hskp21 | (~c2_1(a1149)) | (~c3_1(a1149)) | c0_1(a1149)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.16 tff(845,plain,
% 0.92/1.16 (~hskp19),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[844, 766, 800, 792, 784])).
% 0.92/1.16 tff(846,plain,
% 0.92/1.16 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(847,plain,
% 0.92/1.16 ((hskp14 | hskp19 | (~ndr1_0) | c1_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149))) <=> (hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(848,plain,
% 0.92/1.16 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[847])).
% 0.92/1.16 tff(849,plain,
% 0.92/1.16 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[848, 846])).
% 0.92/1.16 tff(850,plain,
% 0.92/1.16 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(851,plain,
% 0.92/1.16 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.92/1.16 tff(852,plain,
% 0.92/1.16 (hskp19 | c1_1(a1149)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[851, 632, 110, 800, 792, 654])).
% 0.92/1.16 tff(853,plain,
% 0.92/1.16 (c1_1(a1149)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[852, 845])).
% 0.92/1.16 tff(854,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(855,plain,
% 0.92/1.16 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149))) <=> (c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(856,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[855])).
% 0.92/1.16 tff(857,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[856, 854])).
% 0.92/1.16 tff(858,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(859,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[858, 857])).
% 0.92/1.16 tff(860,plain,
% 0.92/1.16 ((~c1_1(a1147)) | (~c1_1(a1149))),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[859, 110, 697, 696, 673, 792, 695, 784, 687, 45])).
% 0.92/1.16 tff(861,plain,
% 0.92/1.16 (~c1_1(a1147)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[860, 853])).
% 0.92/1.16 tff(862,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(863,plain,
% 0.92/1.16 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c2_1(a1149))) <=> (hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(864,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c2_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[863])).
% 0.92/1.16 tff(865,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c2_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[864, 862])).
% 0.92/1.16 tff(866,plain,
% 0.92/1.16 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c2_1(a1149)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(867,plain,
% 0.92/1.16 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.92/1.16 tff(868,plain,
% 0.92/1.16 (c1_1(a1147) | (~c1_1(a1149))),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[867, 110, 698, 800, 695, 784, 687, 717])).
% 0.92/1.16 tff(869,plain,
% 0.92/1.16 ($false),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[868, 861, 853])).
% 0.92/1.16 tff(870,plain,(hskp21 | hskp29 | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | hskp14 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.92/1.16 tff(871,plain,
% 0.92/1.16 (hskp6),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[870, 764, 697, 696, 673, 632, 698])).
% 0.92/1.16 tff(872,plain,
% 0.92/1.16 (~c2_1(a1104)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[502, 871])).
% 0.92/1.16 tff(873,plain,
% 0.92/1.16 (c1_1(a1104)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[535, 871])).
% 0.92/1.16 tff(874,plain,
% 0.92/1.16 (c0_1(a1104)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[510, 871])).
% 0.92/1.16 tff(875,assumption,(c3_1(a1105)), introduced(assumption)).
% 0.92/1.16 tff(876,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(877,plain,
% 0.92/1.16 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(878,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[877])).
% 0.92/1.16 tff(879,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[878, 876])).
% 0.92/1.16 tff(880,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(881,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.92/1.16 tff(882,plain,
% 0.92/1.16 (c2_1(a1105)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[881, 110, 696, 673, 875, 874, 873, 612, 872, 228, 726])).
% 0.92/1.16 tff(883,plain,
% 0.92/1.16 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(884,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[883])).
% 0.92/1.16 tff(885,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(886,plain,
% 0.92/1.16 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_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) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_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) | (~c1_1(U)) | (~c2_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)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(887,plain,
% 0.92/1.16 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[886])).
% 0.92/1.16 tff(888,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.92/1.16 tff(889,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.92/1.16 tff(890,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[889, 885])).
% 0.92/1.16 tff(891,plain,(
% 0.92/1.16 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.16 inference(skolemize,[status(sab)],[890])).
% 0.92/1.16 tff(892,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[891, 884])).
% 0.92/1.16 tff(893,plain,
% 0.92/1.16 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(894,plain,
% 0.92/1.16 ((hskp14 | hskp19 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(895,plain,
% 0.92/1.16 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[894])).
% 0.92/1.16 tff(896,plain,
% 0.92/1.16 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[895, 893])).
% 0.92/1.16 tff(897,plain,
% 0.92/1.16 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(898,plain,
% 0.92/1.16 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.92/1.16 tff(899,plain,
% 0.92/1.16 (hskp14 | hskp19 | (~c2_1(a1105))),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[898, 110, 875, 612, 654])).
% 0.92/1.16 tff(900,plain,
% 0.92/1.16 (hskp19),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[899, 882, 632])).
% 0.92/1.16 tff(901,plain,
% 0.92/1.16 (~c2_1(a1127)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[816, 900])).
% 0.92/1.17 tff(902,assumption,(c0_1(a1105)), introduced(assumption)).
% 0.92/1.17 tff(903,plain,
% 0.92/1.17 (c3_1(a1127)),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[825, 900])).
% 0.92/1.17 tff(904,plain,
% 0.92/1.17 (c1_1(a1127)),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[833, 900])).
% 0.92/1.17 tff(905,assumption,(c2_1(a1105)), introduced(assumption)).
% 0.92/1.17 tff(906,plain,
% 0.92/1.17 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.92/1.17 inference(bind,[status(th)],[])).
% 0.92/1.17 tff(907,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.17 inference(quant_intro,[status(thm)],[906])).
% 0.92/1.17 tff(908,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(909,plain,
% 0.92/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.92/1.17 inference(bind,[status(th)],[])).
% 0.92/1.17 tff(910,plain,
% 0.92/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.17 inference(quant_intro,[status(thm)],[909])).
% 0.92/1.17 tff(911,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.92/1.17 tff(912,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[911, 910])).
% 0.92/1.17 tff(913,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[912, 908])).
% 0.92/1.17 tff(914,plain,(
% 0.92/1.17 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.17 inference(skolemize,[status(sab)],[913])).
% 0.92/1.17 tff(915,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[914, 907])).
% 0.92/1.17 tff(916,assumption,(~c2_1(a1127)), introduced(assumption)).
% 0.92/1.17 tff(917,assumption,(c3_1(a1127)), introduced(assumption)).
% 0.92/1.17 tff(918,plain,
% 0.92/1.17 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(919,plain,
% 0.92/1.17 ((hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105))) <=> (hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(920,plain,
% 0.92/1.17 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 0.92/1.17 inference(monotonicity,[status(thm)],[919])).
% 0.92/1.17 tff(921,plain,
% 0.92/1.17 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 0.92/1.17 inference(transitivity,[status(thm)],[920, 918])).
% 0.92/1.17 tff(922,plain,
% 0.92/1.17 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))),
% 0.92/1.17 inference(quant_inst,[status(thm)],[])).
% 0.92/1.17 tff(923,plain,
% 0.92/1.17 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[922, 921])).
% 0.92/1.17 tff(924,plain,
% 0.92/1.17 (hskp20 | (~c0_1(a1127))),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[923, 110, 917, 902, 916, 612, 915, 905])).
% 0.92/1.17 tff(925,plain,
% 0.92/1.17 (~c0_1(a1127)),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[924, 643])).
% 0.92/1.17 tff(926,assumption,(~c2_1(a1104)), introduced(assumption)).
% 0.92/1.17 tff(927,assumption,(c0_1(a1104)), introduced(assumption)).
% 0.92/1.17 tff(928,plain,
% 0.92/1.17 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(929,plain,
% 0.92/1.17 ((hskp20 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105))) <=> (hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(930,plain,
% 0.92/1.17 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105))))),
% 0.92/1.17 inference(monotonicity,[status(thm)],[929])).
% 0.92/1.17 tff(931,plain,
% 0.92/1.17 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 0.92/1.17 inference(transitivity,[status(thm)],[930, 928])).
% 0.92/1.17 tff(932,plain,
% 0.92/1.17 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))),
% 0.92/1.17 inference(quant_inst,[status(thm)],[])).
% 0.92/1.17 tff(933,plain,
% 0.92/1.17 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[932, 931])).
% 0.92/1.17 tff(934,plain,
% 0.92/1.17 (hskp20 | (~c3_1(a1104))),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[933, 110, 902, 927, 612, 926, 915, 905])).
% 0.92/1.17 tff(935,plain,
% 0.92/1.17 (~c3_1(a1104)),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[934, 643])).
% 0.92/1.17 tff(936,assumption,(c1_1(a1104)), introduced(assumption)).
% 0.92/1.17 tff(937,assumption,(c1_1(a1127)), introduced(assumption)).
% 0.92/1.17 tff(938,plain,
% 0.92/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(939,plain,
% 0.92/1.17 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c0_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127))) <=> ((~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(940,plain,
% 0.92/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c0_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))))),
% 0.92/1.17 inference(monotonicity,[status(thm)],[939])).
% 0.92/1.17 tff(941,plain,
% 0.92/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c0_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 0.92/1.17 inference(transitivity,[status(thm)],[940, 938])).
% 0.92/1.17 tff(942,plain,
% 0.92/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c0_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 0.92/1.17 inference(quant_inst,[status(thm)],[])).
% 0.92/1.17 tff(943,plain,
% 0.92/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[942, 941])).
% 0.92/1.17 tff(944,plain,
% 0.92/1.17 ($false),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[943, 110, 697, 696, 673, 937, 917, 927, 936, 45, 935, 925])).
% 0.92/1.17 tff(945,plain,(hskp20 | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1104)) | (~c1_1(a1104)) | (~c0_1(a1105)) | c2_1(a1127) | c1_1(a1105) | (~c2_1(a1105)) | c2_1(a1104)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.17 tff(946,plain,
% 0.92/1.17 (hskp20),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[945, 904, 696, 673, 697, 903, 874, 873, 902, 901, 612, 882, 872])).
% 0.92/1.17 tff(947,plain,
% 0.92/1.17 (~c3_1(a1130)),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[308, 946])).
% 0.92/1.17 tff(948,plain,
% 0.92/1.17 (~c0_1(a1130)),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[302, 946])).
% 0.92/1.17 tff(949,plain,
% 0.92/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(950,plain,
% 0.92/1.17 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(951,plain,
% 0.92/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147))))),
% 0.92/1.17 inference(monotonicity,[status(thm)],[950])).
% 0.92/1.17 tff(952,plain,
% 0.92/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 0.92/1.17 inference(transitivity,[status(thm)],[951, 949])).
% 0.92/1.17 tff(953,plain,
% 0.92/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 0.92/1.17 inference(quant_inst,[status(thm)],[])).
% 0.92/1.17 tff(954,plain,
% 0.92/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.92/1.17 tff(955,plain,
% 0.92/1.17 (~c1_1(a1130)),
% 0.92/1.17 inference(unit_resolution,[status(thm)],[954, 110, 696, 673, 695, 732, 687, 948, 947, 320, 726])).
% 0.92/1.17 tff(956,plain,
% 0.92/1.17 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.92/1.17 inference(bind,[status(th)],[])).
% 0.92/1.17 tff(957,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.17 inference(quant_intro,[status(thm)],[956])).
% 0.92/1.17 tff(958,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(959,plain,
% 0.92/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~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)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~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)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | 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)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.92/1.17 inference(bind,[status(th)],[])).
% 0.92/1.17 tff(960,plain,
% 0.92/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.17 inference(quant_intro,[status(thm)],[959])).
% 0.92/1.17 tff(961,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.92/1.17 tff(962,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.92/1.17 tff(963,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[962, 958])).
% 0.92/1.17 tff(964,plain,(
% 0.92/1.17 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.17 inference(skolemize,[status(sab)],[963])).
% 0.92/1.17 tff(965,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[964, 957])).
% 0.92/1.17 tff(966,plain,
% 0.92/1.17 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.92/1.17 inference(bind,[status(th)],[])).
% 0.92/1.17 tff(967,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.17 inference(quant_intro,[status(thm)],[966])).
% 0.92/1.17 tff(968,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(969,plain,
% 0.92/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.92/1.17 inference(bind,[status(th)],[])).
% 0.92/1.17 tff(970,plain,
% 0.92/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.17 inference(quant_intro,[status(thm)],[969])).
% 0.92/1.17 tff(971,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.92/1.17 tff(972,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.92/1.17 tff(973,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[972, 968])).
% 0.92/1.17 tff(974,plain,(
% 0.92/1.17 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.17 inference(skolemize,[status(sab)],[973])).
% 0.92/1.17 tff(975,plain,
% 0.92/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.92/1.17 inference(modus_ponens,[status(thm)],[974, 967])).
% 0.92/1.17 tff(976,plain,
% 0.92/1.17 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(977,plain,
% 0.92/1.17 ((hskp2 | (~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.17 inference(rewrite,[status(thm)],[])).
% 0.92/1.17 tff(978,plain,
% 0.92/1.17 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 0.92/1.18 inference(monotonicity,[status(thm)],[977])).
% 0.92/1.18 tff(979,plain,
% 0.92/1.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 0.92/1.18 inference(transitivity,[status(thm)],[978, 976])).
% 0.92/1.18 tff(980,plain,
% 0.92/1.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 0.92/1.18 inference(quant_inst,[status(thm)],[])).
% 0.92/1.18 tff(981,plain,
% 0.92/1.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.92/1.18 tff(982,plain,
% 0.92/1.18 (hskp2 | (~c2_1(a1105))),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[981, 110, 902, 875, 612, 975])).
% 0.92/1.18 tff(983,plain,
% 0.92/1.18 (hskp2),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[982, 882])).
% 0.92/1.18 tff(984,plain,
% 0.92/1.18 (~c3_1(a1100)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[273, 983])).
% 0.92/1.18 tff(985,plain,
% 0.92/1.18 (c2_1(a1100)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[281, 983])).
% 0.92/1.18 tff(986,plain,
% 0.92/1.18 (c0_1(a1100)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[289, 983])).
% 0.92/1.18 tff(987,plain,
% 0.92/1.18 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(988,plain,
% 0.92/1.18 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(989,plain,
% 0.92/1.18 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130)))),
% 0.92/1.18 inference(monotonicity,[status(thm)],[988])).
% 0.92/1.18 tff(990,plain,
% 0.92/1.18 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130))),
% 0.92/1.18 inference(transitivity,[status(thm)],[989, 987])).
% 0.92/1.18 tff(991,plain,
% 0.92/1.18 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 0.92/1.18 inference(quant_inst,[status(thm)],[])).
% 0.92/1.18 tff(992,plain,
% 0.92/1.18 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[991, 990])).
% 0.92/1.18 tff(993,plain,
% 0.92/1.18 (hskp3),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[992, 110, 986, 985, 948, 947, 984, 965, 955])).
% 0.92/1.18 tff(994,plain,
% 0.92/1.18 (((~hskp3) | (~c3_1(a1101))) <=> ((~hskp3) | (~c3_1(a1101)))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(995,plain,
% 0.92/1.18 (((~c3_1(a1101)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1101)))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(996,axiom,((~c3_1(a1101)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.92/1.18 tff(997,plain,
% 0.92/1.18 ((~hskp3) | (~c3_1(a1101))),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[996, 995])).
% 0.92/1.18 tff(998,plain,
% 0.92/1.18 ((~hskp3) | (~c3_1(a1101))),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[997, 994])).
% 0.92/1.18 tff(999,plain,
% 0.92/1.18 (~c3_1(a1101)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[998, 993])).
% 0.92/1.18 tff(1000,plain,
% 0.92/1.18 (((~hskp3) | c2_1(a1101)) <=> ((~hskp3) | c2_1(a1101))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(1001,axiom,((~hskp3) | c2_1(a1101)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.92/1.18 tff(1002,plain,
% 0.92/1.18 ((~hskp3) | c2_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.92/1.18 tff(1003,plain,
% 0.92/1.18 ((~hskp3) | c2_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1002, 1000])).
% 0.92/1.18 tff(1004,plain,
% 0.92/1.18 ((~hskp3) | c2_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1003, 1000])).
% 0.92/1.18 tff(1005,plain,
% 0.92/1.18 ((~hskp3) | c2_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1004, 1000])).
% 0.92/1.18 tff(1006,plain,
% 0.92/1.18 ((~hskp3) | c2_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1005, 1000])).
% 0.92/1.18 tff(1007,plain,
% 0.92/1.18 (c2_1(a1101)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[1006, 993])).
% 0.92/1.18 tff(1008,plain,
% 0.92/1.18 (((~hskp3) | c1_1(a1101)) <=> ((~hskp3) | c1_1(a1101))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(1009,axiom,((~hskp3) | c1_1(a1101)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.92/1.18 tff(1010,plain,
% 0.92/1.18 ((~hskp3) | c1_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.92/1.18 tff(1011,plain,
% 0.92/1.18 ((~hskp3) | c1_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1010, 1008])).
% 0.92/1.18 tff(1012,plain,
% 0.92/1.18 ((~hskp3) | c1_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1011, 1008])).
% 0.92/1.18 tff(1013,plain,
% 0.92/1.18 ((~hskp3) | c1_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1012, 1008])).
% 0.92/1.18 tff(1014,plain,
% 0.92/1.18 ((~hskp3) | c1_1(a1101)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1013, 1008])).
% 0.92/1.18 tff(1015,plain,
% 0.92/1.18 (c1_1(a1101)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[1014, 993])).
% 0.92/1.18 tff(1016,plain,
% 0.92/1.18 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(1017,plain,
% 0.92/1.18 ((hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105))) <=> (hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(1018,plain,
% 0.92/1.18 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105))))),
% 0.92/1.18 inference(monotonicity,[status(thm)],[1017])).
% 0.92/1.18 tff(1019,plain,
% 0.92/1.18 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 0.92/1.18 inference(transitivity,[status(thm)],[1018, 1016])).
% 0.92/1.18 tff(1020,plain,
% 0.92/1.18 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))),
% 0.92/1.18 inference(quant_inst,[status(thm)],[])).
% 0.92/1.18 tff(1021,plain,
% 0.92/1.18 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105))),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.92/1.18 tff(1022,plain,
% 0.92/1.18 (hskp24),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[1021, 110, 902, 1015, 1007, 612, 999, 892, 882])).
% 0.92/1.18 tff(1023,plain,
% 0.92/1.18 (~c0_1(a1149)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[783, 1022])).
% 0.92/1.18 tff(1024,plain,
% 0.92/1.18 (c2_1(a1149)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[799, 1022])).
% 0.92/1.18 tff(1025,plain,
% 0.92/1.18 (c3_1(a1149)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[791, 1022])).
% 0.92/1.18 tff(1026,plain,
% 0.92/1.18 ($false),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[844, 1025, 1024, 764, 900, 1023])).
% 0.92/1.18 tff(1027,plain,(hskp29 | (~c0_1(a1105)) | c1_1(a1105) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | hskp14 | (~c3_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.18 tff(1028,plain,
% 0.92/1.18 (hskp29),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[1027, 632, 583, 672, 664, 631, 656, 655])).
% 0.92/1.18 tff(1029,plain,
% 0.92/1.18 (c3_1(a1116)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[189, 1028])).
% 0.92/1.18 tff(1030,plain,
% 0.92/1.18 (c2_1(a1116)),
% 0.92/1.18 inference(unit_resolution,[status(thm)],[197, 1028])).
% 0.92/1.18 tff(1031,plain,
% 0.92/1.18 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(1032,plain,
% 0.92/1.18 ((hskp14 | hskp19 | (~ndr1_0) | c1_1(a1116) | (~c3_1(a1116)) | (~c2_1(a1116))) <=> (hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116))),
% 0.92/1.18 inference(rewrite,[status(thm)],[])).
% 0.92/1.18 tff(1033,plain,
% 0.92/1.18 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1116) | (~c3_1(a1116)) | (~c2_1(a1116)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116)))),
% 0.92/1.18 inference(monotonicity,[status(thm)],[1032])).
% 0.92/1.18 tff(1034,plain,
% 0.92/1.18 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1116) | (~c3_1(a1116)) | (~c2_1(a1116)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116))),
% 0.92/1.18 inference(transitivity,[status(thm)],[1033, 1031])).
% 0.92/1.18 tff(1035,plain,
% 0.92/1.18 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1116) | (~c3_1(a1116)) | (~c2_1(a1116)))),
% 0.92/1.18 inference(quant_inst,[status(thm)],[])).
% 0.92/1.18 tff(1036,plain,
% 0.92/1.18 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116)),
% 0.92/1.18 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.01/1.18 tff(1037,plain,
% 1.01/1.18 (hskp19 | c1_1(a1116)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1036, 632, 110, 1030, 1029, 654])).
% 1.01/1.18 tff(1038,plain,
% 1.01/1.18 (c1_1(a1116)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1037, 644])).
% 1.01/1.18 tff(1039,plain,
% 1.01/1.18 (hskp14 | hskp19 | (~c2_1(a1105))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[898, 110, 655, 583, 654])).
% 1.01/1.18 tff(1040,plain,
% 1.01/1.18 (~c2_1(a1105)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1039, 644, 632])).
% 1.01/1.18 tff(1041,plain,
% 1.01/1.18 (c0_1(a1116)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[205, 1028])).
% 1.01/1.18 tff(1042,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1043,plain,
% 1.01/1.18 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1044,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[1043])).
% 1.01/1.18 tff(1045,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.01/1.18 inference(transitivity,[status(thm)],[1044, 1042])).
% 1.01/1.18 tff(1046,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(1047,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 1.01/1.18 tff(1048,plain,
% 1.01/1.18 (c2_1(a1105) | (~c1_1(a1147))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1047, 110, 1041, 1030, 1029, 695, 655, 732, 583, 228])).
% 1.01/1.18 tff(1049,plain,
% 1.01/1.18 (~c1_1(a1147)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1048, 1040])).
% 1.01/1.18 tff(1050,plain,
% 1.01/1.18 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(1051,plain,
% 1.01/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[1050])).
% 1.01/1.18 tff(1052,plain,
% 1.01/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1053,plain,
% 1.01/1.18 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(1054,plain,
% 1.01/1.18 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[1053])).
% 1.01/1.18 tff(1055,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.01/1.18 tff(1056,plain,
% 1.01/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 1.01/1.18 tff(1057,plain,
% 1.01/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1056, 1052])).
% 1.01/1.18 tff(1058,plain,(
% 1.01/1.18 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.18 inference(skolemize,[status(sab)],[1057])).
% 1.01/1.18 tff(1059,plain,
% 1.01/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1058, 1051])).
% 1.01/1.18 tff(1060,plain,
% 1.01/1.18 (^[U: $i] : refl((hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(1061,plain,
% 1.01/1.18 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[1060])).
% 1.01/1.18 tff(1062,plain,
% 1.01/1.18 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1063,plain,
% 1.01/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp8))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp8) <=> (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(1064,plain,
% 1.01/1.18 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[1063])).
% 1.01/1.18 tff(1065,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.01/1.18 tff(1066,plain,
% 1.01/1.18 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 1.01/1.18 tff(1067,plain,
% 1.01/1.18 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1066, 1062])).
% 1.01/1.18 tff(1068,plain,(
% 1.01/1.18 ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.01/1.18 inference(skolemize,[status(sab)],[1067])).
% 1.01/1.18 tff(1069,plain,
% 1.01/1.18 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1068, 1061])).
% 1.01/1.18 tff(1070,plain,
% 1.01/1.18 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1071,plain,
% 1.01/1.18 ((hskp19 | hskp8 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098)) <=> (hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1072,plain,
% 1.01/1.18 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0)))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[1071])).
% 1.01/1.18 tff(1073,plain,
% 1.01/1.18 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.01/1.18 inference(transitivity,[status(thm)],[1072, 1070])).
% 1.01/1.18 tff(1074,plain,
% 1.01/1.18 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(1075,plain,
% 1.01/1.18 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 1.01/1.18 tff(1076,plain,
% 1.01/1.18 (hskp19 | hskp8 | c2_1(a1098) | c3_1(a1098)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1075, 110, 34, 1069])).
% 1.01/1.18 tff(1077,plain,
% 1.01/1.18 (hskp8),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1076, 644, 35, 47])).
% 1.01/1.18 tff(1078,assumption,(hskp8), introduced(assumption)).
% 1.01/1.18 tff(1079,plain,
% 1.01/1.18 (((~hskp8) | (~c1_1(a1107))) <=> ((~hskp8) | (~c1_1(a1107)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1080,plain,
% 1.01/1.18 (((~c1_1(a1107)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1107)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1081,axiom,((~c1_1(a1107)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.01/1.18 tff(1082,plain,
% 1.01/1.18 ((~hskp8) | (~c1_1(a1107))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 1.01/1.19 tff(1083,plain,
% 1.01/1.19 ((~hskp8) | (~c1_1(a1107))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[1082, 1079])).
% 1.01/1.19 tff(1084,plain,
% 1.01/1.19 (~c1_1(a1107)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1083, 1078])).
% 1.01/1.19 tff(1085,plain,
% 1.01/1.19 (((~hskp8) | (~c0_1(a1107))) <=> ((~hskp8) | (~c0_1(a1107)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(1086,plain,
% 1.01/1.19 (((~c0_1(a1107)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1107)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(1087,axiom,((~c0_1(a1107)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.01/1.19 tff(1088,plain,
% 1.01/1.19 ((~hskp8) | (~c0_1(a1107))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.01/1.19 tff(1089,plain,
% 1.01/1.19 ((~hskp8) | (~c0_1(a1107))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[1088, 1085])).
% 1.01/1.19 tff(1090,plain,
% 1.01/1.19 (~c0_1(a1107)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1089, 1078])).
% 1.01/1.19 tff(1091,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(1092,plain,
% 1.01/1.19 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107))) <=> (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(1093,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107))))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[1092])).
% 1.01/1.19 tff(1094,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.01/1.19 inference(transitivity,[status(thm)],[1093, 1091])).
% 1.01/1.19 tff(1095,plain,
% 1.01/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(1096,plain,
% 1.01/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 1.02/1.19 tff(1097,plain,
% 1.02/1.19 (~c2_1(a1107)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1096, 110, 231, 230, 229, 902, 875, 1090, 1084, 612, 642])).
% 1.02/1.19 tff(1098,plain,
% 1.02/1.19 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(1099,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[1098])).
% 1.02/1.19 tff(1100,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1101,plain,
% 1.02/1.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(1102,plain,
% 1.02/1.19 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[1101])).
% 1.02/1.19 tff(1103,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.02/1.19 tff(1104,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.02/1.19 tff(1105,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1104, 1100])).
% 1.02/1.19 tff(1106,plain,(
% 1.02/1.19 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.02/1.19 inference(skolemize,[status(sab)],[1105])).
% 1.02/1.19 tff(1107,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1106, 1099])).
% 1.02/1.19 tff(1108,plain,
% 1.02/1.19 (((~hskp8) | c3_1(a1107)) <=> ((~hskp8) | c3_1(a1107))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1109,axiom,((~hskp8) | c3_1(a1107)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.02/1.19 tff(1110,plain,
% 1.02/1.19 ((~hskp8) | c3_1(a1107)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 1.02/1.19 tff(1111,plain,
% 1.02/1.19 ((~hskp8) | c3_1(a1107)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1110, 1108])).
% 1.02/1.19 tff(1112,plain,
% 1.02/1.19 ((~hskp8) | c3_1(a1107)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1111, 1108])).
% 1.02/1.19 tff(1113,plain,
% 1.02/1.19 ((~hskp8) | c3_1(a1107)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1112, 1108])).
% 1.02/1.19 tff(1114,plain,
% 1.02/1.19 ((~hskp8) | c3_1(a1107)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1113, 1108])).
% 1.02/1.19 tff(1115,plain,
% 1.02/1.19 (c3_1(a1107)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1114, 1078])).
% 1.02/1.19 tff(1116,assumption,(~hskp13), introduced(assumption)).
% 1.02/1.19 tff(1117,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1118,plain,
% 1.02/1.19 ((hskp13 | (~ndr1_0) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107))) <=> (hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1119,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1118])).
% 1.02/1.19 tff(1120,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1119, 1117])).
% 1.02/1.19 tff(1121,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1122,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.02/1.19 tff(1123,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1122, 110, 1116, 1115, 1090, 1084, 1107, 1097])).
% 1.02/1.19 tff(1124,plain,((~hskp8) | hskp13 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(1125,plain,
% 1.02/1.19 (hskp13),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1124, 1077, 1041, 1030, 1029, 656, 655, 583])).
% 1.02/1.19 tff(1126,plain,
% 1.02/1.19 (((~hskp13) | (~c1_1(a1115))) <=> ((~hskp13) | (~c1_1(a1115)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1127,plain,
% 1.02/1.19 (((~c1_1(a1115)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1115)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1128,axiom,((~c1_1(a1115)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.02/1.19 tff(1129,plain,
% 1.02/1.19 ((~hskp13) | (~c1_1(a1115))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 1.02/1.19 tff(1130,plain,
% 1.02/1.19 ((~hskp13) | (~c1_1(a1115))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1129, 1126])).
% 1.02/1.19 tff(1131,plain,
% 1.02/1.19 (~c1_1(a1115)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1130, 1125])).
% 1.02/1.19 tff(1132,plain,
% 1.02/1.19 (((~hskp13) | c2_1(a1115)) <=> ((~hskp13) | c2_1(a1115))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1133,axiom,((~hskp13) | c2_1(a1115)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.02/1.19 tff(1134,plain,
% 1.02/1.19 ((~hskp13) | c2_1(a1115)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.02/1.19 tff(1135,plain,
% 1.02/1.19 ((~hskp13) | c2_1(a1115)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1134, 1132])).
% 1.02/1.19 tff(1136,plain,
% 1.02/1.19 ((~hskp13) | c2_1(a1115)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1135, 1132])).
% 1.02/1.19 tff(1137,plain,
% 1.02/1.19 ((~hskp13) | c2_1(a1115)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1136, 1132])).
% 1.02/1.19 tff(1138,plain,
% 1.02/1.19 ((~hskp13) | c2_1(a1115)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1137, 1132])).
% 1.02/1.19 tff(1139,plain,
% 1.02/1.19 (c2_1(a1115)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1138, 1125])).
% 1.02/1.19 tff(1140,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1141,plain,
% 1.02/1.19 (((~ndr1_0) | (~c1_1(a1116)) | (~c3_1(a1116)) | (~c2_1(a1116)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1142,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1116)) | (~c3_1(a1116)) | (~c2_1(a1116)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1141])).
% 1.02/1.19 tff(1143,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1116)) | (~c3_1(a1116)) | (~c2_1(a1116)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1142, 1140])).
% 1.02/1.19 tff(1144,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1116)) | (~c3_1(a1116)) | (~c2_1(a1116)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1145,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 1.02/1.19 tff(1146,plain,
% 1.02/1.19 (c0_1(a1115)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1145, 110, 1030, 1029, 695, 1139, 732, 1131, 1059, 1049, 1038])).
% 1.02/1.19 tff(1147,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1148,plain,
% 1.02/1.19 ((hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115))) <=> (hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1149,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1148])).
% 1.02/1.19 tff(1150,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1149, 1147])).
% 1.02/1.19 tff(1151,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1152,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.02/1.19 tff(1153,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1152, 110, 643, 1139, 656, 655, 1131, 915, 1040, 1146])).
% 1.02/1.19 tff(1154,plain,(hskp19 | hskp20 | hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(1155,plain,
% 1.02/1.19 (hskp19),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1154, 643, 632, 35, 47, 34])).
% 1.02/1.19 tff(1156,plain,
% 1.02/1.19 (~c2_1(a1127)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[816, 1155])).
% 1.02/1.19 tff(1157,plain,
% 1.02/1.19 (c3_1(a1127)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[825, 1155])).
% 1.02/1.19 tff(1158,plain,
% 1.02/1.19 (c1_1(a1127)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[833, 1155])).
% 1.02/1.19 tff(1159,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1160,plain,
% 1.02/1.19 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1161,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[1160])).
% 1.02/1.19 tff(1162,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[1161, 1159])).
% 1.02/1.19 tff(1163,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(1164,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.02/1.19 tff(1165,plain,
% 1.02/1.19 (hskp2),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1164, 110, 1041, 1030, 1029, 1158, 1157, 1156, 260])).
% 1.02/1.19 tff(1166,plain,
% 1.02/1.19 (~c3_1(a1100)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[273, 1165])).
% 1.02/1.19 tff(1167,assumption,(~hskp5), introduced(assumption)).
% 1.02/1.19 tff(1168,plain,
% 1.02/1.19 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(1169,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[1168])).
% 1.02/1.19 tff(1170,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(1171,plain,
% 1.02/1.19 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_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) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_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) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(1172,plain,
% 1.02/1.19 (![V: $i, U: $i] : ((((((((~c1_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) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[1171])).
% 1.02/1.19 tff(1173,axiom,(![V: $i, U: $i] : ((((((((~c1_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','clause188')).
% 1.02/1.19 tff(1174,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 1.02/1.19 tff(1175,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1174, 1170])).
% 1.02/1.19 tff(1176,plain,(
% 1.02/1.19 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.02/1.19 inference(skolemize,[status(sab)],[1175])).
% 1.02/1.19 tff(1177,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[1176, 1169])).
% 1.02/1.19 tff(1178,plain,
% 1.02/1.19 (hskp2),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1164, 110, 231, 230, 229, 834, 826, 817, 260])).
% 1.02/1.19 tff(1179,plain,
% 1.02/1.19 (~c3_1(a1100)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[273, 1178])).
% 1.02/1.20 tff(1180,plain,
% 1.02/1.20 (c2_1(a1100)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[281, 1178])).
% 1.02/1.20 tff(1181,plain,
% 1.02/1.20 (c0_1(a1100)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[289, 1178])).
% 1.02/1.20 tff(1182,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1183,plain,
% 1.02/1.20 ((hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100))) <=> (hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1184,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1183])).
% 1.02/1.20 tff(1185,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1184, 1182])).
% 1.02/1.20 tff(1186,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1187,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 1.02/1.20 tff(1188,plain,
% 1.02/1.20 (~c1_1(a1100)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1187, 110, 1167, 1181, 1180, 1179, 1177])).
% 1.02/1.20 tff(1189,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1190,plain,
% 1.02/1.20 ((hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100))) <=> (hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1191,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1190])).
% 1.02/1.20 tff(1192,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1191, 1189])).
% 1.02/1.20 tff(1193,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1194,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 1.02/1.20 tff(1195,plain,
% 1.02/1.20 (~c0_1(a1127)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1194, 110, 643, 826, 1181, 1180, 817, 915, 1188])).
% 1.02/1.20 tff(1196,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1197,plain,
% 1.02/1.20 ((hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1198,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1197])).
% 1.02/1.20 tff(1199,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1198, 1196])).
% 1.02/1.20 tff(1200,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1201,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.02/1.20 tff(1202,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1201, 110, 643, 834, 826, 1181, 1180, 1179, 250, 1195])).
% 1.02/1.20 tff(1203,plain,((~hskp19) | hskp20 | hskp5 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1204,plain,
% 1.02/1.20 (~hskp19),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1203, 643, 1167, 1041, 1030, 1029])).
% 1.02/1.20 tff(1205,plain,
% 1.02/1.20 (c1_1(a1116)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1037, 1204])).
% 1.02/1.20 tff(1206,plain,
% 1.02/1.20 (~c2_1(a1105)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1039, 1204, 632])).
% 1.02/1.20 tff(1207,plain,
% 1.02/1.20 (~c1_1(a1147)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1048, 1206])).
% 1.02/1.20 tff(1208,plain,
% 1.02/1.20 (hskp8),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1076, 1204, 35, 47])).
% 1.02/1.20 tff(1209,plain,
% 1.02/1.20 (hskp13),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1124, 1208, 1041, 1030, 1029, 656, 655, 583])).
% 1.02/1.20 tff(1210,plain,
% 1.02/1.20 (~c1_1(a1115)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1130, 1209])).
% 1.02/1.20 tff(1211,plain,
% 1.02/1.20 (c2_1(a1115)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1138, 1209])).
% 1.02/1.20 tff(1212,plain,
% 1.02/1.20 (c0_1(a1115)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1145, 110, 1030, 1029, 695, 1211, 732, 1210, 1059, 1207, 1205])).
% 1.02/1.20 tff(1213,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1152, 110, 643, 1211, 656, 655, 1210, 915, 1206, 1212])).
% 1.02/1.20 tff(1214,plain,(hskp20 | hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1215,plain,
% 1.02/1.20 (hskp20),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1214, 1167, 35, 47, 34, 632])).
% 1.02/1.20 tff(1216,plain,
% 1.02/1.20 (~c0_1(a1130)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[302, 1215])).
% 1.02/1.20 tff(1217,plain,
% 1.02/1.20 (~c3_1(a1130)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[308, 1215])).
% 1.02/1.20 tff(1218,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1219,plain,
% 1.02/1.20 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1220,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1219])).
% 1.02/1.20 tff(1221,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1220, 1218])).
% 1.02/1.20 tff(1222,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1223,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 1.02/1.20 tff(1224,plain,
% 1.02/1.20 (c0_1(a1130) | (~c1_1(a1130))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1223, 110, 231, 230, 229, 700, 747, 699, 321, 320])).
% 1.02/1.20 tff(1225,plain,
% 1.02/1.20 (~c1_1(a1130)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1224, 310])).
% 1.02/1.20 tff(1226,assumption,(hskp3), introduced(assumption)).
% 1.02/1.20 tff(1227,plain,
% 1.02/1.20 (~c3_1(a1101)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[998, 1226])).
% 1.02/1.20 tff(1228,plain,
% 1.02/1.20 (c1_1(a1101)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1014, 1226])).
% 1.02/1.20 tff(1229,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1230,plain,
% 1.02/1.20 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1101) | c0_1(a1101) | (~c1_1(a1101))) <=> (c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1231,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1101) | c0_1(a1101) | (~c1_1(a1101)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1230])).
% 1.02/1.20 tff(1232,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1101) | c0_1(a1101) | (~c1_1(a1101)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1231, 1229])).
% 1.02/1.20 tff(1233,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1101) | c0_1(a1101) | (~c1_1(a1101)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1234,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 1.02/1.20 tff(1235,plain,
% 1.02/1.20 (c0_1(a1101)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1234, 110, 231, 230, 229, 700, 1228, 747, 699, 1227, 320])).
% 1.02/1.20 tff(1236,plain,
% 1.02/1.20 (c2_1(a1101)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1006, 1226])).
% 1.02/1.20 tff(1237,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1238,plain,
% 1.02/1.20 ((hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101))) <=> (hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1239,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1238])).
% 1.02/1.20 tff(1240,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1239, 1237])).
% 1.02/1.20 tff(1241,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1242,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 1.02/1.20 tff(1243,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1242, 110, 1167, 1228, 1236, 1227, 1177, 1235])).
% 1.02/1.20 tff(1244,plain,((~hskp3) | hskp5 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1245,plain,
% 1.02/1.20 (~hskp3),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1244, 1167, 231, 230, 229, 700, 747, 699])).
% 1.02/1.20 tff(1246,assumption,(~c1_1(a1130)), introduced(assumption)).
% 1.02/1.20 tff(1247,assumption,(hskp13), introduced(assumption)).
% 1.02/1.20 tff(1248,plain,
% 1.02/1.20 (((~hskp13) | (~c3_1(a1115))) <=> ((~hskp13) | (~c3_1(a1115)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1249,plain,
% 1.02/1.20 (((~c3_1(a1115)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1115)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1250,axiom,((~c3_1(a1115)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.02/1.20 tff(1251,plain,
% 1.02/1.20 ((~hskp13) | (~c3_1(a1115))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 1.02/1.20 tff(1252,plain,
% 1.02/1.20 ((~hskp13) | (~c3_1(a1115))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1251, 1248])).
% 1.02/1.20 tff(1253,plain,
% 1.02/1.20 (~c3_1(a1115)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1252, 1247])).
% 1.02/1.20 tff(1254,plain,
% 1.02/1.20 (c2_1(a1115)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1138, 1247])).
% 1.02/1.20 tff(1255,assumption,(~hskp3), introduced(assumption)).
% 1.02/1.20 tff(1256,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1257,plain,
% 1.02/1.20 ((hskp3 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1258,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130)))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1257])).
% 1.02/1.20 tff(1259,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1258, 1256])).
% 1.02/1.20 tff(1260,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1261,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.02/1.20 tff(1262,plain,
% 1.02/1.20 (~c0_1(a1115)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1261, 110, 1255, 1254, 310, 321, 1253, 965, 1246])).
% 1.02/1.20 tff(1263,plain,
% 1.02/1.20 (~c1_1(a1115)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1130, 1247])).
% 1.02/1.20 tff(1264,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1265,plain,
% 1.02/1.20 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(1266,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[1265])).
% 1.02/1.20 tff(1267,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[1266, 1264])).
% 1.02/1.20 tff(1268,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(1269,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 1.02/1.20 tff(1270,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1269, 110, 231, 230, 229, 1254, 902, 875, 1263, 612, 642, 1262])).
% 1.02/1.20 tff(1271,plain,((~hskp13) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | hskp3 | c0_1(a1130) | c3_1(a1130) | c1_1(a1130)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(1272,plain,
% 1.02/1.20 (~hskp13),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1271, 310, 230, 229, 656, 655, 583, 1245, 231, 321, 1225])).
% 1.02/1.20 tff(1273,plain,
% 1.02/1.20 (~hskp8),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1124, 1272, 231, 230, 229, 656, 655, 583])).
% 1.02/1.20 tff(1274,plain,
% 1.02/1.20 (hskp19),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1076, 1273, 35, 47])).
% 1.02/1.20 tff(1275,plain,
% 1.02/1.20 (~c2_1(a1127)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[816, 1274])).
% 1.02/1.20 tff(1276,plain,
% 1.02/1.20 (c3_1(a1127)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[825, 1274])).
% 1.02/1.20 tff(1277,plain,
% 1.02/1.20 (c1_1(a1127)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[833, 1274])).
% 1.02/1.20 tff(1278,plain,
% 1.02/1.20 (hskp2),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1164, 110, 231, 230, 229, 1277, 1276, 1275, 260])).
% 1.02/1.20 tff(1279,plain,
% 1.02/1.20 (~c3_1(a1100)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[273, 1278])).
% 1.02/1.20 tff(1280,plain,
% 1.02/1.20 (c2_1(a1100)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[281, 1278])).
% 1.02/1.20 tff(1281,plain,
% 1.02/1.20 (c0_1(a1100)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[289, 1278])).
% 1.02/1.20 tff(1282,plain,
% 1.02/1.20 (c0_1(a1130) | (~c1_1(a1130))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[954, 110, 696, 673, 700, 747, 699, 321, 320, 733])).
% 1.02/1.20 tff(1283,plain,
% 1.02/1.20 (~c1_1(a1130)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1282, 310])).
% 1.02/1.20 tff(1284,assumption,(~c3_1(a1100)), introduced(assumption)).
% 1.02/1.20 tff(1285,assumption,(c2_1(a1100)), introduced(assumption)).
% 1.02/1.20 tff(1286,assumption,(c0_1(a1100)), introduced(assumption)).
% 1.02/1.20 tff(1287,plain,
% 1.02/1.20 (hskp3),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[992, 110, 1286, 1285, 310, 321, 1284, 965, 1283])).
% 1.02/1.20 tff(1288,plain,
% 1.02/1.20 (~c3_1(a1101)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[998, 1287])).
% 1.02/1.20 tff(1289,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1290,plain,
% 1.02/1.21 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130))) <=> (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1291,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[1290])).
% 1.02/1.21 tff(1292,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.02/1.21 inference(transitivity,[status(thm)],[1291, 1289])).
% 1.02/1.21 tff(1293,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(1294,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.02/1.21 tff(1295,plain,
% 1.02/1.21 (~c2_1(a1130)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1294, 110, 696, 673, 902, 875, 310, 612, 642, 733, 1283])).
% 1.02/1.21 tff(1296,plain,
% 1.02/1.21 (c2_1(a1101)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1006, 1287])).
% 1.02/1.21 tff(1297,plain,
% 1.02/1.21 (c1_1(a1101)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1014, 1287])).
% 1.02/1.21 tff(1298,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1299,plain,
% 1.02/1.21 ((hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1300,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[1299])).
% 1.02/1.21 tff(1301,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[1300, 1298])).
% 1.02/1.21 tff(1302,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(1303,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.02/1.21 tff(1304,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1303, 110, 1167, 1297, 1296, 310, 1295, 321, 1288, 10])).
% 1.02/1.21 tff(1305,plain,(c0_1(a1130) | hskp5 | c3_1(a1130) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | (~c0_1(a1136)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(1306,plain,
% 1.02/1.21 (~c0_1(a1136)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1305, 1281, 1167, 321, 1280, 1279, 672, 664, 656, 655, 583, 310, 700, 747, 699])).
% 1.02/1.21 tff(1307,plain,
% 1.02/1.21 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_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)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.02/1.21 inference(bind,[status(th)],[])).
% 1.02/1.21 tff(1308,plain,
% 1.02/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.02/1.21 inference(quant_intro,[status(thm)],[1307])).
% 1.02/1.21 tff(1309,plain,
% 1.02/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1310,plain,
% 1.02/1.21 (^[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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.02/1.21 inference(bind,[status(th)],[])).
% 1.02/1.21 tff(1311,plain,
% 1.02/1.21 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.02/1.21 inference(quant_intro,[status(thm)],[1310])).
% 1.02/1.21 tff(1312,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.02/1.21 tff(1313,plain,
% 1.02/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 1.02/1.21 tff(1314,plain,
% 1.02/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1313, 1309])).
% 1.02/1.21 tff(1315,plain,(
% 1.02/1.21 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.02/1.21 inference(skolemize,[status(sab)],[1314])).
% 1.02/1.21 tff(1316,plain,
% 1.02/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1315, 1308])).
% 1.02/1.21 tff(1317,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1318,plain,
% 1.02/1.21 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130))) <=> (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1319,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[1318])).
% 1.02/1.21 tff(1320,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.02/1.21 inference(transitivity,[status(thm)],[1319, 1317])).
% 1.02/1.21 tff(1321,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(1322,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 1.02/1.21 tff(1323,plain,
% 1.02/1.21 (~c2_1(a1130)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1322, 110, 231, 230, 229, 656, 655, 310, 583, 642, 1225])).
% 1.02/1.21 tff(1324,plain,
% 1.02/1.21 (^[U: $i] : refl((hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 1.02/1.21 inference(bind,[status(th)],[])).
% 1.02/1.21 tff(1325,plain,
% 1.02/1.21 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.02/1.21 inference(quant_intro,[status(thm)],[1324])).
% 1.02/1.21 tff(1326,plain,
% 1.02/1.21 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1327,plain,
% 1.02/1.21 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp8) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp8))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp8) <=> (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp8) <=> (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 1.02/1.21 inference(bind,[status(th)],[])).
% 1.02/1.21 tff(1328,plain,
% 1.02/1.21 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp8) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.02/1.21 inference(quant_intro,[status(thm)],[1327])).
% 1.02/1.21 tff(1329,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.02/1.21 tff(1330,plain,
% 1.02/1.21 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 1.02/1.21 tff(1331,plain,
% 1.02/1.21 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1330, 1326])).
% 1.02/1.21 tff(1332,plain,(
% 1.02/1.21 ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.02/1.21 inference(skolemize,[status(sab)],[1331])).
% 1.02/1.21 tff(1333,plain,
% 1.02/1.21 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1332, 1325])).
% 1.02/1.21 tff(1334,plain,
% 1.02/1.21 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1335,plain,
% 1.02/1.21 ((hskp8 | hskp6 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c0_1(a1130)) <=> (hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1336,plain,
% 1.02/1.21 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c0_1(a1130))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0)))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[1335])).
% 1.02/1.21 tff(1337,plain,
% 1.02/1.21 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c0_1(a1130))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0))),
% 1.02/1.21 inference(transitivity,[status(thm)],[1336, 1334])).
% 1.02/1.21 tff(1338,plain,
% 1.02/1.21 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c0_1(a1130))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(1339,plain,
% 1.02/1.21 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0)),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 1.02/1.21 tff(1340,plain,
% 1.02/1.21 (hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1339, 110, 321, 1333])).
% 1.02/1.21 tff(1341,plain,
% 1.02/1.21 (hskp6),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1340, 1273, 310, 1323])).
% 1.02/1.21 tff(1342,plain,
% 1.02/1.21 (~c2_1(a1104)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[502, 1341])).
% 1.02/1.21 tff(1343,plain,
% 1.02/1.21 (c1_1(a1104)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[535, 1341])).
% 1.02/1.21 tff(1344,plain,
% 1.02/1.21 (c0_1(a1104)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[510, 1341])).
% 1.02/1.21 tff(1345,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1346,plain,
% 1.02/1.21 (((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1347,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[1346])).
% 1.02/1.21 tff(1348,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[1347, 1345])).
% 1.02/1.21 tff(1349,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(1350,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 1.02/1.21 tff(1351,plain,
% 1.02/1.21 (~c0_1(a1098)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1350, 110, 631, 672, 1344, 1343, 1342, 34, 47, 1316, 1306])).
% 1.02/1.21 tff(1352,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1353,plain,
% 1.02/1.21 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098)) <=> (hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(1354,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[1353])).
% 1.02/1.21 tff(1355,plain,
% 1.02/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[1354, 1352])).
% 1.02/1.21 tff(1356,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(1357,plain,
% 1.02/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 1.02/1.21 tff(1358,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1357, 110, 1245, 1281, 1280, 1279, 34, 47, 965, 1351])).
% 1.02/1.21 tff(1359,plain,(c0_1(a1130) | c1_1(a1098) | c3_1(a1098) | hskp5 | c3_1(a1130) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(1360,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1359, 1217, 1216, 47, 1167, 34, 695, 732, 687, 1041, 1030, 1029, 35])).
% 1.02/1.21 tff(1361,plain,(hskp5 | c3_1(a1098) | c1_1(a1098) | c2_1(a1098) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(1362,plain,
% 1.02/1.21 (hskp5),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1361, 632, 34, 35, 47])).
% 1.02/1.21 tff(1363,plain,
% 1.02/1.21 (~c0_1(a1103)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[129, 1362])).
% 1.02/1.21 tff(1364,plain,
% 1.02/1.21 (c2_1(a1100)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[281, 1165])).
% 1.02/1.21 tff(1365,plain,
% 1.02/1.21 (c0_1(a1100)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[289, 1165])).
% 1.02/1.21 tff(1366,plain,
% 1.02/1.21 (c3_1(a1103)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[147, 1362])).
% 1.02/1.21 tff(1367,plain,
% 1.02/1.21 (~c1_1(a1103)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[296, 110, 643, 1366, 1365, 1364, 1363, 1166, 250])).
% 1.02/1.22 tff(1368,plain,
% 1.02/1.22 (~c2_1(a1103)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[123, 1362])).
% 1.02/1.22 tff(1369,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(1370,plain,
% 1.02/1.22 ((hskp13 | (~ndr1_0) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103))) <=> (hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(1371,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[1370])).
% 1.02/1.22 tff(1372,plain,
% 1.02/1.22 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[1371, 1369])).
% 1.02/1.22 tff(1373,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(1374,plain,
% 1.02/1.22 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.02/1.22 tff(1375,plain,
% 1.02/1.22 (hskp13 | c1_1(a1103)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1374, 110, 1366, 1363, 1368, 1107])).
% 1.02/1.22 tff(1376,plain,
% 1.02/1.22 (hskp13),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1375, 1367])).
% 1.02/1.22 tff(1377,plain,
% 1.02/1.22 (~c1_1(a1115)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1130, 1376])).
% 1.02/1.22 tff(1378,plain,
% 1.02/1.22 (c2_1(a1115)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1138, 1376])).
% 1.02/1.22 tff(1379,plain,
% 1.02/1.22 (c0_1(a1115)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1269, 110, 1041, 1030, 1029, 1378, 656, 655, 1377, 583, 642])).
% 1.02/1.22 tff(1380,plain,
% 1.02/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(1381,plain,
% 1.02/1.22 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103))) <=> (c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(1382,plain,
% 1.02/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1381])).
% 1.05/1.22 tff(1383,plain,
% 1.05/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.05/1.22 inference(transitivity,[status(thm)],[1382, 1380])).
% 1.05/1.22 tff(1384,plain,
% 1.05/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(1385,plain,
% 1.05/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 1.05/1.22 tff(1386,plain,
% 1.05/1.22 (~c0_1(a1127)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1385, 110, 1041, 1030, 1029, 1158, 1366, 1156, 1368, 228, 1367])).
% 1.05/1.22 tff(1387,plain,
% 1.05/1.22 (~c3_1(a1115)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1252, 1376])).
% 1.05/1.22 tff(1388,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1389,plain,
% 1.05/1.22 ((hskp20 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1390,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1389])).
% 1.05/1.22 tff(1391,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.05/1.22 inference(transitivity,[status(thm)],[1390, 1388])).
% 1.05/1.22 tff(1392,plain,
% 1.05/1.22 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(1393,plain,
% 1.05/1.22 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 1.05/1.22 tff(1394,plain,
% 1.05/1.22 ($false),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1393, 110, 643, 1158, 1157, 1378, 1387, 250, 1386, 1379])).
% 1.05/1.22 tff(1395,plain,(hskp20 | hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.05/1.22 tff(1396,plain,
% 1.05/1.22 (hskp20),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1395, 632, 35, 47, 34])).
% 1.05/1.22 tff(1397,plain,
% 1.05/1.22 (~c0_1(a1130)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[302, 1396])).
% 1.05/1.22 tff(1398,plain,
% 1.05/1.22 (~c3_1(a1130)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[308, 1396])).
% 1.05/1.22 tff(1399,plain,
% 1.05/1.22 (c0_1(a1130) | (~c1_1(a1130))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1223, 110, 1041, 1030, 1029, 695, 732, 687, 321, 320])).
% 1.05/1.22 tff(1400,plain,
% 1.05/1.22 (~c1_1(a1130)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1399, 310])).
% 1.05/1.22 tff(1401,plain,
% 1.05/1.22 (hskp3),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1271, 1125, 1030, 1029, 656, 655, 583, 1400, 310, 321, 1041])).
% 1.05/1.22 tff(1402,plain,
% 1.05/1.22 (~c3_1(a1101)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[998, 1401])).
% 1.05/1.22 tff(1403,plain,
% 1.05/1.22 (c1_1(a1101)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1014, 1401])).
% 1.05/1.22 tff(1404,plain,
% 1.05/1.22 (c0_1(a1101)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1234, 110, 1041, 1030, 1029, 695, 1403, 732, 687, 1402, 320])).
% 1.05/1.22 tff(1405,plain,
% 1.05/1.22 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.05/1.22 inference(bind,[status(th)],[])).
% 1.05/1.22 tff(1406,plain,
% 1.05/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.05/1.22 inference(quant_intro,[status(thm)],[1405])).
% 1.05/1.22 tff(1407,plain,
% 1.05/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1408,plain,
% 1.05/1.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.05/1.22 inference(bind,[status(th)],[])).
% 1.05/1.22 tff(1409,plain,
% 1.05/1.22 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.05/1.22 inference(quant_intro,[status(thm)],[1408])).
% 1.05/1.22 tff(1410,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.05/1.22 tff(1411,plain,
% 1.05/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 1.05/1.22 tff(1412,plain,
% 1.05/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1411, 1407])).
% 1.05/1.22 tff(1413,plain,(
% 1.05/1.22 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.05/1.22 inference(skolemize,[status(sab)],[1412])).
% 1.05/1.22 tff(1414,plain,
% 1.05/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1413, 1406])).
% 1.05/1.22 tff(1415,plain,
% 1.05/1.22 (~c2_1(a1130)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1322, 110, 1041, 1030, 1029, 656, 655, 310, 583, 642, 1400])).
% 1.05/1.22 tff(1416,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1417,plain,
% 1.05/1.22 ((hskp4 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1418,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1417])).
% 1.05/1.22 tff(1419,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)))),
% 1.05/1.22 inference(transitivity,[status(thm)],[1418, 1416])).
% 1.05/1.22 tff(1420,plain,
% 1.05/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(1421,plain,
% 1.05/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.05/1.22 tff(1422,plain,
% 1.05/1.22 (hskp4),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1421, 110, 1403, 310, 1415, 321, 1402, 1414, 1404])).
% 1.05/1.22 tff(1423,plain,
% 1.05/1.22 (((~hskp4) | (~c3_1(a1102))) <=> ((~hskp4) | (~c3_1(a1102)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1424,plain,
% 1.05/1.22 (((~c3_1(a1102)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1102)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1425,axiom,((~c3_1(a1102)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.05/1.22 tff(1426,plain,
% 1.05/1.22 ((~hskp4) | (~c3_1(a1102))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 1.05/1.22 tff(1427,plain,
% 1.05/1.22 ((~hskp4) | (~c3_1(a1102))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1426, 1423])).
% 1.05/1.22 tff(1428,plain,
% 1.05/1.22 (~c3_1(a1102)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1427, 1422])).
% 1.05/1.22 tff(1429,plain,
% 1.05/1.22 (c2_1(a1101)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1006, 1401])).
% 1.05/1.22 tff(1430,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1431,plain,
% 1.05/1.22 ((hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115))) <=> (hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1432,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1431])).
% 1.05/1.22 tff(1433,plain,
% 1.05/1.22 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.05/1.22 inference(transitivity,[status(thm)],[1432, 1430])).
% 1.05/1.22 tff(1434,plain,
% 1.05/1.22 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(1435,plain,
% 1.05/1.22 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.05/1.22 tff(1436,plain,
% 1.05/1.22 (hskp24),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1435, 110, 1139, 1403, 1429, 1131, 1402, 892, 1146])).
% 1.05/1.22 tff(1437,plain,
% 1.05/1.22 (~c0_1(a1149)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[783, 1436])).
% 1.05/1.22 tff(1438,plain,
% 1.05/1.22 (((~hskp4) | c1_1(a1102)) <=> ((~hskp4) | c1_1(a1102))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1439,axiom,((~hskp4) | c1_1(a1102)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.05/1.22 tff(1440,plain,
% 1.05/1.22 ((~hskp4) | c1_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 1.05/1.22 tff(1441,plain,
% 1.05/1.22 ((~hskp4) | c1_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1440, 1438])).
% 1.05/1.22 tff(1442,plain,
% 1.05/1.22 ((~hskp4) | c1_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1441, 1438])).
% 1.05/1.22 tff(1443,plain,
% 1.05/1.22 ((~hskp4) | c1_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1442, 1438])).
% 1.05/1.22 tff(1444,plain,
% 1.05/1.22 ((~hskp4) | c1_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1443, 1438])).
% 1.05/1.22 tff(1445,plain,
% 1.05/1.22 (c1_1(a1102)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1444, 1422])).
% 1.05/1.22 tff(1446,plain,
% 1.05/1.22 (((~hskp4) | c0_1(a1102)) <=> ((~hskp4) | c0_1(a1102))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1447,axiom,((~hskp4) | c0_1(a1102)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.05/1.22 tff(1448,plain,
% 1.05/1.22 ((~hskp4) | c0_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 1.05/1.22 tff(1449,plain,
% 1.05/1.22 ((~hskp4) | c0_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1448, 1446])).
% 1.05/1.22 tff(1450,plain,
% 1.05/1.22 ((~hskp4) | c0_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1449, 1446])).
% 1.05/1.22 tff(1451,plain,
% 1.05/1.22 ((~hskp4) | c0_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1450, 1446])).
% 1.05/1.22 tff(1452,plain,
% 1.05/1.22 ((~hskp4) | c0_1(a1102)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1451, 1446])).
% 1.05/1.22 tff(1453,plain,
% 1.05/1.22 (c0_1(a1102)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1452, 1422])).
% 1.05/1.22 tff(1454,plain,
% 1.05/1.22 (c3_1(a1149)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[791, 1436])).
% 1.05/1.22 tff(1455,plain,
% 1.05/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1456,plain,
% 1.05/1.22 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149))) <=> (c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1457,plain,
% 1.05/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1456])).
% 1.05/1.22 tff(1458,plain,
% 1.05/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.05/1.22 inference(transitivity,[status(thm)],[1457, 1455])).
% 1.05/1.22 tff(1459,plain,
% 1.05/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(1460,plain,
% 1.05/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 1.05/1.22 tff(1461,plain,
% 1.05/1.22 (~c1_1(a1149)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1460, 110, 631, 672, 664, 1454, 1453, 1445, 1437, 1428, 45])).
% 1.05/1.22 tff(1462,plain,
% 1.05/1.22 (c2_1(a1149)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[799, 1436])).
% 1.05/1.22 tff(1463,plain,
% 1.05/1.22 ($false),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[851, 632, 110, 644, 1462, 1454, 654, 1461])).
% 1.05/1.22 tff(1464,plain,(hskp19 | hskp14 | c0_1(a1130) | c3_1(a1130) | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.05/1.22 tff(1465,plain,
% 1.05/1.22 (hskp19),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1464, 310, 632, 321, 35, 47, 34])).
% 1.05/1.22 tff(1466,plain,
% 1.05/1.22 (~c2_1(a1127)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[816, 1465])).
% 1.05/1.22 tff(1467,plain,
% 1.05/1.22 (c3_1(a1127)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[825, 1465])).
% 1.05/1.22 tff(1468,plain,
% 1.05/1.22 (c1_1(a1127)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[833, 1465])).
% 1.05/1.22 tff(1469,plain,
% 1.05/1.22 (hskp2),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1164, 110, 1041, 1030, 1029, 1468, 1467, 1466, 260])).
% 1.05/1.22 tff(1470,plain,
% 1.05/1.22 (~c3_1(a1100)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[273, 1469])).
% 1.05/1.22 tff(1471,plain,
% 1.05/1.22 (c2_1(a1100)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[281, 1469])).
% 1.05/1.22 tff(1472,plain,
% 1.05/1.22 (c0_1(a1100)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[289, 1469])).
% 1.05/1.22 tff(1473,plain,
% 1.05/1.22 (hskp3),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[992, 110, 1472, 1471, 310, 321, 1470, 965, 1400])).
% 1.05/1.22 tff(1474,plain,
% 1.05/1.22 (~c3_1(a1101)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[998, 1473])).
% 1.05/1.22 tff(1475,plain,
% 1.05/1.22 (c1_1(a1101)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1014, 1473])).
% 1.05/1.22 tff(1476,plain,
% 1.05/1.22 (c0_1(a1101)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1234, 110, 1041, 1030, 1029, 695, 1475, 732, 687, 1474, 320])).
% 1.05/1.22 tff(1477,plain,
% 1.05/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(1478,plain,
% 1.05/1.22 (((~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130)) <=> (c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(1479,plain,
% 1.05/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130)))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[1478])).
% 1.05/1.23 tff(1480,plain,
% 1.05/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.05/1.23 inference(transitivity,[status(thm)],[1479, 1477])).
% 1.05/1.23 tff(1481,plain,
% 1.05/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(1482,plain,
% 1.05/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 1.05/1.23 tff(1483,plain,
% 1.05/1.23 (~c1_1(a1103)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[1482, 110, 1366, 1475, 310, 321, 1363, 1474, 339, 1400, 1476])).
% 1.05/1.23 tff(1484,plain,
% 1.05/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(1485,plain,
% 1.05/1.23 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103))) <=> (c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(1486,plain,
% 1.05/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1485])).
% 1.06/1.23 tff(1487,plain,
% 1.06/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1486, 1484])).
% 1.06/1.23 tff(1488,plain,
% 1.06/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1489,plain,
% 1.06/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 1.06/1.23 tff(1490,plain,
% 1.06/1.23 (~c1_1(a1147)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1489, 110, 1041, 1030, 1029, 695, 1366, 732, 1368, 228, 1483])).
% 1.06/1.23 tff(1491,plain,
% 1.06/1.23 (hskp13),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1375, 1483])).
% 1.06/1.23 tff(1492,plain,
% 1.06/1.23 (~c1_1(a1115)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1130, 1491])).
% 1.06/1.23 tff(1493,plain,
% 1.06/1.23 (c2_1(a1115)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1138, 1491])).
% 1.06/1.23 tff(1494,plain,
% 1.06/1.23 (c0_1(a1115)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1269, 110, 1041, 1030, 1029, 1493, 656, 655, 1492, 583, 642])).
% 1.06/1.23 tff(1495,plain,
% 1.06/1.23 (c2_1(a1101)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1006, 1473])).
% 1.06/1.23 tff(1496,plain,
% 1.06/1.23 (hskp24),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1435, 110, 1493, 1475, 1495, 1492, 1474, 892, 1494])).
% 1.06/1.23 tff(1497,plain,
% 1.06/1.23 (~c0_1(a1149)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[783, 1496])).
% 1.06/1.23 tff(1498,plain,
% 1.06/1.23 (c3_1(a1149)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[791, 1496])).
% 1.06/1.23 tff(1499,plain,
% 1.06/1.23 (c2_1(a1149)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[799, 1496])).
% 1.06/1.23 tff(1500,plain,
% 1.06/1.23 (hskp21),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[844, 1499, 1465, 1498, 1497])).
% 1.06/1.23 tff(1501,plain,
% 1.06/1.23 (~c0_1(a1136)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[763, 1500, 664, 695, 732, 687, 672])).
% 1.06/1.23 tff(1502,plain,
% 1.06/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1503,plain,
% 1.06/1.23 (((~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1101)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1504,plain,
% 1.06/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1101)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1503])).
% 1.06/1.23 tff(1505,plain,
% 1.06/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1101)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1504, 1502])).
% 1.06/1.23 tff(1506,plain,
% 1.06/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1101)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1507,plain,
% 1.06/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 1.06/1.23 tff(1508,plain,
% 1.06/1.23 ($false),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1507, 110, 631, 672, 695, 1475, 1495, 687, 57, 1501, 1490, 1476])).
% 1.06/1.23 tff(1509,plain,(c0_1(a1130) | c3_1(a1130) | hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.23 tff(1510,plain,
% 1.06/1.23 ($false),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1509, 1398, 1397, 632, 35, 47, 34])).
% 1.06/1.23 tff(1511,plain,(hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.23 tff(1512,plain,
% 1.06/1.23 (hskp14),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1511, 47, 35, 34])).
% 1.06/1.23 tff(1513,plain,
% 1.06/1.23 (~c3_1(a1118)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[160, 1512])).
% 1.06/1.23 tff(1514,plain,
% 1.06/1.23 (c1_1(a1118)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[174, 1512])).
% 1.06/1.23 tff(1515,plain,
% 1.06/1.23 (~c2_1(a1118)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[166, 1512])).
% 1.06/1.23 tff(1516,plain,
% 1.06/1.23 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.06/1.23 inference(bind,[status(th)],[])).
% 1.06/1.23 tff(1517,plain,
% 1.06/1.23 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.06/1.23 inference(quant_intro,[status(thm)],[1516])).
% 1.06/1.23 tff(1518,plain,
% 1.06/1.23 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1519,plain,
% 1.06/1.23 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.06/1.23 inference(bind,[status(th)],[])).
% 1.06/1.23 tff(1520,plain,
% 1.06/1.23 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.06/1.23 inference(quant_intro,[status(thm)],[1519])).
% 1.06/1.23 tff(1521,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.06/1.23 tff(1522,plain,
% 1.06/1.23 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.06/1.23 tff(1523,plain,
% 1.06/1.23 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1522, 1518])).
% 1.06/1.23 tff(1524,plain,(
% 1.06/1.23 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.06/1.23 inference(skolemize,[status(sab)],[1523])).
% 1.06/1.23 tff(1525,plain,
% 1.06/1.23 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1524, 1517])).
% 1.06/1.23 tff(1526,assumption,(~hskp23), introduced(assumption)).
% 1.06/1.23 tff(1527,assumption,(hskp9), introduced(assumption)).
% 1.06/1.23 tff(1528,plain,
% 1.06/1.23 (~c3_1(a1108)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[464, 1527])).
% 1.06/1.23 tff(1529,plain,
% 1.06/1.23 (~c1_1(a1108)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[470, 1527])).
% 1.06/1.23 tff(1530,plain,
% 1.06/1.23 (c0_1(a1108)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[478, 1527])).
% 1.06/1.23 tff(1531,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1532,plain,
% 1.06/1.23 ((hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108))) <=> (hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1533,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1532])).
% 1.06/1.23 tff(1534,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1533, 1531])).
% 1.06/1.23 tff(1535,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1536,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1535, 1534])).
% 1.06/1.23 tff(1537,plain,
% 1.06/1.23 (~c0_1(a1136)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1536, 1526, 110, 697, 696, 1530, 1529, 1528, 1525])).
% 1.06/1.23 tff(1538,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1539,plain,
% 1.06/1.23 ((hskp29 | (~ndr1_0) | c3_1(a1108) | c1_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136))) <=> (hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1540,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1108) | c1_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1539])).
% 1.06/1.23 tff(1541,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1108) | c1_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1540, 1538])).
% 1.06/1.23 tff(1542,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1108) | c1_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1543,plain,
% 1.06/1.23 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.06/1.23 tff(1544,plain,
% 1.06/1.23 ($false),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1543, 110, 698, 697, 696, 1530, 1529, 1528, 717, 1537])).
% 1.06/1.23 tff(1545,plain,((~hskp9) | hskp29 | (~c1_1(a1136)) | (~c2_1(a1136)) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.06/1.23 tff(1546,plain,
% 1.06/1.23 (~hskp9),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1545, 1526, 697, 696, 698])).
% 1.06/1.23 tff(1547,plain,
% 1.06/1.23 (^[U: $i] : refl((hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 1.06/1.23 inference(bind,[status(th)],[])).
% 1.06/1.23 tff(1548,plain,
% 1.06/1.23 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.06/1.23 inference(quant_intro,[status(thm)],[1547])).
% 1.06/1.23 tff(1549,plain,
% 1.06/1.23 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1550,plain,
% 1.06/1.23 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp9))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp19) <=> ((hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp19))), rewrite(((hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp19) <=> (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.06/1.23 inference(bind,[status(th)],[])).
% 1.06/1.23 tff(1551,plain,
% 1.06/1.23 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp19) <=> ![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.06/1.23 inference(quant_intro,[status(thm)],[1550])).
% 1.06/1.23 tff(1552,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.06/1.23 tff(1553,plain,
% 1.06/1.23 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 1.06/1.23 tff(1554,plain,
% 1.06/1.23 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1553, 1549])).
% 1.06/1.23 tff(1555,plain,(
% 1.06/1.23 ![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.06/1.23 inference(skolemize,[status(sab)],[1554])).
% 1.06/1.23 tff(1556,plain,
% 1.06/1.23 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1555, 1548])).
% 1.06/1.23 tff(1557,plain,
% 1.06/1.23 (((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1558,plain,
% 1.06/1.23 ((hskp19 | hskp9 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136))) <=> (hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1559,plain,
% 1.06/1.23 (((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[1558])).
% 1.06/1.23 tff(1560,plain,
% 1.06/1.23 (((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[1559, 1557])).
% 1.06/1.23 tff(1561,plain,
% 1.06/1.23 ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(1562,plain,
% 1.06/1.23 ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 1.06/1.23 tff(1563,plain,
% 1.06/1.23 (hskp19 | hskp9),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1562, 110, 697, 696, 673, 1556])).
% 1.06/1.23 tff(1564,plain,
% 1.06/1.23 (hskp19),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[1563, 1546])).
% 1.06/1.23 tff(1565,plain,
% 1.06/1.23 (~c2_1(a1127)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[816, 1564])).
% 1.06/1.23 tff(1566,plain,
% 1.06/1.23 (c3_1(a1127)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[825, 1564])).
% 1.06/1.23 tff(1567,plain,
% 1.06/1.23 (c1_1(a1127)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[833, 1564])).
% 1.06/1.23 tff(1568,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1569,plain,
% 1.06/1.23 ((hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127))) <=> (hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(1570,plain,
% 1.06/1.23 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1569])).
% 1.06/1.24 tff(1571,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1570, 1568])).
% 1.06/1.24 tff(1572,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1573,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 1.06/1.24 tff(1574,plain,
% 1.06/1.24 (c0_1(a1127)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1573, 110, 698, 1566, 210, 1565, 212, 208, 67])).
% 1.06/1.24 tff(1575,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1576,plain,
% 1.06/1.24 ((hskp28 | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1127)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1577,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1127)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1576])).
% 1.06/1.24 tff(1578,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1127)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1577, 1575])).
% 1.06/1.24 tff(1579,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1127)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1580,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 1.06/1.24 tff(1581,plain,
% 1.06/1.24 (hskp28 | (~c0_1(a1127))),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1580, 110, 1567, 1566, 1565, 528])).
% 1.06/1.24 tff(1582,plain,
% 1.06/1.24 (hskp28),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1581, 1574])).
% 1.06/1.24 tff(1583,plain,
% 1.06/1.24 (c2_1(a1111)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[551, 1582])).
% 1.06/1.24 tff(1584,plain,
% 1.06/1.24 (c0_1(a1111)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[567, 1582])).
% 1.06/1.24 tff(1585,plain,
% 1.06/1.24 (^[U: $i] : refl((hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.06/1.24 inference(bind,[status(th)],[])).
% 1.06/1.24 tff(1586,plain,
% 1.06/1.24 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.06/1.24 inference(quant_intro,[status(thm)],[1585])).
% 1.06/1.24 tff(1587,plain,
% 1.06/1.24 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1588,plain,
% 1.06/1.24 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp13) <=> ((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp13) <=> (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.06/1.24 inference(bind,[status(th)],[])).
% 1.06/1.24 tff(1589,plain,
% 1.06/1.24 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp13) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.06/1.24 inference(quant_intro,[status(thm)],[1588])).
% 1.06/1.24 tff(1590,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.06/1.24 tff(1591,plain,
% 1.06/1.24 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 1.06/1.24 tff(1592,plain,
% 1.06/1.24 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1591, 1587])).
% 1.06/1.24 tff(1593,plain,(
% 1.06/1.24 ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.06/1.24 inference(skolemize,[status(sab)],[1592])).
% 1.06/1.24 tff(1594,plain,
% 1.06/1.24 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1593, 1586])).
% 1.06/1.24 tff(1595,assumption,(c2_1(a1111)), introduced(assumption)).
% 1.06/1.24 tff(1596,assumption,(c0_1(a1111)), introduced(assumption)).
% 1.06/1.24 tff(1597,assumption,(~hskp9), introduced(assumption)).
% 1.06/1.24 tff(1598,plain,
% 1.06/1.24 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1111) | (~c2_1(a1111)) | (~c0_1(a1111)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | (~ndr1_0) | c3_1(a1111) | (~c2_1(a1111)) | (~c0_1(a1111)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1599,plain,
% 1.06/1.24 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1111) | (~c2_1(a1111)) | (~c0_1(a1111)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1600,plain,
% 1.06/1.24 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | (~ndr1_0) | c3_1(a1111) | (~c2_1(a1111)) | (~c0_1(a1111))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 1.06/1.24 tff(1601,plain,
% 1.06/1.24 (hskp13 | c3_1(a1111)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1600, 110, 1597, 1596, 1595, 1594])).
% 1.06/1.24 tff(1602,plain,
% 1.06/1.24 (c3_1(a1111)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1601, 1116])).
% 1.06/1.24 tff(1603,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1604,plain,
% 1.06/1.24 ((hskp2 | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1605,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1604])).
% 1.06/1.24 tff(1606,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1605, 1603])).
% 1.06/1.24 tff(1607,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1608,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1607, 1606])).
% 1.06/1.24 tff(1609,plain,
% 1.06/1.24 (hskp2),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1608, 110, 1596, 1595, 937, 917, 916, 260, 1602])).
% 1.06/1.24 tff(1610,plain,
% 1.06/1.24 (~c3_1(a1100)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[273, 1609])).
% 1.06/1.24 tff(1611,plain,
% 1.06/1.24 (c2_1(a1100)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[281, 1609])).
% 1.06/1.24 tff(1612,plain,
% 1.06/1.24 (c0_1(a1100)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[289, 1609])).
% 1.06/1.24 tff(1613,plain,
% 1.06/1.24 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1614,plain,
% 1.06/1.24 ((hskp13 | hskp9 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100))) <=> (hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1615,plain,
% 1.06/1.24 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1614])).
% 1.06/1.24 tff(1616,plain,
% 1.06/1.24 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1615, 1613])).
% 1.06/1.24 tff(1617,plain,
% 1.06/1.24 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1618,plain,
% 1.06/1.24 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.06/1.24 tff(1619,plain,
% 1.06/1.24 ($false),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1618, 110, 1116, 1597, 1612, 1611, 1610, 1594])).
% 1.06/1.24 tff(1620,plain,(hskp13 | hskp9 | (~c0_1(a1111)) | (~c2_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)) | c2_1(a1127)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.24 tff(1621,plain,
% 1.06/1.24 (hskp13),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1620, 1546, 1584, 1583, 1567, 1566, 1565])).
% 1.06/1.24 tff(1622,plain,
% 1.06/1.24 (~c3_1(a1115)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1252, 1621])).
% 1.06/1.24 tff(1623,plain,
% 1.06/1.24 (~c1_1(a1115)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1130, 1621])).
% 1.06/1.24 tff(1624,plain,
% 1.06/1.24 (c1_1(a1111)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[559, 1582])).
% 1.06/1.24 tff(1625,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1626,plain,
% 1.06/1.24 ((hskp23 | (~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115))) <=> (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1627,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1626])).
% 1.06/1.24 tff(1628,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1627, 1625])).
% 1.06/1.24 tff(1629,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1630,plain,
% 1.06/1.24 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 1.06/1.24 tff(1631,plain,
% 1.06/1.24 (~c0_1(a1115)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1630, 1526, 110, 1584, 1624, 1583, 1623, 1622, 1525])).
% 1.06/1.24 tff(1632,plain,
% 1.06/1.24 (c2_1(a1115)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1138, 1621])).
% 1.06/1.24 tff(1633,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1634,plain,
% 1.06/1.24 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1635,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1634])).
% 1.06/1.24 tff(1636,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1635, 1633])).
% 1.06/1.24 tff(1637,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1638,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 1.06/1.24 tff(1639,plain,
% 1.06/1.24 ((~c0_1(a1136)) | c0_1(a1115)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1638, 110, 696, 673, 1632, 902, 875, 1623, 612, 642])).
% 1.06/1.24 tff(1640,plain,
% 1.06/1.24 (~c0_1(a1136)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1639, 1631])).
% 1.06/1.24 tff(1641,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1642,plain,
% 1.06/1.24 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136))) <=> (c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1643,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.06/1.24 inference(monotonicity,[status(thm)],[1642])).
% 1.06/1.24 tff(1644,plain,
% 1.06/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.24 inference(transitivity,[status(thm)],[1643, 1641])).
% 1.06/1.24 tff(1645,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))),
% 1.06/1.24 inference(quant_inst,[status(thm)],[])).
% 1.06/1.24 tff(1646,plain,
% 1.06/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.06/1.24 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 1.06/1.24 tff(1647,plain,
% 1.06/1.24 (~c0_1(a1118)),
% 1.06/1.24 inference(unit_resolution,[status(thm)],[1646, 110, 697, 696, 673, 210, 208, 45, 1640])).
% 1.06/1.24 tff(1648,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1649,plain,
% 1.06/1.24 ((hskp9 | (~ndr1_0) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.06/1.24 inference(rewrite,[status(thm)],[])).
% 1.06/1.24 tff(1650,plain,
% 1.06/1.24 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1649])).
% 1.06/1.25 tff(1651,plain,
% 1.06/1.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1650, 1648])).
% 1.06/1.25 tff(1652,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1653,plain,
% 1.06/1.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.06/1.25 tff(1654,plain,
% 1.06/1.25 ($false),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1653, 110, 1546, 697, 696, 210, 212, 398, 1647, 1640])).
% 1.06/1.25 tff(1655,plain,(hskp23 | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c1_1(a1118)) | c2_1(a1118) | (~c3_1(a1136)) | c3_1(a1118) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.06/1.25 tff(1656,plain,
% 1.06/1.25 (hskp23),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1655, 698, 672, 1514, 1515, 664, 1513, 656, 655, 583, 631])).
% 1.06/1.25 tff(1657,plain,
% 1.06/1.25 (~c3_1(a1147)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[686, 1656])).
% 1.06/1.25 tff(1658,plain,
% 1.06/1.25 (c0_1(a1147)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[694, 1656])).
% 1.06/1.25 tff(1659,plain,
% 1.06/1.25 (c0_1(a1136)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[725, 1658, 631, 672, 698, 1657, 664])).
% 1.06/1.25 tff(1660,plain,
% 1.06/1.25 (~c2_1(a1147)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[731, 1656])).
% 1.06/1.25 tff(1661,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1662,plain,
% 1.06/1.25 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1663,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1662])).
% 1.06/1.25 tff(1664,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1663, 1661])).
% 1.06/1.25 tff(1665,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1666,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 1.06/1.25 tff(1667,plain,
% 1.06/1.25 (c0_1(a1118)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1666, 110, 672, 664, 1658, 1514, 1660, 1657, 1513, 320, 1659])).
% 1.06/1.25 tff(1668,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1669,plain,
% 1.06/1.25 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107))) <=> (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1670,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1669])).
% 1.06/1.25 tff(1671,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1670, 1668])).
% 1.06/1.25 tff(1672,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1673,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 1.06/1.25 tff(1674,plain,
% 1.06/1.25 (c2_1(a1107)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1673, 110, 696, 673, 210, 1115, 212, 1084, 228, 209, 733])).
% 1.06/1.25 tff(1675,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1676,plain,
% 1.06/1.25 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107))) <=> (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1677,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1676])).
% 1.06/1.25 tff(1678,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1677, 1675])).
% 1.06/1.25 tff(1679,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1680,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 1.06/1.25 tff(1681,plain,
% 1.06/1.25 ($false),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1680, 110, 696, 673, 902, 875, 1090, 1084, 612, 642, 733, 1674])).
% 1.06/1.25 tff(1682,plain,((~hskp8) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | (~c0_1(a1136)) | (~c1_1(a1118)) | c2_1(a1118) | (~c0_1(a1118))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.25 tff(1683,plain,
% 1.06/1.25 (~hskp8),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1682, 1659, 664, 656, 655, 583, 672, 1514, 1515, 1667])).
% 1.06/1.25 tff(1684,plain,
% 1.06/1.25 (hskp19),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1076, 1683, 35, 47])).
% 1.06/1.25 tff(1685,plain,
% 1.06/1.25 (~c2_1(a1127)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[816, 1684])).
% 1.06/1.25 tff(1686,plain,
% 1.06/1.25 (c3_1(a1127)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[825, 1684])).
% 1.06/1.25 tff(1687,plain,
% 1.06/1.25 (c0_1(a1127)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1573, 110, 698, 1686, 1514, 1685, 1515, 1513, 67])).
% 1.06/1.25 tff(1688,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1689,plain,
% 1.06/1.25 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1690,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1689])).
% 1.06/1.25 tff(1691,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1690, 1688])).
% 1.06/1.25 tff(1692,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1693,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1692, 1691])).
% 1.06/1.25 tff(1694,plain,
% 1.06/1.25 ((~c0_1(a1136)) | c2_1(a1105) | (~c0_1(a1118))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1693, 110, 672, 664, 1514, 655, 1515, 583, 228])).
% 1.06/1.25 tff(1695,plain,
% 1.06/1.25 (c2_1(a1105)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1694, 1667, 1659])).
% 1.06/1.25 tff(1696,plain,
% 1.06/1.25 (hskp20 | (~c0_1(a1127))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[923, 110, 1686, 656, 1685, 583, 915, 1695])).
% 1.06/1.25 tff(1697,plain,
% 1.06/1.25 (hskp20),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1696, 1687])).
% 1.06/1.25 tff(1698,plain,
% 1.06/1.25 (~c3_1(a1130)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[308, 1697])).
% 1.06/1.25 tff(1699,plain,
% 1.06/1.25 (~c0_1(a1130)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[302, 1697])).
% 1.06/1.25 tff(1700,plain,
% 1.06/1.25 (hskp2 | (~c2_1(a1105))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[981, 110, 656, 655, 583, 975])).
% 1.06/1.25 tff(1701,plain,
% 1.06/1.25 (hskp2),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1700, 1695])).
% 1.06/1.25 tff(1702,plain,
% 1.06/1.25 (c0_1(a1100)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[289, 1701])).
% 1.06/1.25 tff(1703,plain,
% 1.06/1.25 (~c3_1(a1100)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[273, 1701])).
% 1.06/1.25 tff(1704,plain,
% 1.06/1.25 (c2_1(a1100)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[281, 1701])).
% 1.06/1.25 tff(1705,plain,
% 1.06/1.25 (hskp5),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1305, 1699, 1659, 1698, 1704, 1703, 672, 664, 656, 655, 583, 1702, 1658, 1660, 1657])).
% 1.06/1.25 tff(1706,plain,
% 1.06/1.25 (~c2_1(a1103)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[123, 1705])).
% 1.06/1.25 tff(1707,plain,
% 1.06/1.25 (c3_1(a1103)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[147, 1705])).
% 1.06/1.25 tff(1708,plain,
% 1.06/1.25 (~c0_1(a1103)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[129, 1705])).
% 1.06/1.25 tff(1709,plain,
% 1.06/1.25 ($false),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[349, 1708, 1707, 1515, 1667, 1706, 1699, 1698, 1513, 1514])).
% 1.06/1.25 tff(1710,plain,(hskp29 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.25 tff(1711,plain,
% 1.06/1.25 (hskp29),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1710, 47, 35, 34])).
% 1.06/1.25 tff(1712,plain,
% 1.06/1.25 (c3_1(a1116)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[189, 1711])).
% 1.06/1.25 tff(1713,plain,
% 1.06/1.25 (c2_1(a1116)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[197, 1711])).
% 1.06/1.25 tff(1714,plain,
% 1.06/1.25 (c0_1(a1116)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[205, 1711])).
% 1.06/1.25 tff(1715,plain,
% 1.06/1.25 (hskp13),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1124, 1078, 1714, 1713, 1712, 656, 655, 583])).
% 1.06/1.25 tff(1716,plain,
% 1.06/1.25 (~c1_1(a1115)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1130, 1715])).
% 1.06/1.25 tff(1717,plain,
% 1.06/1.25 (c2_1(a1115)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1138, 1715])).
% 1.06/1.25 tff(1718,plain,
% 1.06/1.25 (c0_1(a1115)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1269, 110, 1714, 1713, 1712, 1717, 656, 655, 1716, 583, 642])).
% 1.06/1.25 tff(1719,plain,
% 1.06/1.25 (~c2_1(a1107)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1096, 110, 1714, 1713, 1712, 656, 655, 1090, 1084, 583, 642])).
% 1.06/1.25 tff(1720,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1721,plain,
% 1.06/1.25 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107))) <=> (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1722,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1721])).
% 1.06/1.25 tff(1723,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1722, 1720])).
% 1.06/1.25 tff(1724,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1725,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 1.06/1.25 tff(1726,plain,
% 1.06/1.25 (c2_1(a1107) | (~c0_1(a1118))),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1725, 110, 1714, 1713, 1712, 1514, 1115, 1515, 1084, 228])).
% 1.06/1.25 tff(1727,plain,
% 1.06/1.25 (~c0_1(a1118)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1726, 1719])).
% 1.06/1.25 tff(1728,plain,
% 1.06/1.25 (hskp1),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[381, 1727, 1514, 1513, 34, 47, 1714, 1713, 1712, 35])).
% 1.06/1.25 tff(1729,plain,
% 1.06/1.25 (~c0_1(a1099)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[387, 1728])).
% 1.06/1.25 tff(1730,plain,
% 1.06/1.25 (~c3_1(a1115)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1252, 1715])).
% 1.06/1.25 tff(1731,plain,
% 1.06/1.25 (c2_1(a1099)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[435, 1728])).
% 1.06/1.25 tff(1732,plain,
% 1.06/1.25 (c1_1(a1099)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[443, 1728])).
% 1.06/1.25 tff(1733,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1734,plain,
% 1.06/1.25 (((~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099))) <=> (c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1735,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115))))),
% 1.06/1.25 inference(monotonicity,[status(thm)],[1734])).
% 1.06/1.25 tff(1736,plain,
% 1.06/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.06/1.25 inference(transitivity,[status(thm)],[1735, 1733])).
% 1.06/1.25 tff(1737,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))),
% 1.06/1.25 inference(quant_inst,[status(thm)],[])).
% 1.06/1.25 tff(1738,plain,
% 1.06/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115))),
% 1.06/1.25 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 1.06/1.25 tff(1739,plain,
% 1.06/1.25 (~c0_1(a1136)),
% 1.06/1.25 inference(unit_resolution,[status(thm)],[1738, 110, 631, 672, 1732, 1731, 1716, 1730, 1729, 57, 1718])).
% 1.06/1.25 tff(1740,plain,
% 1.06/1.25 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.06/1.25 inference(bind,[status(th)],[])).
% 1.06/1.25 tff(1741,plain,
% 1.06/1.25 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.25 inference(quant_intro,[status(thm)],[1740])).
% 1.06/1.25 tff(1742,plain,
% 1.06/1.25 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.25 inference(rewrite,[status(thm)],[])).
% 1.06/1.25 tff(1743,plain,
% 1.06/1.25 (^[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) | c3_1(U) | 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) | c3_1(U) | c2_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(U) | c2_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(U) | c2_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)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_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)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.06/1.26 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(1744,plain,
% 1.06/1.26 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[1743])).
% 1.06/1.26 tff(1745,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)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.06/1.26 tff(1746,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 1.06/1.26 tff(1747,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1746, 1742])).
% 1.06/1.26 tff(1748,plain,(
% 1.06/1.26 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.26 inference(skolemize,[status(sab)],[1747])).
% 1.06/1.26 tff(1749,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1748, 1741])).
% 1.06/1.26 tff(1750,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1751,plain,
% 1.06/1.26 ((hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107))) <=> (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1752,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1751])).
% 1.06/1.26 tff(1753,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1752, 1750])).
% 1.06/1.26 tff(1754,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1755,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 1.06/1.26 tff(1756,plain,
% 1.06/1.26 (hskp11),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1755, 110, 1514, 1115, 1515, 1513, 1084, 1749, 1719])).
% 1.06/1.26 tff(1757,plain,
% 1.06/1.26 (((~hskp11) | (~c2_1(a1113))) <=> ((~hskp11) | (~c2_1(a1113)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1758,plain,
% 1.06/1.26 (((~c2_1(a1113)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1113)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1759,axiom,((~c2_1(a1113)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.06/1.26 tff(1760,plain,
% 1.06/1.26 ((~hskp11) | (~c2_1(a1113))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 1.06/1.26 tff(1761,plain,
% 1.06/1.26 ((~hskp11) | (~c2_1(a1113))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1760, 1757])).
% 1.06/1.26 tff(1762,plain,
% 1.06/1.26 (~c2_1(a1113)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1761, 1756])).
% 1.06/1.26 tff(1763,plain,
% 1.06/1.26 (((~hskp11) | c0_1(a1113)) <=> ((~hskp11) | c0_1(a1113))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1764,axiom,((~hskp11) | c0_1(a1113)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.06/1.26 tff(1765,plain,
% 1.06/1.26 ((~hskp11) | c0_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 1.06/1.26 tff(1766,plain,
% 1.06/1.26 ((~hskp11) | c0_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1765, 1763])).
% 1.06/1.26 tff(1767,plain,
% 1.06/1.26 ((~hskp11) | c0_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1766, 1763])).
% 1.06/1.26 tff(1768,plain,
% 1.06/1.26 ((~hskp11) | c0_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1767, 1763])).
% 1.06/1.26 tff(1769,plain,
% 1.06/1.26 ((~hskp11) | c0_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1768, 1763])).
% 1.06/1.26 tff(1770,plain,
% 1.06/1.26 (c0_1(a1113)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1769, 1756])).
% 1.06/1.26 tff(1771,plain,
% 1.06/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1772,plain,
% 1.06/1.26 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1773,plain,
% 1.06/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1772])).
% 1.06/1.26 tff(1774,plain,
% 1.06/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1773, 1771])).
% 1.06/1.26 tff(1775,plain,
% 1.06/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1776,plain,
% 1.06/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 1.06/1.26 tff(1777,plain,
% 1.06/1.26 (~c1_1(a1113)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1776, 110, 631, 672, 1770, 1716, 1730, 1762, 1316, 1739, 1718])).
% 1.06/1.26 tff(1778,plain,
% 1.06/1.26 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.06/1.26 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(1779,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[1778])).
% 1.06/1.26 tff(1780,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1781,plain,
% 1.06/1.26 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.06/1.26 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(1782,plain,
% 1.06/1.26 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[1781])).
% 1.06/1.26 tff(1783,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.06/1.26 tff(1784,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1783, 1782])).
% 1.06/1.26 tff(1785,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1784, 1780])).
% 1.06/1.26 tff(1786,plain,(
% 1.06/1.26 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.06/1.26 inference(skolemize,[status(sab)],[1785])).
% 1.06/1.26 tff(1787,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1786, 1779])).
% 1.06/1.26 tff(1788,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1789,plain,
% 1.06/1.26 ((hskp4 | (~ndr1_0) | c2_1(a1113) | c1_1(a1113) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136))) <=> (hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1790,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1113) | c1_1(a1113) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1789])).
% 1.06/1.26 tff(1791,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1113) | c1_1(a1113) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1790, 1788])).
% 1.06/1.26 tff(1792,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1113) | c1_1(a1113) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1793,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 1.06/1.26 tff(1794,plain,
% 1.06/1.26 (hskp4),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1793, 110, 672, 664, 1770, 1762, 1787, 1739, 1777])).
% 1.06/1.26 tff(1795,plain,
% 1.06/1.26 (~c3_1(a1102)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1427, 1794])).
% 1.06/1.26 tff(1796,plain,
% 1.06/1.26 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.06/1.26 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(1797,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[1796])).
% 1.06/1.26 tff(1798,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1799,plain,
% 1.06/1.26 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.06/1.26 inference(bind,[status(th)],[])).
% 1.06/1.26 tff(1800,plain,
% 1.06/1.26 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.06/1.26 inference(quant_intro,[status(thm)],[1799])).
% 1.06/1.26 tff(1801,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.06/1.26 tff(1802,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 1.06/1.26 tff(1803,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1802, 1798])).
% 1.06/1.26 tff(1804,plain,(
% 1.06/1.26 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.06/1.26 inference(skolemize,[status(sab)],[1803])).
% 1.06/1.26 tff(1805,plain,
% 1.06/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1804, 1797])).
% 1.06/1.26 tff(1806,plain,
% 1.06/1.26 (((~hskp11) | c3_1(a1113)) <=> ((~hskp11) | c3_1(a1113))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1807,axiom,((~hskp11) | c3_1(a1113)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.06/1.26 tff(1808,plain,
% 1.06/1.26 ((~hskp11) | c3_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 1.06/1.26 tff(1809,plain,
% 1.06/1.26 ((~hskp11) | c3_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1808, 1806])).
% 1.06/1.26 tff(1810,plain,
% 1.06/1.26 ((~hskp11) | c3_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1809, 1806])).
% 1.06/1.26 tff(1811,plain,
% 1.06/1.26 ((~hskp11) | c3_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1810, 1806])).
% 1.06/1.26 tff(1812,plain,
% 1.06/1.26 ((~hskp11) | c3_1(a1113)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1811, 1806])).
% 1.06/1.26 tff(1813,plain,
% 1.06/1.26 (c3_1(a1113)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1812, 1756])).
% 1.06/1.26 tff(1814,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1815,plain,
% 1.06/1.26 ((hskp16 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136))) <=> (hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1816,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1815])).
% 1.06/1.26 tff(1817,plain,
% 1.06/1.26 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1816, 1814])).
% 1.06/1.26 tff(1818,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1819,plain,
% 1.06/1.26 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.06/1.26 tff(1820,plain,
% 1.06/1.26 (hskp16),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1819, 110, 631, 664, 1770, 1813, 1762, 1805, 1739])).
% 1.06/1.26 tff(1821,plain,
% 1.06/1.26 (((~hskp16) | (~c0_1(a1121))) <=> ((~hskp16) | (~c0_1(a1121)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1822,plain,
% 1.06/1.26 (((~c0_1(a1121)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1121)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1823,axiom,((~c0_1(a1121)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.06/1.26 tff(1824,plain,
% 1.06/1.26 ((~hskp16) | (~c0_1(a1121))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 1.06/1.26 tff(1825,plain,
% 1.06/1.26 ((~hskp16) | (~c0_1(a1121))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1824, 1821])).
% 1.06/1.26 tff(1826,plain,
% 1.06/1.26 (~c0_1(a1121)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1825, 1820])).
% 1.06/1.26 tff(1827,plain,
% 1.06/1.26 (c1_1(a1102)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1444, 1794])).
% 1.06/1.26 tff(1828,plain,
% 1.06/1.26 (c0_1(a1102)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1452, 1794])).
% 1.06/1.26 tff(1829,plain,
% 1.06/1.26 (((~hskp16) | c3_1(a1121)) <=> ((~hskp16) | c3_1(a1121))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1830,axiom,((~hskp16) | c3_1(a1121)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.06/1.26 tff(1831,plain,
% 1.06/1.26 ((~hskp16) | c3_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 1.06/1.26 tff(1832,plain,
% 1.06/1.26 ((~hskp16) | c3_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1831, 1829])).
% 1.06/1.26 tff(1833,plain,
% 1.06/1.26 ((~hskp16) | c3_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1832, 1829])).
% 1.06/1.26 tff(1834,plain,
% 1.06/1.26 ((~hskp16) | c3_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1833, 1829])).
% 1.06/1.26 tff(1835,plain,
% 1.06/1.26 ((~hskp16) | c3_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1834, 1829])).
% 1.06/1.26 tff(1836,plain,
% 1.06/1.26 (c3_1(a1121)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1835, 1820])).
% 1.06/1.26 tff(1837,plain,
% 1.06/1.26 (((~hskp16) | c1_1(a1121)) <=> ((~hskp16) | c1_1(a1121))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1838,axiom,((~hskp16) | c1_1(a1121)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.06/1.26 tff(1839,plain,
% 1.06/1.26 ((~hskp16) | c1_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 1.06/1.26 tff(1840,plain,
% 1.06/1.26 ((~hskp16) | c1_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1839, 1837])).
% 1.06/1.26 tff(1841,plain,
% 1.06/1.26 ((~hskp16) | c1_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1840, 1837])).
% 1.06/1.26 tff(1842,plain,
% 1.06/1.26 ((~hskp16) | c1_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1841, 1837])).
% 1.06/1.26 tff(1843,plain,
% 1.06/1.26 ((~hskp16) | c1_1(a1121)),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1842, 1837])).
% 1.06/1.26 tff(1844,plain,
% 1.06/1.26 (c1_1(a1121)),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1843, 1820])).
% 1.06/1.26 tff(1845,plain,
% 1.06/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1846,plain,
% 1.06/1.26 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121))) <=> (c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1847,plain,
% 1.06/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 1.06/1.26 inference(monotonicity,[status(thm)],[1846])).
% 1.06/1.26 tff(1848,plain,
% 1.06/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.06/1.26 inference(transitivity,[status(thm)],[1847, 1845])).
% 1.06/1.26 tff(1849,plain,
% 1.06/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.06/1.26 inference(quant_inst,[status(thm)],[])).
% 1.06/1.26 tff(1850,plain,
% 1.06/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 1.06/1.26 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 1.06/1.26 tff(1851,plain,
% 1.06/1.26 ($false),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1850, 110, 631, 672, 664, 1844, 1836, 1828, 1827, 1826, 1795, 45])).
% 1.06/1.26 tff(1852,plain,((~hskp8) | c1_1(a1098) | c3_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.26 tff(1853,plain,
% 1.06/1.26 (~hskp8),
% 1.06/1.26 inference(unit_resolution,[status(thm)],[1852, 47, 34, 35])).
% 1.06/1.26 tff(1854,assumption,(~hskp8), introduced(assumption)).
% 1.06/1.26 tff(1855,plain,
% 1.06/1.26 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.06/1.26 inference(rewrite,[status(thm)],[])).
% 1.06/1.26 tff(1856,plain,
% 1.06/1.26 ((hskp8 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118)) <=> (hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1857,plain,
% 1.06/1.27 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118)))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1856])).
% 1.06/1.27 tff(1858,plain,
% 1.06/1.27 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1857, 1855])).
% 1.06/1.27 tff(1859,plain,
% 1.06/1.27 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1860,plain,
% 1.06/1.27 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118)),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 1.06/1.27 tff(1861,plain,
% 1.06/1.27 (hskp8 | hskp6 | c0_1(a1118)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1860, 110, 212, 208, 1333])).
% 1.06/1.27 tff(1862,plain,
% 1.06/1.27 (hskp6),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1861, 354, 1854])).
% 1.06/1.27 tff(1863,plain,
% 1.06/1.27 (~c2_1(a1104)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[502, 1862])).
% 1.06/1.27 tff(1864,plain,
% 1.06/1.27 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(1865,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[1864])).
% 1.06/1.27 tff(1866,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1867,plain,
% 1.06/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(1868,plain,
% 1.06/1.27 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[1867])).
% 1.06/1.27 tff(1869,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.06/1.27 tff(1870,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 1.06/1.27 tff(1871,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1870, 1866])).
% 1.06/1.27 tff(1872,plain,(
% 1.06/1.27 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.27 inference(skolemize,[status(sab)],[1871])).
% 1.06/1.27 tff(1873,plain,
% 1.06/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1872, 1865])).
% 1.06/1.27 tff(1874,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1875,plain,
% 1.06/1.27 ((hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1876,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1875])).
% 1.06/1.27 tff(1877,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1876, 1874])).
% 1.06/1.27 tff(1878,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1879,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 1.06/1.27 tff(1880,plain,
% 1.06/1.27 (hskp10 | c0_1(a1118)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1879, 110, 697, 696, 673, 210, 212, 1873])).
% 1.06/1.27 tff(1881,plain,
% 1.06/1.27 (hskp10),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1880, 354])).
% 1.06/1.27 tff(1882,plain,
% 1.06/1.27 (((~hskp10) | (~c2_1(a1110))) <=> ((~hskp10) | (~c2_1(a1110)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1883,plain,
% 1.06/1.27 (((~c2_1(a1110)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a1110)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1884,axiom,((~c2_1(a1110)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.06/1.27 tff(1885,plain,
% 1.06/1.27 ((~hskp10) | (~c2_1(a1110))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 1.06/1.27 tff(1886,plain,
% 1.06/1.27 ((~hskp10) | (~c2_1(a1110))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1885, 1882])).
% 1.06/1.27 tff(1887,plain,
% 1.06/1.27 (~c2_1(a1110)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1886, 1881])).
% 1.06/1.27 tff(1888,plain,
% 1.06/1.27 (((~hskp10) | (~c1_1(a1110))) <=> ((~hskp10) | (~c1_1(a1110)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1889,plain,
% 1.06/1.27 (((~c1_1(a1110)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1110)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1890,axiom,((~c1_1(a1110)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.06/1.27 tff(1891,plain,
% 1.06/1.27 ((~hskp10) | (~c1_1(a1110))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 1.06/1.27 tff(1892,plain,
% 1.06/1.27 ((~hskp10) | (~c1_1(a1110))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1891, 1888])).
% 1.06/1.27 tff(1893,plain,
% 1.06/1.27 (~c1_1(a1110)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1892, 1881])).
% 1.06/1.27 tff(1894,plain,
% 1.06/1.27 (c1_1(a1104)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[535, 1862])).
% 1.06/1.27 tff(1895,plain,
% 1.06/1.27 (c0_1(a1104)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[510, 1862])).
% 1.06/1.27 tff(1896,plain,
% 1.06/1.27 (((~hskp10) | c3_1(a1110)) <=> ((~hskp10) | c3_1(a1110))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1897,axiom,((~hskp10) | c3_1(a1110)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.06/1.27 tff(1898,plain,
% 1.06/1.27 ((~hskp10) | c3_1(a1110)),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 1.06/1.27 tff(1899,plain,
% 1.06/1.27 ((~hskp10) | c3_1(a1110)),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1898, 1896])).
% 1.06/1.27 tff(1900,plain,
% 1.06/1.27 ((~hskp10) | c3_1(a1110)),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1899, 1896])).
% 1.06/1.27 tff(1901,plain,
% 1.06/1.27 ((~hskp10) | c3_1(a1110)),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1900, 1896])).
% 1.06/1.27 tff(1902,plain,
% 1.06/1.27 ((~hskp10) | c3_1(a1110)),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1901, 1896])).
% 1.06/1.27 tff(1903,plain,
% 1.06/1.27 (c3_1(a1110)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1902, 1881])).
% 1.06/1.27 tff(1904,plain,
% 1.06/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1905,plain,
% 1.06/1.27 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110))) <=> (c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1906,plain,
% 1.06/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1905])).
% 1.06/1.27 tff(1907,plain,
% 1.06/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1906, 1904])).
% 1.06/1.27 tff(1908,plain,
% 1.06/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1909,plain,
% 1.06/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 1.06/1.27 tff(1910,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1909, 110, 231, 230, 229, 1903, 1895, 1894, 1893, 1887, 1863, 228])).
% 1.06/1.27 tff(1911,plain,(c0_1(a1118) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | hskp8 | c2_1(a1118) | c3_1(a1118) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(1912,plain,
% 1.06/1.27 (c0_1(a1118)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1911, 1714, 1713, 1712, 1853, 1515, 1513, 631, 672, 664, 1514])).
% 1.06/1.27 tff(1913,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1646, 110, 697, 696, 673, 210, 208, 45, 209, 46])).
% 1.06/1.27 tff(1914,plain,(c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c3_1(a1118) | (~c0_1(a1118))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(1915,plain,
% 1.06/1.27 (c0_1(a1136)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1914, 1912, 672, 664, 1514, 1513, 631])).
% 1.06/1.27 tff(1916,plain,
% 1.06/1.27 (hskp1),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[381, 354, 1514, 1513, 34, 47, 1714, 1713, 1712, 35])).
% 1.06/1.27 tff(1917,plain,
% 1.06/1.27 (~c0_1(a1099)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[387, 1916])).
% 1.06/1.27 tff(1918,plain,
% 1.06/1.27 (hskp8 | hskp6 | c0_1(a1118)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1860, 110, 1515, 1513, 1333])).
% 1.06/1.27 tff(1919,plain,
% 1.06/1.27 (hskp6),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1918, 354, 1853])).
% 1.06/1.27 tff(1920,plain,
% 1.06/1.27 (~c2_1(a1104)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[502, 1919])).
% 1.06/1.27 tff(1921,assumption,(~c3_1(a1108)), introduced(assumption)).
% 1.06/1.27 tff(1922,assumption,(~c1_1(a1108)), introduced(assumption)).
% 1.06/1.27 tff(1923,plain,
% 1.06/1.27 (c2_1(a1099)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[435, 1916])).
% 1.06/1.27 tff(1924,plain,
% 1.06/1.27 (c1_1(a1099)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[443, 1916])).
% 1.06/1.27 tff(1925,plain,
% 1.06/1.27 (c1_1(a1104)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[535, 1919])).
% 1.06/1.27 tff(1926,plain,
% 1.06/1.27 (c0_1(a1104)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[510, 1919])).
% 1.06/1.27 tff(1927,assumption,(c0_1(a1108)), introduced(assumption)).
% 1.06/1.27 tff(1928,plain,
% 1.06/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1929,plain,
% 1.06/1.27 (((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099))) <=> (c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1930,plain,
% 1.06/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1929])).
% 1.06/1.27 tff(1931,plain,
% 1.06/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1930, 1928])).
% 1.06/1.27 tff(1932,plain,
% 1.06/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1933,plain,
% 1.06/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.06/1.27 tff(1934,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1933, 110, 1927, 1926, 1925, 1924, 1923, 1922, 1921, 1920, 1917, 1316])).
% 1.06/1.27 tff(1935,plain,(c0_1(a1118) | (~c0_1(a1108)) | c1_1(a1108) | c3_1(a1108) | c1_1(a1098) | c3_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(1936,plain,
% 1.06/1.27 (c0_1(a1118)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1935, 1530, 1529, 1528, 34, 47, 35])).
% 1.06/1.27 tff(1937,plain,
% 1.06/1.27 (c0_1(a1136)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1914, 1936, 672, 664, 1514, 1513, 631])).
% 1.06/1.27 tff(1938,plain,
% 1.06/1.27 (hskp23 | (~c0_1(a1136))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1536, 110, 631, 672, 1530, 1529, 1528, 1525])).
% 1.06/1.27 tff(1939,plain,
% 1.06/1.27 (hskp23),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1938, 1937])).
% 1.06/1.27 tff(1940,plain,
% 1.06/1.27 (~c3_1(a1147)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[686, 1939])).
% 1.06/1.27 tff(1941,plain,
% 1.06/1.27 (~c2_1(a1147)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[731, 1939])).
% 1.06/1.27 tff(1942,plain,
% 1.06/1.27 (c0_1(a1147)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[694, 1939])).
% 1.06/1.27 tff(1943,plain,
% 1.06/1.27 (hskp19),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1076, 1853, 35, 47])).
% 1.06/1.27 tff(1944,plain,
% 1.06/1.27 (~c2_1(a1127)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[816, 1943])).
% 1.06/1.27 tff(1945,plain,
% 1.06/1.27 (c3_1(a1127)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[825, 1943])).
% 1.06/1.27 tff(1946,plain,
% 1.06/1.27 (c1_1(a1127)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[833, 1943])).
% 1.06/1.27 tff(1947,plain,
% 1.06/1.27 (hskp2),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1164, 110, 1714, 1713, 1712, 1946, 1945, 1944, 260])).
% 1.06/1.27 tff(1948,plain,
% 1.06/1.27 (c0_1(a1100)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[289, 1947])).
% 1.06/1.27 tff(1949,plain,
% 1.06/1.27 (~c3_1(a1100)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[273, 1947])).
% 1.06/1.27 tff(1950,plain,
% 1.06/1.27 (c2_1(a1100)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[281, 1947])).
% 1.06/1.27 tff(1951,assumption,(hskp5), introduced(assumption)).
% 1.06/1.27 tff(1952,plain,
% 1.06/1.27 (c3_1(a1103)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[147, 1951])).
% 1.06/1.27 tff(1953,plain,
% 1.06/1.27 (~c0_1(a1103)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[129, 1951])).
% 1.06/1.27 tff(1954,plain,
% 1.06/1.27 (~c2_1(a1103)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[123, 1951])).
% 1.06/1.27 tff(1955,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[351, 1954, 1953, 212, 210, 209, 208, 1952])).
% 1.06/1.27 tff(1956,plain,((~hskp5) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c3_1(a1118)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(1957,plain,
% 1.06/1.27 (~hskp5),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1956, 1936, 1514, 1515, 1513])).
% 1.06/1.27 tff(1958,plain,
% 1.06/1.27 (hskp20),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1203, 1957, 1943, 1714, 1713, 1712])).
% 1.06/1.27 tff(1959,plain,
% 1.06/1.27 (~c0_1(a1130)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[302, 1958])).
% 1.06/1.27 tff(1960,plain,
% 1.06/1.27 (~c3_1(a1130)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[308, 1958])).
% 1.06/1.27 tff(1961,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1305, 1960, 1959, 1937, 1957, 1950, 1949, 672, 664, 656, 655, 583, 1948, 1942, 1941, 1940])).
% 1.06/1.27 tff(1962,plain,((~hskp9) | c1_1(a1098) | c3_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(1963,plain,
% 1.06/1.27 (~hskp9),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1962, 47, 34, 35])).
% 1.06/1.27 tff(1964,plain,
% 1.06/1.27 (hskp13 | hskp9),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1618, 110, 1948, 1950, 1949, 1594])).
% 1.06/1.27 tff(1965,plain,
% 1.06/1.27 (hskp13),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1964, 1963])).
% 1.06/1.27 tff(1966,plain,
% 1.06/1.27 (~c1_1(a1115)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1130, 1965])).
% 1.06/1.27 tff(1967,plain,
% 1.06/1.27 (c2_1(a1115)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1138, 1965])).
% 1.06/1.27 tff(1968,plain,
% 1.06/1.27 (c0_1(a1115)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1269, 110, 1714, 1713, 1712, 1967, 656, 655, 1966, 583, 642])).
% 1.06/1.27 tff(1969,plain,
% 1.06/1.27 (~c3_1(a1115)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1252, 1965])).
% 1.06/1.27 tff(1970,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1971,plain,
% 1.06/1.27 ((hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115))) <=> (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1972,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115))))),
% 1.06/1.27 inference(monotonicity,[status(thm)],[1971])).
% 1.06/1.27 tff(1973,plain,
% 1.06/1.27 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.06/1.27 inference(transitivity,[status(thm)],[1972, 1970])).
% 1.06/1.27 tff(1974,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))),
% 1.06/1.27 inference(quant_inst,[status(thm)],[])).
% 1.06/1.27 tff(1975,plain,
% 1.06/1.27 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1974, 1973])).
% 1.06/1.27 tff(1976,plain,
% 1.06/1.27 (hskp23 | (~c0_1(a1136))),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1975, 110, 631, 672, 1966, 1969, 1525, 1968])).
% 1.06/1.27 tff(1977,plain,
% 1.06/1.27 (hskp23),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1976, 1915])).
% 1.06/1.27 tff(1978,plain,
% 1.06/1.27 (~c3_1(a1147)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[686, 1977])).
% 1.06/1.27 tff(1979,plain,
% 1.06/1.27 (~c2_1(a1147)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[731, 1977])).
% 1.06/1.27 tff(1980,plain,
% 1.06/1.27 (c0_1(a1147)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[694, 1977])).
% 1.06/1.27 tff(1981,plain,
% 1.06/1.27 (~hskp5),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1956, 1912, 1514, 1515, 1513])).
% 1.06/1.27 tff(1982,plain,
% 1.06/1.27 (hskp20),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1203, 1981, 1943, 1714, 1713, 1712])).
% 1.06/1.27 tff(1983,plain,
% 1.06/1.27 (~c0_1(a1130)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[302, 1982])).
% 1.06/1.27 tff(1984,plain,
% 1.06/1.27 (~c3_1(a1130)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[308, 1982])).
% 1.06/1.27 tff(1985,plain,
% 1.06/1.27 ($false),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1305, 1984, 1983, 1915, 1981, 1950, 1949, 672, 664, 656, 655, 583, 1948, 1980, 1979, 1978])).
% 1.06/1.27 tff(1986,plain,(c3_1(a1098) | c1_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.27 tff(1987,plain,
% 1.06/1.27 (c3_1(a1098)),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1986, 35, 34])).
% 1.06/1.27 tff(1988,plain,
% 1.06/1.27 (((~hskp0) | (~c3_1(a1098))) <=> ((~hskp0) | (~c3_1(a1098)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1989,plain,
% 1.06/1.27 (((~c3_1(a1098)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1098)))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1990,axiom,((~c3_1(a1098)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.06/1.27 tff(1991,plain,
% 1.06/1.27 ((~hskp0) | (~c3_1(a1098))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 1.06/1.27 tff(1992,plain,
% 1.06/1.27 ((~hskp0) | (~c3_1(a1098))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1991, 1988])).
% 1.06/1.27 tff(1993,plain,
% 1.06/1.27 (~hskp0),
% 1.06/1.27 inference(unit_resolution,[status(thm)],[1992, 1987])).
% 1.06/1.27 tff(1994,plain,
% 1.06/1.27 (^[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)))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(1995,plain,
% 1.06/1.27 (![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))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[1994])).
% 1.06/1.27 tff(1996,plain,
% 1.06/1.27 (![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))),
% 1.06/1.27 inference(rewrite,[status(thm)],[])).
% 1.06/1.27 tff(1997,plain,
% 1.06/1.27 (^[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))))),
% 1.06/1.27 inference(bind,[status(th)],[])).
% 1.06/1.27 tff(1998,plain,
% 1.06/1.27 (![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))),
% 1.06/1.27 inference(quant_intro,[status(thm)],[1997])).
% 1.06/1.27 tff(1999,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','clause162')).
% 1.06/1.27 tff(2000,plain,
% 1.06/1.27 (![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))),
% 1.06/1.27 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 1.06/1.27 tff(2001,plain,
% 1.06/1.27 (![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))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2000, 1996])).
% 1.06/1.28 tff(2002,plain,(
% 1.06/1.28 ![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))),
% 1.06/1.28 inference(skolemize,[status(sab)],[2001])).
% 1.06/1.28 tff(2003,plain,
% 1.06/1.28 (![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))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2002, 1995])).
% 1.06/1.28 tff(2004,plain,
% 1.06/1.28 (((~![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 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098))) <=> ((~![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 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2005,plain,
% 1.06/1.28 ((hskp0 | (~ndr1_0) | c2_1(a1098) | c0_1(a1098) | (~c3_1(a1098)) | c2_1(a1098) | c1_1(a1098) | c0_1(a1098)) <=> (hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2006,plain,
% 1.06/1.28 (((~![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(a1098) | c0_1(a1098) | (~c3_1(a1098)) | c2_1(a1098) | c1_1(a1098) | c0_1(a1098))) <=> ((~![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 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098)))),
% 1.06/1.28 inference(monotonicity,[status(thm)],[2005])).
% 1.06/1.28 tff(2007,plain,
% 1.06/1.28 (((~![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(a1098) | c0_1(a1098) | (~c3_1(a1098)) | c2_1(a1098) | c1_1(a1098) | c0_1(a1098))) <=> ((~![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 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098))),
% 1.06/1.28 inference(transitivity,[status(thm)],[2006, 2004])).
% 1.06/1.28 tff(2008,plain,
% 1.06/1.28 ((~![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(a1098) | c0_1(a1098) | (~c3_1(a1098)) | c2_1(a1098) | c1_1(a1098) | c0_1(a1098))),
% 1.06/1.28 inference(quant_inst,[status(thm)],[])).
% 1.06/1.28 tff(2009,plain,
% 1.06/1.28 ((~![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 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 1.06/1.28 tff(2010,plain,
% 1.06/1.28 (hskp0 | (~c3_1(a1098)) | c0_1(a1098)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2009, 110, 34, 35, 2003])).
% 1.06/1.28 tff(2011,plain,
% 1.06/1.28 (c0_1(a1098)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2010, 1993, 1987])).
% 1.06/1.28 tff(2012,plain,
% 1.06/1.28 (^[U: $i] : refl((hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.06/1.28 inference(bind,[status(th)],[])).
% 1.06/1.28 tff(2013,plain,
% 1.06/1.28 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.06/1.28 inference(quant_intro,[status(thm)],[2012])).
% 1.06/1.28 tff(2014,plain,
% 1.06/1.28 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2015,plain,
% 1.06/1.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp0) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp0))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp0) <=> (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp0) <=> (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.06/1.28 inference(bind,[status(th)],[])).
% 1.06/1.28 tff(2016,plain,
% 1.06/1.28 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp0) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.06/1.28 inference(quant_intro,[status(thm)],[2015])).
% 1.06/1.28 tff(2017,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.06/1.28 tff(2018,plain,
% 1.06/1.28 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.06/1.28 tff(2019,plain,
% 1.06/1.28 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2018, 2014])).
% 1.06/1.28 tff(2020,plain,(
% 1.06/1.28 ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.06/1.28 inference(skolemize,[status(sab)],[2019])).
% 1.06/1.28 tff(2021,plain,
% 1.06/1.28 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2020, 2013])).
% 1.06/1.28 tff(2022,plain,
% 1.06/1.28 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2023,plain,
% 1.06/1.28 ((hskp22 | hskp0 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098))) <=> (hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2024,plain,
% 1.06/1.28 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0)))),
% 1.06/1.28 inference(monotonicity,[status(thm)],[2023])).
% 1.06/1.28 tff(2025,plain,
% 1.06/1.28 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0))),
% 1.06/1.28 inference(transitivity,[status(thm)],[2024, 2022])).
% 1.06/1.28 tff(2026,plain,
% 1.06/1.28 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))),
% 1.06/1.28 inference(quant_inst,[status(thm)],[])).
% 1.06/1.28 tff(2027,plain,
% 1.06/1.28 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2026, 2025])).
% 1.06/1.28 tff(2028,plain,
% 1.06/1.28 (hskp22 | hskp0 | c2_1(a1098) | (~c3_1(a1098))),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2027, 110, 34, 2021])).
% 1.06/1.28 tff(2029,plain,
% 1.06/1.28 (hskp22),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2028, 1993, 35, 1987])).
% 1.06/1.28 tff(2030,plain,
% 1.06/1.28 (((~hskp22) | (~c1_1(a1145))) <=> ((~hskp22) | (~c1_1(a1145)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2031,plain,
% 1.06/1.28 (((~c1_1(a1145)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1145)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2032,axiom,((~c1_1(a1145)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.06/1.28 tff(2033,plain,
% 1.06/1.28 ((~hskp22) | (~c1_1(a1145))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 1.06/1.28 tff(2034,plain,
% 1.06/1.28 ((~hskp22) | (~c1_1(a1145))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2033, 2030])).
% 1.06/1.28 tff(2035,plain,
% 1.06/1.28 (~c1_1(a1145)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2034, 2029])).
% 1.06/1.28 tff(2036,plain,
% 1.06/1.28 (((~hskp22) | c2_1(a1145)) <=> ((~hskp22) | c2_1(a1145))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2037,axiom,((~hskp22) | c2_1(a1145)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.06/1.28 tff(2038,plain,
% 1.06/1.28 ((~hskp22) | c2_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 1.06/1.28 tff(2039,plain,
% 1.06/1.28 ((~hskp22) | c2_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2038, 2036])).
% 1.06/1.28 tff(2040,plain,
% 1.06/1.28 ((~hskp22) | c2_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2039, 2036])).
% 1.06/1.28 tff(2041,plain,
% 1.06/1.28 ((~hskp22) | c2_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2040, 2036])).
% 1.06/1.28 tff(2042,plain,
% 1.06/1.28 ((~hskp22) | c2_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2041, 2036])).
% 1.06/1.28 tff(2043,plain,
% 1.06/1.28 (c2_1(a1145)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2042, 2029])).
% 1.06/1.28 tff(2044,plain,
% 1.06/1.28 ((hskp23 | hskp30 | hskp0) <=> (hskp23 | hskp30 | hskp0)),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2045,plain,
% 1.06/1.28 (((hskp23 | hskp30) | hskp0) <=> (hskp23 | hskp30 | hskp0)),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2046,axiom,((hskp23 | hskp30) | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.06/1.28 tff(2047,plain,
% 1.06/1.28 (hskp23 | hskp30 | hskp0),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 1.06/1.28 tff(2048,plain,
% 1.06/1.28 (hskp23 | hskp30 | hskp0),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2047, 2044])).
% 1.06/1.28 tff(2049,plain,
% 1.06/1.28 (hskp23 | hskp30 | hskp0),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2048, 2044])).
% 1.06/1.28 tff(2050,plain,
% 1.06/1.28 (hskp23 | hskp30 | hskp0),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2049, 2044])).
% 1.06/1.28 tff(2051,plain,
% 1.06/1.28 (hskp23 | hskp30 | hskp0),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2050, 2044])).
% 1.06/1.28 tff(2052,plain,
% 1.06/1.28 (hskp23),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2051, 613, 1993])).
% 1.06/1.28 tff(2053,plain,
% 1.06/1.28 (~c3_1(a1147)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[686, 2052])).
% 1.06/1.28 tff(2054,plain,
% 1.06/1.28 (~c2_1(a1147)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[731, 2052])).
% 1.06/1.28 tff(2055,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2056,plain,
% 1.06/1.28 ((hskp30 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147)) <=> (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2057,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147)))),
% 1.06/1.28 inference(monotonicity,[status(thm)],[2056])).
% 1.06/1.28 tff(2058,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147))),
% 1.06/1.28 inference(transitivity,[status(thm)],[2057, 2055])).
% 1.06/1.28 tff(2059,plain,
% 1.06/1.28 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))),
% 1.06/1.28 inference(quant_inst,[status(thm)],[])).
% 1.06/1.28 tff(2060,plain,
% 1.06/1.28 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 1.06/1.28 tff(2061,plain,
% 1.06/1.28 (c1_1(a1147)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2060, 110, 613, 2054, 2053, 34, 1987, 611, 2011])).
% 1.06/1.28 tff(2062,plain,
% 1.06/1.28 (((~hskp22) | c3_1(a1145)) <=> ((~hskp22) | c3_1(a1145))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2063,axiom,((~hskp22) | c3_1(a1145)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.06/1.28 tff(2064,plain,
% 1.06/1.28 ((~hskp22) | c3_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 1.06/1.28 tff(2065,plain,
% 1.06/1.28 ((~hskp22) | c3_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2064, 2062])).
% 1.06/1.28 tff(2066,plain,
% 1.06/1.28 ((~hskp22) | c3_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2065, 2062])).
% 1.06/1.28 tff(2067,plain,
% 1.06/1.28 ((~hskp22) | c3_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2066, 2062])).
% 1.06/1.28 tff(2068,plain,
% 1.06/1.28 ((~hskp22) | c3_1(a1145)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2067, 2062])).
% 1.06/1.28 tff(2069,plain,
% 1.06/1.28 (c3_1(a1145)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2068, 2029])).
% 1.06/1.28 tff(2070,plain,
% 1.06/1.28 (c0_1(a1147)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[694, 2052])).
% 1.06/1.28 tff(2071,plain,
% 1.06/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2072,plain,
% 1.06/1.28 (((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098))) <=> (c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2073,plain,
% 1.06/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.06/1.28 inference(monotonicity,[status(thm)],[2072])).
% 1.06/1.28 tff(2074,plain,
% 1.06/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.06/1.28 inference(transitivity,[status(thm)],[2073, 2071])).
% 1.06/1.28 tff(2075,plain,
% 1.06/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)))),
% 1.06/1.28 inference(quant_inst,[status(thm)],[])).
% 1.06/1.28 tff(2076,plain,
% 1.06/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.06/1.28 tff(2077,plain,
% 1.06/1.28 ((~c0_1(a1145)) | (~c1_1(a1147))),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2076, 110, 2070, 2043, 2069, 2054, 34, 35, 1987, 228])).
% 1.06/1.28 tff(2078,plain,
% 1.06/1.28 (~c0_1(a1145)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2077, 2061])).
% 1.06/1.28 tff(2079,plain,
% 1.06/1.28 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.06/1.28 inference(bind,[status(th)],[])).
% 1.06/1.28 tff(2080,plain,
% 1.06/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.06/1.28 inference(quant_intro,[status(thm)],[2079])).
% 1.06/1.28 tff(2081,plain,
% 1.06/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2082,plain,
% 1.06/1.28 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.06/1.28 inference(bind,[status(th)],[])).
% 1.06/1.28 tff(2083,plain,
% 1.06/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.06/1.28 inference(quant_intro,[status(thm)],[2082])).
% 1.06/1.28 tff(2084,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.06/1.28 tff(2085,plain,
% 1.06/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 1.06/1.28 tff(2086,plain,
% 1.06/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2085, 2081])).
% 1.06/1.28 tff(2087,plain,(
% 1.06/1.28 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.06/1.28 inference(skolemize,[status(sab)],[2086])).
% 1.06/1.28 tff(2088,plain,
% 1.06/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2087, 2080])).
% 1.06/1.28 tff(2089,plain,
% 1.06/1.28 (^[U: $i] : refl((hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.06/1.28 inference(bind,[status(th)],[])).
% 1.06/1.28 tff(2090,plain,
% 1.06/1.28 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.28 inference(quant_intro,[status(thm)],[2089])).
% 1.06/1.28 tff(2091,plain,
% 1.06/1.28 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2092,plain,
% 1.06/1.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp30) <=> ((hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp30))), rewrite(((hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp30) <=> (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.06/1.28 inference(bind,[status(th)],[])).
% 1.06/1.28 tff(2093,plain,
% 1.06/1.28 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp30) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.28 inference(quant_intro,[status(thm)],[2092])).
% 1.06/1.28 tff(2094,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.06/1.28 tff(2095,plain,
% 1.06/1.28 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 1.06/1.28 tff(2096,plain,
% 1.06/1.28 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2095, 2091])).
% 1.06/1.28 tff(2097,plain,(
% 1.06/1.28 ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.28 inference(skolemize,[status(sab)],[2096])).
% 1.06/1.28 tff(2098,plain,
% 1.06/1.28 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2097, 2090])).
% 1.06/1.28 tff(2099,plain,
% 1.06/1.28 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2100,plain,
% 1.06/1.28 ((hskp30 | hskp18 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098))) <=> (hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2101,plain,
% 1.06/1.28 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098))))),
% 1.06/1.28 inference(monotonicity,[status(thm)],[2100])).
% 1.06/1.28 tff(2102,plain,
% 1.06/1.28 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)))),
% 1.06/1.28 inference(transitivity,[status(thm)],[2101, 2099])).
% 1.06/1.28 tff(2103,plain,
% 1.06/1.28 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)))),
% 1.06/1.28 inference(quant_inst,[status(thm)],[])).
% 1.06/1.28 tff(2104,plain,
% 1.06/1.28 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 1.06/1.28 tff(2105,plain,
% 1.06/1.28 (hskp30 | hskp18 | (~c3_1(a1098)) | (~c0_1(a1098))),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2104, 110, 34, 2098])).
% 1.06/1.28 tff(2106,plain,
% 1.06/1.28 (hskp18),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2105, 613, 1987, 2011])).
% 1.06/1.28 tff(2107,plain,
% 1.06/1.28 (((~hskp18) | (~c1_1(a1125))) <=> ((~hskp18) | (~c1_1(a1125)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2108,plain,
% 1.06/1.28 (((~c1_1(a1125)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a1125)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2109,axiom,((~c1_1(a1125)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.06/1.28 tff(2110,plain,
% 1.06/1.28 ((~hskp18) | (~c1_1(a1125))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 1.06/1.28 tff(2111,plain,
% 1.06/1.28 ((~hskp18) | (~c1_1(a1125))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2110, 2107])).
% 1.06/1.28 tff(2112,plain,
% 1.06/1.28 (~c1_1(a1125)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2111, 2106])).
% 1.06/1.28 tff(2113,plain,
% 1.06/1.28 (((~hskp18) | c2_1(a1125)) <=> ((~hskp18) | c2_1(a1125))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2114,axiom,((~hskp18) | c2_1(a1125)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.06/1.28 tff(2115,plain,
% 1.06/1.28 ((~hskp18) | c2_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2114, 2113])).
% 1.06/1.28 tff(2116,plain,
% 1.06/1.28 ((~hskp18) | c2_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2115, 2113])).
% 1.06/1.28 tff(2117,plain,
% 1.06/1.28 ((~hskp18) | c2_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2116, 2113])).
% 1.06/1.28 tff(2118,plain,
% 1.06/1.28 ((~hskp18) | c2_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2117, 2113])).
% 1.06/1.28 tff(2119,plain,
% 1.06/1.28 ((~hskp18) | c2_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2118, 2113])).
% 1.06/1.28 tff(2120,plain,
% 1.06/1.28 (c2_1(a1125)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2119, 2106])).
% 1.06/1.28 tff(2121,plain,
% 1.06/1.28 (((~hskp18) | c0_1(a1125)) <=> ((~hskp18) | c0_1(a1125))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2122,axiom,((~hskp18) | c0_1(a1125)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.06/1.28 tff(2123,plain,
% 1.06/1.28 ((~hskp18) | c0_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.06/1.28 tff(2124,plain,
% 1.06/1.28 ((~hskp18) | c0_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2123, 2121])).
% 1.06/1.28 tff(2125,plain,
% 1.06/1.28 ((~hskp18) | c0_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2124, 2121])).
% 1.06/1.28 tff(2126,plain,
% 1.06/1.28 ((~hskp18) | c0_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2125, 2121])).
% 1.06/1.28 tff(2127,plain,
% 1.06/1.28 ((~hskp18) | c0_1(a1125)),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2126, 2121])).
% 1.06/1.28 tff(2128,plain,
% 1.06/1.28 (c0_1(a1125)),
% 1.06/1.28 inference(unit_resolution,[status(thm)],[2127, 2106])).
% 1.06/1.28 tff(2129,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2130,plain,
% 1.06/1.28 ((hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.06/1.28 inference(rewrite,[status(thm)],[])).
% 1.06/1.28 tff(2131,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125))))),
% 1.06/1.28 inference(monotonicity,[status(thm)],[2130])).
% 1.06/1.28 tff(2132,plain,
% 1.06/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.06/1.28 inference(transitivity,[status(thm)],[2131, 2129])).
% 1.06/1.28 tff(2133,plain,
% 1.06/1.28 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.06/1.28 inference(quant_inst,[status(thm)],[])).
% 1.06/1.28 tff(2134,plain,
% 1.06/1.28 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125))),
% 1.06/1.28 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 1.06/1.29 tff(2135,plain,
% 1.06/1.29 (hskp7),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2134, 110, 2128, 2120, 2112, 35, 1987, 2088, 2011])).
% 1.06/1.29 tff(2136,plain,
% 1.06/1.29 (~c1_1(a1105)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[582, 2135])).
% 1.06/1.29 tff(2137,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2138,plain,
% 1.06/1.29 ((hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2139,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125))))),
% 1.06/1.29 inference(monotonicity,[status(thm)],[2138])).
% 1.06/1.29 tff(2140,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.06/1.29 inference(transitivity,[status(thm)],[2139, 2137])).
% 1.06/1.29 tff(2141,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.06/1.29 inference(quant_inst,[status(thm)],[])).
% 1.06/1.29 tff(2142,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 1.06/1.29 tff(2143,plain,
% 1.06/1.29 (hskp20),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2142, 110, 2128, 2120, 2112, 35, 1987, 915, 2011])).
% 1.06/1.29 tff(2144,plain,
% 1.06/1.29 (~c3_1(a1130)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[308, 2143])).
% 1.06/1.29 tff(2145,plain,
% 1.06/1.29 (((~hskp20) | (~c2_1(a1130))) <=> ((~hskp20) | (~c2_1(a1130)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2146,plain,
% 1.06/1.29 (((~c2_1(a1130)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a1130)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2147,axiom,((~c2_1(a1130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.06/1.29 tff(2148,plain,
% 1.06/1.29 ((~hskp20) | (~c2_1(a1130))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.06/1.29 tff(2149,plain,
% 1.06/1.29 ((~hskp20) | (~c2_1(a1130))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2148, 2145])).
% 1.06/1.29 tff(2150,plain,
% 1.06/1.29 (~c2_1(a1130)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2149, 2143])).
% 1.06/1.29 tff(2151,plain,
% 1.06/1.29 (c3_1(a1105)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[600, 2135])).
% 1.06/1.29 tff(2152,plain,
% 1.06/1.29 (c0_1(a1105)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[592, 2135])).
% 1.06/1.29 tff(2153,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2154,plain,
% 1.06/1.29 ((hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130)) <=> (hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2155,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)))),
% 1.06/1.29 inference(monotonicity,[status(thm)],[2154])).
% 1.06/1.29 tff(2156,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.06/1.29 inference(transitivity,[status(thm)],[2155, 2153])).
% 1.06/1.29 tff(2157,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))),
% 1.06/1.29 inference(quant_inst,[status(thm)],[])).
% 1.06/1.29 tff(2158,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 1.06/1.29 tff(2159,plain,
% 1.06/1.29 (c1_1(a1130)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2158, 110, 613, 2152, 2151, 2150, 2144, 2136, 611])).
% 1.06/1.29 tff(2160,plain,
% 1.06/1.29 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.06/1.29 inference(bind,[status(th)],[])).
% 1.06/1.29 tff(2161,plain,
% 1.06/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.29 inference(quant_intro,[status(thm)],[2160])).
% 1.06/1.29 tff(2162,plain,
% 1.06/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2163,plain,
% 1.06/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.06/1.29 inference(bind,[status(th)],[])).
% 1.06/1.29 tff(2164,plain,
% 1.06/1.29 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.29 inference(quant_intro,[status(thm)],[2163])).
% 1.06/1.29 tff(2165,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.06/1.29 tff(2166,plain,
% 1.06/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 1.06/1.29 tff(2167,plain,
% 1.06/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2166, 2162])).
% 1.06/1.29 tff(2168,plain,(
% 1.06/1.29 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.29 inference(skolemize,[status(sab)],[2167])).
% 1.06/1.29 tff(2169,plain,
% 1.06/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2168, 2161])).
% 1.06/1.29 tff(2170,plain,
% 1.06/1.29 (~c0_1(a1130)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[302, 2143])).
% 1.06/1.29 tff(2171,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2172,plain,
% 1.06/1.29 ((hskp3 | (~ndr1_0) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2173,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.06/1.29 inference(monotonicity,[status(thm)],[2172])).
% 1.06/1.29 tff(2174,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.29 inference(transitivity,[status(thm)],[2173, 2171])).
% 1.06/1.29 tff(2175,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.06/1.29 inference(quant_inst,[status(thm)],[])).
% 1.06/1.29 tff(2176,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 1.06/1.29 tff(2177,plain,
% 1.06/1.29 (hskp3),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2176, 110, 2043, 2069, 2170, 2150, 2169, 2159, 2078])).
% 1.06/1.29 tff(2178,plain,
% 1.06/1.29 (~c3_1(a1101)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[998, 2177])).
% 1.06/1.29 tff(2179,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2180,plain,
% 1.06/1.29 ((hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145))) <=> (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2181,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.06/1.29 inference(monotonicity,[status(thm)],[2180])).
% 1.06/1.29 tff(2182,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.29 inference(transitivity,[status(thm)],[2181, 2179])).
% 1.06/1.29 tff(2183,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.29 inference(quant_inst,[status(thm)],[])).
% 1.06/1.29 tff(2184,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 1.06/1.29 tff(2185,plain,
% 1.06/1.29 (hskp4),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2184, 110, 2043, 2069, 34, 35, 1787, 2011, 2078])).
% 1.06/1.29 tff(2186,plain,
% 1.06/1.29 (~c3_1(a1102)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[1427, 2185])).
% 1.06/1.29 tff(2187,plain,
% 1.06/1.29 (c2_1(a1101)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[1006, 2177])).
% 1.06/1.29 tff(2188,plain,
% 1.06/1.29 (c1_1(a1101)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[1014, 2177])).
% 1.06/1.29 tff(2189,plain,
% 1.06/1.29 (c1_1(a1102)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[1444, 2185])).
% 1.06/1.29 tff(2190,plain,
% 1.06/1.29 (c0_1(a1102)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[1452, 2185])).
% 1.06/1.29 tff(2191,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2192,plain,
% 1.06/1.29 ((hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102))) <=> (hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2193,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102))))),
% 1.06/1.29 inference(monotonicity,[status(thm)],[2192])).
% 1.06/1.29 tff(2194,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.06/1.29 inference(transitivity,[status(thm)],[2193, 2191])).
% 1.06/1.29 tff(2195,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.06/1.29 inference(quant_inst,[status(thm)],[])).
% 1.06/1.29 tff(2196,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 1.06/1.29 tff(2197,plain,
% 1.06/1.29 (hskp5),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2196, 110, 2190, 2189, 2188, 2187, 2186, 2178, 1177])).
% 1.06/1.29 tff(2198,plain,
% 1.06/1.29 (~c2_1(a1103)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[123, 2197])).
% 1.06/1.29 tff(2199,plain,
% 1.06/1.29 (~c0_1(a1103)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[129, 2197])).
% 1.06/1.29 tff(2200,plain,
% 1.06/1.29 (c3_1(a1103)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[147, 2197])).
% 1.06/1.29 tff(2201,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2202,plain,
% 1.06/1.29 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103))) <=> (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2203,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147))))),
% 1.06/1.29 inference(monotonicity,[status(thm)],[2202])).
% 1.06/1.29 tff(2204,plain,
% 1.06/1.29 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147)))),
% 1.06/1.29 inference(transitivity,[status(thm)],[2203, 2201])).
% 1.06/1.29 tff(2205,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))),
% 1.06/1.29 inference(quant_inst,[status(thm)],[])).
% 1.06/1.29 tff(2206,plain,
% 1.06/1.29 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 1.06/1.29 tff(2207,plain,
% 1.06/1.29 ($false),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2206, 110, 698, 2200, 2054, 2053, 2199, 2198, 67, 2061])).
% 1.06/1.29 tff(2208,plain,(hskp30 | hskp29 | c1_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.29 tff(2209,plain,
% 1.06/1.29 (hskp30),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2208, 698, 34, 35])).
% 1.06/1.29 tff(2210,plain,
% 1.06/1.29 (c1_1(a1136)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[630, 2209])).
% 1.06/1.29 tff(2211,plain,
% 1.06/1.29 (c2_1(a1136)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[671, 2209])).
% 1.06/1.29 tff(2212,plain,
% 1.06/1.29 (c3_1(a1136)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[663, 2209])).
% 1.06/1.29 tff(2213,plain,
% 1.06/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2214,plain,
% 1.06/1.29 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145))) <=> (c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2215,plain,
% 1.06/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145))))),
% 1.06/1.29 inference(monotonicity,[status(thm)],[2214])).
% 1.06/1.29 tff(2216,plain,
% 1.06/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.06/1.29 inference(transitivity,[status(thm)],[2215, 2213])).
% 1.06/1.29 tff(2217,plain,
% 1.06/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.06/1.29 inference(quant_inst,[status(thm)],[])).
% 1.06/1.29 tff(2218,plain,
% 1.06/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145))),
% 1.06/1.29 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 1.06/1.29 tff(2219,plain,
% 1.06/1.29 (c0_1(a1145)),
% 1.06/1.29 inference(unit_resolution,[status(thm)],[2218, 110, 2210, 2211, 2212, 2043, 2035, 34, 35, 1059, 2011])).
% 1.06/1.29 tff(2220,plain,
% 1.06/1.29 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.06/1.29 inference(bind,[status(th)],[])).
% 1.06/1.29 tff(2221,plain,
% 1.06/1.29 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.29 inference(quant_intro,[status(thm)],[2220])).
% 1.06/1.29 tff(2222,plain,
% 1.06/1.29 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.29 inference(rewrite,[status(thm)],[])).
% 1.06/1.29 tff(2223,plain,
% 1.06/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.06/1.30 inference(bind,[status(th)],[])).
% 1.06/1.30 tff(2224,plain,
% 1.06/1.30 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.30 inference(quant_intro,[status(thm)],[2223])).
% 1.06/1.30 tff(2225,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.06/1.30 tff(2226,plain,
% 1.06/1.30 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 1.06/1.30 tff(2227,plain,
% 1.06/1.30 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2226, 2222])).
% 1.06/1.30 tff(2228,plain,(
% 1.06/1.30 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.30 inference(skolemize,[status(sab)],[2227])).
% 1.06/1.30 tff(2229,plain,
% 1.06/1.30 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2228, 2221])).
% 1.06/1.30 tff(2230,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2231,plain,
% 1.06/1.30 ((hskp9 | (~ndr1_0) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098))) <=> (hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2232,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145))))),
% 1.06/1.30 inference(monotonicity,[status(thm)],[2231])).
% 1.06/1.30 tff(2233,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(transitivity,[status(thm)],[2232, 2230])).
% 1.06/1.30 tff(2234,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(2235,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 1.06/1.30 tff(2236,plain,
% 1.06/1.30 (hskp9 | (~c0_1(a1145))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2235, 110, 2043, 2035, 34, 35, 1987, 2229])).
% 1.06/1.30 tff(2237,plain,
% 1.06/1.30 (hskp9),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2236, 2219])).
% 1.06/1.30 tff(2238,plain,
% 1.06/1.30 (hskp23),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[1545, 2237, 698, 2211, 2210])).
% 1.06/1.30 tff(2239,plain,
% 1.06/1.30 (~c3_1(a1147)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[686, 2238])).
% 1.06/1.30 tff(2240,plain,
% 1.06/1.30 (~c2_1(a1147)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[731, 2238])).
% 1.06/1.30 tff(2241,plain,
% 1.06/1.30 (c0_1(a1147)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[694, 2238])).
% 1.06/1.30 tff(2242,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2243,plain,
% 1.06/1.30 ((hskp2 | (~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145))) <=> (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2244,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.06/1.30 inference(monotonicity,[status(thm)],[2243])).
% 1.06/1.30 tff(2245,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.30 inference(transitivity,[status(thm)],[2244, 2242])).
% 1.06/1.30 tff(2246,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(2247,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 1.06/1.30 tff(2248,plain,
% 1.06/1.30 (hskp2 | (~c0_1(a1145))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2247, 110, 2043, 2069, 2035, 975])).
% 1.06/1.30 tff(2249,plain,
% 1.06/1.30 (hskp2),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2248, 2219])).
% 1.06/1.30 tff(2250,plain,
% 1.06/1.30 (c2_1(a1100)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[281, 2249])).
% 1.06/1.30 tff(2251,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2252,plain,
% 1.06/1.30 ((hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145))) <=> (hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2253,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145))))),
% 1.06/1.30 inference(monotonicity,[status(thm)],[2252])).
% 1.06/1.30 tff(2254,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(transitivity,[status(thm)],[2253, 2251])).
% 1.06/1.30 tff(2255,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(2256,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2255, 2254])).
% 1.06/1.30 tff(2257,plain,
% 1.06/1.30 (hskp7 | (~c0_1(a1145))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2256, 110, 2043, 2035, 35, 1987, 2088, 2011])).
% 1.06/1.30 tff(2258,plain,
% 1.06/1.30 (hskp7),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2257, 2219])).
% 1.06/1.30 tff(2259,plain,
% 1.06/1.30 (~c1_1(a1105)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[582, 2258])).
% 1.06/1.30 tff(2260,plain,
% 1.06/1.30 (c3_1(a1105)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[600, 2258])).
% 1.06/1.30 tff(2261,plain,
% 1.06/1.30 (c0_1(a1105)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[592, 2258])).
% 1.06/1.30 tff(2262,plain,
% 1.06/1.30 (~c3_1(a1100)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[273, 2249])).
% 1.06/1.30 tff(2263,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2264,plain,
% 1.06/1.30 ((hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145))) <=> (hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2265,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145))))),
% 1.06/1.30 inference(monotonicity,[status(thm)],[2264])).
% 1.06/1.30 tff(2266,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.06/1.30 inference(transitivity,[status(thm)],[2265, 2263])).
% 1.06/1.30 tff(2267,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(2268,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 1.06/1.30 tff(2269,plain,
% 1.06/1.30 (hskp20 | (~c0_1(a1145))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2268, 110, 2043, 2035, 35, 1987, 915, 2011])).
% 1.06/1.30 tff(2270,plain,
% 1.06/1.30 (hskp20),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2269, 2219])).
% 1.06/1.30 tff(2271,plain,
% 1.06/1.30 (~c3_1(a1130)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[308, 2270])).
% 1.06/1.30 tff(2272,plain,
% 1.06/1.30 (~c0_1(a1130)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[302, 2270])).
% 1.06/1.30 tff(2273,plain,
% 1.06/1.30 (c0_1(a1100)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[289, 2249])).
% 1.06/1.30 tff(2274,plain,
% 1.06/1.30 (c0_1(a1136)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[725, 2241, 2210, 2211, 2212, 2239, 698])).
% 1.06/1.30 tff(2275,plain,
% 1.06/1.30 (hskp5),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[1305, 2274, 2273, 2272, 2271, 2262, 2211, 2212, 2261, 2260, 2259, 2250, 2241, 2240, 2239])).
% 1.06/1.30 tff(2276,plain,
% 1.06/1.30 (~c2_1(a1103)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[123, 2275])).
% 1.06/1.30 tff(2277,plain,
% 1.06/1.30 (~c0_1(a1103)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[129, 2275])).
% 1.06/1.30 tff(2278,plain,
% 1.06/1.30 (~c2_1(a1130)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2149, 2270])).
% 1.06/1.30 tff(2279,plain,
% 1.06/1.30 (c3_1(a1103)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[147, 2275])).
% 1.06/1.30 tff(2280,plain,
% 1.06/1.30 (((~![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(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130))) <=> ((~![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(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2281,plain,
% 1.06/1.30 ((hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130)) <=> (hskp0 | c0_1(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2282,plain,
% 1.06/1.30 (((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![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(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130)))),
% 1.06/1.30 inference(monotonicity,[status(thm)],[2281])).
% 1.06/1.30 tff(2283,plain,
% 1.06/1.30 (((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![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(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.06/1.30 inference(transitivity,[status(thm)],[2282, 2280])).
% 1.06/1.30 tff(2284,plain,
% 1.06/1.30 ((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(2285,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130)),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 1.06/1.30 tff(2286,plain,
% 1.06/1.30 (c1_1(a1130)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2285, 110, 1993, 2279, 2272, 2278, 2277, 2276, 2003])).
% 1.06/1.30 tff(2287,plain,
% 1.06/1.30 ($false),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[954, 110, 2211, 2212, 2241, 2240, 2239, 2272, 2271, 320, 2274, 2286])).
% 1.06/1.30 tff(2288,plain,(hskp29 | c1_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.06/1.30 tff(2289,plain,
% 1.06/1.30 (hskp29),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2288, 35, 34])).
% 1.06/1.30 tff(2290,plain,
% 1.06/1.30 (c3_1(a1116)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[189, 2289])).
% 1.06/1.30 tff(2291,plain,
% 1.06/1.30 (c2_1(a1116)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[197, 2289])).
% 1.06/1.30 tff(2292,plain,
% 1.06/1.30 (c0_1(a1116)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[205, 2289])).
% 1.06/1.30 tff(2293,plain,
% 1.06/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2294,plain,
% 1.06/1.30 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145))) <=> (c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2295,plain,
% 1.06/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145))))),
% 1.06/1.30 inference(monotonicity,[status(thm)],[2294])).
% 1.06/1.30 tff(2296,plain,
% 1.06/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.06/1.30 inference(transitivity,[status(thm)],[2295, 2293])).
% 1.06/1.30 tff(2297,plain,
% 1.06/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(2298,plain,
% 1.06/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 1.06/1.30 tff(2299,plain,
% 1.06/1.30 (c0_1(a1145)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2298, 110, 2292, 2291, 2290, 2043, 2035, 34, 1987, 642, 2011])).
% 1.06/1.30 tff(2300,plain,
% 1.06/1.30 (hskp20),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2269, 2299])).
% 1.06/1.30 tff(2301,plain,
% 1.06/1.30 (~c2_1(a1130)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[2149, 2300])).
% 1.06/1.30 tff(2302,plain,
% 1.06/1.30 (~c3_1(a1130)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[308, 2300])).
% 1.06/1.30 tff(2303,plain,
% 1.06/1.30 (~c0_1(a1130)),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[302, 2300])).
% 1.06/1.30 tff(2304,assumption,(c0_1(a1145)), introduced(assumption)).
% 1.06/1.30 tff(2305,assumption,(~c2_1(a1130)), introduced(assumption)).
% 1.06/1.30 tff(2306,assumption,(~c1_1(a1145)), introduced(assumption)).
% 1.06/1.30 tff(2307,assumption,(c3_1(a1145)), introduced(assumption)).
% 1.06/1.30 tff(2308,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2309,plain,
% 1.06/1.30 ((hskp30 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c0_1(a1145)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130)) <=> (hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(2310,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c0_1(a1145)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145))))),
% 1.06/1.30 inference(monotonicity,[status(thm)],[2309])).
% 1.06/1.30 tff(2311,plain,
% 1.06/1.30 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c0_1(a1145)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145)))),
% 1.06/1.30 inference(transitivity,[status(thm)],[2310, 2308])).
% 1.06/1.30 tff(2312,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c0_1(a1145)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(2313,plain,
% 1.06/1.30 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 1.14/1.31 tff(2314,plain,
% 1.14/1.31 (hskp30 | c1_1(a1130)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2313, 110, 2307, 2306, 2305, 321, 611, 2304])).
% 1.14/1.31 tff(2315,plain,
% 1.14/1.31 (c1_1(a1130)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2314, 613])).
% 1.14/1.31 tff(2316,assumption,(~hskp0), introduced(assumption)).
% 1.14/1.31 tff(2317,plain,
% 1.14/1.31 (hskp23),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2051, 613, 2316])).
% 1.14/1.31 tff(2318,plain,
% 1.14/1.31 (~c3_1(a1147)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[686, 2317])).
% 1.14/1.31 tff(2319,plain,
% 1.14/1.31 (~c2_1(a1147)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[731, 2317])).
% 1.14/1.31 tff(2320,plain,
% 1.14/1.31 (c0_1(a1147)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[694, 2317])).
% 1.14/1.31 tff(2321,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1223, 110, 231, 230, 229, 2320, 2319, 2318, 310, 321, 320, 2315])).
% 1.14/1.31 tff(2322,plain,(hskp30 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c0_1(a1130) | c3_1(a1130) | (~c3_1(a1145)) | c1_1(a1145) | c2_1(a1130) | (~c0_1(a1145)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(2323,plain,
% 1.14/1.31 (hskp30),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2322, 2292, 2291, 2290, 2303, 2302, 2069, 2035, 2301, 2299, 1993])).
% 1.14/1.31 tff(2324,plain,
% 1.14/1.31 (c3_1(a1136)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[663, 2323])).
% 1.14/1.31 tff(2325,plain,
% 1.14/1.31 (c2_1(a1136)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[671, 2323])).
% 1.14/1.31 tff(2326,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2327,plain,
% 1.14/1.31 ((hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136))) <=> (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2328,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2327])).
% 1.14/1.31 tff(2329,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2328, 2326])).
% 1.14/1.31 tff(2330,plain,
% 1.14/1.31 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2331,plain,
% 1.14/1.31 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2330, 2329])).
% 1.14/1.31 tff(2332,plain,
% 1.14/1.31 (hskp4),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2331, 110, 2325, 2324, 34, 35, 1787, 2011, 46])).
% 1.14/1.31 tff(2333,plain,
% 1.14/1.31 (~c3_1(a1102)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1427, 2332])).
% 1.14/1.31 tff(2334,plain,
% 1.14/1.31 (c1_1(a1136)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[630, 2323])).
% 1.14/1.31 tff(2335,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2336,plain,
% 1.14/1.31 ((hskp16 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136))) <=> (hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2337,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2336])).
% 1.14/1.31 tff(2338,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2337, 2335])).
% 1.14/1.31 tff(2339,plain,
% 1.14/1.31 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2340,plain,
% 1.14/1.31 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 1.14/1.31 tff(2341,plain,
% 1.14/1.31 (hskp16),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2340, 110, 2334, 2324, 35, 1987, 1805, 2011, 46])).
% 1.14/1.31 tff(2342,plain,
% 1.14/1.31 (~c0_1(a1121)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1825, 2341])).
% 1.14/1.31 tff(2343,plain,
% 1.14/1.31 (c1_1(a1102)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1444, 2332])).
% 1.14/1.31 tff(2344,plain,
% 1.14/1.31 (c0_1(a1102)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1452, 2332])).
% 1.14/1.31 tff(2345,plain,
% 1.14/1.31 (c3_1(a1121)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1835, 2341])).
% 1.14/1.31 tff(2346,plain,
% 1.14/1.31 (c1_1(a1121)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1843, 2341])).
% 1.14/1.31 tff(2347,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1850, 110, 2334, 2325, 2324, 2346, 2345, 2344, 2343, 2342, 2333, 45])).
% 1.14/1.31 tff(2348,plain,(c0_1(a1136) | c1_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(2349,plain,
% 1.14/1.31 (c0_1(a1136)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2348, 35, 34])).
% 1.14/1.31 tff(2350,plain,
% 1.14/1.31 (hskp9),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2236, 2299])).
% 1.14/1.31 tff(2351,plain,
% 1.14/1.31 (~c3_1(a1108)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[464, 2350])).
% 1.14/1.31 tff(2352,plain,
% 1.14/1.31 (~c1_1(a1108)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[470, 2350])).
% 1.14/1.31 tff(2353,plain,
% 1.14/1.31 (c0_1(a1108)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[478, 2350])).
% 1.14/1.31 tff(2354,plain,
% 1.14/1.31 (hskp23 | (~c0_1(a1136))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1536, 110, 2334, 2325, 2353, 2352, 2351, 1525])).
% 1.14/1.31 tff(2355,plain,
% 1.14/1.31 (hskp23),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2354, 2349])).
% 1.14/1.31 tff(2356,plain,
% 1.14/1.31 (~c3_1(a1147)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[686, 2355])).
% 1.14/1.31 tff(2357,plain,
% 1.14/1.31 (~c2_1(a1147)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[731, 2355])).
% 1.14/1.31 tff(2358,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2359,plain,
% 1.14/1.31 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145))) <=> (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2360,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2359])).
% 1.14/1.31 tff(2361,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2360, 2358])).
% 1.14/1.31 tff(2362,plain,
% 1.14/1.31 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2363,plain,
% 1.14/1.31 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 1.14/1.31 tff(2364,plain,
% 1.14/1.31 (hskp2),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2363, 110, 2292, 2291, 2290, 2043, 2069, 2035, 975])).
% 1.14/1.31 tff(2365,plain,
% 1.14/1.31 (c2_1(a1100)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[281, 2364])).
% 1.14/1.31 tff(2366,plain,
% 1.14/1.31 (hskp7),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2257, 2299])).
% 1.14/1.31 tff(2367,plain,
% 1.14/1.31 (~c1_1(a1105)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[582, 2366])).
% 1.14/1.31 tff(2368,plain,
% 1.14/1.31 (c3_1(a1105)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[600, 2366])).
% 1.14/1.31 tff(2369,plain,
% 1.14/1.31 (c0_1(a1105)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[592, 2366])).
% 1.14/1.31 tff(2370,plain,
% 1.14/1.31 (~c3_1(a1100)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[273, 2364])).
% 1.14/1.31 tff(2371,plain,
% 1.14/1.31 (c0_1(a1100)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[289, 2364])).
% 1.14/1.31 tff(2372,plain,
% 1.14/1.31 (c0_1(a1147)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[694, 2355])).
% 1.14/1.31 tff(2373,plain,
% 1.14/1.31 (hskp5),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1305, 2372, 2371, 2303, 2302, 2370, 2325, 2324, 2369, 2368, 2367, 2365, 2349, 2357, 2356])).
% 1.14/1.31 tff(2374,plain,
% 1.14/1.31 (~c0_1(a1103)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[129, 2373])).
% 1.14/1.31 tff(2375,plain,
% 1.14/1.31 (c3_1(a1103)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[147, 2373])).
% 1.14/1.31 tff(2376,plain,
% 1.14/1.31 (~hskp21),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[763, 2372, 2324, 2349, 2357, 2356, 2325])).
% 1.14/1.31 tff(2377,plain,
% 1.14/1.31 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2378,plain,
% 1.14/1.31 ((hskp21 | hskp0 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c3_1(a1103))) <=> (hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2379,plain,
% 1.14/1.31 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2378])).
% 1.14/1.31 tff(2380,plain,
% 1.14/1.31 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2379, 2377])).
% 1.14/1.31 tff(2381,plain,
% 1.14/1.31 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2382,plain,
% 1.14/1.31 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2381, 2380])).
% 1.14/1.31 tff(2383,plain,
% 1.14/1.31 (~c1_1(a1103)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2382, 110, 2376, 1993, 2375, 2374, 33])).
% 1.14/1.31 tff(2384,plain,
% 1.14/1.31 (~c2_1(a1103)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[123, 2373])).
% 1.14/1.31 tff(2385,plain,
% 1.14/1.31 (((~![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(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))) <=> ((~![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(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2386,plain,
% 1.14/1.31 ((hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c1_1(a1103) | c0_1(a1103)) <=> (hskp0 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2387,plain,
% 1.14/1.31 (((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c1_1(a1103) | c0_1(a1103))) <=> ((~![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(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2386])).
% 1.14/1.31 tff(2388,plain,
% 1.14/1.31 (((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c1_1(a1103) | c0_1(a1103))) <=> ((~![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(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2387, 2385])).
% 1.14/1.31 tff(2389,plain,
% 1.14/1.31 ((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c1_1(a1103) | c0_1(a1103))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2390,plain,
% 1.14/1.31 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 1.14/1.31 tff(2391,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2390, 110, 1993, 2375, 2374, 2384, 2003, 2383])).
% 1.14/1.31 tff(2392,plain,(c2_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(2393,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2392, 23, 17])).
% 1.14/1.31 tff(2394,plain,(~hskp0), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(2395,assumption,(~c0_1(a1147)), introduced(assumption)).
% 1.14/1.31 tff(2396,plain,
% 1.14/1.31 (~hskp23),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[694, 2395])).
% 1.14/1.31 tff(2397,plain,
% 1.14/1.31 (hskp30),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2051, 2396, 2394])).
% 1.14/1.31 tff(2398,plain,
% 1.14/1.31 (c1_1(a1136)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[630, 2397])).
% 1.14/1.31 tff(2399,plain,
% 1.14/1.31 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2400,plain,
% 1.14/1.31 ((hskp7 | hskp6 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c0_1(a1147)) <=> (hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2401,plain,
% 1.14/1.31 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c0_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0)))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2400])).
% 1.14/1.31 tff(2402,plain,
% 1.14/1.31 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c0_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2401, 2399])).
% 1.14/1.31 tff(2403,plain,
% 1.14/1.31 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c0_1(a1147))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2404,plain,
% 1.14/1.31 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.14/1.31 tff(2405,plain,
% 1.14/1.31 (hskp7 | hskp6 | c0_1(a1147) | c3_1(a1147)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2404, 110, 747, 489])).
% 1.14/1.31 tff(2406,plain,
% 1.14/1.31 (hskp6),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2405, 68, 2395, 699])).
% 1.14/1.31 tff(2407,plain,
% 1.14/1.31 (c0_1(a1104)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[510, 2406])).
% 1.14/1.31 tff(2408,plain,
% 1.14/1.31 ((hskp23 | hskp13 | hskp7) <=> (hskp23 | hskp13 | hskp7)),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2409,plain,
% 1.14/1.31 (((hskp23 | hskp7) | hskp13) <=> (hskp23 | hskp13 | hskp7)),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2410,plain,
% 1.14/1.31 ((hskp7 | hskp23) <=> (hskp23 | hskp7)),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2411,plain,
% 1.14/1.31 (((hskp7 | hskp23) | hskp13) <=> ((hskp23 | hskp7) | hskp13)),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2410])).
% 1.14/1.31 tff(2412,plain,
% 1.14/1.31 (((hskp7 | hskp23) | hskp13) <=> (hskp23 | hskp13 | hskp7)),
% 1.14/1.31 inference(transitivity,[status(thm)],[2411, 2409])).
% 1.14/1.31 tff(2413,axiom,((hskp7 | hskp23) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.14/1.31 tff(2414,plain,
% 1.14/1.31 (hskp23 | hskp13 | hskp7),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2413, 2412])).
% 1.14/1.31 tff(2415,plain,
% 1.14/1.31 (hskp23 | hskp13 | hskp7),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2414, 2408])).
% 1.14/1.31 tff(2416,plain,
% 1.14/1.31 (hskp23 | hskp13 | hskp7),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2415, 2408])).
% 1.14/1.31 tff(2417,plain,
% 1.14/1.31 (hskp23 | hskp13 | hskp7),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2416, 2408])).
% 1.14/1.31 tff(2418,plain,
% 1.14/1.31 (hskp23 | hskp13 | hskp7),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2417, 2408])).
% 1.14/1.31 tff(2419,plain,
% 1.14/1.31 (hskp13),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2418, 68, 2396])).
% 1.14/1.31 tff(2420,plain,
% 1.14/1.31 (~c1_1(a1115)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1130, 2419])).
% 1.14/1.31 tff(2421,plain,
% 1.14/1.31 (~c3_1(a1115)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1252, 2419])).
% 1.14/1.31 tff(2422,plain,
% 1.14/1.31 (~c2_1(a1104)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[502, 2406])).
% 1.14/1.31 tff(2423,plain,
% 1.14/1.31 (c1_1(a1104)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[535, 2406])).
% 1.14/1.31 tff(2424,plain,
% 1.14/1.31 (^[U: $i] : refl((hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(2425,plain,
% 1.14/1.31 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[2424])).
% 1.14/1.31 tff(2426,plain,
% 1.14/1.31 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2427,plain,
% 1.14/1.31 (^[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)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp23) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp23) <=> (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.14/1.31 inference(bind,[status(th)],[])).
% 1.14/1.31 tff(2428,plain,
% 1.14/1.31 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp23) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.14/1.31 inference(quant_intro,[status(thm)],[2427])).
% 1.14/1.31 tff(2429,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.14/1.31 tff(2430,plain,
% 1.14/1.31 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2429, 2428])).
% 1.14/1.31 tff(2431,plain,
% 1.14/1.31 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2430, 2426])).
% 1.14/1.31 tff(2432,plain,(
% 1.14/1.31 ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.14/1.31 inference(skolemize,[status(sab)],[2431])).
% 1.14/1.31 tff(2433,plain,
% 1.14/1.31 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2432, 2425])).
% 1.14/1.31 tff(2434,plain,
% 1.14/1.31 (c2_1(a1115)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1138, 2419])).
% 1.14/1.31 tff(2435,plain,
% 1.14/1.31 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2436,plain,
% 1.14/1.31 ((hskp23 | hskp7 | (~ndr1_0) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115))) <=> (hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2437,plain,
% 1.14/1.31 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2436])).
% 1.14/1.31 tff(2438,plain,
% 1.14/1.31 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2437, 2435])).
% 1.14/1.31 tff(2439,plain,
% 1.14/1.31 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2440,plain,
% 1.14/1.31 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2439, 2438])).
% 1.14/1.31 tff(2441,plain,
% 1.14/1.31 (~c0_1(a1115)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2440, 2396, 110, 68, 2434, 2420, 2433])).
% 1.14/1.31 tff(2442,assumption,(~c0_1(a1115)), introduced(assumption)).
% 1.14/1.31 tff(2443,assumption,(c1_1(a1147)), introduced(assumption)).
% 1.14/1.31 tff(2444,assumption,(~c3_1(a1115)), introduced(assumption)).
% 1.14/1.31 tff(2445,assumption,(~c1_1(a1115)), introduced(assumption)).
% 1.14/1.31 tff(2446,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2447,plain,
% 1.14/1.31 ((hskp1 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c1_1(a1147)) | c1_1(a1115) | c0_1(a1115) | c3_1(a1115)) <=> (hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2448,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c1_1(a1147)) | c1_1(a1115) | c0_1(a1115) | c3_1(a1115))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2447])).
% 1.14/1.31 tff(2449,plain,
% 1.14/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c1_1(a1147)) | c1_1(a1115) | c0_1(a1115) | c3_1(a1115))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2448, 2446])).
% 1.14/1.31 tff(2450,plain,
% 1.14/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c1_1(a1147)) | c1_1(a1115) | c0_1(a1115) | c3_1(a1115))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2451,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 1.14/1.32 tff(2452,plain,
% 1.14/1.32 (hskp1 | c0_1(a1115) | (~c1_1(a1147))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2451, 110, 2395, 699, 2445, 2444, 372])).
% 1.14/1.32 tff(2453,plain,
% 1.14/1.32 (hskp1),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2452, 2443, 2442])).
% 1.14/1.32 tff(2454,plain,
% 1.14/1.32 (~c0_1(a1099)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[387, 2453])).
% 1.14/1.32 tff(2455,plain,
% 1.14/1.32 (c2_1(a1099)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[435, 2453])).
% 1.14/1.32 tff(2456,plain,
% 1.14/1.32 (c1_1(a1099)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[443, 2453])).
% 1.14/1.32 tff(2457,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2458,plain,
% 1.14/1.32 ((hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147))) <=> (hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2459,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2458])).
% 1.14/1.32 tff(2460,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2459, 2457])).
% 1.14/1.32 tff(2461,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2462,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 1.14/1.32 tff(2463,plain,
% 1.14/1.32 (hskp9),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2462, 110, 2395, 2456, 2455, 747, 2454, 398, 2443])).
% 1.14/1.32 tff(2464,plain,
% 1.14/1.32 (~c3_1(a1108)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[464, 2463])).
% 1.14/1.32 tff(2465,plain,
% 1.14/1.32 (~c1_1(a1108)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[470, 2463])).
% 1.14/1.32 tff(2466,plain,
% 1.14/1.32 (c0_1(a1108)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[478, 2463])).
% 1.14/1.32 tff(2467,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1933, 110, 2466, 927, 936, 2456, 2455, 2465, 2464, 926, 2454, 1316])).
% 1.14/1.32 tff(2468,plain,((~c1_1(a1147)) | (~c0_1(a1104)) | (~c1_1(a1104)) | c2_1(a1104) | c0_1(a1147) | c2_1(a1147) | c0_1(a1115) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2469,plain,
% 1.14/1.32 (~c1_1(a1147)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2468, 2441, 2423, 2422, 2395, 747, 2421, 699, 2420, 2407])).
% 1.14/1.32 tff(2470,plain,
% 1.14/1.32 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2471,plain,
% 1.14/1.32 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c1_1(a1147)) <=> (hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2472,plain,
% 1.14/1.32 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c1_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2471])).
% 1.14/1.32 tff(2473,plain,
% 1.14/1.32 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c1_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2472, 2470])).
% 1.14/1.32 tff(2474,plain,
% 1.14/1.32 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c1_1(a1147))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2475,plain,
% 1.14/1.32 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2474, 2473])).
% 1.14/1.32 tff(2476,plain,
% 1.14/1.32 (hskp7 | hskp5 | c3_1(a1147) | c1_1(a1147)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2475, 110, 747, 78])).
% 1.14/1.32 tff(2477,plain,
% 1.14/1.32 (hskp5),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2476, 2469, 699, 68])).
% 1.14/1.32 tff(2478,plain,
% 1.14/1.32 (~c2_1(a1103)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[123, 2477])).
% 1.14/1.32 tff(2479,plain,
% 1.14/1.32 (~c0_1(a1103)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[129, 2477])).
% 1.14/1.32 tff(2480,plain,
% 1.14/1.32 (c3_1(a1103)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[147, 2477])).
% 1.14/1.32 tff(2481,plain,
% 1.14/1.32 (((~![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(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147))) <=> ((~![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(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2482,plain,
% 1.14/1.32 ((hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147)) <=> (hskp0 | c0_1(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2483,plain,
% 1.14/1.32 (((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))) <=> ((~![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(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2482])).
% 1.14/1.32 tff(2484,plain,
% 1.14/1.32 (((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))) <=> ((~![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(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2483, 2481])).
% 1.14/1.32 tff(2485,plain,
% 1.14/1.32 ((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2486,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2485, 2484])).
% 1.14/1.32 tff(2487,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2486, 110, 2394, 2395, 2480, 747, 2479, 2478, 2003, 2469])).
% 1.14/1.32 tff(2488,plain,(hskp7 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2489,plain,
% 1.14/1.32 (hskp7),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2488, 2395, 747, 699])).
% 1.14/1.32 tff(2490,plain,
% 1.14/1.32 (~c1_1(a1105)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[582, 2489])).
% 1.14/1.32 tff(2491,plain,
% 1.14/1.32 (c3_1(a1105)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[600, 2489])).
% 1.14/1.32 tff(2492,plain,
% 1.14/1.32 (c3_1(a1136)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[663, 2397])).
% 1.14/1.32 tff(2493,plain,
% 1.14/1.32 (hskp14),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[680, 2396])).
% 1.14/1.32 tff(2494,plain,
% 1.14/1.32 (~c3_1(a1118)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[160, 2493])).
% 1.14/1.32 tff(2495,plain,
% 1.14/1.32 (c2_1(a1136)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[671, 2397])).
% 1.14/1.32 tff(2496,plain,
% 1.14/1.32 (~c2_1(a1118)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[166, 2493])).
% 1.14/1.32 tff(2497,plain,
% 1.14/1.32 (c1_1(a1118)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[174, 2493])).
% 1.14/1.32 tff(2498,plain,
% 1.14/1.32 (c0_1(a1105)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[592, 2489])).
% 1.14/1.32 tff(2499,plain,
% 1.14/1.32 (hskp29),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1655, 2498, 2396, 2497, 2496, 2495, 2494, 2492, 2491, 2490, 2398])).
% 1.14/1.32 tff(2500,plain,
% 1.14/1.32 (c0_1(a1116)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[205, 2499])).
% 1.14/1.32 tff(2501,plain,
% 1.14/1.32 (c3_1(a1116)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[189, 2499])).
% 1.14/1.32 tff(2502,plain,
% 1.14/1.32 (c2_1(a1116)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[197, 2499])).
% 1.14/1.32 tff(2503,plain,
% 1.14/1.32 (((~![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(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![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(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2504,plain,
% 1.14/1.32 ((hskp0 | (~ndr1_0) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c1_1(a1107) | c0_1(a1107)) <=> (hskp0 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2505,plain,
% 1.14/1.32 (((~![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(a1107) | c0_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c1_1(a1107) | c0_1(a1107))) <=> ((~![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(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2504])).
% 1.14/1.32 tff(2506,plain,
% 1.14/1.32 (((~![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(a1107) | c0_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c1_1(a1107) | c0_1(a1107))) <=> ((~![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(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2505, 2503])).
% 1.14/1.32 tff(2507,plain,
% 1.14/1.32 ((~![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(a1107) | c0_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c1_1(a1107) | c0_1(a1107))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2508,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 1.14/1.32 tff(2509,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2508, 110, 2394, 1115, 1090, 1084, 2003, 1097])).
% 1.14/1.32 tff(2510,plain,((~hskp8) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2511,plain,
% 1.14/1.32 (~hskp8),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2510, 2500, 2502, 2501, 2498, 2491, 2490])).
% 1.14/1.32 tff(2512,plain,
% 1.14/1.32 (c0_1(a1118)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1911, 2511, 2497, 2398, 2502, 2496, 2494, 2501, 2495, 2492, 2500])).
% 1.14/1.32 tff(2513,plain,
% 1.14/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2514,plain,
% 1.14/1.32 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2515,plain,
% 1.14/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2514])).
% 1.14/1.32 tff(2516,plain,
% 1.14/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2515, 2513])).
% 1.14/1.32 tff(2517,plain,
% 1.14/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2518,plain,
% 1.14/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 1.14/1.32 tff(2519,plain,
% 1.14/1.32 (c2_1(a1105) | (~c0_1(a1118))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2518, 110, 2500, 2502, 2501, 2497, 2491, 2496, 2490, 228])).
% 1.14/1.32 tff(2520,plain,
% 1.14/1.32 (c2_1(a1105)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2519, 2512])).
% 1.14/1.32 tff(2521,plain,
% 1.14/1.32 (hskp2 | (~c2_1(a1105))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[981, 110, 2498, 2491, 2490, 975])).
% 1.14/1.32 tff(2522,plain,
% 1.14/1.32 (hskp2),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2521, 2520])).
% 1.14/1.32 tff(2523,plain,
% 1.14/1.32 (~c3_1(a1100)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[273, 2522])).
% 1.14/1.32 tff(2524,plain,
% 1.14/1.32 (~hskp5),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1956, 2512, 2497, 2494, 2496])).
% 1.14/1.32 tff(2525,plain,
% 1.14/1.32 (^[U: $i] : refl((hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.14/1.32 inference(bind,[status(th)],[])).
% 1.14/1.32 tff(2526,plain,
% 1.14/1.32 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.14/1.32 inference(quant_intro,[status(thm)],[2525])).
% 1.14/1.32 tff(2527,plain,
% 1.14/1.32 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2528,plain,
% 1.14/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp8) <=> ((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp8))), rewrite(((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp8) <=> (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp8) <=> (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.14/1.32 inference(bind,[status(th)],[])).
% 1.14/1.32 tff(2529,plain,
% 1.14/1.32 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp8) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.14/1.32 inference(quant_intro,[status(thm)],[2528])).
% 1.14/1.32 tff(2530,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.14/1.32 tff(2531,plain,
% 1.14/1.32 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2530, 2529])).
% 1.14/1.32 tff(2532,plain,
% 1.14/1.32 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2531, 2527])).
% 1.14/1.32 tff(2533,plain,(
% 1.14/1.32 ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.14/1.32 inference(skolemize,[status(sab)],[2532])).
% 1.14/1.32 tff(2534,plain,
% 1.14/1.32 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2533, 2526])).
% 1.14/1.32 tff(2535,plain,
% 1.14/1.32 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2536,plain,
% 1.14/1.32 ((hskp19 | hskp8 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2537,plain,
% 1.14/1.32 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2536])).
% 1.14/1.32 tff(2538,plain,
% 1.14/1.32 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2537, 2535])).
% 1.14/1.32 tff(2539,plain,
% 1.14/1.32 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2540,plain,
% 1.14/1.32 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 1.14/1.32 tff(2541,plain,
% 1.14/1.32 (hskp19 | hskp8 | (~c2_1(a1105))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2540, 110, 2491, 2490, 2534])).
% 1.14/1.32 tff(2542,plain,
% 1.14/1.32 (hskp19),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2541, 2520, 2511])).
% 1.14/1.32 tff(2543,plain,
% 1.14/1.32 (hskp20),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1203, 2542, 2500, 2524, 2502, 2501])).
% 1.14/1.32 tff(2544,plain,
% 1.14/1.32 (~c3_1(a1130)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[308, 2543])).
% 1.14/1.32 tff(2545,plain,
% 1.14/1.32 (~c2_1(a1130)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2149, 2543])).
% 1.14/1.32 tff(2546,plain,
% 1.14/1.32 (~c0_1(a1130)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[302, 2543])).
% 1.14/1.32 tff(2547,plain,
% 1.14/1.32 (c2_1(a1100)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[281, 2522])).
% 1.14/1.32 tff(2548,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2549,plain,
% 1.14/1.32 ((hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2550,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2549])).
% 1.14/1.32 tff(2551,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2550, 2548])).
% 1.14/1.32 tff(2552,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2553,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2552, 2551])).
% 1.14/1.32 tff(2554,plain,
% 1.14/1.32 (~c1_1(a1100)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2553, 110, 2524, 2547, 2546, 2545, 2544, 2523, 10])).
% 1.14/1.32 tff(2555,plain,
% 1.14/1.32 (c0_1(a1136)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1914, 2512, 2495, 2492, 2497, 2494, 2398])).
% 1.14/1.32 tff(2556,plain,
% 1.14/1.32 (c0_1(a1100)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[289, 2522])).
% 1.14/1.32 tff(2557,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2558,plain,
% 1.14/1.32 ((hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100))) <=> (hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2559,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2558])).
% 1.14/1.32 tff(2560,plain,
% 1.14/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2559, 2557])).
% 1.14/1.32 tff(2561,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2562,plain,
% 1.14/1.32 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 1.14/1.32 tff(2563,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2562, 2396, 110, 2398, 2495, 2556, 2523, 1525, 2555, 2554])).
% 1.14/1.32 tff(2564,plain,(c0_1(a1147) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2565,plain,
% 1.14/1.32 (c0_1(a1147)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2564, 699, 747])).
% 1.14/1.32 tff(2566,plain,
% 1.14/1.32 (c1_1(a1103)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2390, 110, 2316, 1952, 1953, 1954, 2003])).
% 1.14/1.32 tff(2567,plain,
% 1.14/1.32 (hskp21 | (~c1_1(a1103))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2382, 110, 2316, 1952, 1953, 33])).
% 1.14/1.33 tff(2568,plain,
% 1.14/1.33 (hskp21),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2567, 2566])).
% 1.14/1.33 tff(2569,plain,
% 1.14/1.33 (~c3_1(a1131)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[739, 2568])).
% 1.14/1.33 tff(2570,plain,
% 1.14/1.33 (~c0_1(a1131)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[745, 2568])).
% 1.14/1.33 tff(2571,plain,
% 1.14/1.33 (c1_1(a1131)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[754, 2568])).
% 1.14/1.33 tff(2572,plain,
% 1.14/1.33 (hskp14),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[154, 110, 68, 1952, 1953, 1954, 140])).
% 1.14/1.33 tff(2573,plain,
% 1.14/1.33 (~c3_1(a1118)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[160, 2572])).
% 1.14/1.33 tff(2574,plain,
% 1.14/1.33 (~c2_1(a1118)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[166, 2572])).
% 1.14/1.33 tff(2575,plain,
% 1.14/1.33 (c1_1(a1118)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[174, 2572])).
% 1.14/1.33 tff(2576,plain,
% 1.14/1.33 (hskp29),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[181, 110, 2575, 1952, 2574, 2573, 1953, 1954, 67])).
% 1.14/1.33 tff(2577,plain,
% 1.14/1.33 (c3_1(a1116)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[189, 2576])).
% 1.14/1.33 tff(2578,plain,
% 1.14/1.33 (c2_1(a1116)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[197, 2576])).
% 1.14/1.33 tff(2579,plain,
% 1.14/1.33 (c0_1(a1116)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[205, 2576])).
% 1.14/1.33 tff(2580,plain,
% 1.14/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2581,plain,
% 1.14/1.33 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2582,plain,
% 1.14/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2581])).
% 1.14/1.33 tff(2583,plain,
% 1.14/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2582, 2580])).
% 1.14/1.33 tff(2584,plain,
% 1.14/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2585,plain,
% 1.14/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 1.14/1.33 tff(2586,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2585, 110, 2579, 2578, 2577, 700, 2571, 747, 699, 2570, 2569, 320])).
% 1.14/1.33 tff(2587,plain,((~hskp5) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | hskp0 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2588,plain,
% 1.14/1.33 (~hskp5),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2587, 68, 747, 699, 2394, 2565])).
% 1.14/1.33 tff(2589,plain,
% 1.14/1.33 (c1_1(a1147)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2476, 2588, 699, 68])).
% 1.14/1.33 tff(2590,assumption,(hskp16), introduced(assumption)).
% 1.14/1.33 tff(2591,plain,
% 1.14/1.33 (~c0_1(a1121)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1825, 2590])).
% 1.14/1.33 tff(2592,plain,
% 1.14/1.33 (c3_1(a1121)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1835, 2590])).
% 1.14/1.33 tff(2593,plain,
% 1.14/1.33 (c1_1(a1121)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1843, 2590])).
% 1.14/1.33 tff(2594,plain,
% 1.14/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2595,plain,
% 1.14/1.33 (((~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1121)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121))) <=> (c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2596,plain,
% 1.14/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1121)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2595])).
% 1.14/1.33 tff(2597,plain,
% 1.14/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1121)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2596, 2594])).
% 1.14/1.33 tff(2598,plain,
% 1.14/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1121)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2599,plain,
% 1.14/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 1.14/1.33 tff(2600,plain,
% 1.14/1.33 (~c2_1(a1121)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2599, 110, 700, 2593, 2592, 699, 2591, 45, 2443])).
% 1.14/1.33 tff(2601,plain,
% 1.14/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2602,plain,
% 1.14/1.33 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121))) <=> (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2603,plain,
% 1.14/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2602])).
% 1.14/1.33 tff(2604,plain,
% 1.14/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2603, 2601])).
% 1.14/1.33 tff(2605,plain,
% 1.14/1.33 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2606,plain,
% 1.14/1.33 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 1.14/1.33 tff(2607,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2606, 110, 698, 2592, 747, 699, 2591, 67, 2443, 2600])).
% 1.14/1.33 tff(2608,plain,((~hskp16) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2609,plain,
% 1.14/1.33 (~hskp16),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2608, 698, 747, 699, 2565, 2589])).
% 1.14/1.33 tff(2610,assumption,(hskp26), introduced(assumption)).
% 1.14/1.33 tff(2611,plain,
% 1.14/1.33 (((~hskp26) | (~c2_1(a1180))) <=> ((~hskp26) | (~c2_1(a1180)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2612,plain,
% 1.14/1.33 (((~c2_1(a1180)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a1180)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2613,axiom,((~c2_1(a1180)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.14/1.33 tff(2614,plain,
% 1.14/1.33 ((~hskp26) | (~c2_1(a1180))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 1.14/1.33 tff(2615,plain,
% 1.14/1.33 ((~hskp26) | (~c2_1(a1180))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2614, 2611])).
% 1.14/1.33 tff(2616,plain,
% 1.14/1.33 (~c2_1(a1180)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2615, 2610])).
% 1.14/1.33 tff(2617,plain,
% 1.14/1.33 (((~hskp26) | (~c1_1(a1180))) <=> ((~hskp26) | (~c1_1(a1180)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2618,plain,
% 1.14/1.33 (((~c1_1(a1180)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a1180)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2619,axiom,((~c1_1(a1180)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.14/1.33 tff(2620,plain,
% 1.14/1.33 ((~hskp26) | (~c1_1(a1180))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2619, 2618])).
% 1.14/1.33 tff(2621,plain,
% 1.14/1.33 ((~hskp26) | (~c1_1(a1180))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2620, 2617])).
% 1.14/1.33 tff(2622,plain,
% 1.14/1.33 (~c1_1(a1180)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2621, 2610])).
% 1.14/1.33 tff(2623,plain,
% 1.14/1.33 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2624,plain,
% 1.14/1.33 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180)) <=> (hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2625,plain,
% 1.14/1.33 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180)))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2624])).
% 1.14/1.33 tff(2626,plain,
% 1.14/1.33 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2625, 2623])).
% 1.14/1.33 tff(2627,plain,
% 1.14/1.33 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2628,plain,
% 1.14/1.33 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2627, 2626])).
% 1.14/1.33 tff(2629,plain,
% 1.14/1.33 (c3_1(a1180)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2628, 110, 68, 2588, 2622, 2616, 78])).
% 1.14/1.33 tff(2630,plain,
% 1.14/1.33 (((~hskp26) | (~c0_1(a1180))) <=> ((~hskp26) | (~c0_1(a1180)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2631,plain,
% 1.14/1.33 (((~c0_1(a1180)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1180)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2632,axiom,((~c0_1(a1180)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.14/1.33 tff(2633,plain,
% 1.14/1.33 ((~hskp26) | (~c0_1(a1180))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2632, 2631])).
% 1.14/1.33 tff(2634,plain,
% 1.14/1.33 ((~hskp26) | (~c0_1(a1180))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2633, 2630])).
% 1.14/1.33 tff(2635,plain,
% 1.14/1.33 (~c0_1(a1180)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2634, 2610])).
% 1.14/1.33 tff(2636,plain,
% 1.14/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2637,plain,
% 1.14/1.33 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180))) <=> (hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2638,plain,
% 1.14/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2637])).
% 1.14/1.33 tff(2639,plain,
% 1.14/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2638, 2636])).
% 1.14/1.33 tff(2640,plain,
% 1.14/1.33 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2641,plain,
% 1.14/1.33 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 1.14/1.33 tff(2642,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2641, 110, 698, 2635, 2616, 747, 699, 67, 2629, 2589])).
% 1.14/1.33 tff(2643,plain,((~hskp26) | hskp29 | c2_1(a1147) | c3_1(a1147) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2644,plain,
% 1.14/1.33 (~hskp26),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2643, 698, 747, 699, 68])).
% 1.14/1.33 tff(2645,plain,
% 1.14/1.33 ((hskp26 | hskp18 | hskp16) <=> (hskp26 | hskp18 | hskp16)),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2646,plain,
% 1.14/1.33 (((hskp18 | hskp16) | hskp26) <=> (hskp26 | hskp18 | hskp16)),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2647,plain,
% 1.14/1.33 ((hskp18 | hskp16) <=> (hskp18 | hskp16)),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2648,plain,
% 1.14/1.33 (((hskp18 | hskp16) | hskp26) <=> ((hskp18 | hskp16) | hskp26)),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2647])).
% 1.14/1.33 tff(2649,plain,
% 1.14/1.33 (((hskp18 | hskp16) | hskp26) <=> (hskp26 | hskp18 | hskp16)),
% 1.14/1.33 inference(transitivity,[status(thm)],[2648, 2646])).
% 1.14/1.33 tff(2650,axiom,((hskp18 | hskp16) | hskp26), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.14/1.33 tff(2651,plain,
% 1.14/1.33 (hskp26 | hskp18 | hskp16),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2650, 2649])).
% 1.14/1.33 tff(2652,plain,
% 1.14/1.33 (hskp26 | hskp18 | hskp16),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2651, 2645])).
% 1.14/1.33 tff(2653,plain,
% 1.14/1.33 (hskp26 | hskp18 | hskp16),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2652, 2645])).
% 1.14/1.33 tff(2654,plain,
% 1.14/1.33 (hskp26 | hskp18 | hskp16),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2653, 2645])).
% 1.14/1.33 tff(2655,plain,
% 1.14/1.33 (hskp26 | hskp18 | hskp16),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2654, 2645])).
% 1.14/1.33 tff(2656,plain,
% 1.14/1.33 (hskp18),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2655, 2644, 2609])).
% 1.14/1.33 tff(2657,plain,
% 1.14/1.33 (~c1_1(a1125)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2111, 2656])).
% 1.14/1.33 tff(2658,assumption,(~hskp26), introduced(assumption)).
% 1.14/1.33 tff(2659,assumption,(~hskp16), introduced(assumption)).
% 1.14/1.33 tff(2660,plain,
% 1.14/1.33 (hskp18),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2655, 2659, 2658])).
% 1.14/1.33 tff(2661,plain,
% 1.14/1.33 (~c1_1(a1125)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2111, 2660])).
% 1.14/1.33 tff(2662,assumption,(~hskp2), introduced(assumption)).
% 1.14/1.33 tff(2663,plain,
% 1.14/1.33 (^[U: $i] : refl((hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(2664,plain,
% 1.14/1.33 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[2663])).
% 1.14/1.33 tff(2665,plain,
% 1.14/1.33 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2666,plain,
% 1.14/1.33 (^[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) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp16) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp16) <=> (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(2667,plain,
% 1.14/1.33 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp16) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[2666])).
% 1.14/1.33 tff(2668,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.14/1.33 tff(2669,plain,
% 1.14/1.33 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 1.14/1.33 tff(2670,plain,
% 1.14/1.33 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2669, 2665])).
% 1.14/1.33 tff(2671,plain,(
% 1.14/1.33 ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.14/1.33 inference(skolemize,[status(sab)],[2670])).
% 1.14/1.33 tff(2672,plain,
% 1.14/1.33 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2671, 2664])).
% 1.14/1.33 tff(2673,assumption,(hskp12), introduced(assumption)).
% 1.14/1.33 tff(2674,plain,
% 1.14/1.33 (((~hskp12) | (~c3_1(a1114))) <=> ((~hskp12) | (~c3_1(a1114)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2675,plain,
% 1.14/1.33 (((~c3_1(a1114)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1114)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2676,axiom,((~c3_1(a1114)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.14/1.33 tff(2677,plain,
% 1.14/1.33 ((~hskp12) | (~c3_1(a1114))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 1.14/1.33 tff(2678,plain,
% 1.14/1.33 ((~hskp12) | (~c3_1(a1114))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2677, 2674])).
% 1.14/1.33 tff(2679,plain,
% 1.14/1.33 (~c3_1(a1114)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2678, 2673])).
% 1.14/1.33 tff(2680,plain,
% 1.14/1.33 (((~hskp12) | (~c0_1(a1114))) <=> ((~hskp12) | (~c0_1(a1114)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2681,plain,
% 1.14/1.33 (((~c0_1(a1114)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1114)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2682,axiom,((~c0_1(a1114)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.14/1.33 tff(2683,plain,
% 1.14/1.33 ((~hskp12) | (~c0_1(a1114))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 1.14/1.33 tff(2684,plain,
% 1.14/1.33 ((~hskp12) | (~c0_1(a1114))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2683, 2680])).
% 1.14/1.33 tff(2685,plain,
% 1.14/1.33 (~c0_1(a1114)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2684, 2673])).
% 1.14/1.33 tff(2686,plain,
% 1.14/1.33 (((~hskp12) | c2_1(a1114)) <=> ((~hskp12) | c2_1(a1114))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2687,axiom,((~hskp12) | c2_1(a1114)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.14/1.33 tff(2688,plain,
% 1.14/1.33 ((~hskp12) | c2_1(a1114)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2687, 2686])).
% 1.14/1.33 tff(2689,plain,
% 1.14/1.33 ((~hskp12) | c2_1(a1114)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2688, 2686])).
% 1.14/1.33 tff(2690,plain,
% 1.14/1.33 ((~hskp12) | c2_1(a1114)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2689, 2686])).
% 1.14/1.33 tff(2691,plain,
% 1.14/1.33 ((~hskp12) | c2_1(a1114)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2690, 2686])).
% 1.14/1.33 tff(2692,plain,
% 1.14/1.33 ((~hskp12) | c2_1(a1114)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2691, 2686])).
% 1.14/1.33 tff(2693,plain,
% 1.14/1.33 (c2_1(a1114)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2692, 2673])).
% 1.14/1.33 tff(2694,plain,
% 1.14/1.33 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2695,plain,
% 1.14/1.33 ((hskp16 | hskp2 | (~ndr1_0) | c3_1(a1114) | c0_1(a1114) | (~c2_1(a1114))) <=> (hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2696,plain,
% 1.14/1.33 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1114) | c0_1(a1114) | (~c2_1(a1114)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2695])).
% 1.14/1.33 tff(2697,plain,
% 1.14/1.33 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1114) | c0_1(a1114) | (~c2_1(a1114)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2696, 2694])).
% 1.14/1.33 tff(2698,plain,
% 1.14/1.33 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1114) | c0_1(a1114) | (~c2_1(a1114)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2699,plain,
% 1.14/1.33 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2698, 2697])).
% 1.14/1.33 tff(2700,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2699, 110, 2659, 2662, 2693, 2685, 2679, 2672])).
% 1.14/1.33 tff(2701,plain,((~hskp12) | hskp16 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2702,plain,
% 1.14/1.33 (~hskp12),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2701, 2659, 2662])).
% 1.14/1.33 tff(2703,plain,
% 1.14/1.33 ((hskp26 | hskp19 | hskp12) <=> (hskp26 | hskp19 | hskp12)),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2704,plain,
% 1.14/1.33 (((hskp19 | hskp12) | hskp26) <=> (hskp26 | hskp19 | hskp12)),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2705,plain,
% 1.14/1.33 ((hskp19 | hskp12) <=> (hskp19 | hskp12)),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2706,plain,
% 1.14/1.33 (((hskp19 | hskp12) | hskp26) <=> ((hskp19 | hskp12) | hskp26)),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2705])).
% 1.14/1.33 tff(2707,plain,
% 1.14/1.33 (((hskp19 | hskp12) | hskp26) <=> (hskp26 | hskp19 | hskp12)),
% 1.14/1.33 inference(transitivity,[status(thm)],[2706, 2704])).
% 1.14/1.33 tff(2708,axiom,((hskp19 | hskp12) | hskp26), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.14/1.33 tff(2709,plain,
% 1.14/1.33 (hskp26 | hskp19 | hskp12),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2708, 2707])).
% 1.14/1.33 tff(2710,plain,
% 1.14/1.33 (hskp26 | hskp19 | hskp12),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2709, 2703])).
% 1.14/1.33 tff(2711,plain,
% 1.14/1.33 (hskp26 | hskp19 | hskp12),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2710, 2703])).
% 1.14/1.33 tff(2712,plain,
% 1.14/1.33 (hskp26 | hskp19 | hskp12),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2711, 2703])).
% 1.14/1.33 tff(2713,plain,
% 1.14/1.33 (hskp26 | hskp19 | hskp12),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2712, 2703])).
% 1.14/1.34 tff(2714,plain,
% 1.14/1.34 (hskp19),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2713, 2702, 2658])).
% 1.14/1.34 tff(2715,plain,
% 1.14/1.34 (~c2_1(a1127)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[816, 2714])).
% 1.14/1.34 tff(2716,plain,
% 1.14/1.34 (c2_1(a1125)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2119, 2660])).
% 1.14/1.34 tff(2717,plain,
% 1.14/1.34 (c0_1(a1125)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2127, 2660])).
% 1.14/1.34 tff(2718,plain,
% 1.14/1.34 (c3_1(a1127)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[825, 2714])).
% 1.14/1.34 tff(2719,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2720,plain,
% 1.14/1.34 ((hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2721,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2720])).
% 1.14/1.34 tff(2722,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2721, 2719])).
% 1.14/1.34 tff(2723,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2724,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 1.14/1.34 tff(2725,plain,
% 1.14/1.34 (~c0_1(a1127)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2724, 110, 68, 2718, 2717, 2716, 2715, 2661, 2088])).
% 1.14/1.34 tff(2726,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2727,plain,
% 1.14/1.34 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127))) <=> (hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2728,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2727])).
% 1.14/1.34 tff(2729,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2728, 2726])).
% 1.14/1.34 tff(2730,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2731,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2730, 2729])).
% 1.14/1.34 tff(2732,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2731, 110, 698, 2718, 747, 699, 2715, 67, 2443, 2725])).
% 1.14/1.34 tff(2733,plain,(hskp16 | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp7 | hskp26 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2734,plain,
% 1.14/1.34 (hskp2),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2733, 2644, 747, 699, 2589, 68, 2609, 698])).
% 1.14/1.34 tff(2735,plain,
% 1.14/1.34 (c0_1(a1100)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[289, 2734])).
% 1.14/1.34 tff(2736,plain,
% 1.14/1.34 (~c3_1(a1100)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[273, 2734])).
% 1.14/1.34 tff(2737,plain,
% 1.14/1.34 (c2_1(a1100)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[281, 2734])).
% 1.14/1.34 tff(2738,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2739,plain,
% 1.14/1.34 ((hskp5 | (~ndr1_0) | c3_1(a1114) | (~c1_1(a1114)) | (~c2_1(a1114)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147))) <=> (hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2740,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1114) | (~c1_1(a1114)) | (~c2_1(a1114)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2739])).
% 1.14/1.34 tff(2741,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1114) | (~c1_1(a1114)) | (~c2_1(a1114)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2740, 2738])).
% 1.14/1.34 tff(2742,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1114) | (~c1_1(a1114)) | (~c2_1(a1114)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2743,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2742, 2741])).
% 1.14/1.34 tff(2744,plain,
% 1.14/1.34 (~c1_1(a1114)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2743, 110, 1167, 700, 2693, 699, 2679, 1177, 2443])).
% 1.14/1.34 tff(2745,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2746,plain,
% 1.14/1.34 ((hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147))) <=> (hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2747,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2746])).
% 1.14/1.34 tff(2748,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2747, 2745])).
% 1.14/1.34 tff(2749,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2750,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 1.14/1.34 tff(2751,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2750, 110, 1167, 700, 1228, 1236, 699, 1227, 1177, 2443])).
% 1.14/1.34 tff(2752,plain,((~hskp3) | hskp5 | (~c0_1(a1147)) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2753,plain,
% 1.14/1.34 (~hskp3),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2752, 1167, 700, 699, 2443])).
% 1.14/1.34 tff(2754,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2755,plain,
% 1.14/1.34 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1114) | c0_1(a1114) | c3_1(a1114)) <=> (hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2756,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1114) | c0_1(a1114) | c3_1(a1114))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2755])).
% 1.14/1.34 tff(2757,plain,
% 1.14/1.34 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1114) | c0_1(a1114) | c3_1(a1114))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2756, 2754])).
% 1.14/1.34 tff(2758,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1114) | c0_1(a1114) | c3_1(a1114))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2759,plain,
% 1.14/1.34 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2758, 2757])).
% 1.14/1.34 tff(2760,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2759, 110, 2753, 1286, 1285, 2685, 2679, 1284, 965, 2744])).
% 1.14/1.34 tff(2761,plain,((~hskp12) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | hskp5 | (~c0_1(a1147)) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2762,plain,
% 1.14/1.34 (~hskp12),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2761, 2737, 2589, 2736, 2588, 2565, 699, 2735])).
% 1.14/1.34 tff(2763,plain,
% 1.14/1.34 (hskp19),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2713, 2762, 2644])).
% 1.14/1.34 tff(2764,plain,
% 1.14/1.34 (~c2_1(a1127)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[816, 2763])).
% 1.14/1.34 tff(2765,plain,
% 1.14/1.34 (c2_1(a1125)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2119, 2656])).
% 1.14/1.34 tff(2766,plain,
% 1.14/1.34 (c0_1(a1125)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2127, 2656])).
% 1.14/1.34 tff(2767,plain,
% 1.14/1.34 (c3_1(a1127)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[825, 2763])).
% 1.14/1.34 tff(2768,plain,
% 1.14/1.34 (~c0_1(a1127)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2724, 110, 68, 2767, 2766, 2765, 2764, 2657, 2088])).
% 1.14/1.34 tff(2769,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2731, 110, 698, 2767, 747, 699, 2764, 67, 2589, 2768])).
% 1.14/1.34 tff(2770,plain,(hskp29 | c2_1(a1147) | c3_1(a1147) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2771,plain,
% 1.14/1.34 (hskp29),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2770, 68, 699, 747])).
% 1.14/1.34 tff(2772,plain,
% 1.14/1.34 (c3_1(a1116)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[189, 2771])).
% 1.14/1.34 tff(2773,plain,
% 1.14/1.34 (c2_1(a1116)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[197, 2771])).
% 1.14/1.34 tff(2774,plain,
% 1.14/1.34 (c0_1(a1116)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[205, 2771])).
% 1.14/1.34 tff(2775,assumption,(hskp20), introduced(assumption)).
% 1.14/1.34 tff(2776,plain,
% 1.14/1.34 (~c3_1(a1130)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[308, 2775])).
% 1.14/1.34 tff(2777,plain,
% 1.14/1.34 (~c2_1(a1130)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2149, 2775])).
% 1.14/1.34 tff(2778,plain,
% 1.14/1.34 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2779,plain,
% 1.14/1.34 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c1_1(a1130)) <=> (hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2780,plain,
% 1.14/1.34 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c1_1(a1130))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2779])).
% 1.14/1.34 tff(2781,plain,
% 1.14/1.34 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c1_1(a1130))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2780, 2778])).
% 1.14/1.34 tff(2782,plain,
% 1.14/1.34 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c1_1(a1130))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2783,plain,
% 1.14/1.34 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2782, 2781])).
% 1.14/1.34 tff(2784,plain,
% 1.14/1.34 (c1_1(a1130)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2783, 110, 68, 2588, 2777, 2776, 78])).
% 1.14/1.34 tff(2785,plain,
% 1.14/1.34 (~c0_1(a1130)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[302, 2775])).
% 1.14/1.34 tff(2786,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1223, 110, 2774, 2773, 2772, 2565, 747, 699, 2785, 2776, 320, 2784])).
% 1.14/1.34 tff(2787,plain,((~hskp20) | c2_1(a1147) | c3_1(a1147) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2788,plain,
% 1.14/1.34 (~hskp20),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2787, 68, 699, 747])).
% 1.14/1.34 tff(2789,plain,
% 1.14/1.34 (~hskp19),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1203, 2788, 2774, 2588, 2773, 2772])).
% 1.14/1.34 tff(2790,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1164, 110, 2662, 231, 230, 229, 834, 826, 817, 260])).
% 1.14/1.34 tff(2791,plain,((~hskp19) | hskp2 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2792,plain,
% 1.14/1.34 (~hskp19),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2791, 2662, 231, 230, 229])).
% 1.14/1.34 tff(2793,plain,
% 1.14/1.34 (hskp12),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2713, 2792, 2658])).
% 1.14/1.34 tff(2794,plain,
% 1.14/1.34 (~c3_1(a1114)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2678, 2793])).
% 1.14/1.34 tff(2795,plain,
% 1.14/1.34 (~c0_1(a1114)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2684, 2793])).
% 1.14/1.34 tff(2796,plain,
% 1.14/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2797,plain,
% 1.14/1.34 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1114) | c0_1(a1114) | (~c1_1(a1114))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2798,plain,
% 1.14/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1114) | c0_1(a1114) | (~c1_1(a1114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2797])).
% 1.14/1.34 tff(2799,plain,
% 1.14/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1114) | c0_1(a1114) | (~c1_1(a1114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2798, 2796])).
% 1.14/1.34 tff(2800,plain,
% 1.14/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1114) | c0_1(a1114) | (~c1_1(a1114)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2801,plain,
% 1.14/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2800, 2799])).
% 1.14/1.34 tff(2802,plain,
% 1.14/1.34 (~c1_1(a1114)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2801, 110, 231, 230, 229, 2565, 747, 699, 2795, 2794, 320])).
% 1.14/1.34 tff(2803,plain,
% 1.14/1.34 (hskp16),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2701, 2793, 2662])).
% 1.14/1.34 tff(2804,plain,
% 1.14/1.34 (~c0_1(a1121)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1825, 2803])).
% 1.14/1.34 tff(2805,plain,
% 1.14/1.34 (c3_1(a1121)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1835, 2803])).
% 1.14/1.34 tff(2806,plain,
% 1.14/1.34 (c1_1(a1121)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1843, 2803])).
% 1.14/1.34 tff(2807,plain,
% 1.14/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2808,plain,
% 1.14/1.34 (((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1114) | c1_1(a1114) | c0_1(a1114)) <=> (c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2809,plain,
% 1.14/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1114) | c1_1(a1114) | c0_1(a1114))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2808])).
% 1.14/1.34 tff(2810,plain,
% 1.14/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1114) | c1_1(a1114) | c0_1(a1114))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2809, 2807])).
% 1.14/1.34 tff(2811,plain,
% 1.14/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1114) | c1_1(a1114) | c0_1(a1114))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2812,plain,
% 1.14/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 1.14/1.34 tff(2813,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2812, 110, 2565, 2806, 2805, 699, 2804, 2795, 2794, 339, 2443, 2802])).
% 1.14/1.34 tff(2814,plain,(hskp2 | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c2_1(a1147) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2815,plain,
% 1.14/1.34 (hskp2),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2814, 2658, 2443, 231, 230, 229, 747, 699])).
% 1.14/1.34 tff(2816,plain,
% 1.14/1.34 (c0_1(a1100)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[289, 2815])).
% 1.14/1.34 tff(2817,plain,
% 1.14/1.34 (c2_1(a1100)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[281, 2815])).
% 1.14/1.34 tff(2818,plain,
% 1.14/1.34 (hskp12),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2713, 2658, 644])).
% 1.14/1.34 tff(2819,plain,
% 1.14/1.34 (~c3_1(a1100)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[273, 2815])).
% 1.14/1.34 tff(2820,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2761, 2819, 2818, 2443, 2817, 1167, 2565, 699, 2816])).
% 1.14/1.34 tff(2821,plain,(hskp26 | (~c1_1(a1147)) | hskp5 | c3_1(a1147) | hskp19 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2822,plain,
% 1.14/1.34 (hskp26),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2821, 2589, 2588, 699, 2789, 2774, 2773, 2772, 747])).
% 1.14/1.34 tff(2823,plain,
% 1.14/1.34 (~c2_1(a1180)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2615, 2822])).
% 1.14/1.34 tff(2824,plain,
% 1.14/1.34 (~c1_1(a1180)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2621, 2822])).
% 1.14/1.34 tff(2825,plain,
% 1.14/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2826,plain,
% 1.14/1.34 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1180) | c2_1(a1180) | (~c3_1(a1180))) <=> (c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2827,plain,
% 1.14/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1180) | c2_1(a1180) | (~c3_1(a1180)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2826])).
% 1.14/1.35 tff(2828,plain,
% 1.14/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1180) | c2_1(a1180) | (~c3_1(a1180)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2827, 2825])).
% 1.14/1.35 tff(2829,plain,
% 1.14/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1180) | c2_1(a1180) | (~c3_1(a1180)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2830,plain,
% 1.14/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 1.14/1.35 tff(2831,plain,
% 1.14/1.35 (~c3_1(a1180)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2830, 110, 2774, 2773, 2772, 2565, 2824, 2823, 747, 228, 2589])).
% 1.14/1.35 tff(2832,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2628, 110, 68, 2588, 2824, 2823, 78, 2831])).
% 1.14/1.35 tff(2833,plain,(hskp7 | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2834,plain,
% 1.14/1.35 (hskp7),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2833, 699, 747])).
% 1.14/1.35 tff(2835,plain,
% 1.14/1.35 (c3_1(a1105)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[600, 2834])).
% 1.14/1.35 tff(2836,plain,
% 1.14/1.35 (c0_1(a1105)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[592, 2834])).
% 1.14/1.35 tff(2837,plain,
% 1.14/1.35 (~c1_1(a1105)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[582, 2834])).
% 1.14/1.35 tff(2838,assumption,(~c0_1(a1105)), introduced(assumption)).
% 1.14/1.35 tff(2839,plain,
% 1.14/1.35 (~hskp7),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[592, 2838])).
% 1.14/1.35 tff(2840,plain,
% 1.14/1.35 (hskp7 | hskp5 | c1_1(a1147)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2475, 110, 747, 699, 78])).
% 1.14/1.35 tff(2841,plain,
% 1.14/1.35 (c1_1(a1147)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2840, 1167, 2839])).
% 1.14/1.35 tff(2842,assumption,(~c3_1(a1105)), introduced(assumption)).
% 1.14/1.35 tff(2843,plain,
% 1.14/1.35 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2844,plain,
% 1.14/1.35 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1105) | c2_1(a1105) | c1_1(a1105)) <=> (hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2845,plain,
% 1.14/1.35 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1105) | c2_1(a1105) | c1_1(a1105))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2844])).
% 1.14/1.35 tff(2846,plain,
% 1.14/1.35 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1105) | c2_1(a1105) | c1_1(a1105))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2845, 2843])).
% 1.14/1.35 tff(2847,plain,
% 1.14/1.35 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1105) | c2_1(a1105) | c1_1(a1105))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2848,plain,
% 1.14/1.35 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 1.14/1.35 tff(2849,plain,
% 1.14/1.35 (hskp7 | hskp5 | c3_1(a1105) | c2_1(a1105)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2848, 110, 612, 78])).
% 1.14/1.35 tff(2850,plain,
% 1.14/1.35 (c2_1(a1105)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2849, 1167, 2839, 2842])).
% 1.14/1.35 tff(2851,plain,
% 1.14/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2852,plain,
% 1.14/1.35 (((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1105) | c1_1(a1105) | c0_1(a1105)) <=> (c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2853,plain,
% 1.14/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1105) | c1_1(a1105) | c0_1(a1105))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2852])).
% 1.14/1.35 tff(2854,plain,
% 1.14/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1105) | c1_1(a1105) | c0_1(a1105))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2853, 2851])).
% 1.14/1.35 tff(2855,plain,
% 1.14/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1105) | c1_1(a1105) | c0_1(a1105))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2856,plain,
% 1.14/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2855, 2854])).
% 1.14/1.35 tff(2857,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2856, 110, 700, 2593, 2592, 2838, 2842, 699, 2591, 612, 339, 2443])).
% 1.14/1.35 tff(2858,plain,((~hskp16) | (~c0_1(a1147)) | c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c1_1(a1105) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2859,plain,
% 1.14/1.35 (~hskp16),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2858, 2841, 2838, 2842, 699, 612, 700])).
% 1.14/1.35 tff(2860,plain,
% 1.14/1.35 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2861,plain,
% 1.14/1.35 ((hskp16 | hskp2 | (~ndr1_0) | c3_1(a1105) | c0_1(a1105) | (~c2_1(a1105))) <=> (hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2862,plain,
% 1.14/1.35 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1105) | c0_1(a1105) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2861])).
% 1.14/1.35 tff(2863,plain,
% 1.14/1.35 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1105) | c0_1(a1105) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2862, 2860])).
% 1.14/1.35 tff(2864,plain,
% 1.14/1.35 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1105) | c0_1(a1105) | (~c2_1(a1105)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2865,plain,
% 1.14/1.35 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2864, 2863])).
% 1.14/1.35 tff(2866,plain,
% 1.14/1.35 (hskp16 | hskp2 | c3_1(a1105) | (~c2_1(a1105))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2865, 110, 2838, 2672])).
% 1.14/1.35 tff(2867,plain,
% 1.14/1.35 (hskp2),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2866, 2859, 2842, 2850])).
% 1.14/1.35 tff(2868,plain,
% 1.14/1.35 (~c3_1(a1100)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[273, 2867])).
% 1.14/1.35 tff(2869,plain,
% 1.14/1.35 (c2_1(a1100)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[281, 2867])).
% 1.14/1.35 tff(2870,plain,
% 1.14/1.35 (c0_1(a1100)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[289, 2867])).
% 1.14/1.35 tff(2871,plain,
% 1.14/1.35 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2872,plain,
% 1.14/1.35 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105)) <=> (hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2873,plain,
% 1.14/1.35 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2872])).
% 1.14/1.35 tff(2874,plain,
% 1.14/1.35 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2873, 2871])).
% 1.14/1.35 tff(2875,plain,
% 1.14/1.35 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2876,plain,
% 1.14/1.35 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2875, 2874])).
% 1.14/1.35 tff(2877,plain,
% 1.14/1.35 (hskp3),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2876, 110, 2838, 2842, 2870, 2869, 612, 2868, 965])).
% 1.14/1.35 tff(2878,plain,
% 1.14/1.35 (~c3_1(a1101)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[998, 2877])).
% 1.14/1.35 tff(2879,plain,
% 1.14/1.35 (c2_1(a1101)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1006, 2877])).
% 1.14/1.35 tff(2880,plain,
% 1.14/1.35 (c1_1(a1101)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1014, 2877])).
% 1.14/1.35 tff(2881,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2750, 110, 1167, 700, 2880, 2879, 699, 2878, 1177, 2841])).
% 1.14/1.35 tff(2882,plain,(hskp5 | (~c0_1(a1147)) | c3_1(a1147) | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2883,plain,
% 1.14/1.35 (hskp5),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2882, 2842, 699, 2838, 700, 612, 747])).
% 1.14/1.35 tff(2884,plain,
% 1.14/1.35 (c3_1(a1103)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[147, 2883])).
% 1.14/1.35 tff(2885,plain,
% 1.14/1.35 (~c0_1(a1103)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[129, 2883])).
% 1.14/1.35 tff(2886,plain,
% 1.14/1.35 (~c2_1(a1103)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[123, 2883])).
% 1.14/1.35 tff(2887,plain,
% 1.14/1.35 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2888,plain,
% 1.14/1.35 ((hskp14 | hskp7 | (~ndr1_0) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121))) <=> (hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2889,plain,
% 1.14/1.35 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2888])).
% 1.14/1.35 tff(2890,plain,
% 1.14/1.35 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2889, 2887])).
% 1.14/1.35 tff(2891,plain,
% 1.14/1.35 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2892,plain,
% 1.14/1.35 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 1.14/1.35 tff(2893,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2892, 632, 110, 68, 2592, 2591, 140, 2600])).
% 1.14/1.35 tff(2894,plain,((~hskp16) | hskp14 | hskp7 | (~c0_1(a1147)) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2895,plain,
% 1.14/1.35 (~hskp16),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2894, 2841, 2839, 700, 699, 632])).
% 1.14/1.35 tff(2896,plain,
% 1.14/1.35 (hskp2),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2866, 2895, 2842, 2850])).
% 1.14/1.35 tff(2897,plain,
% 1.14/1.35 (~c3_1(a1100)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[273, 2896])).
% 1.14/1.35 tff(2898,plain,
% 1.14/1.35 (c2_1(a1100)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[281, 2896])).
% 1.14/1.35 tff(2899,plain,
% 1.14/1.35 (c0_1(a1100)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[289, 2896])).
% 1.14/1.35 tff(2900,plain,
% 1.14/1.35 (hskp3),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2876, 110, 2838, 2842, 2899, 2898, 612, 2897, 965])).
% 1.14/1.35 tff(2901,plain,
% 1.14/1.35 (~c3_1(a1101)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[998, 2900])).
% 1.14/1.35 tff(2902,plain,
% 1.14/1.35 (c2_1(a1101)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1006, 2900])).
% 1.14/1.35 tff(2903,plain,
% 1.14/1.35 (c1_1(a1101)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1014, 2900])).
% 1.14/1.35 tff(2904,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2750, 110, 1167, 700, 2903, 2902, 699, 2901, 1177, 2841])).
% 1.14/1.35 tff(2905,plain,(hskp5 | (~c0_1(a1147)) | c3_1(a1147) | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | hskp14 | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2906,plain,
% 1.14/1.35 (hskp5),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2905, 632, 699, 2838, 2842, 612, 700, 747])).
% 1.14/1.35 tff(2907,plain,
% 1.14/1.35 (~c2_1(a1103)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[123, 2906])).
% 1.14/1.35 tff(2908,plain,
% 1.14/1.35 (~c0_1(a1103)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[129, 2906])).
% 1.14/1.35 tff(2909,plain,
% 1.14/1.35 (c3_1(a1103)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[147, 2906])).
% 1.14/1.35 tff(2910,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[154, 632, 110, 2839, 2909, 2908, 2907, 140])).
% 1.14/1.35 tff(2911,plain,(hskp14 | c3_1(a1147) | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | (~c0_1(a1147)) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2912,plain,
% 1.14/1.35 (hskp14),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2911, 2842, 2838, 699, 612, 700, 747])).
% 1.14/1.35 tff(2913,plain,
% 1.14/1.35 (~c2_1(a1118)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[166, 2912])).
% 1.14/1.35 tff(2914,plain,
% 1.14/1.35 (~c3_1(a1118)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[160, 2912])).
% 1.14/1.35 tff(2915,plain,
% 1.14/1.35 (c1_1(a1118)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[174, 2912])).
% 1.14/1.35 tff(2916,plain,
% 1.14/1.35 (~c0_1(a1118)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1956, 2883, 2915, 2914, 2913])).
% 1.14/1.35 tff(2917,plain,
% 1.14/1.35 (hskp14),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[154, 110, 68, 213, 207, 211, 140])).
% 1.14/1.35 tff(2918,plain,
% 1.14/1.35 (~c3_1(a1118)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[160, 2917])).
% 1.14/1.35 tff(2919,plain,
% 1.14/1.35 (~c2_1(a1118)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[166, 2917])).
% 1.14/1.35 tff(2920,plain,
% 1.14/1.35 (hskp6 | c0_1(a1118)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[495, 110, 68, 2919, 2918, 489])).
% 1.14/1.35 tff(2921,plain,
% 1.14/1.35 (hskp6),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2920, 354])).
% 1.14/1.35 tff(2922,plain,
% 1.14/1.35 (~c2_1(a1104)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[502, 2921])).
% 1.14/1.35 tff(2923,plain,
% 1.14/1.35 (c0_1(a1104)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[510, 2921])).
% 1.14/1.35 tff(2924,plain,
% 1.14/1.35 (c1_1(a1118)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[174, 2917])).
% 1.14/1.35 tff(2925,plain,
% 1.14/1.35 (hskp29),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[181, 110, 2924, 213, 2919, 2918, 207, 211, 67])).
% 1.14/1.35 tff(2926,plain,
% 1.14/1.35 (c3_1(a1116)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[189, 2925])).
% 1.14/1.35 tff(2927,plain,
% 1.14/1.35 (c2_1(a1116)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[197, 2925])).
% 1.14/1.35 tff(2928,plain,
% 1.14/1.35 (c0_1(a1116)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[205, 2925])).
% 1.14/1.35 tff(2929,plain,
% 1.14/1.35 (c3_1(a1104)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[517, 110, 2928, 2927, 2926, 2924, 2923, 2918, 2922, 320, 354])).
% 1.14/1.35 tff(2930,plain,
% 1.14/1.35 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2931,plain,
% 1.14/1.35 ((hskp16 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103))) <=> (hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2932,plain,
% 1.14/1.35 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2931])).
% 1.14/1.35 tff(2933,plain,
% 1.14/1.35 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2932, 2930])).
% 1.14/1.35 tff(2934,plain,
% 1.14/1.35 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2935,plain,
% 1.14/1.35 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 1.14/1.35 tff(2936,plain,
% 1.14/1.35 (~c1_1(a1103)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2935, 110, 2659, 2923, 213, 2922, 207, 1805, 2929])).
% 1.14/1.35 tff(2937,plain,
% 1.14/1.35 (c1_1(a1104)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[535, 2921])).
% 1.14/1.35 tff(2938,plain,
% 1.14/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2939,plain,
% 1.14/1.35 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103))) <=> (c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2940,plain,
% 1.14/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2939])).
% 1.14/1.35 tff(2941,plain,
% 1.14/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2940, 2938])).
% 1.14/1.35 tff(2942,plain,
% 1.14/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2943,plain,
% 1.14/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 1.14/1.35 tff(2944,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2943, 110, 2928, 2927, 2926, 2923, 2937, 213, 2922, 211, 228, 2936])).
% 1.14/1.35 tff(2945,plain,(c0_1(a1118) | (~c3_1(a1103)) | c2_1(a1103) | hskp16 | c0_1(a1103) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2946,plain,
% 1.14/1.35 (hskp16),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2945, 2916, 2839, 2886, 2885, 2884])).
% 1.14/1.35 tff(2947,plain,
% 1.14/1.35 (~c1_1(a1147)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2858, 2946, 2838, 2842, 699, 612, 700])).
% 1.14/1.35 tff(2948,plain,
% 1.14/1.35 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2949,plain,
% 1.14/1.35 ((hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105)) <=> (hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2950,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2949])).
% 1.14/1.36 tff(2951,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2950, 2948])).
% 1.14/1.36 tff(2952,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2953,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 1.14/1.36 tff(2954,plain,
% 1.14/1.36 (hskp1 | c0_1(a1118)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2953, 110, 2915, 2838, 2842, 2914, 612, 372])).
% 1.14/1.36 tff(2955,plain,
% 1.14/1.36 (hskp1),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2954, 2916])).
% 1.14/1.36 tff(2956,plain,
% 1.14/1.36 (~c0_1(a1099)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[387, 2955])).
% 1.14/1.36 tff(2957,plain,
% 1.14/1.36 (hskp6 | c0_1(a1118)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[495, 110, 2839, 2913, 2914, 489])).
% 1.14/1.36 tff(2958,plain,
% 1.14/1.36 (hskp6),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2957, 2916])).
% 1.14/1.36 tff(2959,plain,
% 1.14/1.36 (~c2_1(a1104)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[502, 2958])).
% 1.14/1.36 tff(2960,plain,
% 1.14/1.36 (c2_1(a1099)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[435, 2955])).
% 1.14/1.36 tff(2961,plain,
% 1.14/1.36 (c1_1(a1099)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[443, 2955])).
% 1.14/1.36 tff(2962,plain,
% 1.14/1.36 (c1_1(a1104)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[535, 2958])).
% 1.14/1.36 tff(2963,plain,
% 1.14/1.36 (c0_1(a1104)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[510, 2958])).
% 1.14/1.36 tff(2964,plain,
% 1.14/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2965,plain,
% 1.14/1.36 (((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099))) <=> (c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2966,plain,
% 1.14/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2965])).
% 1.14/1.36 tff(2967,plain,
% 1.14/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2966, 2964])).
% 1.14/1.36 tff(2968,plain,
% 1.14/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2969,plain,
% 1.14/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 1.14/1.36 tff(2970,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2969, 110, 700, 2963, 2962, 2961, 2960, 699, 2959, 2956, 1316, 2947])).
% 1.14/1.36 tff(2971,plain,(c3_1(a1105) | (~c0_1(a1147)) | c3_1(a1147) | c0_1(a1105) | c1_1(a1105) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2972,plain,
% 1.14/1.36 (c3_1(a1105)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2971, 2838, 699, 700, 612, 747])).
% 1.14/1.36 tff(2973,plain,
% 1.14/1.36 (~hskp3),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2752, 1167, 700, 699, 2841])).
% 1.14/1.36 tff(2974,assumption,(~c2_1(a1105)), introduced(assumption)).
% 1.14/1.36 tff(2975,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2976,plain,
% 1.14/1.36 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1105) | c0_1(a1105) | (~c3_1(a1105))) <=> (hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2977,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1105) | c0_1(a1105) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2976])).
% 1.14/1.36 tff(2978,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1105) | c0_1(a1105) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2977, 2975])).
% 1.14/1.36 tff(2979,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1105) | c0_1(a1105) | (~c3_1(a1105)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2980,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 1.14/1.36 tff(2981,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2980, 110, 698, 2838, 875, 747, 699, 67, 2974, 2443])).
% 1.14/1.36 tff(2982,plain,(c2_1(a1105) | hskp29 | c0_1(a1105) | (~c3_1(a1105)) | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2983,plain,
% 1.14/1.36 (c2_1(a1105)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2982, 698, 2838, 2972, 747, 699, 2841])).
% 1.14/1.36 tff(2984,plain,
% 1.14/1.36 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.14/1.36 inference(bind,[status(th)],[])).
% 1.14/1.36 tff(2985,plain,
% 1.14/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.14/1.36 inference(quant_intro,[status(thm)],[2984])).
% 1.14/1.36 tff(2986,plain,
% 1.14/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2987,plain,
% 1.14/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.14/1.36 inference(bind,[status(th)],[])).
% 1.14/1.36 tff(2988,plain,
% 1.14/1.36 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.14/1.36 inference(quant_intro,[status(thm)],[2987])).
% 1.14/1.36 tff(2989,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.14/1.36 tff(2990,plain,
% 1.14/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2989, 2988])).
% 1.14/1.36 tff(2991,plain,
% 1.14/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2990, 2986])).
% 1.14/1.36 tff(2992,plain,(
% 1.14/1.36 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.14/1.36 inference(skolemize,[status(sab)],[2991])).
% 1.14/1.36 tff(2993,plain,
% 1.14/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2992, 2985])).
% 1.14/1.36 tff(2994,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2995,plain,
% 1.14/1.36 ((hskp2 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180)) <=> (hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2996,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180)))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2995])).
% 1.14/1.36 tff(2997,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2996, 2994])).
% 1.14/1.36 tff(2998,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2999,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 1.14/1.36 tff(3000,plain,
% 1.14/1.36 (c3_1(a1180)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2999, 110, 2662, 875, 2635, 2622, 612, 2993, 905])).
% 1.14/1.36 tff(3001,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2641, 110, 698, 2635, 2616, 747, 699, 67, 3000, 2443])).
% 1.14/1.36 tff(3002,plain,((~hskp26) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp2 | (~c3_1(a1105)) | c1_1(a1105) | (~c2_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(3003,plain,
% 1.14/1.36 (~hskp26),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[3002, 698, 747, 699, 2841, 2662, 2972, 612, 2983])).
% 1.14/1.36 tff(3004,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(3005,plain,
% 1.14/1.36 ((hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(3006,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[3005])).
% 1.14/1.36 tff(3007,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[3006, 3004])).
% 1.14/1.36 tff(3008,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(3009,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[3008, 3007])).
% 1.14/1.36 tff(3010,plain,
% 1.14/1.36 (~c1_1(a1130)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[3009, 110, 1255, 2838, 875, 2785, 2777, 2169, 905])).
% 1.14/1.36 tff(3011,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2783, 110, 2839, 1167, 2777, 2776, 78, 3010])).
% 1.14/1.36 tff(3012,plain,((~hskp20) | hskp5 | hskp3 | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(3013,plain,
% 1.14/1.36 (~hskp20),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[3012, 2983, 2973, 2838, 2972, 1167])).
% 1.14/1.36 tff(3014,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(3015,plain,
% 1.14/1.36 ((hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(3016,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[3015])).
% 1.14/1.36 tff(3017,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[3016, 3014])).
% 1.14/1.36 tff(3018,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(3019,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 1.14/1.36 tff(3020,plain,
% 1.14/1.36 (~c0_1(a1127)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[3019, 110, 643, 2718, 2717, 2716, 2715, 2661, 915])).
% 1.14/1.36 tff(3021,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2731, 110, 698, 2718, 747, 699, 2715, 67, 2443, 3020])).
% 1.14/1.36 tff(3022,plain,(hskp16 | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp20 | hskp26 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(3023,plain,
% 1.14/1.36 (hskp16),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[3022, 3013, 747, 699, 2841, 2662, 698, 3003])).
% 1.14/1.36 tff(3024,plain,
% 1.14/1.36 (~c0_1(a1121)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1825, 3023])).
% 1.14/1.36 tff(3025,plain,
% 1.14/1.36 (c3_1(a1121)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1835, 3023])).
% 1.14/1.36 tff(3026,plain,
% 1.14/1.36 (c1_1(a1121)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1843, 3023])).
% 1.14/1.36 tff(3027,plain,
% 1.14/1.36 (~c2_1(a1121)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2599, 110, 700, 3026, 3025, 699, 3024, 45, 2841])).
% 1.14/1.36 tff(3028,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(3029,plain,
% 1.14/1.36 ((hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1121) | c0_1(a1121) | (~c1_1(a1121))) <=> (hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(3030,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1121) | c0_1(a1121) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[3029])).
% 1.14/1.36 tff(3031,plain,
% 1.14/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1121) | c0_1(a1121) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[3030, 3028])).
% 1.14/1.36 tff(3032,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1121) | c0_1(a1121) | (~c1_1(a1121)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(3033,plain,
% 1.14/1.36 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3032, 3031])).
% 1.14/1.37 tff(3034,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3033, 110, 2973, 3026, 2838, 2972, 3024, 2169, 2983, 3027])).
% 1.14/1.37 tff(3035,plain,(hskp29 | c0_1(a1105) | (~c0_1(a1147)) | c3_1(a1147) | c2_1(a1147) | hskp2 | hskp5 | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3036,plain,
% 1.14/1.37 (hskp29),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3035, 2662, 700, 699, 747, 2838, 1167, 612])).
% 1.14/1.37 tff(3037,plain,
% 1.14/1.37 (c3_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[189, 3036])).
% 1.14/1.37 tff(3038,plain,
% 1.14/1.37 (c2_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[197, 3036])).
% 1.14/1.37 tff(3039,plain,
% 1.14/1.37 (c0_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[205, 3036])).
% 1.14/1.37 tff(3040,plain,
% 1.14/1.37 (c2_1(a1105)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1047, 110, 3039, 3038, 3037, 700, 2972, 747, 612, 228, 2841])).
% 1.14/1.37 tff(3041,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3042,plain,
% 1.14/1.37 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3043,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[3042])).
% 1.14/1.37 tff(3044,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[3043, 3041])).
% 1.14/1.37 tff(3045,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(3046,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3045, 3044])).
% 1.14/1.37 tff(3047,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3046, 110, 2662, 3039, 3038, 3037, 2972, 612, 975, 3040])).
% 1.14/1.37 tff(3048,plain,(hskp2 | c1_1(a1105) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | c0_1(a1105) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3049,plain,
% 1.14/1.37 (hskp2),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3048, 1167, 700, 747, 699, 2838, 612])).
% 1.14/1.37 tff(3050,plain,
% 1.14/1.37 (~c3_1(a1100)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[273, 3049])).
% 1.14/1.37 tff(3051,plain,
% 1.14/1.37 (c2_1(a1100)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[281, 3049])).
% 1.14/1.37 tff(3052,plain,
% 1.14/1.37 (c0_1(a1100)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[289, 3049])).
% 1.14/1.37 tff(3053,plain,
% 1.14/1.37 (~hskp12),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2761, 3052, 3051, 3050, 1167, 700, 699, 2841])).
% 1.14/1.37 tff(3054,assumption,(~hskp12), introduced(assumption)).
% 1.14/1.37 tff(3055,plain,
% 1.14/1.37 (c2_1(a1105)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2982, 698, 2838, 875, 747, 699, 2841])).
% 1.14/1.37 tff(3056,plain,
% 1.14/1.37 (~hskp20),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3012, 3055, 1255, 2838, 875, 1167])).
% 1.14/1.37 tff(3057,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3058,plain,
% 1.14/1.37 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180)) <=> (hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3059,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[3058])).
% 1.14/1.37 tff(3060,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180))),
% 1.14/1.37 inference(transitivity,[status(thm)],[3059, 3057])).
% 1.14/1.37 tff(3061,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(3062,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 1.14/1.37 tff(3063,plain,
% 1.14/1.37 (c3_1(a1180)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3062, 110, 1255, 1286, 1285, 2635, 2622, 1284, 965])).
% 1.14/1.37 tff(3064,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2641, 110, 698, 2635, 2616, 747, 699, 67, 3063, 2443])).
% 1.14/1.37 tff(3065,plain,((~hskp26) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp3 | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3066,plain,
% 1.14/1.37 (~hskp26),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3065, 698, 747, 699, 2841, 1255, 1286, 1285, 1284])).
% 1.14/1.37 tff(3067,plain,
% 1.14/1.37 (hskp18),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2655, 2658, 2659])).
% 1.14/1.37 tff(3068,plain,
% 1.14/1.37 (~c1_1(a1125)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2111, 3067])).
% 1.14/1.37 tff(3069,plain,
% 1.14/1.37 (hskp19),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2713, 2658, 3054])).
% 1.14/1.37 tff(3070,plain,
% 1.14/1.37 (~c2_1(a1127)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[816, 3069])).
% 1.14/1.37 tff(3071,plain,
% 1.14/1.37 (c2_1(a1125)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2119, 3067])).
% 1.14/1.37 tff(3072,plain,
% 1.14/1.37 (c0_1(a1125)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2127, 3067])).
% 1.14/1.37 tff(3073,plain,
% 1.14/1.37 (c3_1(a1127)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[825, 3069])).
% 1.14/1.37 tff(3074,plain,
% 1.14/1.37 (~c0_1(a1127)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3019, 110, 643, 3073, 3072, 3071, 3070, 3068, 915])).
% 1.14/1.37 tff(3075,plain,
% 1.14/1.37 (c1_1(a1127)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[833, 3069])).
% 1.14/1.37 tff(3076,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3077,plain,
% 1.14/1.37 ((hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127))) <=> (hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3078,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[3077])).
% 1.14/1.37 tff(3079,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.14/1.37 inference(transitivity,[status(thm)],[3078, 3076])).
% 1.14/1.37 tff(3080,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(3081,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3080, 3079])).
% 1.14/1.37 tff(3082,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3081, 110, 1255, 3075, 2838, 875, 3070, 2169, 905, 3074])).
% 1.14/1.37 tff(3083,plain,(hskp26 | hskp3 | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | hskp20 | hskp12 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3084,plain,
% 1.14/1.37 (hskp16),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3083, 3066, 2838, 875, 3055, 3056, 3054, 1255])).
% 1.14/1.37 tff(3085,plain,
% 1.14/1.37 (~c0_1(a1121)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1825, 3084])).
% 1.14/1.37 tff(3086,plain,
% 1.14/1.37 (c3_1(a1121)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1835, 3084])).
% 1.14/1.37 tff(3087,plain,
% 1.14/1.37 (c1_1(a1121)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1843, 3084])).
% 1.14/1.37 tff(3088,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3089,plain,
% 1.14/1.37 ((hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121))) <=> (hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3090,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[3089])).
% 1.14/1.37 tff(3091,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[3090, 3088])).
% 1.14/1.37 tff(3092,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(3093,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 1.14/1.37 tff(3094,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3093, 110, 3056, 3087, 3086, 1286, 1285, 3085, 1284, 250])).
% 1.14/1.37 tff(3095,plain,(hskp29 | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | c0_1(a1105) | (~c3_1(a1105)) | hskp12 | hskp3 | c2_1(a1147) | c3_1(a1147) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3096,plain,
% 1.14/1.37 (hskp29),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3095, 3052, 3051, 3050, 2838, 2972, 3053, 2973, 747, 699, 1167])).
% 1.14/1.37 tff(3097,plain,
% 1.14/1.37 (c3_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[189, 3096])).
% 1.14/1.37 tff(3098,plain,
% 1.14/1.37 (c2_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[197, 3096])).
% 1.14/1.37 tff(3099,plain,
% 1.14/1.37 (c0_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[205, 3096])).
% 1.14/1.37 tff(3100,plain,
% 1.14/1.37 (c2_1(a1105)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1047, 110, 3099, 3098, 3097, 700, 2972, 747, 612, 228, 2841])).
% 1.14/1.37 tff(3101,plain,
% 1.14/1.37 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.14/1.37 inference(bind,[status(th)],[])).
% 1.14/1.37 tff(3102,plain,
% 1.14/1.37 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.37 inference(quant_intro,[status(thm)],[3101])).
% 1.14/1.37 tff(3103,plain,
% 1.14/1.37 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3104,plain,
% 1.14/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.14/1.37 inference(bind,[status(th)],[])).
% 1.14/1.37 tff(3105,plain,
% 1.14/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.37 inference(quant_intro,[status(thm)],[3104])).
% 1.14/1.37 tff(3106,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.14/1.37 tff(3107,plain,
% 1.14/1.37 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3106, 3105])).
% 1.14/1.37 tff(3108,plain,
% 1.14/1.37 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3107, 3103])).
% 1.14/1.37 tff(3109,plain,(
% 1.14/1.37 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.37 inference(skolemize,[status(sab)],[3108])).
% 1.14/1.37 tff(3110,plain,
% 1.14/1.37 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3109, 3102])).
% 1.14/1.37 tff(3111,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3112,plain,
% 1.14/1.37 ((hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3113,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[3112])).
% 1.14/1.37 tff(3114,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[3113, 3111])).
% 1.14/1.37 tff(3115,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(3116,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3115, 3114])).
% 1.14/1.37 tff(3117,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3116, 110, 2839, 3099, 3098, 3097, 2838, 2972, 3110, 3100])).
% 1.14/1.37 tff(3118,plain,(hskp5 | c0_1(a1105) | (~c0_1(a1147)) | c2_1(a1147) | c1_1(a1105) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3119,plain,
% 1.14/1.37 (hskp5),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3118, 2838, 700, 747, 612, 699])).
% 1.14/1.37 tff(3120,plain,
% 1.14/1.37 (~c2_1(a1103)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[123, 3119])).
% 1.14/1.37 tff(3121,plain,
% 1.14/1.37 (~c0_1(a1103)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[129, 3119])).
% 1.14/1.37 tff(3122,plain,
% 1.14/1.37 (c3_1(a1103)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[147, 3119])).
% 1.14/1.37 tff(3123,plain,
% 1.14/1.37 (c1_1(a1103)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2390, 110, 2316, 3122, 3121, 3120, 2003])).
% 1.14/1.37 tff(3124,plain,
% 1.14/1.37 (hskp21 | (~c1_1(a1103))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2382, 110, 2316, 3122, 3121, 33])).
% 1.14/1.37 tff(3125,plain,
% 1.14/1.37 (hskp21),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3124, 3123])).
% 1.14/1.37 tff(3126,plain,
% 1.14/1.37 (~c3_1(a1131)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[739, 3125])).
% 1.14/1.37 tff(3127,plain,
% 1.14/1.37 (~c0_1(a1131)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[745, 3125])).
% 1.14/1.37 tff(3128,plain,
% 1.14/1.37 (c1_1(a1131)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[754, 3125])).
% 1.14/1.37 tff(3129,plain,
% 1.14/1.37 (hskp14),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[154, 110, 2839, 3122, 3121, 3120, 140])).
% 1.14/1.37 tff(3130,plain,
% 1.14/1.37 (~c3_1(a1118)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[160, 3129])).
% 1.14/1.37 tff(3131,plain,
% 1.14/1.37 (~c2_1(a1118)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[166, 3129])).
% 1.14/1.37 tff(3132,plain,
% 1.14/1.37 (c1_1(a1118)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[174, 3129])).
% 1.14/1.37 tff(3133,plain,
% 1.14/1.37 (hskp29),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[181, 110, 3132, 3122, 3131, 3130, 3121, 3120, 67])).
% 1.14/1.37 tff(3134,plain,
% 1.14/1.37 (c3_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[189, 3133])).
% 1.14/1.37 tff(3135,plain,
% 1.14/1.37 (c2_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[197, 3133])).
% 1.14/1.37 tff(3136,plain,
% 1.14/1.37 (c0_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[205, 3133])).
% 1.14/1.37 tff(3137,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2585, 110, 3136, 3135, 3134, 700, 3128, 747, 699, 3127, 3126, 320])).
% 1.14/1.37 tff(3138,plain,(c0_1(a1105) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | hskp0 | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3139,plain,
% 1.14/1.37 (c0_1(a1105)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3138, 612, 2319, 2318, 2316, 2320])).
% 1.14/1.37 tff(3140,plain,
% 1.14/1.37 (~hskp7),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[600, 2842])).
% 1.14/1.37 tff(3141,plain,
% 1.14/1.37 (c2_1(a1105)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2849, 1167, 3140, 2842])).
% 1.14/1.37 tff(3142,plain,
% 1.14/1.37 (c1_1(a1147)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2840, 1167, 3140])).
% 1.14/1.37 tff(3143,plain,
% 1.14/1.37 (c0_1(a1105)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3138, 612, 747, 699, 2316, 700])).
% 1.14/1.37 tff(3144,plain,
% 1.14/1.37 (~hskp3),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2752, 1167, 700, 699, 3142])).
% 1.14/1.37 tff(3145,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3146,plain,
% 1.14/1.37 ((hskp3 | (~ndr1_0) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180)) <=> (hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(3147,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[3146])).
% 1.14/1.37 tff(3148,plain,
% 1.14/1.37 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180))),
% 1.14/1.37 inference(transitivity,[status(thm)],[3147, 3145])).
% 1.14/1.37 tff(3149,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(3150,plain,
% 1.14/1.37 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 1.14/1.37 tff(3151,plain,
% 1.14/1.37 (c3_1(a1180)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3150, 110, 1255, 902, 2842, 2635, 2622, 965, 905])).
% 1.14/1.37 tff(3152,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2641, 110, 698, 2635, 2616, 747, 699, 67, 3151, 2443])).
% 1.14/1.37 tff(3153,plain,((~hskp26) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp3 | (~c0_1(a1105)) | c3_1(a1105) | (~c2_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3154,plain,
% 1.14/1.37 (~hskp26),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3153, 698, 747, 699, 3142, 3144, 902, 2842, 905])).
% 1.14/1.37 tff(3155,plain,
% 1.14/1.37 (~hskp16),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2608, 698, 747, 699, 3142, 700])).
% 1.14/1.37 tff(3156,plain,
% 1.14/1.37 (hskp18),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2655, 3155, 3154])).
% 1.14/1.37 tff(3157,plain,
% 1.14/1.37 (~c1_1(a1125)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2111, 3156])).
% 1.14/1.37 tff(3158,plain,
% 1.14/1.37 (hskp2),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2733, 3155, 747, 699, 3142, 3140, 3154, 698])).
% 1.14/1.37 tff(3159,plain,
% 1.14/1.37 (~c3_1(a1100)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[273, 3158])).
% 1.14/1.37 tff(3160,plain,
% 1.14/1.37 (c2_1(a1100)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[281, 3158])).
% 1.14/1.37 tff(3161,plain,
% 1.14/1.37 (c0_1(a1100)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[289, 3158])).
% 1.14/1.37 tff(3162,plain,
% 1.14/1.37 (~hskp12),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2761, 3161, 3160, 3159, 1167, 700, 699, 3142])).
% 1.14/1.37 tff(3163,plain,
% 1.14/1.37 (hskp19),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2713, 3162, 3154])).
% 1.14/1.37 tff(3164,plain,
% 1.14/1.37 (~c2_1(a1127)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[816, 3163])).
% 1.14/1.37 tff(3165,plain,
% 1.14/1.37 (c2_1(a1125)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2119, 3156])).
% 1.14/1.37 tff(3166,plain,
% 1.14/1.37 (c0_1(a1125)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2127, 3156])).
% 1.14/1.37 tff(3167,plain,
% 1.14/1.37 (c3_1(a1127)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[825, 3163])).
% 1.14/1.37 tff(3168,plain,
% 1.14/1.37 (~c0_1(a1127)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2724, 110, 3140, 3167, 3166, 3165, 3164, 3157, 2088])).
% 1.14/1.37 tff(3169,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2731, 110, 698, 3167, 747, 699, 3164, 67, 3142, 3168])).
% 1.14/1.37 tff(3170,plain,(hskp29 | c2_1(a1147) | c3_1(a1147) | hskp5 | (~c0_1(a1147)) | (~c0_1(a1105)) | c3_1(a1105) | (~c2_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3171,plain,
% 1.14/1.37 (hskp29),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3170, 1167, 699, 747, 700, 3143, 2842, 3141])).
% 1.14/1.37 tff(3172,plain,
% 1.14/1.37 (c3_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[189, 3171])).
% 1.14/1.37 tff(3173,plain,
% 1.14/1.37 (c2_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[197, 3171])).
% 1.14/1.37 tff(3174,plain,
% 1.14/1.37 (c0_1(a1116)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[205, 3171])).
% 1.14/1.37 tff(3175,plain,
% 1.14/1.37 (~c3_1(a1180)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2830, 110, 231, 230, 229, 700, 2622, 2616, 747, 228, 2443])).
% 1.14/1.37 tff(3176,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3150, 110, 1255, 902, 2842, 2635, 2622, 965, 3175, 905])).
% 1.14/1.37 tff(3177,plain,((~hskp26) | hskp3 | (~c0_1(a1105)) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1147)) | c2_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(3178,plain,
% 1.14/1.37 (~hskp26),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[3177, 3144, 3143, 2842, 3141, 3174, 3173, 3172, 700, 747, 3142])).
% 1.14/1.37 tff(3179,plain,
% 1.14/1.37 (c2_1(a1114)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2692, 2793])).
% 1.14/1.37 tff(3180,plain,
% 1.14/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3181,plain,
% 1.21/1.37 (((~ndr1_0) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c3_1(a1105) | (~c0_1(a1105)) | c0_1(a1114) | (~c2_1(a1114)) | (~c1_1(a1114))) <=> (c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(3182,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c3_1(a1105) | (~c0_1(a1105)) | c0_1(a1114) | (~c2_1(a1114)) | (~c1_1(a1114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3181])).
% 1.21/1.38 tff(3183,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c3_1(a1105) | (~c0_1(a1105)) | c0_1(a1114) | (~c2_1(a1114)) | (~c1_1(a1114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3182, 3180])).
% 1.21/1.38 tff(3184,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c3_1(a1105) | (~c0_1(a1105)) | c0_1(a1114) | (~c2_1(a1114)) | (~c1_1(a1114)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3185,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3184, 3183])).
% 1.21/1.38 tff(3186,plain,
% 1.21/1.38 (~c1_1(a1114)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3185, 110, 700, 3179, 902, 2842, 747, 2795, 612, 1316, 2443])).
% 1.21/1.38 tff(3187,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2812, 110, 700, 2806, 2805, 699, 2804, 2795, 2794, 339, 2443, 3186])).
% 1.21/1.38 tff(3188,plain,(hskp2 | (~c0_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1105)) | c3_1(a1105) | c2_1(a1147) | c1_1(a1105) | hskp26 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(3189,plain,
% 1.21/1.38 (hskp2),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3188, 3142, 699, 700, 3143, 2842, 747, 612, 3178, 3174, 3173, 3172])).
% 1.21/1.38 tff(3190,plain,
% 1.21/1.38 (~c3_1(a1100)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[273, 3189])).
% 1.21/1.38 tff(3191,plain,
% 1.21/1.38 (c0_1(a1100)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[289, 3189])).
% 1.21/1.38 tff(3192,plain,
% 1.21/1.38 (c2_1(a1100)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[281, 3189])).
% 1.21/1.38 tff(3193,plain,
% 1.21/1.38 (~hskp12),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2761, 3192, 3191, 3190, 1167, 700, 699, 3142])).
% 1.21/1.38 tff(3194,plain,
% 1.21/1.38 (hskp19),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2713, 3193, 3178])).
% 1.21/1.38 tff(3195,plain,
% 1.21/1.38 (~c2_1(a1127)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[816, 3194])).
% 1.21/1.38 tff(3196,plain,
% 1.21/1.38 (c3_1(a1127)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[825, 3194])).
% 1.21/1.38 tff(3197,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3198,plain,
% 1.21/1.38 ((hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105))) <=> (hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3199,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3198])).
% 1.21/1.38 tff(3200,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3199, 3197])).
% 1.21/1.38 tff(3201,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3202,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3201, 3200])).
% 1.21/1.38 tff(3203,plain,
% 1.21/1.38 (~c0_1(a1127)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3202, 110, 3140, 3196, 3143, 3195, 612, 2088, 3141])).
% 1.21/1.38 tff(3204,plain,
% 1.21/1.38 (hskp20),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1203, 3194, 1167, 3174, 3173, 3172])).
% 1.21/1.38 tff(3205,plain,
% 1.21/1.38 (~c2_1(a1130)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2149, 3204])).
% 1.21/1.38 tff(3206,plain,
% 1.21/1.38 (~c0_1(a1130)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[302, 3204])).
% 1.21/1.38 tff(3207,plain,
% 1.21/1.38 (((~![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(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130))) <=> ((~![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(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3208,plain,
% 1.21/1.38 ((hskp0 | (~ndr1_0) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130)) <=> (hskp0 | c0_1(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3209,plain,
% 1.21/1.38 (((~![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(a1127) | c0_1(a1127) | (~c3_1(a1127)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![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(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130)))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3208])).
% 1.21/1.38 tff(3210,plain,
% 1.21/1.38 (((~![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(a1127) | c0_1(a1127) | (~c3_1(a1127)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![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(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3209, 3207])).
% 1.21/1.38 tff(3211,plain,
% 1.21/1.38 ((~![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(a1127) | c0_1(a1127) | (~c3_1(a1127)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3212,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3211, 3210])).
% 1.21/1.38 tff(3213,plain,
% 1.21/1.38 (c1_1(a1130)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3212, 110, 2316, 3196, 3206, 3205, 3195, 2003, 3203])).
% 1.21/1.38 tff(3214,plain,
% 1.21/1.38 (~c3_1(a1130)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[308, 3204])).
% 1.21/1.38 tff(3215,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1223, 110, 3174, 3173, 3172, 700, 747, 699, 3206, 3214, 320, 3213])).
% 1.21/1.38 tff(3216,plain,(hskp5 | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | hskp0 | c1_1(a1105) | c3_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(3217,plain,
% 1.21/1.38 (hskp5),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3216, 2842, 747, 699, 2316, 612, 700])).
% 1.21/1.38 tff(3218,plain,
% 1.21/1.38 (~c2_1(a1103)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[123, 3217])).
% 1.21/1.38 tff(3219,plain,
% 1.21/1.38 (~c0_1(a1103)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[129, 3217])).
% 1.21/1.38 tff(3220,plain,
% 1.21/1.38 (c3_1(a1103)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[147, 3217])).
% 1.21/1.38 tff(3221,plain,
% 1.21/1.38 (c1_1(a1103)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2390, 110, 2316, 3220, 3219, 3218, 2003])).
% 1.21/1.38 tff(3222,plain,
% 1.21/1.38 (hskp21 | (~c1_1(a1103))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2382, 110, 2316, 3220, 3219, 33])).
% 1.21/1.38 tff(3223,plain,
% 1.21/1.38 (hskp21),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3222, 3221])).
% 1.21/1.38 tff(3224,plain,
% 1.21/1.38 (~c3_1(a1131)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[739, 3223])).
% 1.21/1.38 tff(3225,plain,
% 1.21/1.38 (~c0_1(a1131)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[745, 3223])).
% 1.21/1.38 tff(3226,plain,
% 1.21/1.38 (c1_1(a1131)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[754, 3223])).
% 1.21/1.38 tff(3227,plain,
% 1.21/1.38 (hskp14),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[154, 110, 3140, 3220, 3219, 3218, 140])).
% 1.21/1.38 tff(3228,plain,
% 1.21/1.38 (~c3_1(a1118)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[160, 3227])).
% 1.21/1.38 tff(3229,plain,
% 1.21/1.38 (~c2_1(a1118)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[166, 3227])).
% 1.21/1.38 tff(3230,plain,
% 1.21/1.38 (c1_1(a1118)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[174, 3227])).
% 1.21/1.38 tff(3231,plain,
% 1.21/1.38 (hskp29),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[181, 110, 3230, 3220, 3229, 3228, 3219, 3218, 67])).
% 1.21/1.38 tff(3232,plain,
% 1.21/1.38 (c3_1(a1116)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[189, 3231])).
% 1.21/1.38 tff(3233,plain,
% 1.21/1.38 (c2_1(a1116)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[197, 3231])).
% 1.21/1.38 tff(3234,plain,
% 1.21/1.38 (c0_1(a1116)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[205, 3231])).
% 1.21/1.38 tff(3235,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2585, 110, 3234, 3233, 3232, 700, 3226, 747, 699, 3225, 3224, 320])).
% 1.21/1.38 tff(3236,plain,(c3_1(a1105) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | hskp0 | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(3237,plain,
% 1.21/1.38 (c3_1(a1105)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3236, 612, 2319, 2318, 2316, 2320])).
% 1.21/1.38 tff(3238,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3239,plain,
% 1.21/1.38 ((hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147)) <=> (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3240,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3239])).
% 1.21/1.38 tff(3241,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3240, 3238])).
% 1.21/1.38 tff(3242,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3243,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3242, 3241])).
% 1.21/1.38 tff(3244,plain,
% 1.21/1.38 ((~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3243, 110, 613, 2319, 2318, 612, 611])).
% 1.21/1.38 tff(3245,plain,
% 1.21/1.38 (c1_1(a1147)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3244, 3237, 3139])).
% 1.21/1.38 tff(3246,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2206, 110, 698, 1952, 747, 699, 1953, 1954, 67, 2443])).
% 1.21/1.38 tff(3247,plain,((~hskp5) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(3248,plain,
% 1.21/1.38 (~hskp5),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3247, 698, 2319, 2318, 3245])).
% 1.21/1.38 tff(3249,plain,
% 1.21/1.38 (~hskp3),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2752, 3248, 2320, 2318, 3245])).
% 1.21/1.38 tff(3250,plain,
% 1.21/1.38 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3251,plain,
% 1.21/1.38 ((hskp22 | hskp0 | (~ndr1_0) | c2_1(a1105) | c1_1(a1105) | (~c3_1(a1105))) <=> (hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3252,plain,
% 1.21/1.38 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1105) | c1_1(a1105) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3251])).
% 1.21/1.38 tff(3253,plain,
% 1.21/1.38 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1105) | c1_1(a1105) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3252, 3250])).
% 1.21/1.38 tff(3254,plain,
% 1.21/1.38 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1105) | c1_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3255,plain,
% 1.21/1.38 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3254, 3253])).
% 1.21/1.38 tff(3256,plain,
% 1.21/1.38 (hskp22 | c2_1(a1105) | (~c3_1(a1105))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3255, 110, 2316, 612, 2021])).
% 1.21/1.38 tff(3257,plain,
% 1.21/1.38 (hskp22),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3256, 2974, 3237])).
% 1.21/1.38 tff(3258,plain,
% 1.21/1.38 (c3_1(a1145)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2068, 3257])).
% 1.21/1.38 tff(3259,plain,
% 1.21/1.38 (c2_1(a1145)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2042, 3257])).
% 1.21/1.38 tff(3260,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3261,plain,
% 1.21/1.38 (((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3262,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3261])).
% 1.21/1.38 tff(3263,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3262, 3260])).
% 1.21/1.38 tff(3264,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3265,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3264, 3263])).
% 1.21/1.38 tff(3266,plain,
% 1.21/1.38 (~c0_1(a1145)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3265, 110, 2320, 3259, 3258, 3237, 2319, 612, 228, 2974, 3245])).
% 1.21/1.38 tff(3267,plain,
% 1.21/1.38 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3268,plain,
% 1.21/1.38 ((hskp30 | hskp18 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105))) <=> (hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3269,plain,
% 1.21/1.38 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3268])).
% 1.21/1.38 tff(3270,plain,
% 1.21/1.38 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3269, 3267])).
% 1.21/1.38 tff(3271,plain,
% 1.21/1.38 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3272,plain,
% 1.21/1.38 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3271, 3270])).
% 1.21/1.38 tff(3273,plain,
% 1.21/1.38 (hskp18 | (~c0_1(a1105)) | (~c3_1(a1105))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3272, 110, 613, 612, 2098])).
% 1.21/1.38 tff(3274,plain,
% 1.21/1.38 (hskp18),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3273, 3237, 3139])).
% 1.21/1.38 tff(3275,plain,
% 1.21/1.38 (~c1_1(a1125)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2111, 3274])).
% 1.21/1.38 tff(3276,plain,
% 1.21/1.38 (c2_1(a1125)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2119, 3274])).
% 1.21/1.38 tff(3277,plain,
% 1.21/1.38 (c0_1(a1125)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2127, 3274])).
% 1.21/1.38 tff(3278,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3279,plain,
% 1.21/1.38 ((hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3280,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3279])).
% 1.21/1.38 tff(3281,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[3280, 3278])).
% 1.21/1.38 tff(3282,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(3283,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 1.21/1.38 tff(3284,plain,
% 1.21/1.38 (hskp20),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3283, 110, 3277, 3276, 3139, 3237, 3275, 915, 2974])).
% 1.21/1.38 tff(3285,plain,
% 1.21/1.38 (~c2_1(a1130)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2149, 3284])).
% 1.21/1.38 tff(3286,plain,
% 1.21/1.38 (~c0_1(a1130)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[302, 3284])).
% 1.21/1.38 tff(3287,plain,
% 1.21/1.38 (~c1_1(a1130)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2176, 110, 1255, 3259, 3258, 3286, 3285, 2169, 3266])).
% 1.21/1.38 tff(3288,plain,
% 1.21/1.38 (~c3_1(a1130)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[308, 3284])).
% 1.21/1.38 tff(3289,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2158, 110, 613, 3139, 3237, 3285, 3288, 612, 611, 3287])).
% 1.21/1.38 tff(3290,plain,(c2_1(a1105) | hskp30 | c1_1(a1105) | hskp3 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(3291,plain,
% 1.21/1.38 (c2_1(a1105)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3290, 3249, 612, 613, 2316])).
% 1.21/1.38 tff(3292,plain,
% 1.21/1.38 (hskp2 | (~c2_1(a1105))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[981, 110, 3139, 3237, 612, 975])).
% 1.21/1.38 tff(3293,plain,
% 1.21/1.38 (hskp2),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3292, 3291])).
% 1.21/1.38 tff(3294,plain,
% 1.21/1.38 (~c3_1(a1100)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[273, 3293])).
% 1.21/1.38 tff(3295,plain,
% 1.21/1.38 (c0_1(a1100)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[289, 3293])).
% 1.21/1.38 tff(3296,plain,
% 1.21/1.38 (c2_1(a1100)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[281, 3293])).
% 1.21/1.38 tff(3297,plain,
% 1.21/1.38 (~hskp26),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3065, 3296, 2319, 2318, 3245, 698, 3249, 3295, 3294])).
% 1.21/1.38 tff(3298,plain,
% 1.21/1.38 ((hskp26 | hskp4 | hskp3) <=> (hskp26 | hskp4 | hskp3)),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3299,plain,
% 1.21/1.38 (((hskp4 | hskp3) | hskp26) <=> (hskp26 | hskp4 | hskp3)),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3300,plain,
% 1.21/1.38 ((hskp4 | hskp3) <=> (hskp4 | hskp3)),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(3301,plain,
% 1.21/1.38 (((hskp4 | hskp3) | hskp26) <=> ((hskp4 | hskp3) | hskp26)),
% 1.21/1.38 inference(monotonicity,[status(thm)],[3300])).
% 1.21/1.38 tff(3302,plain,
% 1.21/1.38 (((hskp4 | hskp3) | hskp26) <=> (hskp26 | hskp4 | hskp3)),
% 1.21/1.38 inference(transitivity,[status(thm)],[3301, 3299])).
% 1.21/1.38 tff(3303,axiom,((hskp4 | hskp3) | hskp26), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.21/1.38 tff(3304,plain,
% 1.21/1.38 (hskp26 | hskp4 | hskp3),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 1.21/1.38 tff(3305,plain,
% 1.21/1.38 (hskp26 | hskp4 | hskp3),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3304, 3298])).
% 1.21/1.38 tff(3306,plain,
% 1.21/1.38 (hskp26 | hskp4 | hskp3),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3305, 3298])).
% 1.21/1.38 tff(3307,plain,
% 1.21/1.38 (hskp26 | hskp4 | hskp3),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3306, 3298])).
% 1.21/1.38 tff(3308,plain,
% 1.21/1.38 (hskp26 | hskp4 | hskp3),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[3307, 3298])).
% 1.21/1.38 tff(3309,plain,
% 1.21/1.38 (hskp4),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[3308, 3297, 3249])).
% 1.21/1.38 tff(3310,plain,
% 1.21/1.38 (~c3_1(a1102)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1427, 3309])).
% 1.21/1.38 tff(3311,plain,
% 1.21/1.38 (c1_1(a1102)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1444, 3309])).
% 1.21/1.38 tff(3312,plain,
% 1.21/1.38 (c0_1(a1102)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1452, 3309])).
% 1.21/1.38 tff(3313,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3314,plain,
% 1.21/1.39 ((hskp5 | (~ndr1_0) | c3_1(a1102) | (~c1_1(a1102)) | (~c2_1(a1102)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102))) <=> (hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3315,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1102) | (~c1_1(a1102)) | (~c2_1(a1102)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[3314])).
% 1.21/1.39 tff(3316,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1102) | (~c1_1(a1102)) | (~c2_1(a1102)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[3315, 3313])).
% 1.21/1.39 tff(3317,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1102) | (~c1_1(a1102)) | (~c2_1(a1102)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(3318,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[3317, 3316])).
% 1.21/1.39 tff(3319,plain,
% 1.21/1.39 (~c2_1(a1102)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3318, 110, 3248, 3312, 3311, 3310, 1177])).
% 1.21/1.39 tff(3320,plain,
% 1.21/1.39 (~hskp12),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2761, 3296, 3295, 3294, 3248, 2320, 2318, 3245])).
% 1.21/1.39 tff(3321,plain,
% 1.21/1.39 (hskp19),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2713, 3297, 3320])).
% 1.21/1.39 tff(3322,plain,
% 1.21/1.39 (~c2_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[816, 3321])).
% 1.21/1.39 tff(3323,plain,
% 1.21/1.39 (c3_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[825, 3321])).
% 1.21/1.39 tff(3324,plain,
% 1.21/1.39 (c0_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2731, 110, 698, 3323, 2319, 2318, 3322, 67, 3245])).
% 1.21/1.39 tff(3325,plain,
% 1.21/1.39 (hskp20 | (~c0_1(a1127))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3019, 110, 3323, 3277, 3276, 3322, 3275, 915])).
% 1.21/1.39 tff(3326,plain,
% 1.21/1.39 (hskp20),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3325, 3324])).
% 1.21/1.39 tff(3327,plain,
% 1.21/1.39 (~c3_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[308, 3326])).
% 1.21/1.39 tff(3328,plain,
% 1.21/1.39 (~c0_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[302, 3326])).
% 1.21/1.39 tff(3329,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3330,plain,
% 1.21/1.39 (((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c2_1(a1102) | c3_1(a1102) | (~c0_1(a1102)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3331,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c2_1(a1102) | c3_1(a1102) | (~c0_1(a1102)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[3330])).
% 1.21/1.39 tff(3332,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c2_1(a1102) | c3_1(a1102) | (~c0_1(a1102)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[3331, 3329])).
% 1.21/1.39 tff(3333,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c2_1(a1102) | c3_1(a1102) | (~c0_1(a1102)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(3334,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[3333, 3332])).
% 1.21/1.39 tff(3335,plain,
% 1.21/1.39 (~c1_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3334, 110, 3139, 3237, 3312, 3328, 3327, 3310, 320, 3291, 3319])).
% 1.21/1.39 tff(3336,plain,
% 1.21/1.39 (~c2_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2149, 3326])).
% 1.21/1.39 tff(3337,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2158, 110, 613, 3139, 3237, 3336, 3327, 612, 611, 3335])).
% 1.21/1.39 tff(3338,plain,(hskp29 | hskp30 | c1_1(a1105) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(3339,plain,
% 1.21/1.39 (hskp29),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3338, 612, 613, 2316])).
% 1.21/1.39 tff(3340,plain,
% 1.21/1.39 (c3_1(a1116)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[189, 3339])).
% 1.21/1.39 tff(3341,plain,
% 1.21/1.39 (c2_1(a1116)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[197, 3339])).
% 1.21/1.39 tff(3342,plain,
% 1.21/1.39 (c0_1(a1116)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[205, 3339])).
% 1.21/1.39 tff(3343,plain,
% 1.21/1.39 (c2_1(a1105)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1047, 110, 3342, 3341, 3340, 2320, 3237, 2319, 612, 228, 3245])).
% 1.21/1.39 tff(3344,plain,
% 1.21/1.39 (hskp2),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3046, 110, 3342, 3341, 3340, 3237, 612, 975, 3343])).
% 1.21/1.39 tff(3345,plain,
% 1.21/1.39 (~c3_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[273, 3344])).
% 1.21/1.39 tff(3346,plain,
% 1.21/1.39 (~c1_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1223, 110, 231, 230, 229, 700, 747, 699, 2785, 2776, 320])).
% 1.21/1.39 tff(3347,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2158, 110, 613, 902, 875, 2777, 2776, 612, 611, 3346])).
% 1.21/1.39 tff(3348,plain,((~hskp20) | hskp30 | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(3349,plain,
% 1.21/1.39 (~hskp20),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3348, 3139, 613, 3237, 612, 3342, 3341, 3340, 2320, 2319, 2318])).
% 1.21/1.39 tff(3350,plain,
% 1.21/1.39 (c2_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[281, 3344])).
% 1.21/1.39 tff(3351,plain,
% 1.21/1.39 (c0_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[289, 3344])).
% 1.21/1.39 tff(3352,plain,
% 1.21/1.39 (~hskp12),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2761, 1167, 1286, 1284, 1285, 700, 699, 2443])).
% 1.21/1.39 tff(3353,plain,
% 1.21/1.39 (~hskp19),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1203, 1167, 231, 643, 230, 229])).
% 1.21/1.39 tff(3354,plain,
% 1.21/1.39 (hskp26),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2713, 3353, 3352])).
% 1.21/1.39 tff(3355,plain,
% 1.21/1.39 (~c2_1(a1180)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2615, 3354])).
% 1.21/1.39 tff(3356,plain,
% 1.21/1.39 (~c1_1(a1180)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2621, 3354])).
% 1.21/1.39 tff(3357,plain,
% 1.21/1.39 (~c3_1(a1180)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2830, 110, 231, 230, 229, 700, 3356, 3355, 747, 228, 2443])).
% 1.21/1.39 tff(3358,plain,
% 1.21/1.39 (~c0_1(a1180)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2634, 3354])).
% 1.21/1.39 tff(3359,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3062, 110, 2753, 1286, 1285, 3358, 3356, 1284, 965, 3357])).
% 1.21/1.39 tff(3360,plain,(hskp5 | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1147)) | c2_1(a1147) | (~c1_1(a1147)) | hskp20 | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(3361,plain,
% 1.21/1.39 (hskp5),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3360, 3351, 3350, 3345, 3342, 3341, 3340, 2320, 2319, 3245, 3349, 2318])).
% 1.21/1.39 tff(3362,plain,
% 1.21/1.39 (~c0_1(a1103)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[129, 3361])).
% 1.21/1.39 tff(3363,plain,
% 1.21/1.39 (c3_1(a1103)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[147, 3361])).
% 1.21/1.39 tff(3364,plain,
% 1.21/1.39 (~c1_1(a1103)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[296, 110, 3349, 3363, 3351, 3350, 3362, 3345, 250])).
% 1.21/1.39 tff(3365,plain,
% 1.21/1.39 (~c2_1(a1103)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[123, 3361])).
% 1.21/1.39 tff(3366,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2390, 110, 2316, 3363, 3362, 3365, 2003, 3364])).
% 1.21/1.39 tff(3367,plain,(c1_1(a1105) | hskp0 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(3368,plain,
% 1.21/1.39 (hskp30),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3367, 2837, 2394])).
% 1.21/1.39 tff(3369,plain,
% 1.21/1.39 (c1_1(a1136)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[630, 3368])).
% 1.21/1.39 tff(3370,plain,
% 1.21/1.39 (c3_1(a1136)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[663, 3368])).
% 1.21/1.39 tff(3371,plain,
% 1.21/1.39 (c2_1(a1136)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[671, 3368])).
% 1.21/1.39 tff(3372,plain,
% 1.21/1.39 (hskp14),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1027, 698, 2837, 3371, 3370, 3369, 2836, 2835])).
% 1.21/1.39 tff(3373,plain,
% 1.21/1.39 (~c2_1(a1118)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[166, 3372])).
% 1.21/1.39 tff(3374,plain,
% 1.21/1.39 (c0_1(a1136)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[725, 698, 2565, 3371, 3370, 699, 3369])).
% 1.21/1.39 tff(3375,plain,
% 1.21/1.39 (~c3_1(a1118)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[160, 3372])).
% 1.21/1.39 tff(3376,plain,
% 1.21/1.39 (c1_1(a1118)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[174, 3372])).
% 1.21/1.39 tff(3377,plain,
% 1.21/1.39 (c0_1(a1118)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1666, 110, 3371, 3370, 2565, 3376, 747, 699, 3375, 320, 3374])).
% 1.21/1.39 tff(3378,plain,
% 1.21/1.39 (c2_1(a1105) | (~c0_1(a1118))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1693, 110, 3371, 3370, 3376, 2835, 3373, 2837, 228, 3374])).
% 1.21/1.39 tff(3379,plain,
% 1.21/1.39 (c2_1(a1105)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3378, 3377])).
% 1.21/1.39 tff(3380,plain,
% 1.21/1.39 (hskp2 | (~c2_1(a1105))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[981, 110, 2836, 2835, 2837, 975])).
% 1.21/1.39 tff(3381,plain,
% 1.21/1.39 (hskp2),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3380, 3379])).
% 1.21/1.39 tff(3382,plain,
% 1.21/1.39 (c2_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[281, 3381])).
% 1.21/1.39 tff(3383,plain,
% 1.21/1.39 (c0_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[289, 3381])).
% 1.21/1.39 tff(3384,plain,
% 1.21/1.39 (~c3_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[273, 3381])).
% 1.21/1.39 tff(3385,plain,
% 1.21/1.39 (~hskp8),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1682, 3377, 3370, 2836, 2835, 2837, 3374, 3376, 3373, 3371])).
% 1.21/1.39 tff(3386,plain,
% 1.21/1.39 (hskp19 | hskp8 | (~c2_1(a1105))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2540, 110, 2835, 2837, 2534])).
% 1.21/1.39 tff(3387,plain,
% 1.21/1.39 (hskp19),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3386, 3385, 3379])).
% 1.21/1.39 tff(3388,plain,
% 1.21/1.39 (~c2_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[816, 3387])).
% 1.21/1.39 tff(3389,plain,
% 1.21/1.39 (c3_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[825, 3387])).
% 1.21/1.39 tff(3390,plain,
% 1.21/1.39 (c0_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1573, 110, 698, 3389, 3376, 3388, 3373, 3375, 67])).
% 1.21/1.39 tff(3391,plain,
% 1.21/1.39 (hskp20 | (~c0_1(a1127))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[923, 110, 3389, 2836, 3388, 2837, 915, 3379])).
% 1.21/1.39 tff(3392,plain,
% 1.21/1.39 (hskp20),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3391, 3390])).
% 1.21/1.39 tff(3393,plain,
% 1.21/1.39 (~c0_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[302, 3392])).
% 1.21/1.39 tff(3394,plain,
% 1.21/1.39 (~c3_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[308, 3392])).
% 1.21/1.39 tff(3395,plain,
% 1.21/1.39 (hskp5),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1305, 310, 733, 321, 1285, 1284, 696, 673, 902, 875, 612, 1286, 700, 747, 699])).
% 1.21/1.39 tff(3396,plain,
% 1.21/1.39 (~c2_1(a1103)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[123, 3395])).
% 1.21/1.39 tff(3397,plain,
% 1.21/1.39 (c3_1(a1103)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[147, 3395])).
% 1.21/1.39 tff(3398,plain,
% 1.21/1.39 (~c0_1(a1103)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[129, 3395])).
% 1.21/1.39 tff(3399,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[349, 3398, 3397, 212, 209, 3396, 310, 321, 208, 210])).
% 1.21/1.39 tff(3400,plain,(c0_1(a1130) | c2_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1136)) | (~c2_1(a1100)) | c3_1(a1100) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | (~c0_1(a1100)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(3401,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3400, 3394, 3393, 699, 2565, 3375, 3376, 3374, 3377, 3384, 3371, 3370, 2836, 2835, 2837, 3383, 3382, 747, 3373])).
% 1.21/1.39 tff(3402,plain,(hskp29 | c3_1(a1147) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(3403,plain,
% 1.21/1.39 (hskp29),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3402, 699, 747])).
% 1.21/1.39 tff(3404,plain,
% 1.21/1.39 (c3_1(a1116)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[189, 3403])).
% 1.21/1.39 tff(3405,plain,
% 1.21/1.39 (c2_1(a1116)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[197, 3403])).
% 1.21/1.39 tff(3406,plain,
% 1.21/1.39 (c0_1(a1116)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[205, 3403])).
% 1.21/1.39 tff(3407,plain,
% 1.21/1.39 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(3408,plain,
% 1.21/1.39 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[3407])).
% 1.21/1.39 tff(3409,plain,
% 1.21/1.39 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3410,plain,
% 1.21/1.39 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(3411,plain,
% 1.21/1.39 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[3410])).
% 1.21/1.39 tff(3412,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.21/1.39 tff(3413,plain,
% 1.21/1.39 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 1.21/1.39 tff(3414,plain,
% 1.21/1.39 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[3413, 3409])).
% 1.21/1.39 tff(3415,plain,(
% 1.21/1.39 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.21/1.39 inference(skolemize,[status(sab)],[3414])).
% 1.21/1.39 tff(3416,plain,
% 1.21/1.39 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[3415, 3408])).
% 1.21/1.39 tff(3417,plain,
% 1.21/1.39 (~c2_1(a1105)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[982, 2662])).
% 1.21/1.39 tff(3418,plain,
% 1.21/1.39 (hskp22 | c2_1(a1105)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3255, 110, 2394, 875, 612, 2021])).
% 1.21/1.39 tff(3419,plain,
% 1.21/1.39 (hskp22),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3418, 3417])).
% 1.21/1.39 tff(3420,plain,
% 1.21/1.39 (~c1_1(a1145)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2034, 3419])).
% 1.21/1.39 tff(3421,plain,
% 1.21/1.39 (c3_1(a1145)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2068, 3419])).
% 1.21/1.39 tff(3422,plain,
% 1.21/1.39 (c2_1(a1145)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2042, 3419])).
% 1.21/1.39 tff(3423,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3424,plain,
% 1.21/1.39 ((hskp19 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121))) <=> (hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3425,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[3424])).
% 1.21/1.39 tff(3426,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[3425, 3423])).
% 1.21/1.39 tff(3427,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(3428,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[3427, 3426])).
% 1.21/1.39 tff(3429,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3428, 110, 2792, 3422, 3421, 2806, 2805, 3420, 2804, 3416])).
% 1.21/1.39 tff(3430,plain,(hskp2 | (~c3_1(a1105)) | c1_1(a1105) | hskp26 | (~c0_1(a1105)) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(3431,plain,
% 1.21/1.39 (hskp2),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3430, 2658, 2837, 2835, 2836, 3406, 3405, 3404])).
% 1.21/1.39 tff(3432,plain,
% 1.21/1.39 (~c3_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[273, 3431])).
% 1.21/1.39 tff(3433,plain,
% 1.21/1.39 (c2_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[281, 3431])).
% 1.21/1.39 tff(3434,plain,
% 1.21/1.39 (c0_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[289, 3431])).
% 1.21/1.39 tff(3435,plain,
% 1.21/1.39 (~c1_1(a1100)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1187, 110, 1167, 3434, 3433, 3432, 1177])).
% 1.21/1.39 tff(3436,plain,
% 1.21/1.39 (~hskp8),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2510, 3405, 2836, 3404, 3406, 2835, 2837])).
% 1.21/1.39 tff(3437,plain,
% 1.21/1.39 (~hskp3),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1244, 1167, 2565, 3405, 3404, 3406, 747, 699])).
% 1.21/1.39 tff(3438,plain,
% 1.21/1.39 (hskp4),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3308, 2658, 3437])).
% 1.21/1.39 tff(3439,plain,
% 1.21/1.39 (~c3_1(a1102)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1427, 3438])).
% 1.21/1.39 tff(3440,plain,
% 1.21/1.39 (c1_1(a1102)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1444, 3438])).
% 1.21/1.39 tff(3441,plain,
% 1.21/1.39 (c0_1(a1102)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1452, 3438])).
% 1.21/1.39 tff(3442,plain,
% 1.21/1.39 (~c2_1(a1102)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3318, 110, 1167, 3441, 3440, 3439, 1177])).
% 1.21/1.39 tff(3443,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3444,plain,
% 1.21/1.39 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3445,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[3444])).
% 1.21/1.39 tff(3446,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[3445, 3443])).
% 1.21/1.39 tff(3447,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(3448,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[3447, 3446])).
% 1.21/1.39 tff(3449,plain,
% 1.21/1.39 (c2_1(a1105)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3448, 110, 3406, 3405, 3404, 2835, 3441, 3440, 2837, 228, 3442])).
% 1.21/1.39 tff(3450,plain,
% 1.21/1.39 (hskp19),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3386, 3449, 3436])).
% 1.21/1.39 tff(3451,plain,
% 1.21/1.39 (hskp20),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1203, 3450, 3406, 1167, 3405, 3404])).
% 1.21/1.39 tff(3452,plain,
% 1.21/1.39 (~c0_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[302, 3451])).
% 1.21/1.39 tff(3453,plain,
% 1.21/1.39 (~c3_1(a1130)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[308, 3451])).
% 1.21/1.39 tff(3454,plain,
% 1.21/1.39 (~c0_1(a1136)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1305, 3453, 699, 2565, 3371, 3452, 3433, 3370, 2836, 2835, 2837, 3434, 3432, 747, 1167])).
% 1.21/1.39 tff(3455,plain,
% 1.21/1.39 (~c2_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[816, 3450])).
% 1.21/1.39 tff(3456,plain,
% 1.21/1.39 (c1_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[833, 3450])).
% 1.21/1.39 tff(3457,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3458,plain,
% 1.21/1.39 (((~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3459,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[3458])).
% 1.21/1.39 tff(3460,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[3459, 3457])).
% 1.21/1.39 tff(3461,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(3462,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.21/1.39 tff(3463,plain,
% 1.21/1.39 (~c0_1(a1127)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[3462, 110, 3369, 3371, 3456, 3434, 3455, 3432, 1316, 3454, 3435])).
% 1.21/1.39 tff(3464,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3465,plain,
% 1.21/1.39 ((hskp3 | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127))) <=> (hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(3466,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3465])).
% 1.21/1.40 tff(3467,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3466, 3464])).
% 1.21/1.40 tff(3468,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3469,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127)),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3468, 3467])).
% 1.21/1.40 tff(3470,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3469, 110, 3437, 3371, 3370, 3456, 3455, 2169, 3454, 3463])).
% 1.21/1.40 tff(3471,plain,(hskp26 | c3_1(a1147) | c2_1(a1147) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(3472,plain,
% 1.21/1.40 (hskp26),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3471, 1167, 747, 699])).
% 1.21/1.40 tff(3473,plain,
% 1.21/1.40 (~c2_1(a1180)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2615, 3472])).
% 1.21/1.40 tff(3474,plain,
% 1.21/1.40 (~c1_1(a1180)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2621, 3472])).
% 1.21/1.40 tff(3475,plain,
% 1.21/1.40 (~c0_1(a1180)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2634, 3472])).
% 1.21/1.40 tff(3476,plain,
% 1.21/1.40 (((~![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(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180)))) <=> ((~![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(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3477,plain,
% 1.21/1.40 ((hskp0 | (~ndr1_0) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)) | c2_1(a1180) | c1_1(a1180) | c0_1(a1180)) <=> (hskp0 | c0_1(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3478,plain,
% 1.21/1.40 (((~![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(a1180) | c0_1(a1180) | (~c3_1(a1180)) | c2_1(a1180) | c1_1(a1180) | c0_1(a1180))) <=> ((~![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(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3477])).
% 1.21/1.40 tff(3479,plain,
% 1.21/1.40 (((~![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(a1180) | c0_1(a1180) | (~c3_1(a1180)) | c2_1(a1180) | c1_1(a1180) | c0_1(a1180))) <=> ((~![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(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3478, 3476])).
% 1.21/1.40 tff(3480,plain,
% 1.21/1.40 ((~![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(a1180) | c0_1(a1180) | (~c3_1(a1180)) | c2_1(a1180) | c1_1(a1180) | c0_1(a1180))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3481,plain,
% 1.21/1.40 ((~![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(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3480, 3479])).
% 1.21/1.40 tff(3482,plain,
% 1.21/1.40 (~c3_1(a1180)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3481, 110, 2394, 3475, 3474, 3473, 2003])).
% 1.21/1.40 tff(3483,plain,
% 1.21/1.40 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3484,plain,
% 1.21/1.40 ((hskp19 | hskp8 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180)) <=> (hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3485,plain,
% 1.21/1.40 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3484])).
% 1.21/1.40 tff(3486,plain,
% 1.21/1.40 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3485, 3483])).
% 1.21/1.40 tff(3487,plain,
% 1.21/1.40 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3488,plain,
% 1.21/1.40 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180)),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3487, 3486])).
% 1.21/1.40 tff(3489,plain,
% 1.21/1.40 (hskp19 | c3_1(a1180)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3488, 110, 3436, 3474, 3473, 1069])).
% 1.21/1.40 tff(3490,plain,
% 1.21/1.40 (hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3489, 3482])).
% 1.21/1.40 tff(3491,plain,
% 1.21/1.40 (hskp2),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2791, 3490, 3406, 3405, 3404])).
% 1.21/1.40 tff(3492,plain,
% 1.21/1.40 (~c3_1(a1100)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[273, 3491])).
% 1.21/1.40 tff(3493,plain,
% 1.21/1.40 (c2_1(a1100)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[281, 3491])).
% 1.21/1.40 tff(3494,plain,
% 1.21/1.40 (c0_1(a1100)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[289, 3491])).
% 1.21/1.40 tff(3495,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3062, 110, 3437, 3494, 3493, 3475, 3474, 3492, 965, 3482])).
% 1.21/1.40 tff(3496,plain,(hskp5 | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(3497,plain,
% 1.21/1.40 (hskp5),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3496, 699, 747])).
% 1.21/1.40 tff(3498,plain,
% 1.21/1.40 (~c2_1(a1103)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[123, 3497])).
% 1.21/1.40 tff(3499,plain,
% 1.21/1.40 (~c0_1(a1103)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[129, 3497])).
% 1.21/1.40 tff(3500,plain,
% 1.21/1.40 (c3_1(a1103)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[147, 3497])).
% 1.21/1.40 tff(3501,plain,
% 1.21/1.40 (c1_1(a1103)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2390, 110, 2394, 3500, 3499, 3498, 2003])).
% 1.21/1.40 tff(3502,plain,
% 1.21/1.40 (hskp21 | (~c1_1(a1103))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2382, 110, 2394, 3500, 3499, 33])).
% 1.21/1.40 tff(3503,plain,
% 1.21/1.40 (hskp21),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3502, 3501])).
% 1.21/1.40 tff(3504,plain,
% 1.21/1.40 (~c3_1(a1131)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[739, 3503])).
% 1.21/1.40 tff(3505,plain,
% 1.21/1.40 (~c0_1(a1131)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[745, 3503])).
% 1.21/1.40 tff(3506,plain,
% 1.21/1.40 (c1_1(a1131)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[754, 3503])).
% 1.21/1.40 tff(3507,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2585, 110, 3406, 3405, 3404, 2565, 3506, 747, 699, 3505, 3504, 320])).
% 1.21/1.40 tff(3508,plain,(c3_1(a1147) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(3509,plain,
% 1.21/1.40 (c3_1(a1147)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3508, 747])).
% 1.21/1.40 tff(3510,plain,
% 1.21/1.40 (~hskp23),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[686, 3509])).
% 1.21/1.40 tff(3511,plain,
% 1.21/1.40 (hskp30),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2051, 3510, 2394])).
% 1.21/1.40 tff(3512,plain,
% 1.21/1.40 (c1_1(a1136)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[630, 3511])).
% 1.21/1.40 tff(3513,plain,
% 1.21/1.40 (c2_1(a1136)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[671, 3511])).
% 1.21/1.40 tff(3514,plain,
% 1.21/1.40 (~hskp9),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1545, 698, 3510, 3512, 3513])).
% 1.21/1.40 tff(3515,plain,
% 1.21/1.40 (c3_1(a1136)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[663, 3511])).
% 1.21/1.40 tff(3516,plain,
% 1.21/1.40 (hskp19 | hskp9),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1562, 110, 3512, 3513, 3515, 1556])).
% 1.21/1.40 tff(3517,plain,
% 1.21/1.40 (hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3516, 3514])).
% 1.21/1.40 tff(3518,plain,
% 1.21/1.40 (~c2_1(a1127)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[816, 3517])).
% 1.21/1.40 tff(3519,plain,
% 1.21/1.40 (c3_1(a1127)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[825, 3517])).
% 1.21/1.40 tff(3520,plain,
% 1.21/1.40 (c1_1(a1127)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[833, 3517])).
% 1.21/1.40 tff(3521,plain,
% 1.21/1.40 (hskp14),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[680, 3510])).
% 1.21/1.40 tff(3522,plain,
% 1.21/1.40 (~c3_1(a1118)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[160, 3521])).
% 1.21/1.40 tff(3523,plain,
% 1.21/1.40 (~c2_1(a1118)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[166, 3521])).
% 1.21/1.40 tff(3524,plain,
% 1.21/1.40 (c1_1(a1118)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[174, 3521])).
% 1.21/1.40 tff(3525,plain,
% 1.21/1.40 (c0_1(a1127)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1573, 110, 698, 3519, 3524, 3518, 3523, 3522, 67])).
% 1.21/1.40 tff(3526,plain,
% 1.21/1.40 (hskp28 | (~c0_1(a1127))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1580, 110, 3520, 3519, 3518, 528])).
% 1.21/1.40 tff(3527,plain,
% 1.21/1.40 (hskp28),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3526, 3525])).
% 1.21/1.40 tff(3528,plain,
% 1.21/1.40 (c2_1(a1111)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[551, 3527])).
% 1.21/1.40 tff(3529,plain,
% 1.21/1.40 (c0_1(a1111)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[567, 3527])).
% 1.21/1.40 tff(3530,plain,
% 1.21/1.40 (hskp13),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1620, 3529, 3514, 3528, 3520, 3519, 3518])).
% 1.21/1.40 tff(3531,plain,
% 1.21/1.40 (~c3_1(a1115)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1252, 3530])).
% 1.21/1.40 tff(3532,plain,
% 1.21/1.40 (~c1_1(a1115)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1130, 3530])).
% 1.21/1.40 tff(3533,plain,
% 1.21/1.40 (c1_1(a1111)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[559, 3527])).
% 1.21/1.40 tff(3534,plain,
% 1.21/1.40 (~c0_1(a1115)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1630, 3510, 110, 3529, 3533, 3528, 3532, 3531, 1525])).
% 1.21/1.40 tff(3535,plain,
% 1.21/1.40 (c2_1(a1115)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1138, 3530])).
% 1.21/1.40 tff(3536,plain,
% 1.21/1.40 (((~![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(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))) <=> ((~![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(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3537,plain,
% 1.21/1.40 ((hskp0 | (~ndr1_0) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147)) <=> (hskp0 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3538,plain,
% 1.21/1.40 (((~![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(a1147) | c0_1(a1147) | (~c3_1(a1147)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))) <=> ((~![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(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3537])).
% 1.21/1.40 tff(3539,plain,
% 1.21/1.40 (((~![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(a1147) | c0_1(a1147) | (~c3_1(a1147)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))) <=> ((~![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(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3538, 3536])).
% 1.21/1.40 tff(3540,plain,
% 1.21/1.40 ((~![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(a1147) | c0_1(a1147) | (~c3_1(a1147)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3541,plain,
% 1.21/1.40 ((~![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(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147)),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3540, 3539])).
% 1.21/1.40 tff(3542,plain,
% 1.21/1.40 (c0_1(a1147) | (~c3_1(a1147)) | c1_1(a1147)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3541, 110, 2394, 747, 2003])).
% 1.21/1.40 tff(3543,plain,
% 1.21/1.40 (c1_1(a1147)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3542, 2395, 3509])).
% 1.21/1.40 tff(3544,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3545,plain,
% 1.21/1.40 ((hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147))) <=> (hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3546,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3545])).
% 1.21/1.40 tff(3547,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3546, 3544])).
% 1.21/1.40 tff(3548,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3549,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3548, 3547])).
% 1.21/1.40 tff(3550,plain,
% 1.21/1.40 (hskp29 | c0_1(a1147)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3549, 110, 3524, 747, 3509, 3523, 3522, 67])).
% 1.21/1.40 tff(3551,plain,
% 1.21/1.40 (hskp29),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3550, 2395])).
% 1.21/1.40 tff(3552,plain,
% 1.21/1.40 (c3_1(a1116)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[189, 3551])).
% 1.21/1.40 tff(3553,plain,
% 1.21/1.40 (c2_1(a1116)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[197, 3551])).
% 1.21/1.40 tff(3554,plain,
% 1.21/1.40 (c0_1(a1116)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[205, 3551])).
% 1.21/1.40 tff(3555,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3556,plain,
% 1.21/1.40 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147))) <=> (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3557,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3556])).
% 1.21/1.40 tff(3558,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3557, 3555])).
% 1.21/1.40 tff(3559,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3560,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3559, 3558])).
% 1.21/1.40 tff(3561,plain,
% 1.21/1.40 (hskp2),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3560, 110, 3554, 3553, 3552, 747, 3509, 260, 3543])).
% 1.21/1.40 tff(3562,plain,
% 1.21/1.40 (~c3_1(a1100)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[273, 3561])).
% 1.21/1.40 tff(3563,plain,
% 1.21/1.40 (c0_1(a1100)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[289, 3561])).
% 1.21/1.40 tff(3564,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3565,plain,
% 1.21/1.40 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147))) <=> (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3566,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3565])).
% 1.21/1.40 tff(3567,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3566, 3564])).
% 1.21/1.40 tff(3568,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3569,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 1.21/1.40 tff(3570,plain,
% 1.21/1.40 (~c1_1(a1100)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3569, 110, 3512, 3513, 3515, 2395, 3563, 3509, 3562, 45, 3543])).
% 1.21/1.40 tff(3571,plain,
% 1.21/1.40 (c2_1(a1100)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[281, 3561])).
% 1.21/1.40 tff(3572,plain,
% 1.21/1.40 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3573,plain,
% 1.21/1.40 ((hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100))) <=> (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3574,plain,
% 1.21/1.40 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3573])).
% 1.21/1.40 tff(3575,plain,
% 1.21/1.40 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3574, 3572])).
% 1.21/1.40 tff(3576,plain,
% 1.21/1.40 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3577,plain,
% 1.21/1.40 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3576, 3575])).
% 1.21/1.40 tff(3578,plain,
% 1.21/1.40 (hskp7),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3577, 3510, 110, 3563, 3571, 2433, 3570])).
% 1.21/1.40 tff(3579,plain,
% 1.21/1.40 (~c1_1(a1105)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[582, 3578])).
% 1.21/1.40 tff(3580,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3581,plain,
% 1.21/1.40 ((hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147))) <=> (hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3582,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3581])).
% 1.21/1.40 tff(3583,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3582, 3580])).
% 1.21/1.40 tff(3584,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3585,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3584, 3583])).
% 1.21/1.40 tff(3586,plain,
% 1.21/1.40 (hskp10 | c0_1(a1147) | (~c1_1(a1147))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3585, 110, 3512, 3513, 3515, 747, 1873])).
% 1.21/1.40 tff(3587,plain,
% 1.21/1.40 (hskp10),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3586, 2395, 3543])).
% 1.21/1.40 tff(3588,plain,
% 1.21/1.40 (~c2_1(a1110)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1886, 3587])).
% 1.21/1.40 tff(3589,plain,
% 1.21/1.40 (~c1_1(a1110)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1892, 3587])).
% 1.21/1.40 tff(3590,plain,
% 1.21/1.40 (c3_1(a1110)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1902, 3587])).
% 1.21/1.40 tff(3591,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3592,plain,
% 1.21/1.40 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110))) <=> (c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(3593,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[3592])).
% 1.21/1.40 tff(3594,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[3593, 3591])).
% 1.21/1.40 tff(3595,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(3596,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[3595, 3594])).
% 1.21/1.40 tff(3597,plain,
% 1.21/1.40 (~c0_1(a1118)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[3596, 110, 3554, 3553, 3552, 3524, 3590, 3523, 3589, 3588, 228])).
% 1.21/1.40 tff(3598,plain,
% 1.21/1.40 (hskp8),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1911, 3597, 3524, 3512, 3553, 3523, 3522, 3552, 3513, 3515, 3554])).
% 1.21/1.40 tff(3599,plain,
% 1.21/1.40 (c0_1(a1105)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[592, 3578])).
% 1.21/1.40 tff(3600,plain,
% 1.21/1.40 (c3_1(a1105)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[600, 3578])).
% 1.21/1.40 tff(3601,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2510, 3600, 3599, 3553, 3552, 3554, 3598, 3579])).
% 1.21/1.41 tff(3602,plain,(c0_1(a1147) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(3603,plain,
% 1.21/1.41 (c0_1(a1147)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3602, 747])).
% 1.21/1.41 tff(3604,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3605,plain,
% 1.21/1.41 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3606,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3605])).
% 1.21/1.41 tff(3607,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3606, 3604])).
% 1.21/1.41 tff(3608,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3609,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3608, 3607])).
% 1.21/1.41 tff(3610,plain,
% 1.21/1.41 (c1_1(a1147)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3609, 110, 3512, 3513, 3515, 3603, 3535, 747, 3532, 1059, 3534])).
% 1.21/1.41 tff(3611,assumption,(hskp10), introduced(assumption)).
% 1.21/1.41 tff(3612,plain,
% 1.21/1.41 (~c2_1(a1110)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1886, 3611])).
% 1.21/1.41 tff(3613,plain,
% 1.21/1.41 (~c1_1(a1110)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1892, 3611])).
% 1.21/1.41 tff(3614,assumption,(c2_1(a1115)), introduced(assumption)).
% 1.21/1.41 tff(3615,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3616,plain,
% 1.21/1.41 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1110) | c1_1(a1110) | (~c0_1(a1110)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3617,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1110) | c1_1(a1110) | (~c0_1(a1110)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3616])).
% 1.21/1.41 tff(3618,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1110) | c1_1(a1110) | (~c0_1(a1110)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3617, 3615])).
% 1.21/1.41 tff(3619,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1110) | c1_1(a1110) | (~c0_1(a1110)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3620,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3619, 3618])).
% 1.21/1.41 tff(3621,plain,
% 1.21/1.41 (~c0_1(a1110)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3620, 110, 697, 696, 673, 3614, 2445, 3613, 3612, 1059, 2442])).
% 1.21/1.41 tff(3622,plain,
% 1.21/1.41 (c3_1(a1110)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1902, 3611])).
% 1.21/1.41 tff(3623,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3624,plain,
% 1.21/1.41 ((hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c0_1(a1110) | (~c3_1(a1110))) <=> (hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3625,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c0_1(a1110) | (~c3_1(a1110)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3624])).
% 1.21/1.41 tff(3626,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c0_1(a1110) | (~c3_1(a1110)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3625, 3623])).
% 1.21/1.41 tff(3627,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c0_1(a1110) | (~c3_1(a1110)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3628,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3627, 3626])).
% 1.21/1.41 tff(3629,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3628, 110, 698, 210, 3622, 212, 208, 3612, 67, 3621])).
% 1.21/1.41 tff(3630,plain,((~hskp10) | hskp29 | (~c1_1(a1118)) | c2_1(a1118) | c3_1(a1118) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1115)) | c1_1(a1115) | c0_1(a1115)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(3631,plain,
% 1.21/1.41 (~hskp10),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3630, 698, 3524, 3523, 3522, 3512, 3513, 3515, 3535, 3532, 3534])).
% 1.21/1.41 tff(3632,plain,
% 1.21/1.41 (hskp10 | c0_1(a1118)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1879, 110, 3512, 3513, 3515, 3524, 3523, 1873])).
% 1.21/1.41 tff(3633,plain,
% 1.21/1.41 (c0_1(a1118)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3632, 3631])).
% 1.21/1.41 tff(3634,plain,
% 1.21/1.41 (c0_1(a1136)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1914, 3633, 3513, 3515, 3524, 3522, 3512])).
% 1.21/1.41 tff(3635,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3636,plain,
% 1.21/1.41 ((hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147))) <=> (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3637,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3636])).
% 1.21/1.41 tff(3638,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3637, 3635])).
% 1.21/1.41 tff(3639,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3640,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3639, 3638])).
% 1.21/1.41 tff(3641,plain,
% 1.21/1.41 (hskp2 | (~c0_1(a1136)) | (~c1_1(a1147))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3640, 110, 3513, 3515, 747, 3509, 260])).
% 1.21/1.41 tff(3642,plain,
% 1.21/1.41 (hskp2),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3641, 3634, 3610])).
% 1.21/1.41 tff(3643,plain,
% 1.21/1.41 (~c3_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[273, 3642])).
% 1.21/1.41 tff(3644,plain,
% 1.21/1.41 (c2_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[281, 3642])).
% 1.21/1.41 tff(3645,plain,
% 1.21/1.41 (c0_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[289, 3642])).
% 1.21/1.41 tff(3646,plain,
% 1.21/1.41 (~c1_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1187, 110, 1167, 3645, 3644, 3643, 1177])).
% 1.21/1.41 tff(3647,plain,
% 1.21/1.41 (hskp7 | c1_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3577, 3510, 110, 3645, 3644, 2433])).
% 1.21/1.41 tff(3648,plain,
% 1.21/1.41 (hskp7),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3647, 3646])).
% 1.21/1.41 tff(3649,plain,
% 1.21/1.41 (~c1_1(a1105)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[582, 3648])).
% 1.21/1.41 tff(3650,plain,
% 1.21/1.41 (c0_1(a1105)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[592, 3648])).
% 1.21/1.41 tff(3651,plain,
% 1.21/1.41 (c3_1(a1105)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[600, 3648])).
% 1.21/1.41 tff(3652,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1655, 3651, 3650, 3510, 3524, 3523, 3513, 3522, 3515, 698, 3649, 3512])).
% 1.21/1.41 tff(3653,plain,(hskp29 | hskp5 | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(3654,plain,
% 1.21/1.41 (hskp29),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3653, 1167, 747])).
% 1.21/1.41 tff(3655,plain,
% 1.21/1.41 (c3_1(a1116)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[189, 3654])).
% 1.21/1.41 tff(3656,plain,
% 1.21/1.41 (c2_1(a1116)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[197, 3654])).
% 1.21/1.41 tff(3657,plain,
% 1.21/1.41 (c0_1(a1116)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[205, 3654])).
% 1.21/1.41 tff(3658,plain,
% 1.21/1.41 (hskp2 | (~c1_1(a1147))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3560, 110, 231, 230, 229, 747, 3509, 260])).
% 1.21/1.41 tff(3659,plain,
% 1.21/1.41 (~c1_1(a1147)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3658, 2662])).
% 1.21/1.41 tff(3660,plain,
% 1.21/1.41 (^[U: $i] : refl((hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(3661,plain,
% 1.21/1.41 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[3660])).
% 1.21/1.41 tff(3662,plain,
% 1.21/1.41 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3663,plain,
% 1.21/1.41 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) | hskp19) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) | hskp19) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(3664,plain,
% 1.21/1.41 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) | hskp19) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[3663])).
% 1.21/1.41 tff(3665,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.21/1.41 tff(3666,plain,
% 1.21/1.41 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3665, 3664])).
% 1.21/1.41 tff(3667,plain,
% 1.21/1.41 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3666, 3662])).
% 1.21/1.41 tff(3668,plain,(
% 1.21/1.41 ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.21/1.41 inference(skolemize,[status(sab)],[3667])).
% 1.21/1.41 tff(3669,plain,
% 1.21/1.41 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3668, 3661])).
% 1.21/1.41 tff(3670,plain,
% 1.21/1.41 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3671,plain,
% 1.21/1.41 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147))) <=> (hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3672,plain,
% 1.21/1.41 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3671])).
% 1.21/1.41 tff(3673,plain,
% 1.21/1.41 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3672, 3670])).
% 1.21/1.41 tff(3674,plain,
% 1.21/1.41 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3675,plain,
% 1.21/1.41 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3674, 3673])).
% 1.21/1.41 tff(3676,plain,
% 1.21/1.41 (hskp19 | hskp17 | c1_1(a1147) | (~c0_1(a1147))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3675, 110, 747, 3669])).
% 1.21/1.41 tff(3677,plain,
% 1.21/1.41 (hskp17),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3676, 2792, 3603, 3659])).
% 1.21/1.41 tff(3678,plain,
% 1.21/1.41 (((~hskp17) | (~c2_1(a1124))) <=> ((~hskp17) | (~c2_1(a1124)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3679,plain,
% 1.21/1.41 (((~c2_1(a1124)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1124)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3680,axiom,((~c2_1(a1124)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.21/1.41 tff(3681,plain,
% 1.21/1.41 ((~hskp17) | (~c2_1(a1124))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3680, 3679])).
% 1.21/1.41 tff(3682,plain,
% 1.21/1.41 ((~hskp17) | (~c2_1(a1124))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3681, 3678])).
% 1.21/1.41 tff(3683,plain,
% 1.21/1.41 (~c2_1(a1124)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3682, 3677])).
% 1.21/1.41 tff(3684,plain,
% 1.21/1.41 (((~hskp17) | (~c1_1(a1124))) <=> ((~hskp17) | (~c1_1(a1124)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3685,plain,
% 1.21/1.41 (((~c1_1(a1124)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1124)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3686,axiom,((~c1_1(a1124)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.21/1.41 tff(3687,plain,
% 1.21/1.41 ((~hskp17) | (~c1_1(a1124))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 1.21/1.41 tff(3688,plain,
% 1.21/1.41 ((~hskp17) | (~c1_1(a1124))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3687, 3684])).
% 1.21/1.41 tff(3689,plain,
% 1.21/1.41 (~c1_1(a1124)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3688, 3677])).
% 1.21/1.41 tff(3690,plain,
% 1.21/1.41 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3691,plain,
% 1.21/1.41 ((hskp22 | hskp0 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c3_1(a1147))) <=> (hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3692,plain,
% 1.21/1.41 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c3_1(a1147)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147)))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3691])).
% 1.21/1.41 tff(3693,plain,
% 1.21/1.41 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c3_1(a1147)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3692, 3690])).
% 1.21/1.41 tff(3694,plain,
% 1.21/1.41 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c3_1(a1147)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3695,plain,
% 1.21/1.41 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3694, 3693])).
% 1.21/1.41 tff(3696,plain,
% 1.21/1.41 (hskp22 | (~c3_1(a1147)) | c1_1(a1147)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3695, 110, 2394, 747, 2021])).
% 1.21/1.41 tff(3697,plain,
% 1.21/1.41 (hskp22),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3696, 3659, 3509])).
% 1.21/1.41 tff(3698,plain,
% 1.21/1.41 (~c1_1(a1145)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2034, 3697])).
% 1.21/1.41 tff(3699,plain,
% 1.21/1.41 (((~hskp17) | c0_1(a1124)) <=> ((~hskp17) | c0_1(a1124))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3700,axiom,((~hskp17) | c0_1(a1124)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.21/1.41 tff(3701,plain,
% 1.21/1.41 ((~hskp17) | c0_1(a1124)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3700, 3699])).
% 1.21/1.41 tff(3702,plain,
% 1.21/1.41 ((~hskp17) | c0_1(a1124)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3701, 3699])).
% 1.21/1.41 tff(3703,plain,
% 1.21/1.41 ((~hskp17) | c0_1(a1124)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3702, 3699])).
% 1.21/1.41 tff(3704,plain,
% 1.21/1.41 ((~hskp17) | c0_1(a1124)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3703, 3699])).
% 1.21/1.41 tff(3705,plain,
% 1.21/1.41 ((~hskp17) | c0_1(a1124)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3704, 3699])).
% 1.21/1.41 tff(3706,plain,
% 1.21/1.41 (c0_1(a1124)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3705, 3677])).
% 1.21/1.41 tff(3707,plain,
% 1.21/1.41 (c2_1(a1145)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2042, 3697])).
% 1.21/1.41 tff(3708,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3709,plain,
% 1.21/1.41 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1124) | c1_1(a1124) | (~c0_1(a1124)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145))) <=> (c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3710,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1124) | c1_1(a1124) | (~c0_1(a1124)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3709])).
% 1.21/1.41 tff(3711,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1124) | c1_1(a1124) | (~c0_1(a1124)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3710, 3708])).
% 1.21/1.41 tff(3712,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1124) | c1_1(a1124) | (~c0_1(a1124)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3713,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3712, 3711])).
% 1.21/1.41 tff(3714,plain,
% 1.21/1.41 (c0_1(a1145)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3713, 110, 3512, 3513, 3515, 3707, 3706, 3698, 3689, 3683, 1059])).
% 1.21/1.41 tff(3715,plain,
% 1.21/1.41 (c3_1(a1145)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2068, 3697])).
% 1.21/1.41 tff(3716,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2247, 110, 2662, 3707, 3715, 3698, 975, 3714])).
% 1.21/1.41 tff(3717,plain,(hskp2 | c2_1(a1147) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(3718,plain,
% 1.21/1.41 (hskp2),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3717, 3657, 747, 3656, 3655])).
% 1.21/1.41 tff(3719,plain,
% 1.21/1.41 (~c3_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[273, 3718])).
% 1.21/1.41 tff(3720,plain,
% 1.21/1.41 (c2_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[281, 3718])).
% 1.21/1.41 tff(3721,plain,
% 1.21/1.41 (c0_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[289, 3718])).
% 1.21/1.41 tff(3722,plain,
% 1.21/1.41 (~c1_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1187, 110, 1167, 3721, 3720, 3719, 1177])).
% 1.21/1.41 tff(3723,plain,
% 1.21/1.41 (hskp7 | c1_1(a1100)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3577, 3510, 110, 3721, 3720, 2433])).
% 1.21/1.41 tff(3724,plain,
% 1.21/1.41 (hskp7),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3723, 3722])).
% 1.21/1.41 tff(3725,plain,
% 1.21/1.41 (~c1_1(a1105)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[582, 3724])).
% 1.21/1.41 tff(3726,plain,
% 1.21/1.41 (c0_1(a1105)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[592, 3724])).
% 1.21/1.41 tff(3727,plain,
% 1.21/1.41 (c3_1(a1105)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[600, 3724])).
% 1.21/1.41 tff(3728,plain,
% 1.21/1.41 (~hskp8),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2510, 3727, 3656, 3655, 3657, 3726, 3725])).
% 1.21/1.41 tff(3729,plain,
% 1.21/1.41 (c0_1(a1118)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1911, 3728, 3524, 3512, 3656, 3523, 3522, 3655, 3513, 3515, 3657])).
% 1.21/1.42 tff(3730,plain,
% 1.21/1.42 (c0_1(a1136)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1914, 3729, 3513, 3515, 3524, 3522, 3512])).
% 1.21/1.42 tff(3731,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2562, 3510, 110, 3512, 3513, 3721, 3719, 1525, 3730, 3722])).
% 1.21/1.42 tff(3732,plain,(hskp5 | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(3733,plain,
% 1.21/1.42 (hskp5),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3732, 747])).
% 1.21/1.42 tff(3734,plain,
% 1.21/1.42 (~c2_1(a1103)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[123, 3733])).
% 1.21/1.42 tff(3735,plain,
% 1.21/1.42 (~c0_1(a1103)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[129, 3733])).
% 1.21/1.42 tff(3736,plain,
% 1.21/1.42 (~c0_1(a1118)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1956, 3733, 3524, 3522, 3523])).
% 1.21/1.42 tff(3737,plain,
% 1.21/1.42 (hskp10),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3632, 3736])).
% 1.21/1.42 tff(3738,plain,
% 1.21/1.42 (~c2_1(a1110)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1886, 3737])).
% 1.21/1.42 tff(3739,plain,
% 1.21/1.42 (~c1_1(a1110)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1892, 3737])).
% 1.21/1.42 tff(3740,plain,
% 1.21/1.42 (c3_1(a1103)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[147, 3733])).
% 1.21/1.42 tff(3741,plain,
% 1.21/1.42 (((~![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 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110))) <=> ((~![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 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3742,plain,
% 1.21/1.42 ((hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1110) | c1_1(a1110) | c0_1(a1110)) <=> (hskp0 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3743,plain,
% 1.21/1.42 (((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1110) | c1_1(a1110) | c0_1(a1110))) <=> ((~![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 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110)))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3742])).
% 1.21/1.42 tff(3744,plain,
% 1.21/1.42 (((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1110) | c1_1(a1110) | c0_1(a1110))) <=> ((~![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 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3743, 3741])).
% 1.21/1.42 tff(3745,plain,
% 1.21/1.42 ((~![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(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1110) | c1_1(a1110) | c0_1(a1110))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3746,plain,
% 1.21/1.42 ((~![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 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110)),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3745, 3744])).
% 1.21/1.42 tff(3747,plain,
% 1.21/1.42 (c0_1(a1110)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3746, 110, 2394, 3740, 3739, 3738, 3735, 3734, 2003])).
% 1.21/1.42 tff(3748,plain,
% 1.21/1.42 (c3_1(a1110)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1902, 3737])).
% 1.21/1.42 tff(3749,plain,
% 1.21/1.42 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3750,plain,
% 1.21/1.42 ((hskp22 | hskp0 | (~ndr1_0) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110))) <=> (hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3751,plain,
% 1.21/1.42 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3750])).
% 1.21/1.42 tff(3752,plain,
% 1.21/1.42 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3751, 3749])).
% 1.21/1.42 tff(3753,plain,
% 1.21/1.42 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3754,plain,
% 1.21/1.42 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3753, 3752])).
% 1.21/1.42 tff(3755,plain,
% 1.21/1.42 (hskp22),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3754, 110, 2394, 3748, 3739, 3738, 2021])).
% 1.21/1.42 tff(3756,plain,
% 1.21/1.42 (~c1_1(a1145)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2034, 3755])).
% 1.21/1.42 tff(3757,plain,
% 1.21/1.42 (c2_1(a1145)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2042, 3755])).
% 1.21/1.42 tff(3758,plain,
% 1.21/1.42 (hskp29),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[181, 110, 3524, 3740, 3523, 3522, 3735, 3734, 67])).
% 1.21/1.42 tff(3759,plain,
% 1.21/1.42 (c3_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[189, 3758])).
% 1.21/1.42 tff(3760,plain,
% 1.21/1.42 (c2_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[197, 3758])).
% 1.21/1.42 tff(3761,plain,
% 1.21/1.42 (c0_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[205, 3758])).
% 1.21/1.42 tff(3762,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3763,plain,
% 1.21/1.42 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1110) | (~c3_1(a1110)) | (~c0_1(a1110)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145))) <=> (c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3764,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1110) | (~c3_1(a1110)) | (~c0_1(a1110)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3763])).
% 1.21/1.42 tff(3765,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1110) | (~c3_1(a1110)) | (~c0_1(a1110)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3764, 3762])).
% 1.21/1.42 tff(3766,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1110) | (~c3_1(a1110)) | (~c0_1(a1110)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3767,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3766, 3765])).
% 1.21/1.42 tff(3768,plain,
% 1.21/1.42 (c0_1(a1145)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3767, 110, 3761, 3760, 3759, 3757, 3748, 3756, 3739, 642, 3747])).
% 1.21/1.42 tff(3769,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3770,plain,
% 1.21/1.42 ((hskp7 | (~ndr1_0) | c2_1(a1147) | (~c3_1(a1147)) | (~c0_1(a1147)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145))) <=> (hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3771,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1147) | (~c3_1(a1147)) | (~c0_1(a1147)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3770])).
% 1.21/1.42 tff(3772,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1147) | (~c3_1(a1147)) | (~c0_1(a1147)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3771, 3769])).
% 1.21/1.42 tff(3773,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1147) | (~c3_1(a1147)) | (~c0_1(a1147)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3774,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3773, 3772])).
% 1.21/1.42 tff(3775,plain,
% 1.21/1.42 (hskp7),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3774, 110, 3603, 3757, 747, 3509, 3756, 2088, 3768])).
% 1.21/1.42 tff(3776,plain,
% 1.21/1.42 (~c1_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[582, 3775])).
% 1.21/1.42 tff(3777,plain,
% 1.21/1.42 (hskp8),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1911, 3760, 3524, 3512, 3736, 3523, 3522, 3759, 3513, 3515, 3761])).
% 1.21/1.42 tff(3778,plain,
% 1.21/1.42 (c0_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[592, 3775])).
% 1.21/1.42 tff(3779,plain,
% 1.21/1.42 (c3_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[600, 3775])).
% 1.21/1.42 tff(3780,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2510, 3779, 3778, 3760, 3759, 3761, 3777, 3776])).
% 1.21/1.42 tff(3781,plain,(c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(3782,plain,
% 1.21/1.42 (~hskp23),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[731, 3781])).
% 1.21/1.42 tff(3783,plain,
% 1.21/1.42 (hskp30),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2051, 3782, 2394])).
% 1.21/1.42 tff(3784,plain,
% 1.21/1.42 (c1_1(a1136)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[630, 3783])).
% 1.21/1.42 tff(3785,plain,
% 1.21/1.42 (hskp14),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[680, 3782])).
% 1.21/1.42 tff(3786,plain,
% 1.21/1.42 (~c3_1(a1118)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[160, 3785])).
% 1.21/1.42 tff(3787,plain,
% 1.21/1.42 (c1_1(a1118)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[174, 3785])).
% 1.21/1.42 tff(3788,plain,
% 1.21/1.42 (c3_1(a1136)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[663, 3783])).
% 1.21/1.42 tff(3789,plain,
% 1.21/1.42 (c2_1(a1136)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[671, 3783])).
% 1.21/1.42 tff(3790,plain,
% 1.21/1.42 (~c2_1(a1118)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[166, 3785])).
% 1.21/1.42 tff(3791,plain,
% 1.21/1.42 (~c0_1(a1118)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1956, 1951, 3787, 3786, 3790])).
% 1.21/1.42 tff(3792,plain,
% 1.21/1.42 (hskp10 | c0_1(a1118)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1879, 110, 3784, 3789, 3788, 3787, 3790, 1873])).
% 1.21/1.42 tff(3793,plain,
% 1.21/1.42 (hskp10),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3792, 3791])).
% 1.21/1.42 tff(3794,plain,
% 1.21/1.42 (~c2_1(a1110)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1886, 3793])).
% 1.21/1.42 tff(3795,plain,
% 1.21/1.42 (~c1_1(a1110)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1892, 3793])).
% 1.21/1.42 tff(3796,plain,
% 1.21/1.42 (c0_1(a1110)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3746, 110, 2394, 1952, 3795, 3794, 1953, 1954, 2003])).
% 1.21/1.42 tff(3797,plain,
% 1.21/1.42 (c3_1(a1110)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1902, 3793])).
% 1.21/1.42 tff(3798,plain,
% 1.21/1.42 (hskp22),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3754, 110, 2394, 3797, 3795, 3794, 2021])).
% 1.21/1.42 tff(3799,plain,
% 1.21/1.42 (~c1_1(a1145)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2034, 3798])).
% 1.21/1.42 tff(3800,plain,
% 1.21/1.42 (c2_1(a1145)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2042, 3798])).
% 1.21/1.42 tff(3801,plain,
% 1.21/1.42 (hskp29),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[181, 110, 3787, 1952, 3790, 3786, 1953, 1954, 67])).
% 1.21/1.42 tff(3802,plain,
% 1.21/1.42 (c3_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[189, 3801])).
% 1.21/1.42 tff(3803,plain,
% 1.21/1.42 (c2_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[197, 3801])).
% 1.21/1.42 tff(3804,plain,
% 1.21/1.42 (c0_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[205, 3801])).
% 1.21/1.42 tff(3805,plain,
% 1.21/1.42 (c0_1(a1145)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3767, 110, 3804, 3803, 3802, 3800, 3797, 3799, 3795, 642, 3796])).
% 1.21/1.42 tff(3806,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3807,plain,
% 1.21/1.42 ((hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110))) <=> (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3808,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3807])).
% 1.21/1.42 tff(3809,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3808, 3806])).
% 1.21/1.42 tff(3810,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3811,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 1.21/1.42 tff(3812,plain,
% 1.21/1.42 (hskp11),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3811, 110, 3787, 3797, 3790, 3786, 3795, 3794, 1749])).
% 1.21/1.42 tff(3813,plain,
% 1.21/1.42 (~c2_1(a1113)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1761, 3812])).
% 1.21/1.42 tff(3814,plain,
% 1.21/1.42 (c3_1(a1113)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1812, 3812])).
% 1.21/1.42 tff(3815,plain,
% 1.21/1.42 (c0_1(a1113)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1769, 3812])).
% 1.21/1.42 tff(3816,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3817,plain,
% 1.21/1.42 ((hskp7 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145))) <=> (hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3818,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3817])).
% 1.21/1.42 tff(3819,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3818, 3816])).
% 1.21/1.42 tff(3820,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3821,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 1.21/1.42 tff(3822,plain,
% 1.21/1.42 (hskp7),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3821, 110, 3800, 3815, 3814, 3799, 3813, 2088, 3805])).
% 1.21/1.42 tff(3823,plain,
% 1.21/1.42 (~c1_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[582, 3822])).
% 1.21/1.42 tff(3824,plain,
% 1.21/1.42 (hskp8),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1911, 3803, 3787, 3784, 3791, 3790, 3786, 3802, 3789, 3788, 3804])).
% 1.21/1.42 tff(3825,plain,
% 1.21/1.42 (c0_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[592, 3822])).
% 1.21/1.42 tff(3826,plain,
% 1.21/1.42 (c3_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[600, 3822])).
% 1.21/1.42 tff(3827,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2510, 3826, 3825, 3803, 3802, 3804, 3824, 3823])).
% 1.21/1.42 tff(3828,plain,(~hskp5), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(3829,plain,
% 1.21/1.42 (~hskp9),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1545, 698, 3782, 3784, 3789])).
% 1.21/1.42 tff(3830,plain,
% 1.21/1.42 (hskp19 | hskp9),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1562, 110, 3784, 3789, 3788, 1556])).
% 1.21/1.42 tff(3831,plain,
% 1.21/1.42 (hskp19),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3830, 3829])).
% 1.21/1.42 tff(3832,plain,
% 1.21/1.42 (~c2_1(a1127)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[816, 3831])).
% 1.21/1.42 tff(3833,plain,
% 1.21/1.42 (c3_1(a1127)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[825, 3831])).
% 1.21/1.42 tff(3834,plain,
% 1.21/1.42 (c1_1(a1127)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[833, 3831])).
% 1.21/1.42 tff(3835,plain,
% 1.21/1.42 (c0_1(a1127)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1573, 110, 698, 3833, 3787, 3832, 3790, 3786, 67])).
% 1.21/1.42 tff(3836,plain,
% 1.21/1.42 (hskp28 | (~c0_1(a1127))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1580, 110, 3834, 3833, 3832, 528])).
% 1.21/1.42 tff(3837,plain,
% 1.21/1.42 (hskp28),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3836, 3835])).
% 1.21/1.42 tff(3838,plain,
% 1.21/1.42 (c2_1(a1111)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[551, 3837])).
% 1.21/1.42 tff(3839,plain,
% 1.21/1.42 (c0_1(a1111)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[567, 3837])).
% 1.21/1.42 tff(3840,plain,
% 1.21/1.42 (hskp13),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1620, 3839, 3829, 3838, 3834, 3833, 3832])).
% 1.21/1.42 tff(3841,plain,
% 1.21/1.42 (c2_1(a1115)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1138, 3840])).
% 1.21/1.42 tff(3842,plain,
% 1.21/1.42 (~c1_1(a1115)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1130, 3840])).
% 1.21/1.42 tff(3843,plain,
% 1.21/1.42 (~c3_1(a1115)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1252, 3840])).
% 1.21/1.42 tff(3844,plain,
% 1.21/1.42 (c1_1(a1111)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[559, 3837])).
% 1.21/1.42 tff(3845,plain,
% 1.21/1.42 (~c0_1(a1115)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1630, 3782, 110, 3839, 3844, 3838, 3842, 3843, 1525])).
% 1.21/1.42 tff(3846,plain,
% 1.21/1.42 (~hskp10),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3630, 3845, 3787, 3790, 3786, 3784, 3789, 3788, 698, 3842, 3841])).
% 1.21/1.42 tff(3847,plain,
% 1.21/1.42 (c0_1(a1118)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3792, 3846])).
% 1.21/1.42 tff(3848,plain,
% 1.21/1.42 (c0_1(a1136)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1914, 3847, 3789, 3788, 3787, 3786, 3784])).
% 1.21/1.42 tff(3849,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3850,plain,
% 1.21/1.42 ((hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3851,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3850])).
% 1.21/1.42 tff(3852,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3851, 3849])).
% 1.21/1.42 tff(3853,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3854,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3853, 3852])).
% 1.21/1.42 tff(3855,plain,
% 1.21/1.42 (hskp2 | (~c0_1(a1136))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3854, 110, 3789, 3788, 3834, 3833, 3832, 260])).
% 1.21/1.42 tff(3856,plain,
% 1.21/1.42 (hskp2),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3855, 3848])).
% 1.21/1.42 tff(3857,plain,
% 1.21/1.42 (~c3_1(a1100)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[273, 3856])).
% 1.21/1.42 tff(3858,plain,
% 1.21/1.42 (c2_1(a1100)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[281, 3856])).
% 1.21/1.42 tff(3859,plain,
% 1.21/1.42 (c0_1(a1100)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[289, 3856])).
% 1.21/1.42 tff(3860,plain,
% 1.21/1.42 (~c1_1(a1100)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1187, 110, 1167, 3859, 3858, 3857, 1177])).
% 1.21/1.42 tff(3861,plain,
% 1.21/1.42 (hskp7 | c1_1(a1100)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3577, 3782, 110, 3859, 3858, 2433])).
% 1.21/1.42 tff(3862,plain,
% 1.21/1.42 (hskp7),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3861, 3860])).
% 1.21/1.42 tff(3863,plain,
% 1.21/1.42 (~c1_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[582, 3862])).
% 1.21/1.42 tff(3864,plain,
% 1.21/1.42 (c0_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[592, 3862])).
% 1.21/1.42 tff(3865,plain,
% 1.21/1.42 (c3_1(a1105)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[600, 3862])).
% 1.21/1.42 tff(3866,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1655, 3865, 3864, 3782, 3787, 3790, 3789, 3786, 3788, 698, 3863, 3784])).
% 1.21/1.42 tff(3867,plain,(hskp29 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(3868,plain,
% 1.21/1.42 (hskp29),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3867, 3828])).
% 1.21/1.42 tff(3869,plain,
% 1.21/1.42 (c0_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[205, 3868])).
% 1.21/1.42 tff(3870,plain,
% 1.21/1.42 (c3_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[189, 3868])).
% 1.21/1.42 tff(3871,plain,
% 1.21/1.42 (c2_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[197, 3868])).
% 1.21/1.42 tff(3872,plain,
% 1.21/1.42 (hskp29),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3867, 1167])).
% 1.21/1.42 tff(3873,plain,
% 1.21/1.42 (c3_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[189, 3872])).
% 1.21/1.42 tff(3874,plain,
% 1.21/1.42 (c2_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[197, 3872])).
% 1.21/1.42 tff(3875,plain,
% 1.21/1.42 (c0_1(a1116)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[205, 3872])).
% 1.21/1.42 tff(3876,plain,
% 1.21/1.42 (hskp9),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3830, 2792])).
% 1.21/1.42 tff(3877,plain,
% 1.21/1.42 (~c3_1(a1108)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[464, 3876])).
% 1.21/1.42 tff(3878,plain,
% 1.21/1.42 (~c1_1(a1108)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[470, 3876])).
% 1.21/1.43 tff(3879,plain,
% 1.21/1.43 (c0_1(a1108)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[478, 3876])).
% 1.21/1.43 tff(3880,plain,
% 1.21/1.43 (~c0_1(a1136)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1536, 3782, 110, 3784, 3789, 3879, 3878, 3877, 1525])).
% 1.21/1.43 tff(3881,plain,
% 1.21/1.43 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3882,plain,
% 1.21/1.43 ((hskp16 | hskp2 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c2_1(a1147))) <=> (hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3883,plain,
% 1.21/1.43 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0)))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[3882])).
% 1.21/1.43 tff(3884,plain,
% 1.21/1.43 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0))),
% 1.21/1.43 inference(transitivity,[status(thm)],[3883, 3881])).
% 1.21/1.43 tff(3885,plain,
% 1.21/1.43 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(3886,plain,
% 1.21/1.43 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0)),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 1.21/1.43 tff(3887,plain,
% 1.21/1.43 (hskp16 | hskp2 | c0_1(a1147) | c3_1(a1147)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3886, 110, 3781, 2672])).
% 1.21/1.43 tff(3888,plain,
% 1.21/1.43 (hskp16),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3887, 2662, 2395, 699])).
% 1.21/1.43 tff(3889,plain,
% 1.21/1.43 (~c0_1(a1121)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1825, 3888])).
% 1.21/1.43 tff(3890,plain,
% 1.21/1.43 (c3_1(a1121)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1835, 3888])).
% 1.21/1.43 tff(3891,plain,
% 1.21/1.43 (c1_1(a1121)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1843, 3888])).
% 1.21/1.43 tff(3892,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3893,plain,
% 1.21/1.43 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121))) <=> (c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3894,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[3893])).
% 1.21/1.43 tff(3895,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[3894, 3892])).
% 1.21/1.43 tff(3896,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(3897,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3896, 3895])).
% 1.21/1.43 tff(3898,plain,
% 1.21/1.43 (~c0_1(a1118)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3897, 110, 3784, 3789, 3788, 3891, 3890, 3787, 3889, 3786, 45])).
% 1.21/1.43 tff(3899,plain,
% 1.21/1.43 (^[U: $i] : refl((hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.21/1.43 inference(bind,[status(th)],[])).
% 1.21/1.43 tff(3900,plain,
% 1.21/1.43 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.43 inference(quant_intro,[status(thm)],[3899])).
% 1.21/1.43 tff(3901,plain,
% 1.21/1.43 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3902,plain,
% 1.21/1.43 (^[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)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp2) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp2))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp2) <=> (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp2) <=> (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.21/1.43 inference(bind,[status(th)],[])).
% 1.21/1.43 tff(3903,plain,
% 1.21/1.43 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp2) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.43 inference(quant_intro,[status(thm)],[3902])).
% 1.21/1.43 tff(3904,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.21/1.43 tff(3905,plain,
% 1.21/1.43 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3904, 3903])).
% 1.21/1.43 tff(3906,plain,
% 1.21/1.43 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3905, 3901])).
% 1.21/1.43 tff(3907,plain,(
% 1.21/1.43 ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.43 inference(skolemize,[status(sab)],[3906])).
% 1.21/1.43 tff(3908,plain,
% 1.21/1.43 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3907, 3900])).
% 1.21/1.43 tff(3909,plain,
% 1.21/1.43 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3910,plain,
% 1.21/1.43 ((hskp28 | hskp2 | (~ndr1_0) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3911,plain,
% 1.21/1.43 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | (~ndr1_0) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[3910])).
% 1.21/1.43 tff(3912,plain,
% 1.21/1.43 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | (~ndr1_0) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.21/1.43 inference(transitivity,[status(thm)],[3911, 3909])).
% 1.21/1.43 tff(3913,plain,
% 1.21/1.43 ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | (~ndr1_0) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(3914,plain,
% 1.21/1.43 ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3913, 3912])).
% 1.21/1.43 tff(3915,plain,
% 1.21/1.43 (hskp28 | hskp2 | c0_1(a1118)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3914, 110, 3787, 3790, 3908])).
% 1.21/1.43 tff(3916,plain,
% 1.21/1.43 (hskp28),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3915, 3898, 2662])).
% 1.21/1.43 tff(3917,plain,
% 1.21/1.43 (c2_1(a1111)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[551, 3916])).
% 1.21/1.43 tff(3918,plain,
% 1.21/1.43 (c1_1(a1111)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[559, 3916])).
% 1.21/1.43 tff(3919,plain,
% 1.21/1.43 (c0_1(a1111)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[567, 3916])).
% 1.21/1.43 tff(3920,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3921,plain,
% 1.21/1.43 (((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3922,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[3921])).
% 1.21/1.43 tff(3923,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[3922, 3920])).
% 1.21/1.43 tff(3924,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(3925,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3924, 3923])).
% 1.21/1.43 tff(3926,plain,
% 1.21/1.43 ($false),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3925, 110, 3784, 3789, 3919, 3918, 3917, 3879, 3878, 3877, 57, 3880])).
% 1.21/1.43 tff(3927,plain,(hskp2 | c0_1(a1147) | c3_1(a1147) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.43 tff(3928,plain,
% 1.21/1.43 (hskp2),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3927, 3875, 699, 2395, 3874, 3873])).
% 1.21/1.43 tff(3929,plain,
% 1.21/1.43 (~c3_1(a1100)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[273, 3928])).
% 1.21/1.43 tff(3930,plain,
% 1.21/1.43 (c2_1(a1100)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[281, 3928])).
% 1.21/1.43 tff(3931,plain,
% 1.21/1.43 (c0_1(a1100)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[289, 3928])).
% 1.21/1.43 tff(3932,plain,
% 1.21/1.43 (~c1_1(a1100)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1187, 110, 1167, 3931, 3930, 3929, 1177])).
% 1.21/1.43 tff(3933,plain,
% 1.21/1.43 (hskp7 | c1_1(a1100)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3577, 3782, 110, 3931, 3930, 2433])).
% 1.21/1.43 tff(3934,plain,
% 1.21/1.43 (hskp7),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3933, 3932])).
% 1.21/1.43 tff(3935,plain,
% 1.21/1.43 (~c1_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[582, 3934])).
% 1.21/1.43 tff(3936,plain,
% 1.21/1.43 (c0_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[592, 3934])).
% 1.21/1.43 tff(3937,plain,
% 1.21/1.43 (c3_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[600, 3934])).
% 1.21/1.43 tff(3938,plain,
% 1.21/1.43 (~hskp8),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2510, 3937, 3874, 3873, 3875, 3936, 3935])).
% 1.21/1.43 tff(3939,plain,
% 1.21/1.43 (c0_1(a1118)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1911, 3938, 3787, 3784, 3874, 3790, 3786, 3873, 3789, 3788, 3875])).
% 1.21/1.43 tff(3940,plain,
% 1.21/1.43 (c0_1(a1136)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1914, 3939, 3789, 3788, 3787, 3786, 3784])).
% 1.21/1.43 tff(3941,plain,
% 1.21/1.43 ($false),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2562, 3782, 110, 3784, 3789, 3931, 3929, 1525, 3940, 3932])).
% 1.21/1.43 tff(3942,plain,(hskp5 | c3_1(a1147) | c0_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.43 tff(3943,plain,
% 1.21/1.43 (c0_1(a1147)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3942, 699, 3828])).
% 1.21/1.43 tff(3944,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3945,plain,
% 1.21/1.43 ((hskp5 | (~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c2_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147))) <=> (hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3946,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c2_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[3945])).
% 1.21/1.43 tff(3947,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c2_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[3946, 3944])).
% 1.21/1.43 tff(3948,plain,
% 1.21/1.43 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c2_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(3949,plain,
% 1.21/1.43 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 1.21/1.43 tff(3950,plain,
% 1.21/1.43 (~c1_1(a1147)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3949, 110, 3828, 3943, 3781, 699, 1177])).
% 1.21/1.43 tff(3951,plain,
% 1.21/1.43 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3952,plain,
% 1.21/1.43 ((hskp23 | hskp7 | (~ndr1_0) | c1_1(a1147) | (~c2_1(a1147)) | (~c0_1(a1147))) <=> (hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3953,plain,
% 1.21/1.43 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1147) | (~c2_1(a1147)) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[3952])).
% 1.21/1.43 tff(3954,plain,
% 1.21/1.43 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1147) | (~c2_1(a1147)) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[3953, 3951])).
% 1.21/1.43 tff(3955,plain,
% 1.21/1.43 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1147) | (~c2_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(3956,plain,
% 1.21/1.43 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3955, 3954])).
% 1.21/1.43 tff(3957,plain,
% 1.21/1.43 (hskp7 | c1_1(a1147) | (~c0_1(a1147))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3956, 3782, 110, 3781, 2433])).
% 1.21/1.43 tff(3958,plain,
% 1.21/1.43 (hskp7),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3957, 3950, 3943])).
% 1.21/1.43 tff(3959,plain,
% 1.21/1.43 (~c1_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[582, 3958])).
% 1.21/1.43 tff(3960,plain,
% 1.21/1.43 (c0_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[592, 3958])).
% 1.21/1.43 tff(3961,plain,
% 1.21/1.43 (c3_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[600, 3958])).
% 1.21/1.43 tff(3962,plain,
% 1.21/1.43 (~hskp8),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2510, 3961, 3871, 3870, 3869, 3960, 3959])).
% 1.21/1.43 tff(3963,plain,
% 1.21/1.43 (c0_1(a1118)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1911, 3962, 3787, 3784, 3871, 3790, 3786, 3870, 3789, 3788, 3869])).
% 1.21/1.43 tff(3964,plain,
% 1.21/1.43 (c0_1(a1136)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1914, 3963, 3789, 3788, 3787, 3786, 3784])).
% 1.21/1.43 tff(3965,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3966,plain,
% 1.21/1.43 ((hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147))) <=> (hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3967,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[3966])).
% 1.21/1.43 tff(3968,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[3967, 3965])).
% 1.21/1.43 tff(3969,plain,
% 1.21/1.43 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(3970,plain,
% 1.21/1.43 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3969, 3968])).
% 1.21/1.43 tff(3971,plain,
% 1.21/1.43 ($false),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3970, 3782, 110, 3784, 3789, 3943, 699, 1525, 3964, 3950])).
% 1.21/1.43 tff(3972,plain,(c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.43 tff(3973,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3974,plain,
% 1.21/1.43 ((hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1147) | (~c3_1(a1147)) | (~c2_1(a1147))) <=> (hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(3975,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1147) | (~c3_1(a1147)) | (~c2_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[3974])).
% 1.21/1.43 tff(3976,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1147) | (~c3_1(a1147)) | (~c2_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[3975, 3973])).
% 1.21/1.43 tff(3977,plain,
% 1.21/1.43 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1147) | (~c3_1(a1147)) | (~c2_1(a1147)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(3978,plain,
% 1.21/1.43 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[3977, 3976])).
% 1.21/1.43 tff(3979,plain,
% 1.21/1.43 (hskp7),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[3978, 110, 3869, 3871, 3870, 2395, 3781, 3972, 3110])).
% 1.21/1.43 tff(3980,plain,
% 1.21/1.43 (~c1_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[582, 3979])).
% 1.21/1.43 tff(3981,plain,
% 1.21/1.43 (c0_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[592, 3979])).
% 1.21/1.43 tff(3982,plain,
% 1.21/1.43 (c3_1(a1105)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[600, 3979])).
% 1.21/1.43 tff(3983,plain,
% 1.21/1.43 (~hskp8),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2510, 3982, 3871, 3870, 3869, 3981, 3980])).
% 1.21/1.43 tff(3984,plain,
% 1.21/1.43 (c0_1(a1118)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1911, 3983, 3787, 3784, 3871, 3790, 3786, 3870, 3789, 3788, 3869])).
% 1.21/1.43 tff(3985,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147)))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(3986,plain,
% 1.21/1.44 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147))) <=> (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147)))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(3987,plain,
% 1.21/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147))))),
% 1.21/1.44 inference(monotonicity,[status(thm)],[3986])).
% 1.21/1.44 tff(3988,plain,
% 1.21/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147)))),
% 1.21/1.44 inference(transitivity,[status(thm)],[3987, 3985])).
% 1.21/1.44 tff(3989,plain,
% 1.21/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))),
% 1.21/1.44 inference(quant_inst,[status(thm)],[])).
% 1.21/1.44 tff(3990,plain,
% 1.21/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[3989, 3988])).
% 1.21/1.44 tff(3991,plain,
% 1.21/1.44 ((~c0_1(a1118)) | (~c1_1(a1147))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[3990, 110, 3784, 3789, 3788, 2395, 3787, 3972, 3786, 45])).
% 1.21/1.44 tff(3992,plain,
% 1.21/1.44 (~c1_1(a1147)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[3991, 3984])).
% 1.21/1.44 tff(3993,plain,
% 1.21/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(3994,plain,
% 1.21/1.44 (((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1147) | c0_1(a1147) | (~c2_1(a1147))) <=> (c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(3995,plain,
% 1.21/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)))),
% 1.21/1.44 inference(monotonicity,[status(thm)],[3994])).
% 1.21/1.44 tff(3996,plain,
% 1.21/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.21/1.44 inference(transitivity,[status(thm)],[3995, 3993])).
% 1.21/1.44 tff(3997,plain,
% 1.21/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))),
% 1.21/1.44 inference(quant_inst,[status(thm)],[])).
% 1.21/1.44 tff(3998,plain,
% 1.21/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[3997, 3996])).
% 1.21/1.44 tff(3999,plain,
% 1.21/1.44 (~c2_1(a1105)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[3998, 110, 2395, 3981, 3982, 3781, 3980, 642, 3992])).
% 1.21/1.44 tff(4000,plain,
% 1.21/1.44 (c0_1(a1136)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1914, 3984, 3789, 3788, 3787, 3786, 3784])).
% 1.21/1.44 tff(4001,plain,
% 1.21/1.44 ($false),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1693, 110, 3789, 3788, 3787, 3982, 3790, 3980, 228, 3984, 4000, 3999])).
% 1.21/1.44 tff(4002,plain,(c0_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.44 tff(4003,plain,
% 1.21/1.44 (c1_1(a1147)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[3957, 68, 4002])).
% 1.21/1.44 tff(4004,plain,
% 1.21/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(4005,plain,
% 1.21/1.44 ((hskp23 | (~ndr1_0) | (~c1_1(a1147)) | (~c2_1(a1147)) | (~c0_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108))) <=> (hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(4006,plain,
% 1.21/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1147)) | (~c2_1(a1147)) | (~c0_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.21/1.44 inference(monotonicity,[status(thm)],[4005])).
% 1.21/1.44 tff(4007,plain,
% 1.21/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1147)) | (~c2_1(a1147)) | (~c0_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.21/1.44 inference(transitivity,[status(thm)],[4006, 4004])).
% 1.21/1.44 tff(4008,plain,
% 1.21/1.44 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1147)) | (~c2_1(a1147)) | (~c0_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))),
% 1.21/1.44 inference(quant_inst,[status(thm)],[])).
% 1.21/1.44 tff(4009,plain,
% 1.21/1.44 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[4008, 4007])).
% 1.21/1.44 tff(4010,plain,
% 1.21/1.44 ($false),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[4009, 3782, 110, 4002, 1530, 3781, 1529, 1528, 1525, 2443])).
% 1.21/1.44 tff(4011,plain,((~hskp9) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.44 tff(4012,plain,
% 1.21/1.44 (~hskp9),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[4011, 4003])).
% 1.21/1.44 tff(4013,plain,
% 1.21/1.44 (hskp19),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[3830, 4012])).
% 1.21/1.44 tff(4014,plain,
% 1.21/1.44 (hskp2),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2791, 4013, 3869, 3871, 3870])).
% 1.21/1.44 tff(4015,plain,
% 1.21/1.44 (~c3_1(a1100)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[273, 4014])).
% 1.21/1.44 tff(4016,plain,
% 1.21/1.44 (c2_1(a1100)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[281, 4014])).
% 1.21/1.44 tff(4017,plain,
% 1.21/1.44 (c0_1(a1100)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[289, 4014])).
% 1.21/1.44 tff(4018,plain,
% 1.21/1.44 (~c1_1(a1100)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1187, 110, 3828, 4017, 4016, 4015, 1177])).
% 1.21/1.44 tff(4019,plain,
% 1.21/1.44 ($false),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[3577, 3782, 110, 68, 4017, 4016, 2433, 4018])).
% 1.21/1.44 tff(4020,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 1.21/1.44 tff(4021,plain,
% 1.21/1.44 (~c1_1(a1105)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[582, 4020])).
% 1.21/1.44 tff(4022,plain,
% 1.21/1.44 (c0_1(a1105)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[592, 4020])).
% 1.21/1.44 tff(4023,plain,
% 1.21/1.44 (c3_1(a1105)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[600, 4020])).
% 1.21/1.44 tff(4024,plain,
% 1.21/1.44 (~hskp8),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2510, 4023, 3871, 3870, 3869, 4022, 4021])).
% 1.21/1.44 tff(4025,plain,
% 1.21/1.44 (c0_1(a1118)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1911, 4024, 3787, 3784, 3871, 3790, 3786, 3870, 3789, 3788, 3869])).
% 1.21/1.44 tff(4026,plain,
% 1.21/1.44 (c0_1(a1136)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1914, 4025, 3789, 3788, 3787, 3786, 3784])).
% 1.21/1.44 tff(4027,plain,
% 1.21/1.44 (c2_1(a1105)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1693, 110, 3789, 3788, 3787, 4023, 3790, 4021, 228, 4025, 4026])).
% 1.21/1.44 tff(4028,plain,
% 1.21/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(4029,plain,
% 1.21/1.44 ((hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(4030,plain,
% 1.21/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.21/1.44 inference(monotonicity,[status(thm)],[4029])).
% 1.21/1.44 tff(4031,plain,
% 1.21/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.21/1.44 inference(transitivity,[status(thm)],[4030, 4028])).
% 1.21/1.44 tff(4032,plain,
% 1.21/1.44 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.21/1.44 inference(quant_inst,[status(thm)],[])).
% 1.21/1.44 tff(4033,plain,
% 1.21/1.44 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[4032, 4031])).
% 1.21/1.44 tff(4034,plain,
% 1.21/1.44 (hskp2),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[4033, 110, 3789, 3788, 4023, 4021, 975, 4026, 4027])).
% 1.21/1.44 tff(4035,plain,
% 1.21/1.44 (~c3_1(a1100)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[273, 4034])).
% 1.21/1.44 tff(4036,plain,
% 1.21/1.44 (hskp19 | (~c2_1(a1105))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2540, 110, 4024, 4023, 4021, 2534])).
% 1.21/1.44 tff(4037,plain,
% 1.21/1.44 (hskp19),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[4036, 4027])).
% 1.21/1.44 tff(4038,plain,
% 1.21/1.44 (hskp20),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1203, 4037, 3828, 3869, 3871, 3870])).
% 1.21/1.44 tff(4039,plain,
% 1.21/1.44 (~c3_1(a1130)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[308, 4038])).
% 1.21/1.44 tff(4040,plain,
% 1.21/1.44 (~c2_1(a1130)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2149, 4038])).
% 1.21/1.44 tff(4041,plain,
% 1.21/1.44 (~c0_1(a1130)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[302, 4038])).
% 1.21/1.44 tff(4042,plain,
% 1.21/1.44 (c2_1(a1100)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[281, 4034])).
% 1.21/1.44 tff(4043,plain,
% 1.21/1.44 (~c1_1(a1100)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2553, 110, 3828, 4042, 4041, 4040, 4039, 4035, 10])).
% 1.21/1.44 tff(4044,plain,
% 1.21/1.44 (c0_1(a1100)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[289, 4034])).
% 1.21/1.44 tff(4045,plain,
% 1.21/1.44 ($false),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2562, 3782, 110, 3784, 3789, 4044, 4035, 1525, 4026, 4043])).
% 1.21/1.44 % SZS output end Proof
% 1.21/1.45 % E exiting
%------------------------------------------------------------------------------