TSTP Solution File: SYN458-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN458-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Thu Sep 29 23:55:34 EDT 2022
% Result : Unsatisfiable 1.80s 1.37s
% Output : Proof 2.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SYN458-1 : TPTP v8.1.0. Released v2.1.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.29 % Computer : n007.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Sep 5 03:41:35 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.30 Usage: tptp [options] [-file:]file
% 0.10/0.30 -h, -? prints this message.
% 0.10/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.30 -m, -model generate model.
% 0.10/0.30 -p, -proof generate proof.
% 0.10/0.30 -c, -core generate unsat core of named formulas.
% 0.10/0.30 -st, -statistics display statistics.
% 0.10/0.30 -t:timeout set timeout (in second).
% 0.10/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.30 -<param>:<value> configuration parameter and value.
% 0.10/0.30 -o:<output-file> file to place output in.
% 1.80/1.37 % SZS status Unsatisfiable
% 1.80/1.37 % SZS output start Proof
% 1.80/1.37 tff(c0_1_type, type, (
% 1.80/1.37 c0_1: $i > $o)).
% 1.80/1.37 tff(a1089_type, type, (
% 1.80/1.37 a1089: $i)).
% 1.80/1.37 tff(c1_1_type, type, (
% 1.80/1.37 c1_1: $i > $o)).
% 1.80/1.37 tff(c2_1_type, type, (
% 1.80/1.37 c2_1: $i > $o)).
% 1.80/1.37 tff(c3_1_type, type, (
% 1.80/1.37 c3_1: $i > $o)).
% 1.80/1.37 tff(ndr1_0_type, type, (
% 1.80/1.37 ndr1_0: $o)).
% 1.80/1.37 tff(hskp5_type, type, (
% 1.80/1.37 hskp5: $o)).
% 1.80/1.37 tff(a1080_type, type, (
% 1.80/1.37 a1080: $i)).
% 1.80/1.37 tff(hskp0_type, type, (
% 1.80/1.37 hskp0: $o)).
% 1.80/1.37 tff(a1085_type, type, (
% 1.80/1.37 a1085: $i)).
% 1.80/1.37 tff(hskp3_type, type, (
% 1.80/1.37 hskp3: $o)).
% 1.80/1.37 tff(a1120_type, type, (
% 1.80/1.37 a1120: $i)).
% 1.80/1.37 tff(hskp21_type, type, (
% 1.80/1.37 hskp21: $o)).
% 1.80/1.37 tff(hskp9_type, type, (
% 1.80/1.37 hskp9: $o)).
% 1.80/1.37 tff(a1082_type, type, (
% 1.80/1.37 a1082: $i)).
% 1.80/1.37 tff(hskp2_type, type, (
% 1.80/1.37 hskp2: $o)).
% 1.80/1.37 tff(a1146_type, type, (
% 1.80/1.37 a1146: $i)).
% 1.80/1.37 tff(hskp26_type, type, (
% 1.80/1.37 hskp26: $o)).
% 1.80/1.37 tff(a1113_type, type, (
% 1.80/1.37 a1113: $i)).
% 1.80/1.37 tff(hskp19_type, type, (
% 1.80/1.37 hskp19: $o)).
% 1.80/1.37 tff(a1092_type, type, (
% 1.80/1.37 a1092: $i)).
% 1.80/1.37 tff(a1109_type, type, (
% 1.80/1.37 a1109: $i)).
% 1.80/1.37 tff(hskp30_type, type, (
% 1.80/1.37 hskp30: $o)).
% 1.80/1.37 tff(a1097_type, type, (
% 1.80/1.37 a1097: $i)).
% 1.80/1.37 tff(hskp14_type, type, (
% 1.80/1.37 hskp14: $o)).
% 1.80/1.37 tff(a1103_type, type, (
% 1.80/1.37 a1103: $i)).
% 1.80/1.37 tff(hskp18_type, type, (
% 1.80/1.37 hskp18: $o)).
% 1.80/1.37 tff(hskp13_type, type, (
% 1.80/1.37 hskp13: $o)).
% 1.80/1.37 tff(hskp27_type, type, (
% 1.80/1.37 hskp27: $o)).
% 1.80/1.37 tff(hskp20_type, type, (
% 1.80/1.37 hskp20: $o)).
% 1.80/1.37 tff(a1098_type, type, (
% 1.80/1.37 a1098: $i)).
% 1.80/1.37 tff(hskp15_type, type, (
% 1.80/1.37 hskp15: $o)).
% 1.80/1.37 tff(hskp28_type, type, (
% 1.80/1.37 hskp28: $o)).
% 1.80/1.37 tff(hskp1_type, type, (
% 1.80/1.37 hskp1: $o)).
% 1.80/1.37 tff(a1081_type, type, (
% 1.80/1.37 a1081: $i)).
% 1.80/1.37 tff(hskp11_type, type, (
% 1.80/1.37 hskp11: $o)).
% 1.80/1.37 tff(a1091_type, type, (
% 1.80/1.37 a1091: $i)).
% 1.80/1.37 tff(a1095_type, type, (
% 1.80/1.37 a1095: $i)).
% 1.80/1.37 tff(a1083_type, type, (
% 1.80/1.37 a1083: $i)).
% 1.80/1.37 tff(a1090_type, type, (
% 1.80/1.37 a1090: $i)).
% 1.80/1.37 tff(hskp10_type, type, (
% 1.80/1.37 hskp10: $o)).
% 1.80/1.37 tff(a1088_type, type, (
% 1.80/1.37 a1088: $i)).
% 1.80/1.37 tff(hskp8_type, type, (
% 1.80/1.37 hskp8: $o)).
% 1.80/1.37 tff(a1084_type, type, (
% 1.80/1.37 a1084: $i)).
% 1.80/1.37 tff(hskp4_type, type, (
% 1.80/1.37 hskp4: $o)).
% 1.80/1.37 tff(a1122_type, type, (
% 1.80/1.37 a1122: $i)).
% 1.80/1.37 tff(hskp23_type, type, (
% 1.80/1.37 hskp23: $o)).
% 1.80/1.37 tff(a1102_type, type, (
% 1.80/1.37 a1102: $i)).
% 1.80/1.37 tff(hskp17_type, type, (
% 1.80/1.37 hskp17: $o)).
% 1.80/1.37 tff(a1100_type, type, (
% 1.80/1.37 a1100: $i)).
% 1.80/1.37 tff(hskp16_type, type, (
% 1.80/1.37 hskp16: $o)).
% 1.80/1.37 tff(a1148_type, type, (
% 1.80/1.37 a1148: $i)).
% 1.80/1.37 tff(hskp31_type, type, (
% 1.80/1.37 hskp31: $o)).
% 1.80/1.37 tff(a1121_type, type, (
% 1.80/1.37 a1121: $i)).
% 1.80/1.37 tff(hskp22_type, type, (
% 1.80/1.37 hskp22: $o)).
% 1.80/1.37 tff(1,plain,
% 1.80/1.37 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.80/1.37 inference(bind,[status(th)],[])).
% 1.80/1.37 tff(2,plain,
% 1.80/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.80/1.37 inference(quant_intro,[status(thm)],[1])).
% 1.80/1.37 tff(3,plain,
% 1.80/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.80/1.37 inference(rewrite,[status(thm)],[])).
% 1.80/1.37 tff(4,plain,
% 1.80/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.86/1.37 inference(bind,[status(th)],[])).
% 1.86/1.37 tff(5,plain,
% 1.86/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.86/1.37 inference(quant_intro,[status(thm)],[4])).
% 1.86/1.37 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.86/1.37 tff(7,plain,
% 1.86/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.86/1.37 tff(8,plain,
% 1.86/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.86/1.37 tff(9,plain,(
% 1.86/1.37 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.86/1.37 inference(skolemize,[status(sab)],[8])).
% 1.86/1.37 tff(10,plain,
% 1.86/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.86/1.37 tff(11,assumption,(~c1_1(a1085)), introduced(assumption)).
% 1.86/1.37 tff(12,assumption,(~c0_1(a1085)), introduced(assumption)).
% 1.86/1.37 tff(13,plain,
% 1.86/1.37 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.86/1.37 inference(bind,[status(th)],[])).
% 1.86/1.37 tff(14,plain,
% 1.86/1.37 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.86/1.37 inference(quant_intro,[status(thm)],[13])).
% 1.86/1.37 tff(15,plain,
% 1.86/1.37 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.86/1.37 inference(rewrite,[status(thm)],[])).
% 1.86/1.37 tff(16,plain,
% 1.86/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.86/1.37 inference(bind,[status(th)],[])).
% 1.86/1.37 tff(17,plain,
% 1.86/1.37 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.86/1.37 inference(quant_intro,[status(thm)],[16])).
% 1.86/1.37 tff(18,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.86/1.37 tff(19,plain,
% 1.86/1.37 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.86/1.37 tff(20,plain,
% 1.86/1.37 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.86/1.37 tff(21,plain,(
% 1.86/1.37 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.86/1.37 inference(skolemize,[status(sab)],[20])).
% 1.86/1.37 tff(22,plain,
% 1.86/1.37 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.86/1.37 tff(23,assumption,(hskp0), introduced(assumption)).
% 1.86/1.37 tff(24,plain,
% 1.86/1.37 (((~hskp0) | (~c2_1(a1080))) <=> ((~hskp0) | (~c2_1(a1080)))),
% 1.86/1.37 inference(rewrite,[status(thm)],[])).
% 1.86/1.37 tff(25,plain,
% 1.86/1.37 (((~c2_1(a1080)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1080)))),
% 1.86/1.37 inference(rewrite,[status(thm)],[])).
% 1.86/1.37 tff(26,axiom,((~c2_1(a1080)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.86/1.37 tff(27,plain,
% 1.86/1.37 ((~hskp0) | (~c2_1(a1080))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.86/1.37 tff(28,plain,
% 1.86/1.37 ((~hskp0) | (~c2_1(a1080))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[27, 24])).
% 1.86/1.37 tff(29,plain,
% 1.86/1.37 (~c2_1(a1080)),
% 1.86/1.37 inference(unit_resolution,[status(thm)],[28, 23])).
% 1.86/1.37 tff(30,plain,
% 1.86/1.37 (((~hskp0) | (~c0_1(a1080))) <=> ((~hskp0) | (~c0_1(a1080)))),
% 1.86/1.37 inference(rewrite,[status(thm)],[])).
% 1.86/1.37 tff(31,plain,
% 1.86/1.37 (((~c0_1(a1080)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1080)))),
% 1.86/1.37 inference(rewrite,[status(thm)],[])).
% 1.86/1.37 tff(32,axiom,((~c0_1(a1080)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.86/1.37 tff(33,plain,
% 1.86/1.37 ((~hskp0) | (~c0_1(a1080))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.86/1.37 tff(34,plain,
% 1.86/1.37 ((~hskp0) | (~c0_1(a1080))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[33, 30])).
% 1.86/1.37 tff(35,plain,
% 1.86/1.37 (~c0_1(a1080)),
% 1.86/1.37 inference(unit_resolution,[status(thm)],[34, 23])).
% 1.86/1.37 tff(36,plain,
% 1.86/1.37 (((~hskp0) | c1_1(a1080)) <=> ((~hskp0) | c1_1(a1080))),
% 1.86/1.37 inference(rewrite,[status(thm)],[])).
% 1.86/1.37 tff(37,axiom,((~hskp0) | c1_1(a1080)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.86/1.37 tff(38,plain,
% 1.86/1.37 ((~hskp0) | c1_1(a1080)),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.86/1.37 tff(39,plain,
% 1.86/1.37 ((~hskp0) | c1_1(a1080)),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[38, 36])).
% 1.86/1.37 tff(40,plain,
% 1.86/1.37 ((~hskp0) | c1_1(a1080)),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[39, 36])).
% 1.86/1.37 tff(41,plain,
% 1.86/1.37 ((~hskp0) | c1_1(a1080)),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.86/1.37 tff(42,plain,
% 1.86/1.37 ((~hskp0) | c1_1(a1080)),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[41, 36])).
% 1.86/1.37 tff(43,plain,
% 1.86/1.37 ((~hskp0) | c1_1(a1080)),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[42, 36])).
% 1.86/1.37 tff(44,plain,
% 1.86/1.37 ((~hskp0) | c1_1(a1080)),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[43, 36])).
% 1.86/1.37 tff(45,plain,
% 1.86/1.37 ((~hskp0) | c1_1(a1080)),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[44, 36])).
% 1.86/1.37 tff(46,plain,
% 1.86/1.37 (c1_1(a1080)),
% 1.86/1.37 inference(unit_resolution,[status(thm)],[45, 23])).
% 1.86/1.37 tff(47,plain,
% 1.86/1.37 (^[U: $i] : refl((hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.86/1.37 inference(bind,[status(th)],[])).
% 1.86/1.37 tff(48,plain,
% 1.86/1.37 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.37 inference(quant_intro,[status(thm)],[47])).
% 1.86/1.37 tff(49,plain,
% 1.86/1.37 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.37 inference(rewrite,[status(thm)],[])).
% 1.86/1.37 tff(50,plain,
% 1.86/1.37 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.86/1.37 inference(bind,[status(th)],[])).
% 1.86/1.37 tff(51,plain,
% 1.86/1.37 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.37 inference(quant_intro,[status(thm)],[50])).
% 1.86/1.37 tff(52,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.86/1.37 tff(53,plain,
% 1.86/1.37 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.86/1.38 tff(54,plain,
% 1.86/1.38 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.86/1.38 tff(55,plain,(
% 1.86/1.38 ![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(skolemize,[status(sab)],[54])).
% 1.86/1.38 tff(56,plain,
% 1.86/1.38 (![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.86/1.38 tff(57,assumption,(~hskp9), introduced(assumption)).
% 1.86/1.38 tff(58,plain,
% 1.86/1.38 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.86/1.38 inference(bind,[status(th)],[])).
% 1.86/1.38 tff(59,plain,
% 1.86/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.86/1.38 inference(quant_intro,[status(thm)],[58])).
% 1.86/1.38 tff(60,plain,
% 1.86/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.86/1.38 inference(rewrite,[status(thm)],[])).
% 1.86/1.38 tff(61,plain,
% 1.86/1.38 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.86/1.38 inference(bind,[status(th)],[])).
% 1.86/1.38 tff(62,plain,
% 1.86/1.38 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.86/1.38 inference(quant_intro,[status(thm)],[61])).
% 1.86/1.38 tff(63,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.86/1.38 tff(64,plain,
% 1.86/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.86/1.38 tff(65,plain,
% 1.86/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.86/1.38 tff(66,plain,(
% 1.86/1.38 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.86/1.38 inference(skolemize,[status(sab)],[65])).
% 1.86/1.38 tff(67,plain,
% 1.86/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.86/1.38 tff(68,assumption,(~hskp2), introduced(assumption)).
% 1.86/1.38 tff(69,assumption,(~c2_1(a1080)), introduced(assumption)).
% 1.86/1.38 tff(70,plain,
% 1.86/1.38 (^[U: $i] : refl((hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.86/1.38 inference(bind,[status(th)],[])).
% 1.86/1.38 tff(71,plain,
% 1.86/1.38 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(quant_intro,[status(thm)],[70])).
% 1.86/1.38 tff(72,plain,
% 1.86/1.38 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(rewrite,[status(thm)],[])).
% 1.86/1.38 tff(73,plain,
% 1.86/1.38 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.86/1.38 inference(bind,[status(th)],[])).
% 1.86/1.38 tff(74,plain,
% 1.86/1.38 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(quant_intro,[status(thm)],[73])).
% 1.86/1.38 tff(75,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.86/1.38 tff(76,plain,
% 1.86/1.38 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.86/1.38 tff(77,plain,
% 1.86/1.38 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.86/1.38 tff(78,plain,(
% 1.86/1.38 ![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(skolemize,[status(sab)],[77])).
% 1.86/1.38 tff(79,plain,
% 1.86/1.38 (![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[78, 71])).
% 1.86/1.38 tff(80,plain,
% 1.86/1.38 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.86/1.38 inference(bind,[status(th)],[])).
% 1.86/1.38 tff(81,plain,
% 1.86/1.38 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.86/1.38 inference(quant_intro,[status(thm)],[80])).
% 1.86/1.38 tff(82,plain,
% 1.86/1.38 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.86/1.38 inference(rewrite,[status(thm)],[])).
% 1.86/1.38 tff(83,plain,
% 1.86/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.86/1.38 inference(bind,[status(th)],[])).
% 1.86/1.38 tff(84,plain,
% 1.86/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.86/1.38 inference(quant_intro,[status(thm)],[83])).
% 1.86/1.38 tff(85,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.86/1.38 tff(86,plain,
% 1.86/1.38 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.86/1.38 tff(87,plain,
% 1.86/1.38 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[86, 82])).
% 1.86/1.38 tff(88,plain,(
% 1.86/1.38 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.86/1.38 inference(skolemize,[status(sab)],[87])).
% 1.86/1.38 tff(89,plain,
% 1.86/1.38 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[88, 81])).
% 1.86/1.38 tff(90,assumption,(~c0_1(a1080)), introduced(assumption)).
% 1.86/1.38 tff(91,assumption,(~c2_1(a1085)), introduced(assumption)).
% 1.86/1.38 tff(92,assumption,(c0_1(a1097)), introduced(assumption)).
% 1.86/1.38 tff(93,plain,
% 1.86/1.38 (^[U: $i] : refl((hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.86/1.38 inference(bind,[status(th)],[])).
% 1.86/1.38 tff(94,plain,
% 1.86/1.38 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.86/1.38 inference(quant_intro,[status(thm)],[93])).
% 1.86/1.38 tff(95,plain,
% 1.86/1.38 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.86/1.38 inference(rewrite,[status(thm)],[])).
% 1.86/1.38 tff(96,plain,
% 1.86/1.38 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.86/1.38 inference(bind,[status(th)],[])).
% 1.86/1.38 tff(97,plain,
% 1.86/1.38 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.86/1.38 inference(quant_intro,[status(thm)],[96])).
% 1.86/1.38 tff(98,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.86/1.38 tff(99,plain,
% 1.86/1.38 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.86/1.38 tff(100,plain,
% 1.86/1.38 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[99, 95])).
% 1.86/1.38 tff(101,plain,(
% 1.86/1.38 ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.86/1.38 inference(skolemize,[status(sab)],[100])).
% 1.86/1.38 tff(102,plain,
% 1.86/1.38 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[101, 94])).
% 1.86/1.38 tff(103,plain,
% 1.86/1.38 (((~hskp5) | c2_1(a1085)) <=> ((~hskp5) | c2_1(a1085))),
% 1.86/1.38 inference(rewrite,[status(thm)],[])).
% 1.86/1.38 tff(104,axiom,((~hskp5) | c2_1(a1085)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.86/1.38 tff(105,plain,
% 1.86/1.38 ((~hskp5) | c2_1(a1085)),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.86/1.38 tff(106,plain,
% 1.86/1.38 ((~hskp5) | c2_1(a1085)),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[105, 103])).
% 1.86/1.38 tff(107,plain,
% 1.86/1.38 ((~hskp5) | c2_1(a1085)),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[106, 103])).
% 1.86/1.38 tff(108,plain,
% 1.86/1.38 ((~hskp5) | c2_1(a1085)),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[107, 103])).
% 1.86/1.38 tff(109,plain,
% 1.86/1.38 ((~hskp5) | c2_1(a1085)),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[108, 103])).
% 1.86/1.38 tff(110,plain,
% 1.86/1.38 ((~hskp5) | c2_1(a1085)),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[109, 103])).
% 1.86/1.38 tff(111,plain,
% 1.86/1.38 ((~hskp5) | c2_1(a1085)),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[110, 103])).
% 1.86/1.38 tff(112,plain,
% 1.86/1.38 ((~hskp5) | c2_1(a1085)),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[111, 103])).
% 1.86/1.38 tff(113,plain,
% 1.86/1.38 (~hskp5),
% 1.86/1.38 inference(unit_resolution,[status(thm)],[112, 91])).
% 1.86/1.38 tff(114,plain,
% 1.86/1.38 ((hskp0 | hskp5) <=> (hskp0 | hskp5)),
% 1.86/1.38 inference(rewrite,[status(thm)],[])).
% 1.86/1.38 tff(115,axiom,(hskp0 | hskp5), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.86/1.38 tff(116,plain,
% 1.86/1.38 (hskp0 | hskp5),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.86/1.38 tff(117,plain,
% 1.86/1.38 (hskp0),
% 1.86/1.38 inference(unit_resolution,[status(thm)],[116, 113])).
% 1.86/1.38 tff(118,plain,
% 1.86/1.38 (~c2_1(a1080)),
% 1.86/1.38 inference(unit_resolution,[status(thm)],[28, 117])).
% 1.86/1.38 tff(119,plain,
% 1.86/1.38 (~c0_1(a1080)),
% 1.86/1.38 inference(unit_resolution,[status(thm)],[34, 117])).
% 1.86/1.38 tff(120,plain,
% 1.86/1.38 (c1_1(a1080)),
% 1.86/1.38 inference(unit_resolution,[status(thm)],[45, 117])).
% 1.86/1.38 tff(121,assumption,(~hskp5), introduced(assumption)).
% 1.86/1.38 tff(122,plain,
% 1.86/1.38 (hskp0),
% 1.86/1.38 inference(unit_resolution,[status(thm)],[116, 121])).
% 1.86/1.38 tff(123,plain,
% 1.86/1.38 (~c2_1(a1080)),
% 1.86/1.38 inference(unit_resolution,[status(thm)],[28, 122])).
% 1.86/1.38 tff(124,plain,
% 1.86/1.38 (~c0_1(a1080)),
% 1.86/1.38 inference(unit_resolution,[status(thm)],[34, 122])).
% 1.86/1.38 tff(125,assumption,(hskp18), introduced(assumption)).
% 1.86/1.38 tff(126,plain,
% 1.86/1.38 (((~hskp18) | (~c1_1(a1103))) <=> ((~hskp18) | (~c1_1(a1103)))),
% 1.86/1.38 inference(rewrite,[status(thm)],[])).
% 1.86/1.38 tff(127,plain,
% 1.86/1.38 (((~c1_1(a1103)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a1103)))),
% 1.86/1.38 inference(rewrite,[status(thm)],[])).
% 1.86/1.38 tff(128,axiom,((~c1_1(a1103)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.86/1.38 tff(129,plain,
% 1.86/1.38 ((~hskp18) | (~c1_1(a1103))),
% 1.86/1.38 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.86/1.38 tff(130,plain,
% 1.86/1.38 ((~hskp18) | (~c1_1(a1103))),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[129, 126])).
% 1.86/1.39 tff(131,plain,
% 1.86/1.39 (~c1_1(a1103)),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[130, 125])).
% 1.86/1.39 tff(132,plain,
% 1.86/1.39 (c1_1(a1080)),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[45, 122])).
% 1.86/1.39 tff(133,plain,
% 1.86/1.39 (((~hskp18) | c3_1(a1103)) <=> ((~hskp18) | c3_1(a1103))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(134,axiom,((~hskp18) | c3_1(a1103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.86/1.39 tff(135,plain,
% 1.86/1.39 ((~hskp18) | c3_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.86/1.39 tff(136,plain,
% 1.86/1.39 ((~hskp18) | c3_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[135, 133])).
% 1.86/1.39 tff(137,plain,
% 1.86/1.39 ((~hskp18) | c3_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[136, 133])).
% 1.86/1.39 tff(138,plain,
% 1.86/1.39 ((~hskp18) | c3_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[137, 133])).
% 1.86/1.39 tff(139,plain,
% 1.86/1.39 ((~hskp18) | c3_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[138, 133])).
% 1.86/1.39 tff(140,plain,
% 1.86/1.39 ((~hskp18) | c3_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[139, 133])).
% 1.86/1.39 tff(141,plain,
% 1.86/1.39 ((~hskp18) | c3_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.86/1.39 tff(142,plain,
% 1.86/1.39 ((~hskp18) | c3_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[141, 133])).
% 1.86/1.39 tff(143,plain,
% 1.86/1.39 (c3_1(a1103)),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[142, 125])).
% 1.86/1.39 tff(144,plain,
% 1.86/1.39 (((~hskp18) | c0_1(a1103)) <=> ((~hskp18) | c0_1(a1103))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(145,axiom,((~hskp18) | c0_1(a1103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.86/1.39 tff(146,plain,
% 1.86/1.39 ((~hskp18) | c0_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.86/1.39 tff(147,plain,
% 1.86/1.39 ((~hskp18) | c0_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[146, 144])).
% 1.86/1.39 tff(148,plain,
% 1.86/1.39 ((~hskp18) | c0_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[147, 144])).
% 1.86/1.39 tff(149,plain,
% 1.86/1.39 ((~hskp18) | c0_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[148, 144])).
% 1.86/1.39 tff(150,plain,
% 1.86/1.39 ((~hskp18) | c0_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[149, 144])).
% 1.86/1.39 tff(151,plain,
% 1.86/1.39 ((~hskp18) | c0_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[150, 144])).
% 1.86/1.39 tff(152,plain,
% 1.86/1.39 ((~hskp18) | c0_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[151, 144])).
% 1.86/1.39 tff(153,plain,
% 1.86/1.39 ((~hskp18) | c0_1(a1103)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[152, 144])).
% 1.86/1.39 tff(154,plain,
% 1.86/1.39 (c0_1(a1103)),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[153, 125])).
% 1.86/1.39 tff(155,assumption,(~ndr1_0), introduced(assumption)).
% 1.86/1.39 tff(156,plain,
% 1.86/1.39 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(157,plain,
% 1.86/1.39 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(158,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 1.86/1.39 tff(159,plain,
% 1.86/1.39 (ndr1_0 | (~hskp13)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.86/1.39 tff(160,plain,
% 1.86/1.39 (ndr1_0 | (~hskp13)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[159, 156])).
% 1.86/1.39 tff(161,plain,
% 1.86/1.39 (~hskp13),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[160, 155])).
% 1.86/1.39 tff(162,plain,
% 1.86/1.39 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(163,plain,
% 1.86/1.39 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(164,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 1.86/1.39 tff(165,plain,
% 1.86/1.39 (ndr1_0 | (~hskp27)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[164, 163])).
% 1.86/1.39 tff(166,plain,
% 1.86/1.39 (ndr1_0 | (~hskp27)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[165, 162])).
% 1.86/1.39 tff(167,plain,
% 1.86/1.39 (~hskp27),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[166, 155])).
% 1.86/1.39 tff(168,plain,
% 1.86/1.39 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(169,plain,
% 1.86/1.39 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(170,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 1.86/1.39 tff(171,plain,
% 1.86/1.39 (ndr1_0 | (~hskp20)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.86/1.39 tff(172,plain,
% 1.86/1.39 (ndr1_0 | (~hskp20)),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[171, 168])).
% 1.86/1.39 tff(173,plain,
% 1.86/1.39 (~hskp20),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[172, 155])).
% 1.86/1.39 tff(174,plain,
% 1.86/1.39 ((hskp27 | hskp20 | hskp13) <=> (hskp27 | hskp20 | hskp13)),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(175,plain,
% 1.86/1.39 (((hskp20 | hskp27) | hskp13) <=> (hskp27 | hskp20 | hskp13)),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(176,axiom,((hskp20 | hskp27) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.86/1.39 tff(177,plain,
% 1.86/1.39 (hskp27 | hskp20 | hskp13),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.86/1.39 tff(178,plain,
% 1.86/1.39 (hskp27 | hskp20 | hskp13),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[177, 174])).
% 1.86/1.39 tff(179,plain,
% 1.86/1.39 (hskp27 | hskp20 | hskp13),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[178, 174])).
% 1.86/1.39 tff(180,plain,
% 1.86/1.39 (hskp27 | hskp20 | hskp13),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[179, 174])).
% 1.86/1.39 tff(181,plain,
% 1.86/1.39 (hskp27 | hskp20 | hskp13),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[180, 174])).
% 1.86/1.39 tff(182,plain,
% 1.86/1.39 (hskp27 | hskp20 | hskp13),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[181, 174])).
% 1.86/1.39 tff(183,plain,
% 1.86/1.39 (hskp27 | hskp20 | hskp13),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[182, 174])).
% 1.86/1.39 tff(184,plain,
% 1.86/1.39 (hskp27 | hskp20 | hskp13),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[183, 174])).
% 1.86/1.39 tff(185,plain,
% 1.86/1.39 ($false),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[184, 173, 167, 161])).
% 1.86/1.39 tff(186,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.86/1.39 tff(187,plain,
% 1.86/1.39 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103)))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(188,plain,
% 1.86/1.39 ((hskp5 | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)) | (~c0_1(a1103)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103)))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(189,plain,
% 1.86/1.39 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)) | (~c0_1(a1103)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103))))),
% 1.86/1.39 inference(monotonicity,[status(thm)],[188])).
% 1.86/1.39 tff(190,plain,
% 1.86/1.39 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)) | (~c0_1(a1103)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103)))),
% 1.86/1.39 inference(transitivity,[status(thm)],[189, 187])).
% 1.86/1.39 tff(191,plain,
% 1.86/1.39 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)) | (~c0_1(a1103)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 1.86/1.39 inference(quant_inst,[status(thm)],[])).
% 1.86/1.39 tff(192,plain,
% 1.86/1.39 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1103) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1103)) | (~c3_1(a1103))),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.86/1.39 tff(193,plain,
% 1.86/1.39 ($false),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[192, 121, 186, 154, 143, 132, 131, 124, 123, 10])).
% 1.86/1.39 tff(194,plain,((~hskp18) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.86/1.39 tff(195,plain,
% 1.86/1.39 (~hskp18),
% 1.86/1.39 inference(unit_resolution,[status(thm)],[194, 113])).
% 1.86/1.39 tff(196,plain,
% 1.86/1.39 (^[U: $i] : refl((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.86/1.39 inference(bind,[status(th)],[])).
% 1.86/1.39 tff(197,plain,
% 1.86/1.39 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.86/1.39 inference(quant_intro,[status(thm)],[196])).
% 1.86/1.39 tff(198,plain,
% 1.86/1.39 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(199,plain,
% 1.86/1.39 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.86/1.39 inference(bind,[status(th)],[])).
% 1.86/1.39 tff(200,plain,
% 1.86/1.39 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.86/1.39 inference(quant_intro,[status(thm)],[199])).
% 1.86/1.39 tff(201,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.86/1.39 tff(202,plain,
% 1.86/1.39 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.86/1.39 tff(203,plain,
% 1.86/1.39 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[202, 198])).
% 1.86/1.39 tff(204,plain,(
% 1.86/1.39 ![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.86/1.39 inference(skolemize,[status(sab)],[203])).
% 1.86/1.39 tff(205,plain,
% 1.86/1.39 (![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.86/1.39 inference(modus_ponens,[status(thm)],[204, 197])).
% 1.86/1.39 tff(206,assumption,(c1_1(a1080)), introduced(assumption)).
% 1.86/1.39 tff(207,assumption,(ndr1_0), introduced(assumption)).
% 1.86/1.39 tff(208,assumption,(~hskp14), introduced(assumption)).
% 1.86/1.39 tff(209,plain,
% 1.86/1.39 (^[U: $i] : refl((hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.86/1.39 inference(bind,[status(th)],[])).
% 1.86/1.39 tff(210,plain,
% 1.86/1.39 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.86/1.39 inference(quant_intro,[status(thm)],[209])).
% 1.86/1.39 tff(211,plain,
% 1.86/1.39 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.86/1.39 inference(rewrite,[status(thm)],[])).
% 1.86/1.39 tff(212,plain,
% 1.86/1.39 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.86/1.40 inference(bind,[status(th)],[])).
% 1.86/1.40 tff(213,plain,
% 1.86/1.40 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.86/1.40 inference(quant_intro,[status(thm)],[212])).
% 1.86/1.40 tff(214,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.86/1.40 tff(215,plain,
% 1.86/1.40 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.86/1.40 tff(216,plain,
% 1.86/1.40 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[215, 211])).
% 1.86/1.40 tff(217,plain,(
% 1.86/1.40 ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.86/1.40 inference(skolemize,[status(sab)],[216])).
% 1.86/1.40 tff(218,plain,
% 1.86/1.40 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[217, 210])).
% 1.86/1.40 tff(219,plain,
% 1.86/1.40 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(220,plain,
% 1.86/1.40 ((hskp15 | hskp14 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(221,plain,
% 1.86/1.40 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080))))),
% 1.86/1.40 inference(monotonicity,[status(thm)],[220])).
% 1.86/1.40 tff(222,plain,
% 1.86/1.40 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 1.86/1.40 inference(transitivity,[status(thm)],[221, 219])).
% 1.86/1.40 tff(223,plain,
% 1.86/1.40 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 1.86/1.40 inference(quant_inst,[status(thm)],[])).
% 1.86/1.40 tff(224,plain,
% 1.86/1.40 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp14 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.86/1.40 tff(225,plain,
% 1.86/1.40 (hskp15 | hskp14 | c0_1(a1080) | (~ndr1_0) | (~c1_1(a1080))),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[224, 69, 218])).
% 1.86/1.40 tff(226,plain,
% 1.86/1.40 (hskp15),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[225, 208, 207, 206, 90])).
% 1.86/1.40 tff(227,plain,
% 1.86/1.40 (((~hskp15) | (~c1_1(a1098))) <=> ((~hskp15) | (~c1_1(a1098)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(228,plain,
% 1.86/1.40 (((~c1_1(a1098)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a1098)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(229,axiom,((~c1_1(a1098)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.86/1.40 tff(230,plain,
% 1.86/1.40 ((~hskp15) | (~c1_1(a1098))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.86/1.40 tff(231,plain,
% 1.86/1.40 ((~hskp15) | (~c1_1(a1098))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[230, 227])).
% 1.86/1.40 tff(232,plain,
% 1.86/1.40 (~c1_1(a1098)),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[231, 226])).
% 1.86/1.40 tff(233,plain,
% 1.86/1.40 (((~hskp15) | c2_1(a1098)) <=> ((~hskp15) | c2_1(a1098))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(234,axiom,((~hskp15) | c2_1(a1098)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.86/1.40 tff(235,plain,
% 1.86/1.40 ((~hskp15) | c2_1(a1098)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.86/1.40 tff(236,plain,
% 1.86/1.40 ((~hskp15) | c2_1(a1098)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[235, 233])).
% 1.86/1.40 tff(237,plain,
% 1.86/1.40 ((~hskp15) | c2_1(a1098)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[236, 233])).
% 1.86/1.40 tff(238,plain,
% 1.86/1.40 ((~hskp15) | c2_1(a1098)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[237, 233])).
% 1.86/1.40 tff(239,plain,
% 1.86/1.40 ((~hskp15) | c2_1(a1098)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[238, 233])).
% 1.86/1.40 tff(240,plain,
% 1.86/1.40 ((~hskp15) | c2_1(a1098)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[239, 233])).
% 1.86/1.40 tff(241,plain,
% 1.86/1.40 ((~hskp15) | c2_1(a1098)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[240, 233])).
% 1.86/1.40 tff(242,plain,
% 1.86/1.40 ((~hskp15) | c2_1(a1098)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[241, 233])).
% 1.86/1.40 tff(243,plain,
% 1.86/1.40 (c2_1(a1098)),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[242, 226])).
% 1.86/1.40 tff(244,plain,
% 1.86/1.40 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(245,plain,
% 1.86/1.40 ((hskp14 | (~ndr1_0) | c1_1(a1098) | (~c2_1(a1098)) | (~c0_1(a1098))) <=> (hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(246,plain,
% 1.86/1.40 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1098) | (~c2_1(a1098)) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098))))),
% 1.86/1.40 inference(monotonicity,[status(thm)],[245])).
% 1.86/1.40 tff(247,plain,
% 1.86/1.40 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1098) | (~c2_1(a1098)) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098)))),
% 1.86/1.40 inference(transitivity,[status(thm)],[246, 244])).
% 1.86/1.40 tff(248,plain,
% 1.86/1.40 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1098) | (~c2_1(a1098)) | (~c0_1(a1098)))),
% 1.86/1.40 inference(quant_inst,[status(thm)],[])).
% 1.86/1.40 tff(249,plain,
% 1.86/1.40 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1098))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.86/1.40 tff(250,plain,
% 1.86/1.40 (~c0_1(a1098)),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[249, 207, 208, 243, 232, 205])).
% 1.86/1.40 tff(251,plain,
% 1.86/1.40 (^[U: $i] : refl((hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.86/1.40 inference(bind,[status(th)],[])).
% 1.86/1.40 tff(252,plain,
% 1.86/1.40 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.86/1.40 inference(quant_intro,[status(thm)],[251])).
% 1.86/1.40 tff(253,plain,
% 1.86/1.40 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(254,plain,
% 1.86/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.86/1.40 inference(bind,[status(th)],[])).
% 1.86/1.40 tff(255,plain,
% 1.86/1.40 (![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp18) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.86/1.40 inference(quant_intro,[status(thm)],[254])).
% 1.86/1.40 tff(256,axiom,(![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.86/1.40 tff(257,plain,
% 1.86/1.40 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.86/1.40 tff(258,plain,
% 1.86/1.40 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[257, 253])).
% 1.86/1.40 tff(259,plain,(
% 1.86/1.40 ![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.86/1.40 inference(skolemize,[status(sab)],[258])).
% 1.86/1.40 tff(260,plain,
% 1.86/1.40 (![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[259, 252])).
% 1.86/1.40 tff(261,plain,
% 1.86/1.40 (((~hskp15) | (~c3_1(a1098))) <=> ((~hskp15) | (~c3_1(a1098)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(262,plain,
% 1.86/1.40 (((~c3_1(a1098)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1098)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(263,axiom,((~c3_1(a1098)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.86/1.40 tff(264,plain,
% 1.86/1.40 ((~hskp15) | (~c3_1(a1098))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[263, 262])).
% 1.86/1.40 tff(265,plain,
% 1.86/1.40 ((~hskp15) | (~c3_1(a1098))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[264, 261])).
% 1.86/1.40 tff(266,plain,
% 1.86/1.40 (~c3_1(a1098)),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[265, 226])).
% 1.86/1.40 tff(267,assumption,(~hskp18), introduced(assumption)).
% 1.86/1.40 tff(268,plain,
% 1.86/1.40 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(269,plain,
% 1.86/1.40 ((hskp18 | (~ndr1_0) | c0_1(a1098) | c3_1(a1098) | (~c2_1(a1098))) <=> (hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(270,plain,
% 1.86/1.40 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1098) | c3_1(a1098) | (~c2_1(a1098)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098))))),
% 1.86/1.40 inference(monotonicity,[status(thm)],[269])).
% 1.86/1.40 tff(271,plain,
% 1.86/1.40 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1098) | c3_1(a1098) | (~c2_1(a1098)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098)))),
% 1.86/1.40 inference(transitivity,[status(thm)],[270, 268])).
% 1.86/1.40 tff(272,plain,
% 1.86/1.40 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1098) | c3_1(a1098) | (~c2_1(a1098)))),
% 1.86/1.40 inference(quant_inst,[status(thm)],[])).
% 1.86/1.40 tff(273,plain,
% 1.86/1.40 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c2_1(a1098))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.86/1.40 tff(274,plain,
% 1.86/1.40 ($false),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[273, 207, 267, 243, 266, 260, 250])).
% 1.86/1.40 tff(275,plain,(hskp14 | (~ndr1_0) | hskp18 | (~c1_1(a1080)) | c0_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 1.86/1.40 tff(276,plain,
% 1.86/1.40 (hskp14 | hskp18 | (~c1_1(a1080)) | c0_1(a1080) | c2_1(a1080)),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[275, 186])).
% 1.86/1.40 tff(277,plain,
% 1.86/1.40 (hskp14),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[276, 195, 120, 119, 118])).
% 1.86/1.40 tff(278,plain,
% 1.86/1.40 (((~hskp14) | (~c2_1(a1097))) <=> ((~hskp14) | (~c2_1(a1097)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(279,plain,
% 1.86/1.40 (((~c2_1(a1097)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1097)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(280,axiom,((~c2_1(a1097)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.86/1.40 tff(281,plain,
% 1.86/1.40 ((~hskp14) | (~c2_1(a1097))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.86/1.40 tff(282,plain,
% 1.86/1.40 ((~hskp14) | (~c2_1(a1097))),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[281, 278])).
% 1.86/1.40 tff(283,plain,
% 1.86/1.40 (~c2_1(a1097)),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[282, 277])).
% 1.86/1.40 tff(284,plain,
% 1.86/1.40 (((~hskp14) | c1_1(a1097)) <=> ((~hskp14) | c1_1(a1097))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(285,axiom,((~hskp14) | c1_1(a1097)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.86/1.40 tff(286,plain,
% 1.86/1.40 ((~hskp14) | c1_1(a1097)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[285, 284])).
% 1.86/1.40 tff(287,plain,
% 1.86/1.40 ((~hskp14) | c1_1(a1097)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[286, 284])).
% 1.86/1.40 tff(288,plain,
% 1.86/1.40 ((~hskp14) | c1_1(a1097)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[287, 284])).
% 1.86/1.40 tff(289,plain,
% 1.86/1.40 ((~hskp14) | c1_1(a1097)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[288, 284])).
% 1.86/1.40 tff(290,plain,
% 1.86/1.40 ((~hskp14) | c1_1(a1097)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[289, 284])).
% 1.86/1.40 tff(291,plain,
% 1.86/1.40 ((~hskp14) | c1_1(a1097)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[290, 284])).
% 1.86/1.40 tff(292,plain,
% 1.86/1.40 ((~hskp14) | c1_1(a1097)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[291, 284])).
% 1.86/1.40 tff(293,plain,
% 1.86/1.40 ((~hskp14) | c1_1(a1097)),
% 1.86/1.40 inference(modus_ponens,[status(thm)],[292, 284])).
% 1.86/1.40 tff(294,plain,
% 1.86/1.40 (c1_1(a1097)),
% 1.86/1.40 inference(unit_resolution,[status(thm)],[293, 277])).
% 1.86/1.40 tff(295,plain,
% 1.86/1.40 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(296,plain,
% 1.86/1.40 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097))) <=> (hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 1.86/1.40 inference(rewrite,[status(thm)],[])).
% 1.86/1.40 tff(297,plain,
% 1.86/1.40 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097))))),
% 1.86/1.40 inference(monotonicity,[status(thm)],[296])).
% 1.86/1.40 tff(298,plain,
% 1.86/1.40 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 1.86/1.41 inference(transitivity,[status(thm)],[297, 295])).
% 1.86/1.41 tff(299,plain,
% 1.86/1.41 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)))),
% 1.86/1.41 inference(quant_inst,[status(thm)],[])).
% 1.86/1.41 tff(300,plain,
% 1.86/1.41 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c1_1(a1097))),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.86/1.41 tff(301,plain,
% 1.86/1.41 (hskp30 | (~c0_1(a1097))),
% 1.86/1.41 inference(unit_resolution,[status(thm)],[300, 186, 57, 294, 283, 102])).
% 1.86/1.41 tff(302,plain,
% 1.86/1.41 (hskp30),
% 1.86/1.41 inference(unit_resolution,[status(thm)],[301, 92])).
% 1.86/1.41 tff(303,plain,
% 1.86/1.41 (((~hskp30) | c1_1(a1109)) <=> ((~hskp30) | c1_1(a1109))),
% 1.86/1.41 inference(rewrite,[status(thm)],[])).
% 1.86/1.41 tff(304,axiom,((~hskp30) | c1_1(a1109)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.86/1.41 tff(305,plain,
% 1.86/1.41 ((~hskp30) | c1_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[304, 303])).
% 1.86/1.41 tff(306,plain,
% 1.86/1.41 ((~hskp30) | c1_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[305, 303])).
% 1.86/1.41 tff(307,plain,
% 1.86/1.41 ((~hskp30) | c1_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[306, 303])).
% 1.86/1.41 tff(308,plain,
% 1.86/1.41 ((~hskp30) | c1_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[307, 303])).
% 1.86/1.41 tff(309,plain,
% 1.86/1.41 ((~hskp30) | c1_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[308, 303])).
% 1.86/1.41 tff(310,plain,
% 1.86/1.41 ((~hskp30) | c1_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[309, 303])).
% 1.86/1.41 tff(311,plain,
% 1.86/1.41 ((~hskp30) | c1_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[310, 303])).
% 1.86/1.41 tff(312,plain,
% 1.86/1.41 ((~hskp30) | c1_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[311, 303])).
% 1.86/1.41 tff(313,plain,
% 1.86/1.41 (c1_1(a1109)),
% 1.86/1.41 inference(unit_resolution,[status(thm)],[312, 302])).
% 1.86/1.41 tff(314,plain,
% 1.86/1.41 (^[U: $i] : refl((hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.86/1.41 inference(bind,[status(th)],[])).
% 1.86/1.41 tff(315,plain,
% 1.86/1.41 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.86/1.41 inference(quant_intro,[status(thm)],[314])).
% 1.86/1.41 tff(316,plain,
% 1.86/1.41 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.86/1.41 inference(rewrite,[status(thm)],[])).
% 1.86/1.41 tff(317,plain,
% 1.86/1.41 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp9) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp9))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp9) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.86/1.41 inference(bind,[status(th)],[])).
% 1.86/1.41 tff(318,plain,
% 1.86/1.41 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp9) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.86/1.41 inference(quant_intro,[status(thm)],[317])).
% 1.86/1.41 tff(319,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.86/1.41 tff(320,plain,
% 1.86/1.41 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.86/1.41 tff(321,plain,
% 1.86/1.41 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[320, 316])).
% 1.86/1.41 tff(322,plain,(
% 1.86/1.41 ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.86/1.41 inference(skolemize,[status(sab)],[321])).
% 1.86/1.41 tff(323,plain,
% 1.86/1.41 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[322, 315])).
% 1.86/1.41 tff(324,plain,
% 1.86/1.41 (((~hskp14) | c3_1(a1097)) <=> ((~hskp14) | c3_1(a1097))),
% 1.86/1.41 inference(rewrite,[status(thm)],[])).
% 1.86/1.41 tff(325,axiom,((~hskp14) | c3_1(a1097)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.86/1.41 tff(326,plain,
% 1.86/1.41 ((~hskp14) | c3_1(a1097)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.86/1.41 tff(327,plain,
% 1.86/1.41 ((~hskp14) | c3_1(a1097)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[326, 324])).
% 1.86/1.41 tff(328,plain,
% 1.86/1.41 ((~hskp14) | c3_1(a1097)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[327, 324])).
% 1.86/1.41 tff(329,plain,
% 1.86/1.41 ((~hskp14) | c3_1(a1097)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[328, 324])).
% 1.86/1.41 tff(330,plain,
% 1.86/1.41 ((~hskp14) | c3_1(a1097)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[329, 324])).
% 1.86/1.41 tff(331,plain,
% 1.86/1.41 ((~hskp14) | c3_1(a1097)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[330, 324])).
% 1.86/1.41 tff(332,plain,
% 1.86/1.41 ((~hskp14) | c3_1(a1097)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[331, 324])).
% 1.86/1.41 tff(333,plain,
% 1.86/1.41 ((~hskp14) | c3_1(a1097)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[332, 324])).
% 1.86/1.41 tff(334,plain,
% 1.86/1.41 (c3_1(a1097)),
% 1.86/1.41 inference(unit_resolution,[status(thm)],[333, 277])).
% 1.86/1.41 tff(335,plain,
% 1.86/1.41 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.41 inference(rewrite,[status(thm)],[])).
% 1.86/1.41 tff(336,plain,
% 1.86/1.41 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c0_1(a1097))) <=> (hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.41 inference(rewrite,[status(thm)],[])).
% 1.86/1.41 tff(337,plain,
% 1.86/1.41 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c0_1(a1097)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097))))),
% 1.86/1.41 inference(monotonicity,[status(thm)],[336])).
% 1.86/1.41 tff(338,plain,
% 1.86/1.41 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c0_1(a1097)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.41 inference(transitivity,[status(thm)],[337, 335])).
% 1.86/1.41 tff(339,plain,
% 1.86/1.41 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c0_1(a1097)))),
% 1.86/1.41 inference(quant_inst,[status(thm)],[])).
% 1.86/1.41 tff(340,plain,
% 1.86/1.41 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1097) | (~ndr1_0) | (~c0_1(a1097)) | (~c3_1(a1097))),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.86/1.41 tff(341,plain,
% 1.86/1.41 (hskp28 | (~c0_1(a1097))),
% 1.86/1.41 inference(unit_resolution,[status(thm)],[340, 186, 57, 334, 283, 323])).
% 1.86/1.41 tff(342,plain,
% 1.86/1.41 (hskp28),
% 1.86/1.41 inference(unit_resolution,[status(thm)],[341, 92])).
% 1.86/1.41 tff(343,plain,
% 1.86/1.41 (((~hskp30) | c0_1(a1109)) <=> ((~hskp30) | c0_1(a1109))),
% 1.86/1.41 inference(rewrite,[status(thm)],[])).
% 1.86/1.41 tff(344,axiom,((~hskp30) | c0_1(a1109)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.86/1.41 tff(345,plain,
% 1.86/1.41 ((~hskp30) | c0_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.86/1.41 tff(346,plain,
% 1.86/1.41 ((~hskp30) | c0_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[345, 343])).
% 1.86/1.41 tff(347,plain,
% 1.86/1.41 ((~hskp30) | c0_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[346, 343])).
% 1.86/1.41 tff(348,plain,
% 1.86/1.41 ((~hskp30) | c0_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[347, 343])).
% 1.86/1.41 tff(349,plain,
% 1.86/1.41 ((~hskp30) | c0_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[348, 343])).
% 1.86/1.41 tff(350,plain,
% 1.86/1.41 ((~hskp30) | c0_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[349, 343])).
% 1.86/1.41 tff(351,plain,
% 1.86/1.41 ((~hskp30) | c0_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[350, 343])).
% 1.86/1.41 tff(352,plain,
% 1.86/1.41 ((~hskp30) | c0_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[351, 343])).
% 1.86/1.41 tff(353,plain,
% 1.86/1.41 (c0_1(a1109)),
% 1.86/1.41 inference(unit_resolution,[status(thm)],[352, 302])).
% 1.86/1.41 tff(354,plain,
% 1.86/1.41 (((~hskp30) | c3_1(a1109)) <=> ((~hskp30) | c3_1(a1109))),
% 1.86/1.41 inference(rewrite,[status(thm)],[])).
% 1.86/1.41 tff(355,axiom,((~hskp30) | c3_1(a1109)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.86/1.41 tff(356,plain,
% 1.86/1.41 ((~hskp30) | c3_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[355, 354])).
% 1.86/1.41 tff(357,plain,
% 1.86/1.41 ((~hskp30) | c3_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[356, 354])).
% 1.86/1.41 tff(358,plain,
% 1.86/1.41 ((~hskp30) | c3_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[357, 354])).
% 1.86/1.41 tff(359,plain,
% 1.86/1.41 ((~hskp30) | c3_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[358, 354])).
% 1.86/1.41 tff(360,plain,
% 1.86/1.41 ((~hskp30) | c3_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[359, 354])).
% 1.86/1.41 tff(361,plain,
% 1.86/1.41 ((~hskp30) | c3_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[360, 354])).
% 1.86/1.41 tff(362,plain,
% 1.86/1.41 ((~hskp30) | c3_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[361, 354])).
% 1.86/1.41 tff(363,plain,
% 1.86/1.41 ((~hskp30) | c3_1(a1109)),
% 1.86/1.41 inference(modus_ponens,[status(thm)],[362, 354])).
% 1.86/1.41 tff(364,plain,
% 1.86/1.41 (c3_1(a1109)),
% 1.86/1.41 inference(unit_resolution,[status(thm)],[363, 302])).
% 1.86/1.41 tff(365,plain,
% 1.86/1.41 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.86/1.41 inference(bind,[status(th)],[])).
% 1.86/1.41 tff(366,plain,
% 1.86/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.41 inference(quant_intro,[status(thm)],[365])).
% 1.86/1.41 tff(367,plain,
% 1.86/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.41 inference(rewrite,[status(thm)],[])).
% 1.86/1.41 tff(368,plain,
% 1.86/1.41 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.86/1.41 inference(bind,[status(th)],[])).
% 1.86/1.41 tff(369,plain,
% 1.86/1.41 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.41 inference(quant_intro,[status(thm)],[368])).
% 1.86/1.41 tff(370,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.86/1.42 tff(371,plain,
% 1.86/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[370, 369])).
% 1.86/1.42 tff(372,plain,
% 1.86/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[371, 367])).
% 1.86/1.42 tff(373,plain,(
% 1.86/1.42 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.42 inference(skolemize,[status(sab)],[372])).
% 1.86/1.42 tff(374,plain,
% 1.86/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[373, 366])).
% 1.86/1.42 tff(375,assumption,(hskp28), introduced(assumption)).
% 1.86/1.42 tff(376,plain,
% 1.86/1.42 (((~hskp28) | c3_1(a1092)) <=> ((~hskp28) | c3_1(a1092))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(377,axiom,((~hskp28) | c3_1(a1092)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.86/1.42 tff(378,plain,
% 1.86/1.42 ((~hskp28) | c3_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.86/1.42 tff(379,plain,
% 1.86/1.42 ((~hskp28) | c3_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[378, 376])).
% 1.86/1.42 tff(380,plain,
% 1.86/1.42 ((~hskp28) | c3_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[379, 376])).
% 1.86/1.42 tff(381,plain,
% 1.86/1.42 ((~hskp28) | c3_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[380, 376])).
% 1.86/1.42 tff(382,plain,
% 1.86/1.42 ((~hskp28) | c3_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[381, 376])).
% 1.86/1.42 tff(383,plain,
% 1.86/1.42 ((~hskp28) | c3_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[382, 376])).
% 1.86/1.42 tff(384,plain,
% 1.86/1.42 ((~hskp28) | c3_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[383, 376])).
% 1.86/1.42 tff(385,plain,
% 1.86/1.42 ((~hskp28) | c3_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[384, 376])).
% 1.86/1.42 tff(386,plain,
% 1.86/1.42 (c3_1(a1092)),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[385, 375])).
% 1.86/1.42 tff(387,plain,
% 1.86/1.42 (((~hskp28) | c2_1(a1092)) <=> ((~hskp28) | c2_1(a1092))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(388,axiom,((~hskp28) | c2_1(a1092)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.86/1.42 tff(389,plain,
% 1.86/1.42 ((~hskp28) | c2_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.86/1.42 tff(390,plain,
% 1.86/1.42 ((~hskp28) | c2_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[389, 387])).
% 1.86/1.42 tff(391,plain,
% 1.86/1.42 ((~hskp28) | c2_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[390, 387])).
% 1.86/1.42 tff(392,plain,
% 1.86/1.42 ((~hskp28) | c2_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[391, 387])).
% 1.86/1.42 tff(393,plain,
% 1.86/1.42 ((~hskp28) | c2_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[392, 387])).
% 1.86/1.42 tff(394,plain,
% 1.86/1.42 ((~hskp28) | c2_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[393, 387])).
% 1.86/1.42 tff(395,plain,
% 1.86/1.42 ((~hskp28) | c2_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[394, 387])).
% 1.86/1.42 tff(396,plain,
% 1.86/1.42 ((~hskp28) | c2_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[395, 387])).
% 1.86/1.42 tff(397,plain,
% 1.86/1.42 (c2_1(a1092)),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[396, 375])).
% 1.86/1.42 tff(398,plain,
% 1.86/1.42 (((~hskp28) | c0_1(a1092)) <=> ((~hskp28) | c0_1(a1092))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(399,axiom,((~hskp28) | c0_1(a1092)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.86/1.42 tff(400,plain,
% 1.86/1.42 ((~hskp28) | c0_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[399, 398])).
% 1.86/1.42 tff(401,plain,
% 1.86/1.42 ((~hskp28) | c0_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[400, 398])).
% 1.86/1.42 tff(402,plain,
% 1.86/1.42 ((~hskp28) | c0_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[401, 398])).
% 1.86/1.42 tff(403,plain,
% 1.86/1.42 ((~hskp28) | c0_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[402, 398])).
% 1.86/1.42 tff(404,plain,
% 1.86/1.42 ((~hskp28) | c0_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[403, 398])).
% 1.86/1.42 tff(405,plain,
% 1.86/1.42 ((~hskp28) | c0_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[404, 398])).
% 1.86/1.42 tff(406,plain,
% 1.86/1.42 ((~hskp28) | c0_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[405, 398])).
% 1.86/1.42 tff(407,plain,
% 1.86/1.42 ((~hskp28) | c0_1(a1092)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[406, 398])).
% 1.86/1.42 tff(408,plain,
% 1.86/1.42 (c0_1(a1092)),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[407, 375])).
% 1.86/1.42 tff(409,assumption,(c3_1(a1109)), introduced(assumption)).
% 1.86/1.42 tff(410,assumption,(c1_1(a1109)), introduced(assumption)).
% 1.86/1.42 tff(411,assumption,(c0_1(a1109)), introduced(assumption)).
% 1.86/1.42 tff(412,plain,
% 1.86/1.42 ((ndr1_0 | (~hskp0)) <=> (ndr1_0 | (~hskp0))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(413,plain,
% 1.86/1.42 (((~hskp0) | ndr1_0) <=> (ndr1_0 | (~hskp0))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(414,axiom,((~hskp0) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.86/1.42 tff(415,plain,
% 1.86/1.42 (ndr1_0 | (~hskp0)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.86/1.42 tff(416,plain,
% 1.86/1.42 (ndr1_0 | (~hskp0)),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[415, 412])).
% 1.86/1.42 tff(417,plain,
% 1.86/1.42 (ndr1_0),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[416, 117])).
% 1.86/1.42 tff(418,plain,
% 1.86/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(419,plain,
% 1.86/1.42 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085)) <=> (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(420,plain,
% 1.86/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 1.86/1.42 inference(monotonicity,[status(thm)],[419])).
% 1.86/1.42 tff(421,plain,
% 1.86/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.86/1.42 inference(transitivity,[status(thm)],[420, 418])).
% 1.86/1.42 tff(422,plain,
% 1.86/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))),
% 1.86/1.42 inference(quant_inst,[status(thm)],[])).
% 1.86/1.42 tff(423,plain,
% 1.86/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.86/1.42 tff(424,plain,
% 1.86/1.42 ($false),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[423, 417, 411, 410, 409, 408, 397, 386, 91, 12, 11, 374])).
% 1.86/1.42 tff(425,plain,((~hskp28) | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 1.86/1.42 tff(426,plain,
% 1.86/1.42 ($false),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[425, 364, 353, 12, 91, 342, 313, 11])).
% 1.86/1.42 tff(427,plain,((~c0_1(a1097)) | c0_1(a1085) | c2_1(a1085) | c1_1(a1085) | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.86/1.42 tff(428,plain,
% 1.86/1.42 (~c0_1(a1097)),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[427, 91, 12, 11, 57])).
% 1.86/1.42 tff(429,plain,
% 1.86/1.42 (^[U: $i] : refl((hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.86/1.42 inference(bind,[status(th)],[])).
% 1.86/1.42 tff(430,plain,
% 1.86/1.42 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.42 inference(quant_intro,[status(thm)],[429])).
% 1.86/1.42 tff(431,plain,
% 1.86/1.42 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(432,plain,
% 1.86/1.42 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp2) <=> ((hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp2))), rewrite(((hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.86/1.42 inference(bind,[status(th)],[])).
% 1.86/1.42 tff(433,plain,
% 1.86/1.42 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp2) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.42 inference(quant_intro,[status(thm)],[432])).
% 1.86/1.42 tff(434,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 1.86/1.42 tff(435,plain,
% 1.86/1.42 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.86/1.42 tff(436,plain,
% 1.86/1.42 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[435, 431])).
% 1.86/1.42 tff(437,plain,(
% 1.86/1.42 ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.42 inference(skolemize,[status(sab)],[436])).
% 1.86/1.42 tff(438,plain,
% 1.86/1.42 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[437, 430])).
% 1.86/1.42 tff(439,plain,
% 1.86/1.42 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(440,plain,
% 1.86/1.42 ((hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097))) <=> (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(441,plain,
% 1.86/1.42 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 1.86/1.42 inference(monotonicity,[status(thm)],[440])).
% 1.86/1.42 tff(442,plain,
% 1.86/1.42 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.42 inference(transitivity,[status(thm)],[441, 439])).
% 1.86/1.42 tff(443,plain,
% 1.86/1.42 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))),
% 1.86/1.42 inference(quant_inst,[status(thm)],[])).
% 1.86/1.42 tff(444,plain,
% 1.86/1.42 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[443, 442])).
% 1.86/1.42 tff(445,plain,
% 1.86/1.42 (hskp2 | c0_1(a1097)),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[444, 186, 57, 294, 334, 438])).
% 1.86/1.42 tff(446,plain,
% 1.86/1.42 (hskp2),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[445, 428])).
% 1.86/1.42 tff(447,plain,
% 1.86/1.42 (((~hskp2) | (~c3_1(a1082))) <=> ((~hskp2) | (~c3_1(a1082)))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(448,plain,
% 1.86/1.42 (((~c3_1(a1082)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a1082)))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(449,axiom,((~c3_1(a1082)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.86/1.42 tff(450,plain,
% 1.86/1.42 ((~hskp2) | (~c3_1(a1082))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[449, 448])).
% 1.86/1.42 tff(451,plain,
% 1.86/1.42 ((~hskp2) | (~c3_1(a1082))),
% 1.86/1.42 inference(modus_ponens,[status(thm)],[450, 447])).
% 1.86/1.42 tff(452,plain,
% 1.86/1.42 (~c3_1(a1082)),
% 1.86/1.42 inference(unit_resolution,[status(thm)],[451, 446])).
% 1.86/1.42 tff(453,assumption,(~hskp1), introduced(assumption)).
% 1.86/1.42 tff(454,assumption,(~c3_1(a1085)), introduced(assumption)).
% 1.86/1.42 tff(455,plain,
% 1.86/1.42 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.86/1.42 inference(bind,[status(th)],[])).
% 1.86/1.42 tff(456,plain,
% 1.86/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.42 inference(quant_intro,[status(thm)],[455])).
% 1.86/1.42 tff(457,plain,
% 1.86/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.42 inference(rewrite,[status(thm)],[])).
% 1.86/1.42 tff(458,plain,
% 1.86/1.42 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.86/1.43 inference(bind,[status(th)],[])).
% 1.86/1.43 tff(459,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.43 inference(quant_intro,[status(thm)],[458])).
% 1.86/1.43 tff(460,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.86/1.43 tff(461,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.43 inference(modus_ponens,[status(thm)],[460, 459])).
% 1.86/1.43 tff(462,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.43 inference(modus_ponens,[status(thm)],[461, 457])).
% 1.86/1.43 tff(463,plain,(
% 1.86/1.43 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.43 inference(skolemize,[status(sab)],[462])).
% 1.86/1.43 tff(464,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.86/1.43 inference(modus_ponens,[status(thm)],[463, 456])).
% 1.86/1.43 tff(465,plain,
% 1.86/1.43 (hskp14),
% 1.86/1.43 inference(unit_resolution,[status(thm)],[275, 417, 267, 206, 90, 69])).
% 1.86/1.43 tff(466,assumption,(~c3_1(a1080)), introduced(assumption)).
% 1.86/1.43 tff(467,plain,
% 1.86/1.43 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.86/1.43 inference(bind,[status(th)],[])).
% 1.86/1.43 tff(468,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.86/1.43 inference(quant_intro,[status(thm)],[467])).
% 1.86/1.43 tff(469,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.86/1.43 inference(rewrite,[status(thm)],[])).
% 1.86/1.43 tff(470,plain,
% 1.86/1.43 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.86/1.43 inference(bind,[status(th)],[])).
% 1.86/1.43 tff(471,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.86/1.43 inference(quant_intro,[status(thm)],[470])).
% 1.86/1.43 tff(472,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.86/1.43 tff(473,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.86/1.43 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.86/1.43 tff(474,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.86/1.43 inference(modus_ponens,[status(thm)],[473, 469])).
% 1.86/1.43 tff(475,plain,(
% 1.86/1.43 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.86/1.43 inference(skolemize,[status(sab)],[474])).
% 1.86/1.43 tff(476,plain,
% 1.86/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.86/1.43 inference(modus_ponens,[status(thm)],[475, 468])).
% 1.86/1.43 tff(477,assumption,(hskp14), introduced(assumption)).
% 1.86/1.43 tff(478,plain,
% 1.86/1.43 (~c2_1(a1097)),
% 1.86/1.43 inference(unit_resolution,[status(thm)],[282, 477])).
% 1.86/1.43 tff(479,plain,
% 1.86/1.43 (c3_1(a1097)),
% 1.86/1.43 inference(unit_resolution,[status(thm)],[333, 477])).
% 1.86/1.43 tff(480,plain,
% 1.86/1.43 (c1_1(a1097)),
% 1.86/1.43 inference(unit_resolution,[status(thm)],[293, 477])).
% 1.86/1.43 tff(481,plain,
% 1.86/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.43 inference(rewrite,[status(thm)],[])).
% 1.86/1.43 tff(482,plain,
% 1.86/1.43 (((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085)) <=> (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.43 inference(rewrite,[status(thm)],[])).
% 1.86/1.43 tff(483,plain,
% 1.86/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 1.86/1.43 inference(monotonicity,[status(thm)],[482])).
% 1.86/1.43 tff(484,plain,
% 1.86/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.86/1.43 inference(transitivity,[status(thm)],[483, 481])).
% 1.86/1.43 tff(485,plain,
% 1.86/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))),
% 1.86/1.43 inference(quant_inst,[status(thm)],[])).
% 1.86/1.43 tff(486,plain,
% 1.86/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 1.86/1.43 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.86/1.43 tff(487,plain,
% 1.86/1.43 ($false),
% 1.86/1.43 inference(unit_resolution,[status(thm)],[486, 207, 480, 479, 206, 478, 12, 11, 69, 476, 466, 454])).
% 1.86/1.43 tff(488,plain,((~hskp14) | (~ndr1_0) | (~c1_1(a1080)) | c0_1(a1085) | c1_1(a1085) | c2_1(a1080) | c3_1(a1080) | c3_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 1.86/1.43 tff(489,plain,
% 1.86/1.43 (c3_1(a1080)),
% 1.86/1.43 inference(unit_resolution,[status(thm)],[488, 454, 206, 12, 11, 69, 417, 465])).
% 1.86/1.43 tff(490,plain,
% 1.86/1.43 (^[U: $i] : refl((hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.86/1.43 inference(bind,[status(th)],[])).
% 1.86/1.43 tff(491,plain,
% 1.86/1.43 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.43 inference(quant_intro,[status(thm)],[490])).
% 1.86/1.43 tff(492,plain,
% 1.86/1.43 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.43 inference(rewrite,[status(thm)],[])).
% 1.86/1.43 tff(493,plain,
% 1.86/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp30))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) | hskp18) <=> ((hskp30 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp30 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) | hskp18) <=> (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.86/1.44 inference(bind,[status(th)],[])).
% 1.86/1.44 tff(494,plain,
% 1.86/1.44 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) | hskp18) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.44 inference(quant_intro,[status(thm)],[493])).
% 1.86/1.44 tff(495,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp30) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.86/1.44 tff(496,plain,
% 1.86/1.44 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.44 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.86/1.44 tff(497,plain,
% 1.86/1.44 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.44 inference(modus_ponens,[status(thm)],[496, 492])).
% 1.86/1.44 tff(498,plain,(
% 1.86/1.44 ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.44 inference(skolemize,[status(sab)],[497])).
% 1.86/1.44 tff(499,plain,
% 1.86/1.44 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.86/1.44 inference(modus_ponens,[status(thm)],[498, 491])).
% 1.86/1.44 tff(500,plain,
% 1.86/1.44 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 1.86/1.44 inference(rewrite,[status(thm)],[])).
% 1.86/1.44 tff(501,plain,
% 1.86/1.44 ((hskp30 | hskp18 | (~ndr1_0) | c0_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080))) <=> (hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 1.86/1.44 inference(rewrite,[status(thm)],[])).
% 1.86/1.44 tff(502,plain,
% 1.86/1.44 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080))))),
% 1.86/1.44 inference(monotonicity,[status(thm)],[501])).
% 1.86/1.44 tff(503,plain,
% 1.86/1.44 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 1.86/1.44 inference(transitivity,[status(thm)],[502, 500])).
% 1.86/1.44 tff(504,plain,
% 1.86/1.44 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 1.86/1.44 inference(quant_inst,[status(thm)],[])).
% 1.86/1.44 tff(505,plain,
% 1.86/1.44 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080))),
% 1.86/1.44 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.86/1.44 tff(506,plain,
% 1.86/1.44 (hskp30 | hskp18 | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080))),
% 1.86/1.44 inference(unit_resolution,[status(thm)],[505, 90, 499])).
% 1.86/1.44 tff(507,plain,
% 1.86/1.44 (hskp30),
% 1.86/1.44 inference(unit_resolution,[status(thm)],[506, 489, 267, 206, 417])).
% 1.93/1.44 tff(508,plain,
% 1.93/1.44 (c3_1(a1109)),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[363, 507])).
% 1.93/1.44 tff(509,plain,
% 1.93/1.44 (c1_1(a1109)),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[312, 507])).
% 1.93/1.44 tff(510,plain,
% 1.93/1.44 (c0_1(a1109)),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[352, 507])).
% 1.93/1.44 tff(511,assumption,(c2_1(a1109)), introduced(assumption)).
% 1.93/1.44 tff(512,plain,
% 1.93/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.93/1.44 inference(rewrite,[status(thm)],[])).
% 1.93/1.44 tff(513,plain,
% 1.93/1.44 (((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085)) <=> (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.93/1.44 inference(rewrite,[status(thm)],[])).
% 1.93/1.44 tff(514,plain,
% 1.93/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))))),
% 1.93/1.44 inference(monotonicity,[status(thm)],[513])).
% 1.93/1.44 tff(515,plain,
% 1.93/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.93/1.44 inference(transitivity,[status(thm)],[514, 512])).
% 1.93/1.44 tff(516,plain,
% 1.93/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))),
% 1.93/1.44 inference(quant_inst,[status(thm)],[])).
% 1.93/1.44 tff(517,plain,
% 1.93/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[516, 515])).
% 1.93/1.44 tff(518,plain,
% 1.93/1.44 ($false),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[517, 417, 411, 410, 409, 91, 12, 11, 374, 511])).
% 1.93/1.44 tff(519,plain,((~c2_1(a1109)) | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.44 tff(520,plain,
% 1.93/1.44 (~c2_1(a1109)),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[519, 510, 509, 508, 91, 12, 11])).
% 1.93/1.44 tff(521,plain,
% 1.93/1.44 (~hskp28),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[425, 510, 509, 508, 91, 12, 11])).
% 1.93/1.44 tff(522,plain,
% 1.93/1.44 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109))),
% 1.93/1.44 inference(rewrite,[status(thm)],[])).
% 1.93/1.44 tff(523,plain,
% 1.93/1.44 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a1109) | (~c3_1(a1109)) | (~c0_1(a1109))) <=> (hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109))),
% 1.93/1.44 inference(rewrite,[status(thm)],[])).
% 1.93/1.44 tff(524,plain,
% 1.93/1.44 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1109) | (~c3_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109)))),
% 1.93/1.44 inference(monotonicity,[status(thm)],[523])).
% 1.93/1.44 tff(525,plain,
% 1.93/1.44 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1109) | (~c3_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109))),
% 1.93/1.44 inference(transitivity,[status(thm)],[524, 522])).
% 1.93/1.44 tff(526,plain,
% 1.93/1.44 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1109) | (~c3_1(a1109)) | (~c0_1(a1109)))),
% 1.93/1.44 inference(quant_inst,[status(thm)],[])).
% 1.93/1.44 tff(527,plain,
% 1.93/1.44 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | (~ndr1_0) | (~c3_1(a1109)) | (~c0_1(a1109)) | c2_1(a1109)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[526, 525])).
% 1.93/1.44 tff(528,plain,
% 1.93/1.44 (hskp28 | hskp9 | c2_1(a1109)),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[527, 417, 510, 508, 323])).
% 1.93/1.44 tff(529,plain,
% 1.93/1.44 (hskp9),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[528, 521, 520])).
% 1.93/1.44 tff(530,plain,
% 1.93/1.44 (((~hskp9) | (~c1_1(a1089))) <=> ((~hskp9) | (~c1_1(a1089)))),
% 1.93/1.44 inference(rewrite,[status(thm)],[])).
% 1.93/1.44 tff(531,plain,
% 1.93/1.44 (((~c1_1(a1089)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1089)))),
% 1.93/1.44 inference(rewrite,[status(thm)],[])).
% 1.93/1.44 tff(532,axiom,((~c1_1(a1089)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.93/1.44 tff(533,plain,
% 1.93/1.44 ((~hskp9) | (~c1_1(a1089))),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[532, 531])).
% 1.93/1.44 tff(534,plain,
% 1.93/1.44 ((~hskp9) | (~c1_1(a1089))),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[533, 530])).
% 1.93/1.44 tff(535,plain,
% 1.93/1.44 (~c1_1(a1089)),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[534, 529])).
% 1.93/1.44 tff(536,plain,
% 1.93/1.44 (((~hskp9) | c3_1(a1089)) <=> ((~hskp9) | c3_1(a1089))),
% 1.93/1.44 inference(rewrite,[status(thm)],[])).
% 1.93/1.44 tff(537,axiom,((~hskp9) | c3_1(a1089)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.93/1.44 tff(538,plain,
% 1.93/1.44 ((~hskp9) | c3_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[537, 536])).
% 1.93/1.44 tff(539,plain,
% 1.93/1.44 ((~hskp9) | c3_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[538, 536])).
% 1.93/1.44 tff(540,plain,
% 1.93/1.44 ((~hskp9) | c3_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[539, 536])).
% 1.93/1.44 tff(541,plain,
% 1.93/1.44 ((~hskp9) | c3_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[540, 536])).
% 1.93/1.44 tff(542,plain,
% 1.93/1.44 ((~hskp9) | c3_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[541, 536])).
% 1.93/1.44 tff(543,plain,
% 1.93/1.44 ((~hskp9) | c3_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[542, 536])).
% 1.93/1.44 tff(544,plain,
% 1.93/1.44 ((~hskp9) | c3_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[543, 536])).
% 1.93/1.44 tff(545,plain,
% 1.93/1.44 ((~hskp9) | c3_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[544, 536])).
% 1.93/1.44 tff(546,plain,
% 1.93/1.44 (c3_1(a1089)),
% 1.93/1.44 inference(unit_resolution,[status(thm)],[545, 529])).
% 1.93/1.44 tff(547,plain,
% 1.93/1.44 (((~hskp9) | c2_1(a1089)) <=> ((~hskp9) | c2_1(a1089))),
% 1.93/1.44 inference(rewrite,[status(thm)],[])).
% 1.93/1.44 tff(548,axiom,((~hskp9) | c2_1(a1089)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.93/1.44 tff(549,plain,
% 1.93/1.44 ((~hskp9) | c2_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[548, 547])).
% 1.93/1.44 tff(550,plain,
% 1.93/1.44 ((~hskp9) | c2_1(a1089)),
% 1.93/1.44 inference(modus_ponens,[status(thm)],[549, 547])).
% 1.93/1.45 tff(551,plain,
% 1.93/1.45 ((~hskp9) | c2_1(a1089)),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[550, 547])).
% 1.93/1.45 tff(552,plain,
% 1.93/1.45 ((~hskp9) | c2_1(a1089)),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[551, 547])).
% 1.93/1.45 tff(553,plain,
% 1.93/1.45 ((~hskp9) | c2_1(a1089)),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[552, 547])).
% 1.93/1.45 tff(554,plain,
% 1.93/1.45 ((~hskp9) | c2_1(a1089)),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[553, 547])).
% 1.93/1.45 tff(555,plain,
% 1.93/1.45 ((~hskp9) | c2_1(a1089)),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[554, 547])).
% 1.93/1.45 tff(556,plain,
% 1.93/1.45 ((~hskp9) | c2_1(a1089)),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[555, 547])).
% 1.93/1.45 tff(557,plain,
% 1.93/1.45 (c2_1(a1089)),
% 1.93/1.45 inference(unit_resolution,[status(thm)],[556, 529])).
% 1.93/1.45 tff(558,plain,
% 1.93/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.93/1.45 inference(rewrite,[status(thm)],[])).
% 1.93/1.45 tff(559,plain,
% 1.93/1.45 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1085) | c0_1(a1085) | c3_1(a1085) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085)) <=> (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.93/1.45 inference(rewrite,[status(thm)],[])).
% 1.93/1.45 tff(560,plain,
% 1.93/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1085) | c0_1(a1085) | c3_1(a1085) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 1.93/1.45 inference(monotonicity,[status(thm)],[559])).
% 1.93/1.45 tff(561,plain,
% 1.93/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1085) | c0_1(a1085) | c3_1(a1085) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.93/1.45 inference(transitivity,[status(thm)],[560, 558])).
% 1.93/1.45 tff(562,plain,
% 1.93/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1085) | c0_1(a1085) | c3_1(a1085) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))),
% 1.93/1.45 inference(quant_inst,[status(thm)],[])).
% 1.93/1.45 tff(563,plain,
% 1.93/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | c3_1(a1085) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.93/1.45 tff(564,plain,
% 1.93/1.45 ($false),
% 1.93/1.45 inference(unit_resolution,[status(thm)],[563, 417, 557, 546, 91, 535, 12, 11, 464, 454])).
% 1.93/1.45 tff(565,plain,(c3_1(a1085) | c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | hskp18 | (~c1_1(a1080)) | c0_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.45 tff(566,plain,
% 1.93/1.45 (c3_1(a1085)),
% 1.93/1.45 inference(unit_resolution,[status(thm)],[565, 195, 12, 11, 118, 120, 119, 91])).
% 1.93/1.45 tff(567,plain,
% 1.93/1.45 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.93/1.45 inference(bind,[status(th)],[])).
% 1.93/1.45 tff(568,plain,
% 1.93/1.45 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.93/1.45 inference(quant_intro,[status(thm)],[567])).
% 1.93/1.45 tff(569,plain,
% 1.93/1.45 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.93/1.45 inference(rewrite,[status(thm)],[])).
% 1.93/1.45 tff(570,plain,
% 1.93/1.45 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.93/1.45 inference(bind,[status(th)],[])).
% 1.93/1.45 tff(571,plain,
% 1.93/1.45 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.93/1.45 inference(quant_intro,[status(thm)],[570])).
% 1.93/1.45 tff(572,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.93/1.45 tff(573,plain,
% 1.93/1.45 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.93/1.45 tff(574,plain,
% 1.93/1.45 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[573, 569])).
% 1.93/1.45 tff(575,plain,(
% 1.93/1.45 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.93/1.45 inference(skolemize,[status(sab)],[574])).
% 1.93/1.45 tff(576,plain,
% 1.93/1.45 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[575, 568])).
% 1.93/1.45 tff(577,plain,
% 1.93/1.45 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 1.93/1.45 inference(rewrite,[status(thm)],[])).
% 1.93/1.45 tff(578,plain,
% 1.93/1.45 ((hskp1 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)) | c2_1(a1085) | c1_1(a1085) | (~c3_1(a1085))) <=> (hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 1.93/1.45 inference(rewrite,[status(thm)],[])).
% 1.93/1.45 tff(579,plain,
% 1.93/1.45 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)) | c2_1(a1085) | c1_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097))))),
% 1.93/1.45 inference(monotonicity,[status(thm)],[578])).
% 1.93/1.45 tff(580,plain,
% 1.93/1.45 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)) | c2_1(a1085) | c1_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097)))),
% 1.93/1.45 inference(transitivity,[status(thm)],[579, 577])).
% 1.93/1.45 tff(581,plain,
% 1.93/1.45 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1097) | (~c1_1(a1097)) | (~c0_1(a1097)) | c2_1(a1085) | c1_1(a1085) | (~c3_1(a1085)))),
% 1.93/1.45 inference(quant_inst,[status(thm)],[])).
% 1.93/1.45 tff(582,plain,
% 1.93/1.45 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a1085) | c2_1(a1097) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c0_1(a1097)) | (~c1_1(a1097))),
% 1.93/1.45 inference(modus_ponens,[status(thm)],[581, 580])).
% 1.93/1.45 tff(583,plain,
% 1.93/1.45 (hskp1 | (~c0_1(a1097))),
% 1.93/1.45 inference(unit_resolution,[status(thm)],[582, 186, 294, 91, 283, 11, 576, 566])).
% 1.93/1.45 tff(584,plain,
% 1.93/1.45 (~c0_1(a1097)),
% 1.93/1.45 inference(unit_resolution,[status(thm)],[583, 453])).
% 1.93/1.45 tff(585,plain,
% 1.93/1.45 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.93/1.45 inference(rewrite,[status(thm)],[])).
% 1.93/1.45 tff(586,plain,
% 1.93/1.45 ((hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097))) <=> (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.93/1.45 inference(rewrite,[status(thm)],[])).
% 1.93/1.45 tff(587,plain,
% 1.93/1.45 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 1.93/1.46 inference(monotonicity,[status(thm)],[586])).
% 1.93/1.46 tff(588,plain,
% 1.93/1.46 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.93/1.46 inference(transitivity,[status(thm)],[587, 585])).
% 1.93/1.46 tff(589,plain,
% 1.93/1.46 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))),
% 1.93/1.46 inference(quant_inst,[status(thm)],[])).
% 1.93/1.46 tff(590,plain,
% 1.93/1.46 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | (~ndr1_0) | c0_1(a1097) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.93/1.46 tff(591,plain,
% 1.93/1.46 (hskp30 | c0_1(a1097)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[590, 186, 195, 294, 334, 499])).
% 1.93/1.46 tff(592,plain,
% 1.93/1.46 (hskp30),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[591, 584])).
% 1.93/1.46 tff(593,plain,
% 1.93/1.46 (c1_1(a1109)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[312, 592])).
% 1.93/1.46 tff(594,plain,
% 1.93/1.46 (^[U: $i] : refl((hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.93/1.46 inference(bind,[status(th)],[])).
% 1.93/1.46 tff(595,plain,
% 1.93/1.46 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.93/1.46 inference(quant_intro,[status(thm)],[594])).
% 1.93/1.46 tff(596,plain,
% 1.93/1.46 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(597,plain,
% 1.93/1.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) | hskp1) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp1))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp1) <=> (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) | hskp1) <=> (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.93/1.46 inference(bind,[status(th)],[])).
% 1.93/1.46 tff(598,plain,
% 1.93/1.46 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) | hskp1) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.93/1.46 inference(quant_intro,[status(thm)],[597])).
% 1.93/1.46 tff(599,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp28) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.93/1.46 tff(600,plain,
% 1.93/1.46 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[599, 598])).
% 1.93/1.46 tff(601,plain,
% 1.93/1.46 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[600, 596])).
% 1.93/1.46 tff(602,plain,(
% 1.93/1.46 ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.93/1.46 inference(skolemize,[status(sab)],[601])).
% 1.93/1.46 tff(603,plain,
% 1.93/1.46 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[602, 595])).
% 1.93/1.46 tff(604,plain,
% 1.93/1.46 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(605,plain,
% 1.93/1.46 ((hskp28 | hskp1 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085))) <=> (hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(606,plain,
% 1.93/1.46 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085))))),
% 1.93/1.46 inference(monotonicity,[status(thm)],[605])).
% 1.93/1.46 tff(607,plain,
% 1.93/1.46 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)))),
% 1.93/1.46 inference(transitivity,[status(thm)],[606, 604])).
% 1.93/1.46 tff(608,plain,
% 1.93/1.46 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))),
% 1.93/1.46 inference(quant_inst,[status(thm)],[])).
% 1.93/1.46 tff(609,plain,
% 1.93/1.46 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.93/1.46 tff(610,plain,
% 1.93/1.46 (hskp28 | hskp1 | c0_1(a1085) | (~c3_1(a1085))),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[609, 186, 11, 603])).
% 1.93/1.46 tff(611,plain,
% 1.93/1.46 (hskp28),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[610, 453, 12, 566])).
% 1.93/1.46 tff(612,plain,
% 1.93/1.46 (c0_1(a1109)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[352, 592])).
% 1.93/1.46 tff(613,plain,
% 1.93/1.46 (c3_1(a1109)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[363, 592])).
% 1.93/1.46 tff(614,plain,
% 1.93/1.46 ($false),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[425, 613, 612, 12, 91, 611, 593, 11])).
% 1.93/1.46 tff(615,plain,(hskp1 | c0_1(a1085) | c2_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.46 tff(616,plain,
% 1.93/1.46 (hskp1),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[615, 91, 12, 11])).
% 1.93/1.46 tff(617,plain,
% 1.93/1.46 (((~hskp2) | (~c0_1(a1082))) <=> ((~hskp2) | (~c0_1(a1082)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(618,plain,
% 1.93/1.46 (((~c0_1(a1082)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1082)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(619,axiom,((~c0_1(a1082)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.93/1.46 tff(620,plain,
% 1.93/1.46 ((~hskp2) | (~c0_1(a1082))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[619, 618])).
% 1.93/1.46 tff(621,plain,
% 1.93/1.46 ((~hskp2) | (~c0_1(a1082))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[620, 617])).
% 1.93/1.46 tff(622,plain,
% 1.93/1.46 (~c0_1(a1082)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[621, 446])).
% 1.93/1.46 tff(623,plain,
% 1.93/1.46 (((~hskp2) | (~c2_1(a1082))) <=> ((~hskp2) | (~c2_1(a1082)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(624,plain,
% 1.93/1.46 (((~c2_1(a1082)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1082)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(625,axiom,((~c2_1(a1082)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.93/1.46 tff(626,plain,
% 1.93/1.46 ((~hskp2) | (~c2_1(a1082))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.93/1.46 tff(627,plain,
% 1.93/1.46 ((~hskp2) | (~c2_1(a1082))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[626, 623])).
% 1.93/1.46 tff(628,plain,
% 1.93/1.46 (~c2_1(a1082)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[627, 446])).
% 1.93/1.46 tff(629,assumption,(~c2_1(a1082)), introduced(assumption)).
% 1.93/1.46 tff(630,assumption,(~c3_1(a1082)), introduced(assumption)).
% 1.93/1.46 tff(631,assumption,(~c0_1(a1082)), introduced(assumption)).
% 1.93/1.46 tff(632,assumption,(hskp1), introduced(assumption)).
% 1.93/1.46 tff(633,plain,
% 1.93/1.46 (((~hskp1) | (~c0_1(a1081))) <=> ((~hskp1) | (~c0_1(a1081)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(634,plain,
% 1.93/1.46 (((~c0_1(a1081)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1081)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(635,axiom,((~c0_1(a1081)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.93/1.46 tff(636,plain,
% 1.93/1.46 ((~hskp1) | (~c0_1(a1081))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.93/1.46 tff(637,plain,
% 1.93/1.46 ((~hskp1) | (~c0_1(a1081))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[636, 633])).
% 1.93/1.46 tff(638,plain,
% 1.93/1.46 (~c0_1(a1081)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[637, 632])).
% 1.93/1.46 tff(639,plain,
% 1.93/1.46 (((~hskp1) | (~c1_1(a1081))) <=> ((~hskp1) | (~c1_1(a1081)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(640,plain,
% 1.93/1.46 (((~c1_1(a1081)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1081)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(641,axiom,((~c1_1(a1081)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.93/1.46 tff(642,plain,
% 1.93/1.46 ((~hskp1) | (~c1_1(a1081))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[641, 640])).
% 1.93/1.46 tff(643,plain,
% 1.93/1.46 ((~hskp1) | (~c1_1(a1081))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[642, 639])).
% 1.93/1.46 tff(644,plain,
% 1.93/1.46 (~c1_1(a1081)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[643, 632])).
% 1.93/1.46 tff(645,assumption,(~c1_1(a1081)), introduced(assumption)).
% 1.93/1.46 tff(646,assumption,(~c0_1(a1081)), introduced(assumption)).
% 1.93/1.46 tff(647,plain,
% 1.93/1.46 (ndr1_0),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[416, 122])).
% 1.93/1.46 tff(648,assumption,(~hskp30), introduced(assumption)).
% 1.93/1.46 tff(649,plain,
% 1.93/1.46 (~c3_1(a1080)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[506, 648, 267, 206, 647])).
% 1.93/1.46 tff(650,plain,
% 1.93/1.46 (hskp14),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[275, 647, 267, 206, 90, 69])).
% 1.93/1.46 tff(651,plain,
% 1.93/1.46 (~c2_1(a1097)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[282, 650])).
% 1.93/1.46 tff(652,plain,
% 1.93/1.46 (c3_1(a1097)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[333, 650])).
% 1.93/1.46 tff(653,plain,
% 1.93/1.46 (c1_1(a1097)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[293, 650])).
% 1.93/1.46 tff(654,plain,
% 1.93/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(655,plain,
% 1.93/1.46 (((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081)) <=> (c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(656,plain,
% 1.93/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 1.93/1.46 inference(monotonicity,[status(thm)],[655])).
% 1.93/1.46 tff(657,plain,
% 1.93/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.93/1.46 inference(transitivity,[status(thm)],[656, 654])).
% 1.93/1.46 tff(658,plain,
% 1.93/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))),
% 1.93/1.46 inference(quant_inst,[status(thm)],[])).
% 1.93/1.46 tff(659,plain,
% 1.93/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[658, 657])).
% 1.93/1.46 tff(660,plain,
% 1.93/1.46 (c3_1(a1081) | c3_1(a1080)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[659, 647, 653, 652, 206, 651, 646, 645, 69, 476])).
% 1.93/1.46 tff(661,plain,
% 1.93/1.46 (c3_1(a1081)),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[660, 649])).
% 1.93/1.46 tff(662,plain,
% 1.93/1.46 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.93/1.46 inference(bind,[status(th)],[])).
% 1.93/1.46 tff(663,plain,
% 1.93/1.46 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.93/1.46 inference(quant_intro,[status(thm)],[662])).
% 1.93/1.46 tff(664,plain,
% 1.93/1.46 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(665,plain,
% 1.93/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.93/1.47 inference(bind,[status(th)],[])).
% 1.93/1.47 tff(666,plain,
% 1.93/1.47 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.93/1.47 inference(quant_intro,[status(thm)],[665])).
% 1.93/1.47 tff(667,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.93/1.47 tff(668,plain,
% 1.93/1.47 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.93/1.47 tff(669,plain,
% 1.93/1.47 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[668, 664])).
% 1.93/1.47 tff(670,plain,(
% 1.93/1.47 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.93/1.47 inference(skolemize,[status(sab)],[669])).
% 1.93/1.47 tff(671,plain,
% 1.93/1.47 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[670, 663])).
% 1.93/1.47 tff(672,plain,
% 1.93/1.47 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081)))),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(673,plain,
% 1.93/1.47 ((hskp5 | (~ndr1_0) | c1_1(a1081) | (~c2_1(a1081)) | (~c3_1(a1081)) | c1_1(a1081) | c0_1(a1081) | (~c2_1(a1081))) <=> (hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081)))),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(674,plain,
% 1.93/1.47 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1081) | (~c2_1(a1081)) | (~c3_1(a1081)) | c1_1(a1081) | c0_1(a1081) | (~c2_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081))))),
% 1.93/1.47 inference(monotonicity,[status(thm)],[673])).
% 1.93/1.47 tff(675,plain,
% 1.93/1.47 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1081) | (~c2_1(a1081)) | (~c3_1(a1081)) | c1_1(a1081) | c0_1(a1081) | (~c2_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081)))),
% 1.93/1.47 inference(transitivity,[status(thm)],[674, 672])).
% 1.93/1.47 tff(676,plain,
% 1.93/1.47 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1081) | (~c2_1(a1081)) | (~c3_1(a1081)) | c1_1(a1081) | c0_1(a1081) | (~c2_1(a1081)))),
% 1.96/1.47 inference(quant_inst,[status(thm)],[])).
% 1.96/1.47 tff(677,plain,
% 1.96/1.47 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081))),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[676, 675])).
% 1.96/1.47 tff(678,plain,
% 1.96/1.47 (hskp5 | c0_1(a1081) | (~ndr1_0) | (~c2_1(a1081)) | (~c3_1(a1081))),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[677, 645, 671])).
% 1.96/1.47 tff(679,plain,
% 1.96/1.47 (~c2_1(a1081)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[678, 661, 121, 646, 647])).
% 1.96/1.47 tff(680,plain,
% 1.96/1.47 (hskp30 | c0_1(a1097)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[590, 647, 267, 653, 652, 499])).
% 1.96/1.47 tff(681,plain,
% 1.96/1.47 (c0_1(a1097)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[680, 648])).
% 1.96/1.47 tff(682,plain,
% 1.96/1.47 (hskp30 | hskp9 | (~c0_1(a1097))),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[300, 647, 653, 651, 102])).
% 1.96/1.47 tff(683,plain,
% 1.96/1.47 (hskp9),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[682, 681, 648])).
% 1.96/1.47 tff(684,plain,
% 1.96/1.47 (~c1_1(a1089)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[534, 683])).
% 1.96/1.47 tff(685,plain,
% 1.96/1.47 (c3_1(a1089)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[545, 683])).
% 1.96/1.47 tff(686,plain,
% 1.96/1.47 (c2_1(a1089)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[556, 683])).
% 1.96/1.47 tff(687,plain,
% 1.96/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(688,plain,
% 1.96/1.47 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1081) | c1_1(a1081) | c0_1(a1081)) <=> (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(689,plain,
% 1.96/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1081) | c1_1(a1081) | c0_1(a1081))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 1.96/1.47 inference(monotonicity,[status(thm)],[688])).
% 1.96/1.47 tff(690,plain,
% 1.96/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1081) | c1_1(a1081) | c0_1(a1081))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.47 inference(transitivity,[status(thm)],[689, 687])).
% 1.96/1.47 tff(691,plain,
% 1.96/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1081) | c1_1(a1081) | c0_1(a1081))),
% 1.96/1.47 inference(quant_inst,[status(thm)],[])).
% 1.96/1.47 tff(692,plain,
% 1.96/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | c2_1(a1081) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[691, 690])).
% 1.96/1.47 tff(693,plain,
% 1.96/1.47 ($false),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[692, 647, 686, 685, 684, 631, 629, 630, 646, 645, 464, 679])).
% 1.96/1.47 tff(694,plain,(hskp30 | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | hskp5 | (~c1_1(a1080)) | c2_1(a1080) | hskp18 | c0_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.47 tff(695,plain,
% 1.96/1.47 (hskp30),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[694, 132, 629, 630, 646, 645, 631, 121, 69, 267, 90])).
% 1.96/1.47 tff(696,plain,
% 1.96/1.47 (c3_1(a1109)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[363, 695])).
% 1.96/1.47 tff(697,plain,
% 1.96/1.47 (c1_1(a1109)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[312, 695])).
% 1.96/1.47 tff(698,plain,
% 1.96/1.47 (c0_1(a1109)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[352, 695])).
% 1.96/1.47 tff(699,assumption,(hskp11), introduced(assumption)).
% 1.96/1.47 tff(700,plain,
% 1.96/1.47 (((~hskp11) | (~c3_1(a1091))) <=> ((~hskp11) | (~c3_1(a1091)))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(701,plain,
% 1.96/1.47 (((~c3_1(a1091)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a1091)))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(702,axiom,((~c3_1(a1091)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.96/1.47 tff(703,plain,
% 1.96/1.47 ((~hskp11) | (~c3_1(a1091))),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[702, 701])).
% 1.96/1.47 tff(704,plain,
% 1.96/1.47 ((~hskp11) | (~c3_1(a1091))),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[703, 700])).
% 1.96/1.47 tff(705,plain,
% 1.96/1.47 (~c3_1(a1091)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[704, 699])).
% 1.96/1.47 tff(706,plain,
% 1.96/1.47 (((~hskp11) | (~c0_1(a1091))) <=> ((~hskp11) | (~c0_1(a1091)))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(707,plain,
% 1.96/1.47 (((~c0_1(a1091)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a1091)))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(708,axiom,((~c0_1(a1091)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.96/1.47 tff(709,plain,
% 1.96/1.47 ((~hskp11) | (~c0_1(a1091))),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[708, 707])).
% 1.96/1.47 tff(710,plain,
% 1.96/1.47 ((~hskp11) | (~c0_1(a1091))),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[709, 706])).
% 1.96/1.47 tff(711,plain,
% 1.96/1.47 (~c0_1(a1091)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[710, 699])).
% 1.96/1.47 tff(712,plain,
% 1.96/1.47 (((~hskp11) | c2_1(a1091)) <=> ((~hskp11) | c2_1(a1091))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(713,axiom,((~hskp11) | c2_1(a1091)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.96/1.47 tff(714,plain,
% 1.96/1.47 ((~hskp11) | c2_1(a1091)),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[713, 712])).
% 1.96/1.47 tff(715,plain,
% 1.96/1.47 ((~hskp11) | c2_1(a1091)),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[714, 712])).
% 1.96/1.47 tff(716,plain,
% 1.96/1.47 ((~hskp11) | c2_1(a1091)),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[715, 712])).
% 1.96/1.47 tff(717,plain,
% 1.96/1.47 ((~hskp11) | c2_1(a1091)),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[716, 712])).
% 1.96/1.47 tff(718,plain,
% 1.96/1.47 ((~hskp11) | c2_1(a1091)),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[717, 712])).
% 1.96/1.47 tff(719,plain,
% 1.96/1.47 ((~hskp11) | c2_1(a1091)),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[718, 712])).
% 1.96/1.47 tff(720,plain,
% 1.96/1.47 ((~hskp11) | c2_1(a1091)),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[719, 712])).
% 1.96/1.47 tff(721,plain,
% 1.96/1.47 ((~hskp11) | c2_1(a1091)),
% 1.96/1.47 inference(modus_ponens,[status(thm)],[720, 712])).
% 1.96/1.47 tff(722,plain,
% 1.96/1.47 (c2_1(a1091)),
% 1.96/1.47 inference(unit_resolution,[status(thm)],[721, 699])).
% 1.96/1.47 tff(723,plain,
% 1.96/1.47 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(724,plain,
% 1.96/1.47 ((hskp18 | (~ndr1_0) | c0_1(a1091) | c3_1(a1091) | (~c2_1(a1091))) <=> (hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)))),
% 1.96/1.47 inference(rewrite,[status(thm)],[])).
% 1.96/1.47 tff(725,plain,
% 1.96/1.47 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1091) | c3_1(a1091) | (~c2_1(a1091)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091))))),
% 1.96/1.48 inference(monotonicity,[status(thm)],[724])).
% 1.96/1.48 tff(726,plain,
% 1.96/1.48 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1091) | c3_1(a1091) | (~c2_1(a1091)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)))),
% 1.96/1.48 inference(transitivity,[status(thm)],[725, 723])).
% 1.96/1.48 tff(727,plain,
% 1.96/1.48 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1091) | c3_1(a1091) | (~c2_1(a1091)))),
% 1.96/1.48 inference(quant_inst,[status(thm)],[])).
% 1.96/1.48 tff(728,plain,
% 1.96/1.48 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091))),
% 1.96/1.48 inference(modus_ponens,[status(thm)],[727, 726])).
% 1.96/1.48 tff(729,plain,
% 1.96/1.48 ($false),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[728, 207, 267, 722, 711, 705, 260])).
% 1.96/1.48 tff(730,plain,((~hskp11) | (~ndr1_0) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.96/1.48 tff(731,plain,
% 1.96/1.48 (~hskp11),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[730, 647, 267])).
% 1.96/1.48 tff(732,plain,
% 1.96/1.48 (hskp14),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[275, 647, 267, 132, 90, 69])).
% 1.96/1.48 tff(733,plain,
% 1.96/1.48 (~c2_1(a1097)),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[282, 732])).
% 1.96/1.48 tff(734,plain,
% 1.96/1.48 (c3_1(a1097)),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[333, 732])).
% 1.96/1.48 tff(735,plain,
% 1.96/1.48 (c1_1(a1097)),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[293, 732])).
% 1.96/1.48 tff(736,plain,
% 1.96/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.96/1.48 inference(rewrite,[status(thm)],[])).
% 1.96/1.48 tff(737,plain,
% 1.96/1.48 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.96/1.48 inference(rewrite,[status(thm)],[])).
% 1.96/1.48 tff(738,plain,
% 1.96/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 1.96/1.48 inference(monotonicity,[status(thm)],[737])).
% 1.96/1.48 tff(739,plain,
% 1.96/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.96/1.48 inference(transitivity,[status(thm)],[738, 736])).
% 1.96/1.48 tff(740,plain,
% 1.96/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 1.96/1.48 inference(quant_inst,[status(thm)],[])).
% 1.96/1.48 tff(741,plain,
% 1.96/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 1.96/1.48 inference(modus_ponens,[status(thm)],[740, 739])).
% 1.96/1.48 tff(742,plain,
% 1.96/1.48 (c1_1(a1082)),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[741, 207, 411, 410, 409, 408, 397, 386, 631, 629, 374])).
% 1.96/1.48 tff(743,plain,
% 1.96/1.48 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.96/1.48 inference(bind,[status(th)],[])).
% 1.96/1.48 tff(744,plain,
% 1.96/1.48 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.48 inference(quant_intro,[status(thm)],[743])).
% 1.96/1.48 tff(745,plain,
% 1.96/1.48 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.48 inference(rewrite,[status(thm)],[])).
% 1.96/1.48 tff(746,plain,
% 1.96/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.96/1.48 inference(bind,[status(th)],[])).
% 1.96/1.48 tff(747,plain,
% 1.96/1.48 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.48 inference(quant_intro,[status(thm)],[746])).
% 1.96/1.48 tff(748,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.96/1.48 tff(749,plain,
% 1.96/1.48 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.48 inference(modus_ponens,[status(thm)],[748, 747])).
% 1.96/1.48 tff(750,plain,
% 1.96/1.48 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.48 inference(modus_ponens,[status(thm)],[749, 745])).
% 1.96/1.48 tff(751,plain,(
% 1.96/1.48 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.48 inference(skolemize,[status(sab)],[750])).
% 1.96/1.48 tff(752,plain,
% 1.96/1.48 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.96/1.48 inference(modus_ponens,[status(thm)],[751, 744])).
% 1.96/1.48 tff(753,assumption,(~hskp11), introduced(assumption)).
% 1.96/1.48 tff(754,plain,
% 1.96/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.96/1.48 inference(rewrite,[status(thm)],[])).
% 1.96/1.48 tff(755,plain,
% 1.96/1.48 ((hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1081) | c0_1(a1081) | (~c3_1(a1081))) <=> (hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.96/1.48 inference(rewrite,[status(thm)],[])).
% 1.96/1.48 tff(756,plain,
% 1.96/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1081) | c0_1(a1081) | (~c3_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 1.96/1.48 inference(monotonicity,[status(thm)],[755])).
% 1.96/1.48 tff(757,plain,
% 1.96/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1081) | c0_1(a1081) | (~c3_1(a1081)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 1.96/1.48 inference(transitivity,[status(thm)],[756, 754])).
% 1.96/1.48 tff(758,plain,
% 1.96/1.48 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1081) | c0_1(a1081) | (~c3_1(a1081)))),
% 1.96/1.48 inference(quant_inst,[status(thm)],[])).
% 1.96/1.48 tff(759,plain,
% 1.96/1.48 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c3_1(a1081)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 1.96/1.48 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.96/1.48 tff(760,plain,
% 1.96/1.48 (~c3_1(a1081)),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[759, 207, 753, 408, 397, 386, 646, 645, 752])).
% 1.96/1.48 tff(761,assumption,(~c2_1(a1097)), introduced(assumption)).
% 1.96/1.48 tff(762,assumption,(c3_1(a1097)), introduced(assumption)).
% 1.96/1.48 tff(763,assumption,(c1_1(a1097)), introduced(assumption)).
% 1.96/1.48 tff(764,plain,
% 1.96/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.96/1.48 inference(rewrite,[status(thm)],[])).
% 1.96/1.48 tff(765,plain,
% 1.96/1.48 (((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1082) | c3_1(a1082) | (~c1_1(a1082)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081)) <=> (c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.96/1.48 inference(rewrite,[status(thm)],[])).
% 1.96/1.48 tff(766,plain,
% 1.96/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1082) | c3_1(a1082) | (~c1_1(a1082)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 1.96/1.48 inference(monotonicity,[status(thm)],[765])).
% 1.96/1.48 tff(767,plain,
% 1.96/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1082) | c3_1(a1082) | (~c1_1(a1082)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 1.96/1.48 inference(transitivity,[status(thm)],[766, 764])).
% 1.96/1.48 tff(768,plain,
% 1.96/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1082) | c3_1(a1082) | (~c1_1(a1082)) | c1_1(a1081) | c0_1(a1081) | c3_1(a1081))),
% 1.96/1.48 inference(quant_inst,[status(thm)],[])).
% 1.96/1.48 tff(769,plain,
% 1.96/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1081) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | (~ndr1_0) | (~c1_1(a1082)) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 1.96/1.48 inference(modus_ponens,[status(thm)],[768, 767])).
% 1.96/1.48 tff(770,plain,
% 1.96/1.48 (c3_1(a1081) | (~c1_1(a1082))),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[769, 207, 763, 762, 761, 629, 630, 646, 645, 476])).
% 1.96/1.48 tff(771,plain,
% 1.96/1.48 ($false),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[770, 760, 742])).
% 1.96/1.48 tff(772,plain,((~hskp28) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | c2_1(a1097) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | hskp11 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | c0_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.48 tff(773,plain,
% 1.96/1.48 (~hskp28),
% 1.96/1.48 inference(unit_resolution,[status(thm)],[772, 647, 735, 734, 733, 629, 630, 646, 645, 731, 698, 697, 696, 631])).
% 1.96/1.49 tff(774,assumption,(~hskp28), introduced(assumption)).
% 1.96/1.49 tff(775,plain,
% 1.96/1.49 (hskp28 | hskp9 | c2_1(a1109)),
% 1.96/1.49 inference(unit_resolution,[status(thm)],[527, 647, 411, 409, 323])).
% 1.96/1.49 tff(776,plain,
% 1.96/1.49 (c2_1(a1109)),
% 1.96/1.49 inference(unit_resolution,[status(thm)],[775, 774, 57])).
% 1.96/1.49 tff(777,plain,
% 1.96/1.49 (^[U: $i] : refl((hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.96/1.49 inference(bind,[status(th)],[])).
% 1.96/1.49 tff(778,plain,
% 1.96/1.49 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.96/1.49 inference(quant_intro,[status(thm)],[777])).
% 1.96/1.49 tff(779,plain,
% 1.96/1.49 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(780,plain,
% 1.96/1.49 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) | hskp13) <=> ((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) | hskp13) <=> (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.96/1.49 inference(bind,[status(th)],[])).
% 1.96/1.49 tff(781,plain,
% 1.96/1.49 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) | hskp13) <=> ![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.96/1.49 inference(quant_intro,[status(thm)],[780])).
% 1.96/1.49 tff(782,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp5) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.96/1.49 tff(783,plain,
% 1.96/1.49 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[782, 781])).
% 1.96/1.49 tff(784,plain,
% 1.96/1.49 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[783, 779])).
% 1.96/1.49 tff(785,plain,(
% 1.96/1.49 ![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.96/1.49 inference(skolemize,[status(sab)],[784])).
% 1.96/1.49 tff(786,plain,
% 1.96/1.49 (![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[785, 778])).
% 1.96/1.49 tff(787,plain,
% 1.96/1.49 (((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))) <=> ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(788,plain,
% 1.96/1.49 ((hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109))) <=> (hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(789,plain,
% 1.96/1.49 (((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))))),
% 1.96/1.49 inference(monotonicity,[status(thm)],[788])).
% 1.96/1.49 tff(790,plain,
% 1.96/1.49 (((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.96/1.49 inference(transitivity,[status(thm)],[789, 787])).
% 1.96/1.49 tff(791,plain,
% 1.96/1.49 ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 1.96/1.49 inference(quant_inst,[status(thm)],[])).
% 1.96/1.49 tff(792,plain,
% 1.96/1.49 ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[791, 790])).
% 1.96/1.49 tff(793,plain,
% 1.96/1.49 (hskp13 | (~c2_1(a1109))),
% 1.96/1.49 inference(unit_resolution,[status(thm)],[792, 121, 647, 411, 410, 786])).
% 1.96/1.49 tff(794,plain,
% 1.96/1.49 (hskp13),
% 1.96/1.49 inference(unit_resolution,[status(thm)],[793, 776])).
% 1.96/1.49 tff(795,plain,
% 1.96/1.49 (((~hskp13) | (~c2_1(a1095))) <=> ((~hskp13) | (~c2_1(a1095)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(796,plain,
% 1.96/1.49 (((~c2_1(a1095)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1095)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(797,axiom,((~c2_1(a1095)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.96/1.49 tff(798,plain,
% 1.96/1.49 ((~hskp13) | (~c2_1(a1095))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[797, 796])).
% 1.96/1.49 tff(799,plain,
% 1.96/1.49 ((~hskp13) | (~c2_1(a1095))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[798, 795])).
% 1.96/1.49 tff(800,plain,
% 1.96/1.49 (~c2_1(a1095)),
% 1.96/1.49 inference(unit_resolution,[status(thm)],[799, 794])).
% 1.96/1.49 tff(801,plain,
% 1.96/1.49 (((~hskp13) | (~c1_1(a1095))) <=> ((~hskp13) | (~c1_1(a1095)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(802,plain,
% 1.96/1.49 (((~c1_1(a1095)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1095)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(803,axiom,((~c1_1(a1095)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.96/1.49 tff(804,plain,
% 1.96/1.49 ((~hskp13) | (~c1_1(a1095))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.96/1.49 tff(805,plain,
% 1.96/1.49 ((~hskp13) | (~c1_1(a1095))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[804, 801])).
% 1.96/1.49 tff(806,plain,
% 1.96/1.49 (~c1_1(a1095)),
% 1.96/1.49 inference(unit_resolution,[status(thm)],[805, 794])).
% 1.96/1.49 tff(807,plain,
% 1.96/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(808,plain,
% 1.96/1.49 (((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1095) | c1_1(a1095) | c0_1(a1095)) <=> (c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(809,plain,
% 1.96/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1095) | c1_1(a1095) | c0_1(a1095))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))))),
% 1.96/1.49 inference(monotonicity,[status(thm)],[808])).
% 1.96/1.49 tff(810,plain,
% 1.96/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1095) | c1_1(a1095) | c0_1(a1095))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109)))),
% 1.96/1.49 inference(transitivity,[status(thm)],[809, 807])).
% 1.96/1.49 tff(811,plain,
% 1.96/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1095) | c1_1(a1095) | c0_1(a1095))),
% 1.96/1.49 inference(quant_inst,[status(thm)],[])).
% 1.96/1.49 tff(812,plain,
% 1.96/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1095) | c2_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c2_1(a1109))),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[811, 810])).
% 1.96/1.49 tff(813,plain,
% 1.96/1.49 (c0_1(a1095)),
% 1.96/1.49 inference(unit_resolution,[status(thm)],[812, 647, 411, 410, 409, 806, 800, 374, 776])).
% 1.96/1.49 tff(814,plain,
% 1.96/1.49 (((~hskp13) | c3_1(a1095)) <=> ((~hskp13) | c3_1(a1095))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(815,axiom,((~hskp13) | c3_1(a1095)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.96/1.49 tff(816,plain,
% 1.96/1.49 ((~hskp13) | c3_1(a1095)),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[815, 814])).
% 1.96/1.49 tff(817,plain,
% 1.96/1.49 ((~hskp13) | c3_1(a1095)),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[816, 814])).
% 1.96/1.49 tff(818,plain,
% 1.96/1.49 ((~hskp13) | c3_1(a1095)),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[817, 814])).
% 1.96/1.49 tff(819,plain,
% 1.96/1.49 ((~hskp13) | c3_1(a1095)),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[818, 814])).
% 1.96/1.49 tff(820,plain,
% 1.96/1.49 ((~hskp13) | c3_1(a1095)),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[819, 814])).
% 1.96/1.49 tff(821,plain,
% 1.96/1.49 ((~hskp13) | c3_1(a1095)),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[820, 814])).
% 1.96/1.49 tff(822,plain,
% 1.96/1.49 ((~hskp13) | c3_1(a1095)),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[821, 814])).
% 1.96/1.49 tff(823,plain,
% 1.96/1.49 ((~hskp13) | c3_1(a1095)),
% 1.96/1.49 inference(modus_ponens,[status(thm)],[822, 814])).
% 1.96/1.49 tff(824,plain,
% 1.96/1.49 (c3_1(a1095)),
% 1.96/1.49 inference(unit_resolution,[status(thm)],[823, 794])).
% 1.96/1.49 tff(825,plain,
% 1.96/1.49 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(826,plain,
% 1.96/1.49 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095))) <=> (hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 1.96/1.49 inference(rewrite,[status(thm)],[])).
% 1.96/1.49 tff(827,plain,
% 1.96/1.49 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095))))),
% 1.96/1.49 inference(monotonicity,[status(thm)],[826])).
% 1.96/1.49 tff(828,plain,
% 1.96/1.49 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 1.96/1.50 inference(transitivity,[status(thm)],[827, 825])).
% 1.96/1.50 tff(829,plain,
% 1.96/1.50 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)))),
% 1.96/1.50 inference(quant_inst,[status(thm)],[])).
% 1.96/1.50 tff(830,plain,
% 1.96/1.50 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.96/1.50 tff(831,plain,
% 1.96/1.50 ($false),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[830, 647, 774, 57, 824, 800, 323, 813])).
% 1.96/1.50 tff(832,plain,(hskp28 | hskp9 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.96/1.50 tff(833,plain,
% 1.96/1.50 (hskp9),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[832, 773, 698, 697, 696, 121])).
% 1.96/1.50 tff(834,plain,
% 1.96/1.50 (~c1_1(a1089)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[534, 833])).
% 1.96/1.50 tff(835,plain,
% 1.96/1.50 (c3_1(a1089)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[545, 833])).
% 1.96/1.50 tff(836,plain,
% 1.96/1.50 (c2_1(a1089)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[556, 833])).
% 1.96/1.50 tff(837,plain,
% 1.96/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(838,plain,
% 1.96/1.50 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(839,plain,
% 1.96/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 1.96/1.50 inference(monotonicity,[status(thm)],[838])).
% 1.96/1.50 tff(840,plain,
% 1.96/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.50 inference(transitivity,[status(thm)],[839, 837])).
% 1.96/1.50 tff(841,plain,
% 1.96/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 1.96/1.50 inference(quant_inst,[status(thm)],[])).
% 1.96/1.50 tff(842,plain,
% 1.96/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[841, 840])).
% 1.96/1.50 tff(843,plain,
% 1.96/1.50 (c1_1(a1082)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[842, 647, 836, 835, 834, 631, 629, 630, 464])).
% 1.96/1.50 tff(844,plain,
% 1.96/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(845,plain,
% 1.96/1.50 ((hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082))) <=> (hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(846,plain,
% 1.96/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089))))),
% 1.96/1.50 inference(monotonicity,[status(thm)],[845])).
% 1.96/1.50 tff(847,plain,
% 1.96/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 1.96/1.50 inference(transitivity,[status(thm)],[846, 844])).
% 1.96/1.50 tff(848,plain,
% 1.96/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))),
% 1.96/1.50 inference(quant_inst,[status(thm)],[])).
% 1.96/1.50 tff(849,plain,
% 1.96/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c3_1(a1089)) | (~c0_1(a1089))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[848, 847])).
% 1.96/1.50 tff(850,plain,
% 1.96/1.50 (~c0_1(a1089)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[849, 121, 647, 835, 834, 631, 629, 10, 843])).
% 1.96/1.50 tff(851,plain,
% 1.96/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(852,plain,
% 1.96/1.50 ((hskp5 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089))) <=> (hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(853,plain,
% 1.96/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 1.96/1.50 inference(monotonicity,[status(thm)],[852])).
% 1.96/1.50 tff(854,plain,
% 1.96/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.50 inference(transitivity,[status(thm)],[853, 851])).
% 1.96/1.50 tff(855,plain,
% 1.96/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))),
% 1.96/1.50 inference(quant_inst,[status(thm)],[])).
% 1.96/1.50 tff(856,plain,
% 1.96/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[855, 854])).
% 1.96/1.50 tff(857,plain,
% 1.96/1.50 ($false),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[856, 121, 647, 836, 835, 834, 671, 850])).
% 1.96/1.50 tff(858,plain,(hskp5 | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | hskp18 | c2_1(a1080) | c0_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.50 tff(859,plain,
% 1.96/1.50 (hskp5),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[858, 267, 629, 630, 646, 645, 631, 69, 90])).
% 1.96/1.50 tff(860,plain,
% 1.96/1.50 (((~hskp5) | (~c1_1(a1085))) <=> ((~hskp5) | (~c1_1(a1085)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(861,plain,
% 1.96/1.50 (((~c1_1(a1085)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a1085)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(862,axiom,((~c1_1(a1085)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.96/1.50 tff(863,plain,
% 1.96/1.50 ((~hskp5) | (~c1_1(a1085))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.96/1.50 tff(864,plain,
% 1.96/1.50 ((~hskp5) | (~c1_1(a1085))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[863, 860])).
% 1.96/1.50 tff(865,plain,
% 1.96/1.50 (~c1_1(a1085)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[864, 859])).
% 1.96/1.50 tff(866,plain,
% 1.96/1.50 (((~hskp5) | (~c0_1(a1085))) <=> ((~hskp5) | (~c0_1(a1085)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(867,plain,
% 1.96/1.50 (((~c0_1(a1085)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1085)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(868,axiom,((~c0_1(a1085)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.96/1.50 tff(869,plain,
% 1.96/1.50 ((~hskp5) | (~c0_1(a1085))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.96/1.50 tff(870,plain,
% 1.96/1.50 ((~hskp5) | (~c0_1(a1085))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[869, 866])).
% 1.96/1.50 tff(871,plain,
% 1.96/1.50 (~c0_1(a1085)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[870, 859])).
% 1.96/1.50 tff(872,plain,
% 1.96/1.50 (c2_1(a1085)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[112, 859])).
% 1.96/1.50 tff(873,plain,
% 1.96/1.50 ((ndr1_0 | (~hskp5)) <=> (ndr1_0 | (~hskp5))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(874,plain,
% 1.96/1.50 (((~hskp5) | ndr1_0) <=> (ndr1_0 | (~hskp5))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(875,axiom,((~hskp5) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 1.96/1.50 tff(876,plain,
% 1.96/1.50 (ndr1_0 | (~hskp5)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[875, 874])).
% 1.96/1.50 tff(877,plain,
% 1.96/1.50 (ndr1_0 | (~hskp5)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[876, 873])).
% 1.96/1.50 tff(878,plain,
% 1.96/1.50 (ndr1_0),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[877, 859])).
% 1.96/1.50 tff(879,plain,
% 1.96/1.50 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(880,plain,
% 1.96/1.50 ((hskp18 | (~ndr1_0) | c0_1(a1085) | c3_1(a1085) | (~c2_1(a1085))) <=> (hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(881,plain,
% 1.96/1.50 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1085) | c3_1(a1085) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[880])).
% 1.96/1.51 tff(882,plain,
% 1.96/1.51 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1085) | c3_1(a1085) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 1.96/1.51 inference(transitivity,[status(thm)],[881, 879])).
% 1.96/1.51 tff(883,plain,
% 1.96/1.51 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1085) | c3_1(a1085) | (~c2_1(a1085)))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(884,plain,
% 1.96/1.51 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.96/1.51 tff(885,plain,
% 1.96/1.51 (c3_1(a1085)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[884, 878, 267, 872, 871, 260])).
% 1.96/1.51 tff(886,plain,
% 1.96/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(887,plain,
% 1.96/1.51 (((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(888,plain,
% 1.96/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[887])).
% 1.96/1.51 tff(889,plain,
% 1.96/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.51 inference(transitivity,[status(thm)],[888, 886])).
% 1.96/1.51 tff(890,plain,
% 1.96/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(891,plain,
% 1.96/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[890, 889])).
% 1.96/1.51 tff(892,plain,
% 1.96/1.51 (c1_1(a1082)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[891, 878, 872, 865, 631, 629, 630, 464, 885])).
% 1.96/1.51 tff(893,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(894,plain,
% 1.96/1.51 ((hskp3 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(895,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085))))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[894])).
% 1.96/1.51 tff(896,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085)))),
% 1.96/1.51 inference(transitivity,[status(thm)],[895, 893])).
% 1.96/1.51 tff(897,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(898,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c2_1(a1085))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.96/1.51 tff(899,plain,
% 1.96/1.51 (hskp3),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[898, 878, 872, 871, 865, 631, 629, 22, 892])).
% 1.96/1.51 tff(900,plain,
% 1.96/1.51 (((~hskp3) | (~c2_1(a1083))) <=> ((~hskp3) | (~c2_1(a1083)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(901,plain,
% 1.96/1.51 (((~c2_1(a1083)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1083)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(902,axiom,((~c2_1(a1083)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.96/1.51 tff(903,plain,
% 1.96/1.51 ((~hskp3) | (~c2_1(a1083))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[902, 901])).
% 1.96/1.51 tff(904,plain,
% 1.96/1.51 ((~hskp3) | (~c2_1(a1083))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[903, 900])).
% 1.96/1.51 tff(905,plain,
% 1.96/1.51 (~c2_1(a1083)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[904, 899])).
% 1.96/1.51 tff(906,plain,
% 1.96/1.51 (((~hskp3) | (~c3_1(a1083))) <=> ((~hskp3) | (~c3_1(a1083)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(907,plain,
% 1.96/1.51 (((~c3_1(a1083)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1083)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(908,axiom,((~c3_1(a1083)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.96/1.51 tff(909,plain,
% 1.96/1.51 ((~hskp3) | (~c3_1(a1083))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[908, 907])).
% 1.96/1.51 tff(910,plain,
% 1.96/1.51 ((~hskp3) | (~c3_1(a1083))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[909, 906])).
% 1.96/1.51 tff(911,plain,
% 1.96/1.51 (~c3_1(a1083)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[910, 899])).
% 1.96/1.51 tff(912,assumption,(~c1_1(a1080)), introduced(assumption)).
% 1.96/1.51 tff(913,plain,
% 1.96/1.51 (~hskp0),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[45, 912])).
% 1.96/1.51 tff(914,plain,
% 1.96/1.51 (hskp5),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[116, 913])).
% 1.96/1.51 tff(915,plain,
% 1.96/1.51 (ndr1_0),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[877, 914])).
% 1.96/1.51 tff(916,plain,
% 1.96/1.51 (c2_1(a1085)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[112, 914])).
% 1.96/1.51 tff(917,plain,
% 1.96/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(918,plain,
% 1.96/1.51 (((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080)) <=> (c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(919,plain,
% 1.96/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[918])).
% 1.96/1.51 tff(920,plain,
% 1.96/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.51 inference(transitivity,[status(thm)],[919, 917])).
% 1.96/1.51 tff(921,plain,
% 1.96/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(922,plain,
% 1.96/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[921, 920])).
% 1.96/1.51 tff(923,plain,
% 1.96/1.51 (c1_1(a1080) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[922, 11, 631, 629, 630, 90, 69, 464])).
% 1.96/1.51 tff(924,plain,
% 1.96/1.51 (~c3_1(a1085)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[923, 916, 912, 915])).
% 1.96/1.51 tff(925,plain,
% 1.96/1.51 ((~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[884, 267, 12, 260])).
% 1.96/1.51 tff(926,plain,
% 1.96/1.51 ($false),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[925, 924, 916, 915])).
% 1.96/1.51 tff(927,plain,(c1_1(a1080) | hskp18 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.51 tff(928,plain,
% 1.96/1.51 (c1_1(a1080)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[927, 12, 267, 11, 631, 629, 630, 90, 69])).
% 1.96/1.51 tff(929,plain,
% 1.96/1.51 ((ndr1_0 | (~hskp30)) <=> (ndr1_0 | (~hskp30))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(930,plain,
% 1.96/1.52 (((~hskp30) | ndr1_0) <=> (ndr1_0 | (~hskp30))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(931,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 1.96/1.52 tff(932,plain,
% 1.96/1.52 (ndr1_0 | (~hskp30)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[931, 930])).
% 1.96/1.52 tff(933,plain,
% 1.96/1.52 (ndr1_0 | (~hskp30)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[932, 929])).
% 1.96/1.52 tff(934,plain,
% 1.96/1.52 (~hskp30),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[933, 155])).
% 1.96/1.52 tff(935,plain,
% 1.96/1.52 (~hskp5),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[877, 155])).
% 1.96/1.52 tff(936,plain,
% 1.96/1.52 ($false),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[694, 935, 934, 629, 630, 646, 645, 631, 206, 69, 267, 90])).
% 1.96/1.52 tff(937,plain,(ndr1_0 | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | (~c1_1(a1080)) | c2_1(a1080) | hskp18 | c0_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.52 tff(938,plain,
% 1.96/1.52 (ndr1_0),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[937, 928, 630, 646, 645, 631, 629, 69, 267, 90])).
% 1.96/1.52 tff(939,plain,
% 1.96/1.52 (hskp30),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[694, 113, 629, 630, 646, 645, 631, 928, 69, 267, 90])).
% 1.96/1.52 tff(940,plain,
% 1.96/1.52 (c0_1(a1109)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[352, 939])).
% 1.96/1.52 tff(941,plain,
% 1.96/1.52 (c1_1(a1109)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[312, 939])).
% 1.96/1.52 tff(942,plain,
% 1.96/1.52 (c3_1(a1109)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[363, 939])).
% 1.96/1.52 tff(943,plain,
% 1.96/1.52 (~c2_1(a1109)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[519, 942, 941, 940, 91, 12, 11])).
% 1.96/1.52 tff(944,plain,
% 1.96/1.52 (~hskp28),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[425, 940, 941, 942, 91, 12, 11])).
% 1.96/1.52 tff(945,plain,
% 1.96/1.52 (hskp9),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[527, 417, 944, 940, 942, 323, 943])).
% 1.96/1.52 tff(946,plain,
% 1.96/1.52 (~c1_1(a1089)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[534, 945])).
% 1.96/1.52 tff(947,plain,
% 1.96/1.52 (c3_1(a1089)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[545, 945])).
% 1.96/1.52 tff(948,plain,
% 1.96/1.52 (c2_1(a1089)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[556, 945])).
% 1.96/1.52 tff(949,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(950,plain,
% 1.96/1.52 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085)) <=> (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(951,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[950])).
% 1.96/1.52 tff(952,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[951, 949])).
% 1.96/1.52 tff(953,plain,
% 1.96/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1082) | c0_1(a1082) | c3_1(a1082) | c2_1(a1085) | c1_1(a1085) | c0_1(a1085))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(954,plain,
% 1.96/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1085) | c1_1(a1089) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[953, 952])).
% 1.96/1.52 tff(955,plain,
% 1.96/1.52 ($false),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[954, 417, 948, 947, 91, 946, 12, 11, 631, 629, 630, 464])).
% 1.96/1.52 tff(956,plain,(c2_1(a1085) | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c2_1(a1080) | hskp18 | c0_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.52 tff(957,plain,
% 1.96/1.52 (c2_1(a1085)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[956, 12, 11, 631, 629, 630, 646, 645, 69, 267, 90])).
% 1.96/1.52 tff(958,plain,
% 1.96/1.52 (c3_1(a1085)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[925, 938, 957])).
% 1.96/1.52 tff(959,plain,
% 1.96/1.52 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(960,plain,
% 1.96/1.52 ((hskp19 | (~ndr1_0) | c0_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085))) <=> (hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(961,plain,
% 1.96/1.52 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[960])).
% 1.96/1.52 tff(962,plain,
% 1.96/1.52 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[961, 959])).
% 1.96/1.52 tff(963,plain,
% 1.96/1.52 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(964,plain,
% 1.96/1.52 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[963, 962])).
% 1.96/1.52 tff(965,plain,
% 1.96/1.52 (hskp19 | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[964, 12, 79])).
% 1.96/1.52 tff(966,plain,
% 1.96/1.52 (hskp19),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[965, 958, 957, 938])).
% 1.96/1.52 tff(967,plain,
% 1.96/1.52 (((~hskp19) | (~c2_1(a1113))) <=> ((~hskp19) | (~c2_1(a1113)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(968,plain,
% 1.96/1.52 (((~c2_1(a1113)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1113)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(969,axiom,((~c2_1(a1113)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.96/1.52 tff(970,plain,
% 1.96/1.52 ((~hskp19) | (~c2_1(a1113))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[969, 968])).
% 1.96/1.52 tff(971,plain,
% 1.96/1.52 ((~hskp19) | (~c2_1(a1113))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[970, 967])).
% 1.96/1.52 tff(972,plain,
% 1.96/1.52 (~c2_1(a1113)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[971, 966])).
% 1.96/1.52 tff(973,plain,
% 1.96/1.52 (((~hskp19) | c1_1(a1113)) <=> ((~hskp19) | c1_1(a1113))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(974,axiom,((~hskp19) | c1_1(a1113)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.96/1.52 tff(975,plain,
% 1.96/1.52 ((~hskp19) | c1_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[974, 973])).
% 1.96/1.52 tff(976,plain,
% 1.96/1.52 ((~hskp19) | c1_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[975, 973])).
% 1.96/1.52 tff(977,plain,
% 1.96/1.52 ((~hskp19) | c1_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[976, 973])).
% 1.96/1.52 tff(978,plain,
% 1.96/1.52 ((~hskp19) | c1_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[977, 973])).
% 1.96/1.52 tff(979,plain,
% 1.96/1.52 ((~hskp19) | c1_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[978, 973])).
% 1.96/1.52 tff(980,plain,
% 1.96/1.52 ((~hskp19) | c1_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[979, 973])).
% 1.96/1.52 tff(981,plain,
% 1.96/1.52 ((~hskp19) | c1_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[980, 973])).
% 1.96/1.52 tff(982,plain,
% 1.96/1.52 ((~hskp19) | c1_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[981, 973])).
% 1.96/1.52 tff(983,plain,
% 1.96/1.52 (c1_1(a1113)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[982, 966])).
% 1.96/1.52 tff(984,plain,
% 1.96/1.52 (((~hskp19) | c0_1(a1113)) <=> ((~hskp19) | c0_1(a1113))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(985,axiom,((~hskp19) | c0_1(a1113)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.96/1.52 tff(986,plain,
% 1.96/1.52 ((~hskp19) | c0_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[985, 984])).
% 1.96/1.52 tff(987,plain,
% 1.96/1.52 ((~hskp19) | c0_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[986, 984])).
% 1.96/1.52 tff(988,plain,
% 1.96/1.52 ((~hskp19) | c0_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[987, 984])).
% 1.96/1.52 tff(989,plain,
% 1.96/1.52 ((~hskp19) | c0_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[988, 984])).
% 1.96/1.52 tff(990,plain,
% 1.96/1.52 ((~hskp19) | c0_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[989, 984])).
% 1.96/1.52 tff(991,plain,
% 1.96/1.52 ((~hskp19) | c0_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[990, 984])).
% 1.96/1.52 tff(992,plain,
% 1.96/1.52 ((~hskp19) | c0_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[991, 984])).
% 1.96/1.52 tff(993,plain,
% 1.96/1.52 ((~hskp19) | c0_1(a1113)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[992, 984])).
% 1.96/1.52 tff(994,plain,
% 1.96/1.52 (c0_1(a1113)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[993, 966])).
% 1.96/1.52 tff(995,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(996,plain,
% 1.96/1.52 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1113) | c3_1(a1113) | (~c0_1(a1113)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(997,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1113) | c3_1(a1113) | (~c0_1(a1113)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[996])).
% 1.96/1.52 tff(998,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1113) | c3_1(a1113) | (~c0_1(a1113)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.02/1.53 inference(transitivity,[status(thm)],[997, 995])).
% 2.02/1.53 tff(999,plain,
% 2.02/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1113) | c3_1(a1113) | (~c0_1(a1113)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.02/1.53 inference(quant_inst,[status(thm)],[])).
% 2.02/1.53 tff(1000,plain,
% 2.02/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1113) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[999, 998])).
% 2.02/1.53 tff(1001,plain,
% 2.02/1.53 (c3_1(a1113)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1000, 938, 994, 983, 957, 972, 12, 11, 67])).
% 2.02/1.53 tff(1002,assumption,(~c3_1(a1083)), introduced(assumption)).
% 2.02/1.53 tff(1003,assumption,(~c2_1(a1083)), introduced(assumption)).
% 2.02/1.53 tff(1004,plain,
% 2.02/1.53 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1005,plain,
% 2.02/1.53 ((hskp21 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085))) <=> (hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1006,plain,
% 2.02/1.53 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 2.02/1.53 inference(monotonicity,[status(thm)],[1005])).
% 2.02/1.53 tff(1007,plain,
% 2.02/1.53 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 2.02/1.53 inference(transitivity,[status(thm)],[1006, 1004])).
% 2.02/1.53 tff(1008,plain,
% 2.02/1.53 ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 2.02/1.53 inference(quant_inst,[status(thm)],[])).
% 2.02/1.53 tff(1009,plain,
% 2.02/1.53 ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 2.02/1.53 tff(1010,plain,
% 2.02/1.53 (hskp21 | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1009, 11, 56])).
% 2.02/1.53 tff(1011,plain,
% 2.02/1.53 (hskp21),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1010, 958, 957, 938])).
% 2.02/1.53 tff(1012,plain,
% 2.02/1.53 (((~hskp21) | (~c3_1(a1120))) <=> ((~hskp21) | (~c3_1(a1120)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1013,plain,
% 2.02/1.53 (((~c3_1(a1120)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a1120)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1014,axiom,((~c3_1(a1120)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 2.02/1.53 tff(1015,plain,
% 2.02/1.53 ((~hskp21) | (~c3_1(a1120))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 2.02/1.53 tff(1016,plain,
% 2.02/1.53 ((~hskp21) | (~c3_1(a1120))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1015, 1012])).
% 2.02/1.53 tff(1017,plain,
% 2.02/1.53 (~c3_1(a1120)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1016, 1011])).
% 2.02/1.53 tff(1018,plain,
% 2.02/1.53 (((~hskp21) | c2_1(a1120)) <=> ((~hskp21) | c2_1(a1120))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1019,axiom,((~hskp21) | c2_1(a1120)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 2.02/1.53 tff(1020,plain,
% 2.02/1.53 ((~hskp21) | c2_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 2.02/1.53 tff(1021,plain,
% 2.02/1.53 ((~hskp21) | c2_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1020, 1018])).
% 2.02/1.53 tff(1022,plain,
% 2.02/1.53 ((~hskp21) | c2_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1021, 1018])).
% 2.02/1.53 tff(1023,plain,
% 2.02/1.53 ((~hskp21) | c2_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1022, 1018])).
% 2.02/1.53 tff(1024,plain,
% 2.02/1.53 ((~hskp21) | c2_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1023, 1018])).
% 2.02/1.53 tff(1025,plain,
% 2.02/1.53 ((~hskp21) | c2_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1024, 1018])).
% 2.02/1.53 tff(1026,plain,
% 2.02/1.53 ((~hskp21) | c2_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1025, 1018])).
% 2.02/1.53 tff(1027,plain,
% 2.02/1.53 ((~hskp21) | c2_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1026, 1018])).
% 2.02/1.53 tff(1028,plain,
% 2.02/1.53 (c2_1(a1120)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1027, 1011])).
% 2.02/1.53 tff(1029,plain,
% 2.02/1.53 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1030,plain,
% 2.02/1.53 ((hskp18 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120))) <=> (hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1031,plain,
% 2.02/1.53 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120))))),
% 2.02/1.53 inference(monotonicity,[status(thm)],[1030])).
% 2.02/1.53 tff(1032,plain,
% 2.02/1.53 (((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 2.02/1.53 inference(transitivity,[status(thm)],[1031, 1029])).
% 2.02/1.53 tff(1033,plain,
% 2.02/1.53 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))),
% 2.02/1.53 inference(quant_inst,[status(thm)],[])).
% 2.02/1.53 tff(1034,plain,
% 2.02/1.53 ((~![U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 2.02/1.53 tff(1035,plain,
% 2.02/1.53 (c0_1(a1120)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1034, 938, 267, 1028, 1017, 260])).
% 2.02/1.53 tff(1036,plain,
% 2.02/1.53 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.02/1.53 inference(bind,[status(th)],[])).
% 2.02/1.53 tff(1037,plain,
% 2.02/1.53 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.02/1.53 inference(quant_intro,[status(thm)],[1036])).
% 2.02/1.53 tff(1038,plain,
% 2.02/1.53 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1039,plain,
% 2.02/1.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.02/1.53 inference(bind,[status(th)],[])).
% 2.02/1.53 tff(1040,plain,
% 2.02/1.53 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.02/1.53 inference(quant_intro,[status(thm)],[1039])).
% 2.02/1.53 tff(1041,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 2.02/1.53 tff(1042,plain,
% 2.02/1.53 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 2.02/1.53 tff(1043,plain,
% 2.02/1.53 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1042, 1038])).
% 2.02/1.53 tff(1044,plain,(
% 2.02/1.53 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.02/1.53 inference(skolemize,[status(sab)],[1043])).
% 2.02/1.53 tff(1045,plain,
% 2.02/1.53 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1044, 1037])).
% 2.02/1.53 tff(1046,plain,
% 2.02/1.53 (((~hskp21) | c1_1(a1120)) <=> ((~hskp21) | c1_1(a1120))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1047,axiom,((~hskp21) | c1_1(a1120)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 2.02/1.53 tff(1048,plain,
% 2.02/1.53 ((~hskp21) | c1_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 2.02/1.53 tff(1049,plain,
% 2.02/1.53 ((~hskp21) | c1_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1048, 1046])).
% 2.02/1.53 tff(1050,plain,
% 2.02/1.53 ((~hskp21) | c1_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1049, 1046])).
% 2.02/1.53 tff(1051,plain,
% 2.02/1.53 ((~hskp21) | c1_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1050, 1046])).
% 2.02/1.53 tff(1052,plain,
% 2.02/1.53 ((~hskp21) | c1_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1051, 1046])).
% 2.02/1.53 tff(1053,plain,
% 2.02/1.53 ((~hskp21) | c1_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1052, 1046])).
% 2.02/1.53 tff(1054,plain,
% 2.02/1.53 ((~hskp21) | c1_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1053, 1046])).
% 2.02/1.53 tff(1055,plain,
% 2.02/1.53 ((~hskp21) | c1_1(a1120)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1054, 1046])).
% 2.02/1.53 tff(1056,plain,
% 2.02/1.53 (c1_1(a1120)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1055, 1011])).
% 2.02/1.53 tff(1057,plain,
% 2.02/1.53 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1058,plain,
% 2.02/1.53 ((hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085))) <=> (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1059,plain,
% 2.02/1.53 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))))),
% 2.02/1.53 inference(monotonicity,[status(thm)],[1058])).
% 2.02/1.53 tff(1060,plain,
% 2.02/1.53 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.02/1.53 inference(transitivity,[status(thm)],[1059, 1057])).
% 2.02/1.53 tff(1061,plain,
% 2.02/1.53 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))),
% 2.02/1.53 inference(quant_inst,[status(thm)],[])).
% 2.02/1.53 tff(1062,plain,
% 2.02/1.53 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 2.02/1.53 tff(1063,plain,
% 2.02/1.53 (hskp10),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1062, 938, 1056, 1028, 12, 11, 1045, 958, 1035])).
% 2.02/1.53 tff(1064,plain,
% 2.02/1.53 (((~hskp10) | (~c3_1(a1090))) <=> ((~hskp10) | (~c3_1(a1090)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1065,plain,
% 2.02/1.53 (((~c3_1(a1090)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a1090)))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(1066,axiom,((~c3_1(a1090)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 2.02/1.53 tff(1067,plain,
% 2.02/1.53 ((~hskp10) | (~c3_1(a1090))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 2.02/1.53 tff(1068,plain,
% 2.02/1.53 ((~hskp10) | (~c3_1(a1090))),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[1067, 1064])).
% 2.02/1.53 tff(1069,plain,
% 2.02/1.53 (~c3_1(a1090)),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[1068, 1063])).
% 2.02/1.53 tff(1070,plain,
% 2.02/1.53 (((~hskp10) | (~c1_1(a1090))) <=> ((~hskp10) | (~c1_1(a1090)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1071,plain,
% 2.02/1.54 (((~c1_1(a1090)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1090)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1072,axiom,((~c1_1(a1090)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 2.02/1.54 tff(1073,plain,
% 2.02/1.54 ((~hskp10) | (~c1_1(a1090))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 2.02/1.54 tff(1074,plain,
% 2.02/1.54 ((~hskp10) | (~c1_1(a1090))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1073, 1070])).
% 2.02/1.54 tff(1075,plain,
% 2.02/1.54 (~c1_1(a1090)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1074, 1063])).
% 2.02/1.54 tff(1076,plain,
% 2.02/1.54 (((~hskp10) | (~c0_1(a1090))) <=> ((~hskp10) | (~c0_1(a1090)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1077,plain,
% 2.02/1.54 (((~c0_1(a1090)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a1090)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1078,axiom,((~c0_1(a1090)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 2.02/1.54 tff(1079,plain,
% 2.02/1.54 ((~hskp10) | (~c0_1(a1090))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 2.02/1.54 tff(1080,plain,
% 2.02/1.54 ((~hskp10) | (~c0_1(a1090))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1079, 1076])).
% 2.02/1.54 tff(1081,plain,
% 2.02/1.54 (~c0_1(a1090)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1080, 1063])).
% 2.02/1.54 tff(1082,plain,
% 2.02/1.54 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1083,plain,
% 2.02/1.54 ((hskp3 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1084,plain,
% 2.02/1.54 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085))))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[1083])).
% 2.02/1.54 tff(1085,plain,
% 2.02/1.54 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.02/1.54 inference(transitivity,[status(thm)],[1084, 1082])).
% 2.02/1.54 tff(1086,plain,
% 2.02/1.54 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(1087,plain,
% 2.02/1.54 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 2.02/1.54 tff(1088,plain,
% 2.02/1.54 (hskp3 | c0_1(a1085) | (~ndr1_0) | (~c1_1(a1080)) | (~c2_1(a1085))),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1087, 11, 90, 69, 22])).
% 2.02/1.54 tff(1089,plain,
% 2.02/1.54 (hskp3),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1088, 938, 928, 957, 12])).
% 2.02/1.54 tff(1090,plain,
% 2.02/1.54 (((~hskp3) | c1_1(a1083)) <=> ((~hskp3) | c1_1(a1083))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1091,axiom,((~hskp3) | c1_1(a1083)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 2.02/1.54 tff(1092,plain,
% 2.02/1.54 ((~hskp3) | c1_1(a1083)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 2.02/1.54 tff(1093,plain,
% 2.02/1.54 ((~hskp3) | c1_1(a1083)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1092, 1090])).
% 2.02/1.54 tff(1094,plain,
% 2.02/1.54 ((~hskp3) | c1_1(a1083)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1093, 1090])).
% 2.02/1.54 tff(1095,plain,
% 2.02/1.54 ((~hskp3) | c1_1(a1083)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1094, 1090])).
% 2.02/1.54 tff(1096,plain,
% 2.02/1.54 ((~hskp3) | c1_1(a1083)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1095, 1090])).
% 2.02/1.54 tff(1097,plain,
% 2.02/1.54 ((~hskp3) | c1_1(a1083)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1096, 1090])).
% 2.02/1.54 tff(1098,plain,
% 2.02/1.54 ((~hskp3) | c1_1(a1083)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1097, 1090])).
% 2.02/1.54 tff(1099,plain,
% 2.02/1.54 ((~hskp3) | c1_1(a1083)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1098, 1090])).
% 2.02/1.54 tff(1100,plain,
% 2.02/1.54 (c1_1(a1083)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1099, 1089])).
% 2.02/1.54 tff(1101,plain,
% 2.02/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1102,plain,
% 2.02/1.54 (((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090)) <=> (c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1103,plain,
% 2.02/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113))))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[1102])).
% 2.02/1.54 tff(1104,plain,
% 2.02/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.02/1.54 inference(transitivity,[status(thm)],[1103, 1101])).
% 2.02/1.54 tff(1105,plain,
% 2.02/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(1106,plain,
% 2.02/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c1_1(a1113)) | (~c3_1(a1113))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 2.02/1.54 tff(1107,plain,
% 2.02/1.54 ($false),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1106, 938, 983, 1100, 972, 1081, 1075, 1069, 1003, 1002, 476, 1001])).
% 2.02/1.54 tff(1108,plain,(c0_1(a1085) | c2_1(a1083) | c3_1(a1083) | c1_1(a1085) | hskp18 | c0_1(a1080) | c2_1(a1080) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.54 tff(1109,plain,
% 2.02/1.54 ($false),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1108, 911, 905, 871, 865, 267, 90, 69, 630, 646, 645, 631, 629])).
% 2.02/1.54 tff(1110,plain,(hskp18 | c0_1(a1080) | c2_1(a1080) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.54 tff(1111,plain,
% 2.02/1.54 ($false),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1110, 644, 638, 69, 267, 631, 630, 90, 629])).
% 2.02/1.54 tff(1112,plain,((~hskp1) | c2_1(a1080) | hskp18 | c0_1(a1082) | c3_1(a1082) | c0_1(a1080) | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.54 tff(1113,plain,
% 2.02/1.54 ($false),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1112, 628, 622, 195, 616, 118, 119, 452])).
% 2.02/1.54 tff(1114,plain,(c2_1(a1085) | hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.54 tff(1115,plain,
% 2.02/1.54 (c2_1(a1085)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1114, 57, 12, 11])).
% 2.02/1.54 tff(1116,plain,
% 2.02/1.54 ((~hskp11) | hskp18),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[730, 186])).
% 2.02/1.54 tff(1117,plain,
% 2.02/1.54 (~hskp11),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1116, 267])).
% 2.02/1.54 tff(1118,plain,
% 2.02/1.54 (hskp18 | (~c2_1(a1085)) | c3_1(a1085)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[884, 186, 12, 260])).
% 2.02/1.54 tff(1119,plain,
% 2.02/1.54 (c3_1(a1085)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[1118, 267, 1115])).
% 2.02/1.54 tff(1120,plain,
% 2.02/1.54 (^[U: $i] : refl((hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(1121,plain,
% 2.02/1.54 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[1120])).
% 2.02/1.54 tff(1122,plain,
% 2.02/1.54 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(1123,plain,
% 2.02/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) | hskp11) <=> ((hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp11))), rewrite(((hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) | hskp11) <=> (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(1124,plain,
% 2.02/1.54 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) | hskp11) <=> ![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[1123])).
% 2.02/1.54 tff(1125,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp9) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 2.02/1.55 tff(1126,plain,
% 2.02/1.55 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 2.02/1.55 tff(1127,plain,
% 2.02/1.55 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1126, 1122])).
% 2.02/1.55 tff(1128,plain,(
% 2.02/1.55 ![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.02/1.55 inference(skolemize,[status(sab)],[1127])).
% 2.02/1.55 tff(1129,plain,
% 2.02/1.55 (![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1128, 1121])).
% 2.02/1.55 tff(1130,plain,
% 2.02/1.55 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1131,plain,
% 2.02/1.55 ((hskp11 | hskp9 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085))) <=> (hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1132,plain,
% 2.02/1.55 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[1131])).
% 2.02/1.55 tff(1133,plain,
% 2.02/1.55 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 2.02/1.55 inference(transitivity,[status(thm)],[1132, 1130])).
% 2.02/1.55 tff(1134,plain,
% 2.02/1.55 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c3_1(a1085)))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(1135,plain,
% 2.02/1.55 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c3_1(a1085))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 2.02/1.55 tff(1136,plain,
% 2.02/1.55 (hskp11 | hskp9 | (~c2_1(a1085)) | (~c3_1(a1085))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[1135, 186, 11, 1129])).
% 2.02/1.55 tff(1137,plain,
% 2.02/1.55 ($false),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[1136, 1119, 1117, 57, 1115])).
% 2.02/1.55 tff(1138,plain,(hskp18 | hskp9 | c1_1(a1085) | c0_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.55 tff(1139,plain,
% 2.02/1.55 (hskp18),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[1138, 57, 11, 12])).
% 2.02/1.55 tff(1140,plain,
% 2.02/1.55 (c0_1(a1103)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[153, 1139])).
% 2.02/1.55 tff(1141,plain,
% 2.02/1.55 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(1142,plain,
% 2.02/1.55 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[1141])).
% 2.02/1.55 tff(1143,plain,
% 2.02/1.55 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1144,plain,
% 2.02/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(1145,plain,
% 2.02/1.55 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[1144])).
% 2.02/1.55 tff(1146,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 2.02/1.55 tff(1147,plain,
% 2.02/1.55 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 2.02/1.55 tff(1148,plain,
% 2.02/1.55 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1147, 1143])).
% 2.02/1.55 tff(1149,plain,(
% 2.02/1.55 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.02/1.55 inference(skolemize,[status(sab)],[1148])).
% 2.02/1.55 tff(1150,plain,
% 2.02/1.55 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1149, 1142])).
% 2.02/1.55 tff(1151,plain,
% 2.02/1.55 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1152,plain,
% 2.02/1.55 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1153,plain,
% 2.02/1.55 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085))))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[1152])).
% 2.02/1.55 tff(1154,plain,
% 2.02/1.55 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)))),
% 2.02/1.55 inference(transitivity,[status(thm)],[1153, 1151])).
% 2.02/1.55 tff(1155,plain,
% 2.02/1.55 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(1156,plain,
% 2.02/1.55 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 2.02/1.55 tff(1157,plain,
% 2.02/1.55 (hskp9 | hskp8 | c0_1(a1085) | (~c2_1(a1085))),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[1156, 186, 11, 1150])).
% 2.02/1.55 tff(1158,plain,
% 2.02/1.55 (hskp8),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[1157, 1115, 57, 12])).
% 2.02/1.55 tff(1159,plain,
% 2.02/1.55 (((~hskp8) | (~c2_1(a1088))) <=> ((~hskp8) | (~c2_1(a1088)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1160,plain,
% 2.02/1.55 (((~c2_1(a1088)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a1088)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1161,axiom,((~c2_1(a1088)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 2.02/1.55 tff(1162,plain,
% 2.02/1.55 ((~hskp8) | (~c2_1(a1088))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 2.02/1.55 tff(1163,plain,
% 2.02/1.55 ((~hskp8) | (~c2_1(a1088))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1162, 1159])).
% 2.02/1.55 tff(1164,plain,
% 2.02/1.55 (~c2_1(a1088)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[1163, 1158])).
% 2.02/1.55 tff(1165,plain,
% 2.02/1.55 (((~hskp8) | c3_1(a1088)) <=> ((~hskp8) | c3_1(a1088))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1166,axiom,((~hskp8) | c3_1(a1088)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 2.02/1.55 tff(1167,plain,
% 2.02/1.55 ((~hskp8) | c3_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 2.02/1.55 tff(1168,plain,
% 2.02/1.55 ((~hskp8) | c3_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1167, 1165])).
% 2.02/1.55 tff(1169,plain,
% 2.02/1.55 ((~hskp8) | c3_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1168, 1165])).
% 2.02/1.55 tff(1170,plain,
% 2.02/1.55 ((~hskp8) | c3_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1169, 1165])).
% 2.02/1.55 tff(1171,plain,
% 2.02/1.55 ((~hskp8) | c3_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1170, 1165])).
% 2.02/1.55 tff(1172,plain,
% 2.02/1.55 ((~hskp8) | c3_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1171, 1165])).
% 2.02/1.55 tff(1173,plain,
% 2.02/1.55 ((~hskp8) | c3_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1172, 1165])).
% 2.02/1.55 tff(1174,plain,
% 2.02/1.55 ((~hskp8) | c3_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1173, 1165])).
% 2.02/1.55 tff(1175,plain,
% 2.02/1.55 (c3_1(a1088)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[1174, 1158])).
% 2.02/1.55 tff(1176,plain,
% 2.02/1.55 (((~hskp8) | c0_1(a1088)) <=> ((~hskp8) | c0_1(a1088))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1177,axiom,((~hskp8) | c0_1(a1088)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 2.02/1.55 tff(1178,plain,
% 2.02/1.55 ((~hskp8) | c0_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 2.02/1.55 tff(1179,plain,
% 2.02/1.55 ((~hskp8) | c0_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1178, 1176])).
% 2.02/1.55 tff(1180,plain,
% 2.02/1.55 ((~hskp8) | c0_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1179, 1176])).
% 2.02/1.55 tff(1181,plain,
% 2.02/1.55 ((~hskp8) | c0_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1180, 1176])).
% 2.02/1.55 tff(1182,plain,
% 2.02/1.55 ((~hskp8) | c0_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1181, 1176])).
% 2.02/1.55 tff(1183,plain,
% 2.02/1.55 ((~hskp8) | c0_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1182, 1176])).
% 2.02/1.55 tff(1184,plain,
% 2.02/1.55 ((~hskp8) | c0_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1183, 1176])).
% 2.02/1.55 tff(1185,plain,
% 2.02/1.55 ((~hskp8) | c0_1(a1088)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[1184, 1176])).
% 2.02/1.55 tff(1186,plain,
% 2.02/1.55 (c0_1(a1088)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[1185, 1158])).
% 2.02/1.55 tff(1187,plain,
% 2.02/1.55 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1188,plain,
% 2.02/1.55 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088))) <=> (hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(1189,plain,
% 2.02/1.55 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088))))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[1188])).
% 2.02/1.55 tff(1190,plain,
% 2.02/1.55 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088)))),
% 2.04/1.55 inference(transitivity,[status(thm)],[1189, 1187])).
% 2.04/1.55 tff(1191,plain,
% 2.04/1.55 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(1192,plain,
% 2.04/1.55 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c3_1(a1088))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 2.04/1.55 tff(1193,plain,
% 2.04/1.55 (hskp28),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[1192, 186, 57, 1186, 1175, 1164, 323])).
% 2.04/1.55 tff(1194,plain,
% 2.04/1.55 (c2_1(a1092)),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[396, 1193])).
% 2.04/1.55 tff(1195,plain,
% 2.04/1.55 (c0_1(a1092)),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[407, 1193])).
% 2.04/1.55 tff(1196,plain,
% 2.04/1.55 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(1197,plain,
% 2.04/1.55 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.55 inference(quant_inst,[status(thm)],[])).
% 2.04/1.55 tff(1198,plain,
% 2.04/1.55 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 2.04/1.55 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 2.04/1.55 tff(1199,plain,
% 2.04/1.55 (hskp14 | c1_1(a1092)),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[1198, 186, 1195, 1194, 205])).
% 2.04/1.55 tff(1200,plain,
% 2.04/1.55 (c1_1(a1092)),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[1199, 208])).
% 2.04/1.55 tff(1201,plain,
% 2.04/1.55 (c3_1(a1092)),
% 2.04/1.55 inference(unit_resolution,[status(thm)],[385, 1193])).
% 2.04/1.55 tff(1202,plain,
% 2.04/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(1203,plain,
% 2.04/1.55 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080)) <=> (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.55 inference(rewrite,[status(thm)],[])).
% 2.04/1.55 tff(1204,plain,
% 2.04/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))))),
% 2.04/1.55 inference(monotonicity,[status(thm)],[1203])).
% 2.04/1.55 tff(1205,plain,
% 2.04/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.56 inference(transitivity,[status(thm)],[1204, 1202])).
% 2.04/1.56 tff(1206,plain,
% 2.04/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))),
% 2.04/1.56 inference(quant_inst,[status(thm)],[])).
% 2.04/1.56 tff(1207,plain,
% 2.04/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 2.04/1.56 tff(1208,plain,
% 2.04/1.56 (c1_1(a1080) | c0_1(a1080) | (~c1_1(a1092))),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[1207, 186, 1195, 1194, 1201, 69, 374])).
% 2.04/1.56 tff(1209,plain,
% 2.04/1.56 (c1_1(a1080)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[1208, 1200, 90])).
% 2.04/1.56 tff(1210,plain,
% 2.04/1.56 (hskp3 | c0_1(a1080) | (~c1_1(a1080))),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[1087, 186, 1115, 12, 11, 69, 22])).
% 2.04/1.56 tff(1211,plain,
% 2.04/1.56 (hskp3),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[1210, 1209, 90])).
% 2.04/1.56 tff(1212,plain,
% 2.04/1.56 (~c3_1(a1083)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[910, 1211])).
% 2.04/1.56 tff(1213,plain,
% 2.04/1.56 (~c2_1(a1083)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[904, 1211])).
% 2.04/1.56 tff(1214,plain,
% 2.04/1.56 (~c1_1(a1103)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[130, 1139])).
% 2.04/1.56 tff(1215,plain,
% 2.04/1.56 (c1_1(a1083)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[1099, 1211])).
% 2.04/1.56 tff(1216,plain,
% 2.04/1.56 (c3_1(a1103)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[142, 1139])).
% 2.04/1.56 tff(1217,plain,
% 2.04/1.56 (hskp15 | hskp14 | c0_1(a1080) | (~c1_1(a1080))),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[224, 186, 69, 218])).
% 2.04/1.56 tff(1218,plain,
% 2.04/1.56 (hskp15),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[1217, 1209, 208, 90])).
% 2.04/1.56 tff(1219,plain,
% 2.04/1.56 (~c1_1(a1098)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[231, 1218])).
% 2.04/1.56 tff(1220,plain,
% 2.04/1.56 (c2_1(a1098)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[242, 1218])).
% 2.04/1.56 tff(1221,plain,
% 2.04/1.56 (~c0_1(a1098)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[249, 186, 208, 1220, 1219, 205])).
% 2.04/1.56 tff(1222,plain,
% 2.04/1.56 (~c3_1(a1098)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[265, 1218])).
% 2.04/1.56 tff(1223,plain,
% 2.04/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(1224,plain,
% 2.04/1.56 (((~ndr1_0) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098)) <=> (c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(1225,plain,
% 2.04/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098)))),
% 2.04/1.56 inference(monotonicity,[status(thm)],[1224])).
% 2.04/1.56 tff(1226,plain,
% 2.04/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098))),
% 2.04/1.56 inference(transitivity,[status(thm)],[1225, 1223])).
% 2.04/1.56 tff(1227,plain,
% 2.04/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))),
% 2.04/1.56 inference(quant_inst,[status(thm)],[])).
% 2.04/1.56 tff(1228,plain,
% 2.04/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1098) | c3_1(a1098) | c2_1(a1083) | c3_1(a1083) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c1_1(a1083)) | c0_1(a1098)),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 2.04/1.56 tff(1229,plain,
% 2.04/1.56 ((~c3_1(a1080)) | c0_1(a1098)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[1228, 186, 1215, 1209, 1219, 1222, 1213, 1212, 69, 476])).
% 2.04/1.56 tff(1230,plain,
% 2.04/1.56 (~c3_1(a1080)),
% 2.04/1.56 inference(unit_resolution,[status(thm)],[1229, 1221])).
% 2.04/1.56 tff(1231,plain,
% 2.04/1.56 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(1232,plain,
% 2.04/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.04/1.56 inference(quant_intro,[status(thm)],[1231])).
% 2.04/1.56 tff(1233,plain,
% 2.04/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(1234,plain,
% 2.04/1.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.04/1.56 inference(bind,[status(th)],[])).
% 2.04/1.56 tff(1235,plain,
% 2.04/1.56 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.04/1.56 inference(quant_intro,[status(thm)],[1234])).
% 2.04/1.56 tff(1236,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 2.04/1.56 tff(1237,plain,
% 2.04/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 2.04/1.56 tff(1238,plain,
% 2.04/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[1237, 1233])).
% 2.04/1.56 tff(1239,plain,(
% 2.04/1.56 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.04/1.56 inference(skolemize,[status(sab)],[1238])).
% 2.04/1.56 tff(1240,plain,
% 2.04/1.56 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.04/1.56 inference(modus_ponens,[status(thm)],[1239, 1232])).
% 2.04/1.56 tff(1241,plain,
% 2.04/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(1242,plain,
% 2.04/1.56 ((hskp4 | (~ndr1_0) | c0_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.04/1.56 inference(rewrite,[status(thm)],[])).
% 2.04/1.56 tff(1243,plain,
% 2.04/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085))))),
% 2.04/1.56 inference(monotonicity,[status(thm)],[1242])).
% 2.04/1.56 tff(1244,plain,
% 2.04/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.04/1.57 inference(transitivity,[status(thm)],[1243, 1241])).
% 2.04/1.57 tff(1245,plain,
% 2.04/1.57 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1080) | c3_1(a1080) | (~c1_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.04/1.57 inference(quant_inst,[status(thm)],[])).
% 2.04/1.57 tff(1246,plain,
% 2.04/1.57 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 2.04/1.57 tff(1247,plain,
% 2.04/1.57 (hskp4 | c3_1(a1080) | (~c1_1(a1080))),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1246, 186, 1115, 12, 11, 90, 1240])).
% 2.04/1.57 tff(1248,plain,
% 2.04/1.57 (hskp4),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1247, 1230, 1209])).
% 2.04/1.57 tff(1249,plain,
% 2.04/1.57 (((~hskp4) | c0_1(a1084)) <=> ((~hskp4) | c0_1(a1084))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1250,axiom,((~hskp4) | c0_1(a1084)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 2.04/1.57 tff(1251,plain,
% 2.04/1.57 ((~hskp4) | c0_1(a1084)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 2.04/1.57 tff(1252,plain,
% 2.04/1.57 ((~hskp4) | c0_1(a1084)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1251, 1249])).
% 2.04/1.57 tff(1253,plain,
% 2.04/1.57 ((~hskp4) | c0_1(a1084)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1252, 1249])).
% 2.04/1.57 tff(1254,plain,
% 2.04/1.57 ((~hskp4) | c0_1(a1084)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1253, 1249])).
% 2.04/1.57 tff(1255,plain,
% 2.04/1.57 ((~hskp4) | c0_1(a1084)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1254, 1249])).
% 2.04/1.57 tff(1256,plain,
% 2.04/1.57 ((~hskp4) | c0_1(a1084)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1255, 1249])).
% 2.04/1.57 tff(1257,plain,
% 2.04/1.57 ((~hskp4) | c0_1(a1084)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1256, 1249])).
% 2.04/1.57 tff(1258,plain,
% 2.04/1.57 ((~hskp4) | c0_1(a1084)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1257, 1249])).
% 2.04/1.57 tff(1259,plain,
% 2.04/1.57 (c0_1(a1084)),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1258, 1248])).
% 2.04/1.57 tff(1260,plain,
% 2.04/1.57 (((~hskp4) | (~c1_1(a1084))) <=> ((~hskp4) | (~c1_1(a1084)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1261,plain,
% 2.04/1.57 (((~c1_1(a1084)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a1084)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1262,axiom,((~c1_1(a1084)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 2.04/1.57 tff(1263,plain,
% 2.04/1.57 ((~hskp4) | (~c1_1(a1084))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 2.04/1.57 tff(1264,plain,
% 2.04/1.57 ((~hskp4) | (~c1_1(a1084))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1263, 1260])).
% 2.04/1.57 tff(1265,plain,
% 2.04/1.57 (~c1_1(a1084)),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1264, 1248])).
% 2.04/1.57 tff(1266,plain,
% 2.04/1.57 (((~hskp4) | (~c3_1(a1084))) <=> ((~hskp4) | (~c3_1(a1084)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1267,plain,
% 2.04/1.57 (((~c3_1(a1084)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1084)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1268,axiom,((~c3_1(a1084)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 2.04/1.57 tff(1269,plain,
% 2.04/1.57 ((~hskp4) | (~c3_1(a1084))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 2.04/1.57 tff(1270,plain,
% 2.04/1.57 ((~hskp4) | (~c3_1(a1084))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1269, 1266])).
% 2.04/1.57 tff(1271,plain,
% 2.04/1.57 (~c3_1(a1084)),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1270, 1248])).
% 2.04/1.57 tff(1272,assumption,(c0_1(a1084)), introduced(assumption)).
% 2.04/1.57 tff(1273,assumption,(~c1_1(a1103)), introduced(assumption)).
% 2.04/1.57 tff(1274,assumption,(c0_1(a1103)), introduced(assumption)).
% 2.04/1.57 tff(1275,plain,
% 2.04/1.57 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1276,plain,
% 2.04/1.57 ((hskp14 | (~ndr1_0) | c1_1(a1103) | (~c2_1(a1103)) | (~c0_1(a1103))) <=> (hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1277,plain,
% 2.04/1.57 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1103) | (~c2_1(a1103)) | (~c0_1(a1103)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103))))),
% 2.04/1.57 inference(monotonicity,[status(thm)],[1276])).
% 2.04/1.57 tff(1278,plain,
% 2.04/1.57 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1103) | (~c2_1(a1103)) | (~c0_1(a1103)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103)))),
% 2.04/1.57 inference(transitivity,[status(thm)],[1277, 1275])).
% 2.04/1.57 tff(1279,plain,
% 2.04/1.57 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1103) | (~c2_1(a1103)) | (~c0_1(a1103)))),
% 2.04/1.57 inference(quant_inst,[status(thm)],[])).
% 2.04/1.57 tff(1280,plain,
% 2.04/1.57 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1103) | (~ndr1_0) | (~c0_1(a1103)) | (~c2_1(a1103))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 2.04/1.57 tff(1281,plain,
% 2.04/1.57 (hskp14 | (~c2_1(a1103))),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1280, 207, 1274, 1273, 205])).
% 2.04/1.57 tff(1282,plain,
% 2.04/1.57 (~c2_1(a1103)),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1281, 208])).
% 2.04/1.57 tff(1283,plain,
% 2.04/1.57 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 2.04/1.57 inference(bind,[status(th)],[])).
% 2.04/1.57 tff(1284,plain,
% 2.04/1.57 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.04/1.57 inference(quant_intro,[status(thm)],[1283])).
% 2.04/1.57 tff(1285,plain,
% 2.04/1.57 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1286,plain,
% 2.04/1.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 2.04/1.57 inference(bind,[status(th)],[])).
% 2.04/1.57 tff(1287,plain,
% 2.04/1.57 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.04/1.57 inference(quant_intro,[status(thm)],[1286])).
% 2.04/1.57 tff(1288,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 2.04/1.57 tff(1289,plain,
% 2.04/1.57 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 2.04/1.57 tff(1290,plain,
% 2.04/1.57 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1289, 1285])).
% 2.04/1.57 tff(1291,plain,(
% 2.04/1.57 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.04/1.57 inference(skolemize,[status(sab)],[1290])).
% 2.04/1.57 tff(1292,plain,
% 2.04/1.57 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1291, 1284])).
% 2.04/1.57 tff(1293,assumption,(c1_1(a1083)), introduced(assumption)).
% 2.04/1.57 tff(1294,assumption,(c3_1(a1103)), introduced(assumption)).
% 2.04/1.57 tff(1295,plain,
% 2.04/1.57 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1296,plain,
% 2.04/1.57 ((hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103))) <=> (hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1297,plain,
% 2.04/1.57 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103))))),
% 2.04/1.57 inference(monotonicity,[status(thm)],[1296])).
% 2.04/1.57 tff(1298,plain,
% 2.04/1.57 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103)))),
% 2.04/1.57 inference(transitivity,[status(thm)],[1297, 1295])).
% 2.04/1.57 tff(1299,plain,
% 2.04/1.57 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)))),
% 2.04/1.57 inference(quant_inst,[status(thm)],[])).
% 2.04/1.57 tff(1300,plain,
% 2.04/1.57 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1103) | (~c3_1(a1103))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 2.04/1.57 tff(1301,plain,
% 2.04/1.57 (hskp23),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1300, 207, 1294, 1293, 1273, 1003, 1002, 1292, 1282])).
% 2.04/1.57 tff(1302,plain,
% 2.04/1.57 (((~hskp23) | c2_1(a1122)) <=> ((~hskp23) | c2_1(a1122))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1303,axiom,((~hskp23) | c2_1(a1122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 2.04/1.57 tff(1304,plain,
% 2.04/1.57 ((~hskp23) | c2_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 2.04/1.57 tff(1305,plain,
% 2.04/1.57 ((~hskp23) | c2_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1304, 1302])).
% 2.04/1.57 tff(1306,plain,
% 2.04/1.57 ((~hskp23) | c2_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1305, 1302])).
% 2.04/1.57 tff(1307,plain,
% 2.04/1.57 ((~hskp23) | c2_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1306, 1302])).
% 2.04/1.57 tff(1308,plain,
% 2.04/1.57 ((~hskp23) | c2_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1307, 1302])).
% 2.04/1.57 tff(1309,plain,
% 2.04/1.57 ((~hskp23) | c2_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1308, 1302])).
% 2.04/1.57 tff(1310,plain,
% 2.04/1.57 ((~hskp23) | c2_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1309, 1302])).
% 2.04/1.57 tff(1311,plain,
% 2.04/1.57 ((~hskp23) | c2_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1310, 1302])).
% 2.04/1.57 tff(1312,plain,
% 2.04/1.57 (c2_1(a1122)),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1311, 1301])).
% 2.04/1.57 tff(1313,assumption,(~c3_1(a1084)), introduced(assumption)).
% 2.04/1.57 tff(1314,assumption,(~c1_1(a1084)), introduced(assumption)).
% 2.04/1.57 tff(1315,plain,
% 2.04/1.57 (((~hskp23) | c0_1(a1122)) <=> ((~hskp23) | c0_1(a1122))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1316,axiom,((~hskp23) | c0_1(a1122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 2.04/1.57 tff(1317,plain,
% 2.04/1.57 ((~hskp23) | c0_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 2.04/1.57 tff(1318,plain,
% 2.04/1.57 ((~hskp23) | c0_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1317, 1315])).
% 2.04/1.57 tff(1319,plain,
% 2.04/1.57 ((~hskp23) | c0_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1318, 1315])).
% 2.04/1.57 tff(1320,plain,
% 2.04/1.57 ((~hskp23) | c0_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1319, 1315])).
% 2.04/1.57 tff(1321,plain,
% 2.04/1.57 ((~hskp23) | c0_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1320, 1315])).
% 2.04/1.57 tff(1322,plain,
% 2.04/1.57 ((~hskp23) | c0_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1321, 1315])).
% 2.04/1.57 tff(1323,plain,
% 2.04/1.57 ((~hskp23) | c0_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1322, 1315])).
% 2.04/1.57 tff(1324,plain,
% 2.04/1.57 ((~hskp23) | c0_1(a1122)),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1323, 1315])).
% 2.04/1.57 tff(1325,plain,
% 2.04/1.57 (c0_1(a1122)),
% 2.04/1.57 inference(unit_resolution,[status(thm)],[1324, 1301])).
% 2.04/1.57 tff(1326,plain,
% 2.04/1.57 (((~hskp23) | (~c3_1(a1122))) <=> ((~hskp23) | (~c3_1(a1122)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1327,plain,
% 2.04/1.57 (((~c3_1(a1122)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1122)))),
% 2.04/1.57 inference(rewrite,[status(thm)],[])).
% 2.04/1.57 tff(1328,axiom,((~c3_1(a1122)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 2.04/1.57 tff(1329,plain,
% 2.04/1.57 ((~hskp23) | (~c3_1(a1122))),
% 2.04/1.57 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 2.04/1.57 tff(1330,plain,
% 2.04/1.58 ((~hskp23) | (~c3_1(a1122))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1329, 1326])).
% 2.04/1.58 tff(1331,plain,
% 2.04/1.58 (~c3_1(a1122)),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1330, 1301])).
% 2.04/1.58 tff(1332,assumption,(c2_1(a1122)), introduced(assumption)).
% 2.04/1.58 tff(1333,assumption,(c0_1(a1122)), introduced(assumption)).
% 2.04/1.58 tff(1334,plain,
% 2.04/1.58 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1335,plain,
% 2.04/1.58 ((hskp14 | (~ndr1_0) | c1_1(a1122) | (~c2_1(a1122)) | (~c0_1(a1122))) <=> (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1336,plain,
% 2.04/1.58 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c2_1(a1122)) | (~c0_1(a1122)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122))))),
% 2.04/1.58 inference(monotonicity,[status(thm)],[1335])).
% 2.04/1.58 tff(1337,plain,
% 2.04/1.58 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c2_1(a1122)) | (~c0_1(a1122)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122)))),
% 2.04/1.58 inference(transitivity,[status(thm)],[1336, 1334])).
% 2.04/1.58 tff(1338,plain,
% 2.04/1.58 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1122) | (~c2_1(a1122)) | (~c0_1(a1122)))),
% 2.04/1.58 inference(quant_inst,[status(thm)],[])).
% 2.04/1.58 tff(1339,plain,
% 2.04/1.58 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | (~ndr1_0) | c1_1(a1122) | (~c0_1(a1122)) | (~c2_1(a1122))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 2.04/1.58 tff(1340,plain,
% 2.04/1.58 (hskp14 | c1_1(a1122)),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1339, 207, 1333, 1332, 205])).
% 2.04/1.58 tff(1341,plain,
% 2.04/1.58 (c1_1(a1122)),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1340, 208])).
% 2.04/1.58 tff(1342,plain,
% 2.04/1.58 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1343,plain,
% 2.04/1.58 ((hskp14 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084))) <=> (hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1344,plain,
% 2.04/1.58 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084))))),
% 2.04/1.58 inference(monotonicity,[status(thm)],[1343])).
% 2.04/1.58 tff(1345,plain,
% 2.04/1.58 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 2.04/1.58 inference(transitivity,[status(thm)],[1344, 1342])).
% 2.04/1.58 tff(1346,plain,
% 2.04/1.58 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.04/1.58 inference(quant_inst,[status(thm)],[])).
% 2.04/1.58 tff(1347,plain,
% 2.04/1.58 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 2.04/1.58 tff(1348,plain,
% 2.04/1.58 (hskp14 | (~c2_1(a1084))),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1347, 207, 1272, 1314, 205])).
% 2.04/1.58 tff(1349,plain,
% 2.04/1.58 (~c2_1(a1084)),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1348, 208])).
% 2.04/1.58 tff(1350,plain,
% 2.04/1.58 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 2.04/1.58 inference(bind,[status(th)],[])).
% 2.04/1.58 tff(1351,plain,
% 2.04/1.58 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.04/1.58 inference(quant_intro,[status(thm)],[1350])).
% 2.04/1.58 tff(1352,plain,
% 2.04/1.58 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1353,plain,
% 2.04/1.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 2.04/1.58 inference(bind,[status(th)],[])).
% 2.04/1.58 tff(1354,plain,
% 2.04/1.58 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.04/1.58 inference(quant_intro,[status(thm)],[1353])).
% 2.04/1.58 tff(1355,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 2.04/1.58 tff(1356,plain,
% 2.04/1.58 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 2.04/1.58 tff(1357,plain,
% 2.04/1.58 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1356, 1352])).
% 2.04/1.58 tff(1358,plain,(
% 2.04/1.58 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.04/1.58 inference(skolemize,[status(sab)],[1357])).
% 2.04/1.58 tff(1359,plain,
% 2.04/1.58 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1358, 1351])).
% 2.04/1.58 tff(1360,assumption,(~c3_1(a1122)), introduced(assumption)).
% 2.04/1.58 tff(1361,plain,
% 2.04/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1362,plain,
% 2.04/1.58 ((hskp9 | (~ndr1_0) | c3_1(a1122) | (~c1_1(a1122)) | (~c0_1(a1122)) | c2_1(a1084) | c1_1(a1084) | c3_1(a1084)) <=> (hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1363,plain,
% 2.04/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a1122) | (~c1_1(a1122)) | (~c0_1(a1122)) | c2_1(a1084) | c1_1(a1084) | c3_1(a1084))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122))))),
% 2.04/1.58 inference(monotonicity,[status(thm)],[1362])).
% 2.04/1.58 tff(1364,plain,
% 2.04/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a1122) | (~c1_1(a1122)) | (~c0_1(a1122)) | c2_1(a1084) | c1_1(a1084) | c3_1(a1084))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122)))),
% 2.04/1.58 inference(transitivity,[status(thm)],[1363, 1361])).
% 2.04/1.58 tff(1365,plain,
% 2.04/1.58 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a1122) | (~c1_1(a1122)) | (~c0_1(a1122)) | c2_1(a1084) | c1_1(a1084) | c3_1(a1084))),
% 2.04/1.58 inference(quant_inst,[status(thm)],[])).
% 2.04/1.58 tff(1366,plain,
% 2.04/1.58 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp9 | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | c2_1(a1084) | (~c1_1(a1122)) | (~c0_1(a1122))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 2.04/1.58 tff(1367,plain,
% 2.04/1.58 ($false),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1366, 207, 57, 1333, 1360, 1314, 1313, 1359, 1349, 1341])).
% 2.04/1.58 tff(1368,plain,(hskp14 | (~ndr1_0) | hskp9 | (~c0_1(a1122)) | c3_1(a1122) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1122)) | (~c0_1(a1084))), inference(lemma,lemma(discharge,[]))).
% 2.04/1.58 tff(1369,plain,
% 2.04/1.58 ($false),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1368, 1331, 1325, 57, 207, 208, 1314, 1313, 1312, 1272])).
% 2.04/1.58 tff(1370,plain,(hskp14 | hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | (~c3_1(a1103)) | (~c1_1(a1083)) | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1103))), inference(lemma,lemma(discharge,[]))).
% 2.04/1.58 tff(1371,plain,
% 2.04/1.58 (hskp14 | hskp9 | c1_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | (~c3_1(a1103)) | (~c1_1(a1083)) | c1_1(a1103) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1103))),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1370, 186])).
% 2.04/1.58 tff(1372,plain,
% 2.04/1.58 ($false),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1371, 1271, 1265, 57, 208, 1259, 1216, 1215, 1214, 1213, 1212, 1140])).
% 2.04/1.58 tff(1373,plain,(hskp14 | hskp9 | c0_1(a1085) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 2.04/1.58 tff(1374,plain,
% 2.04/1.58 (hskp14),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1373, 90, 12, 11, 57, 69])).
% 2.04/1.58 tff(1375,plain,
% 2.04/1.58 (~c2_1(a1097)),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[282, 1374])).
% 2.04/1.58 tff(1376,plain,
% 2.04/1.58 (c3_1(a1097)),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[333, 1374])).
% 2.04/1.58 tff(1377,plain,
% 2.04/1.58 (c1_1(a1097)),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[293, 1374])).
% 2.04/1.58 tff(1378,plain,
% 2.04/1.58 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1379,plain,
% 2.04/1.58 ((hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097))) <=> (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1380,plain,
% 2.04/1.58 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 2.04/1.58 inference(monotonicity,[status(thm)],[1379])).
% 2.04/1.58 tff(1381,plain,
% 2.04/1.58 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.58 inference(transitivity,[status(thm)],[1380, 1378])).
% 2.04/1.58 tff(1382,plain,
% 2.04/1.58 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))),
% 2.04/1.58 inference(quant_inst,[status(thm)],[])).
% 2.04/1.58 tff(1383,plain,
% 2.04/1.58 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c1_1(a1097)) | (~c3_1(a1097)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 2.04/1.58 tff(1384,plain,
% 2.04/1.58 (hskp26),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1383, 186, 1195, 1194, 1201, 1377, 1376, 1375, 89])).
% 2.04/1.58 tff(1385,plain,
% 2.04/1.58 (((~hskp26) | (~c0_1(a1146))) <=> ((~hskp26) | (~c0_1(a1146)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1386,plain,
% 2.04/1.58 (((~c0_1(a1146)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1146)))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.58 tff(1387,axiom,((~c0_1(a1146)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 2.04/1.58 tff(1388,plain,
% 2.04/1.58 ((~hskp26) | (~c0_1(a1146))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 2.04/1.58 tff(1389,plain,
% 2.04/1.58 ((~hskp26) | (~c0_1(a1146))),
% 2.04/1.58 inference(modus_ponens,[status(thm)],[1388, 1385])).
% 2.04/1.58 tff(1390,plain,
% 2.04/1.58 (~c0_1(a1146)),
% 2.04/1.58 inference(unit_resolution,[status(thm)],[1389, 1384])).
% 2.04/1.58 tff(1391,plain,
% 2.04/1.58 (((~hskp26) | c3_1(a1146)) <=> ((~hskp26) | c3_1(a1146))),
% 2.04/1.58 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1392,axiom,((~hskp26) | c3_1(a1146)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 2.04/1.59 tff(1393,plain,
% 2.04/1.59 ((~hskp26) | c3_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 2.04/1.59 tff(1394,plain,
% 2.04/1.59 ((~hskp26) | c3_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1393, 1391])).
% 2.04/1.59 tff(1395,plain,
% 2.04/1.59 ((~hskp26) | c3_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1394, 1391])).
% 2.04/1.59 tff(1396,plain,
% 2.04/1.59 ((~hskp26) | c3_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1395, 1391])).
% 2.04/1.59 tff(1397,plain,
% 2.04/1.59 ((~hskp26) | c3_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1396, 1391])).
% 2.04/1.59 tff(1398,plain,
% 2.04/1.59 ((~hskp26) | c3_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1397, 1391])).
% 2.04/1.59 tff(1399,plain,
% 2.04/1.59 ((~hskp26) | c3_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1398, 1391])).
% 2.04/1.59 tff(1400,plain,
% 2.04/1.59 ((~hskp26) | c3_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1399, 1391])).
% 2.04/1.59 tff(1401,plain,
% 2.04/1.59 (c3_1(a1146)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[1400, 1384])).
% 2.04/1.59 tff(1402,plain,
% 2.04/1.59 (((~hskp26) | c2_1(a1146)) <=> ((~hskp26) | c2_1(a1146))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1403,axiom,((~hskp26) | c2_1(a1146)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 2.04/1.59 tff(1404,plain,
% 2.04/1.59 ((~hskp26) | c2_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 2.04/1.59 tff(1405,plain,
% 2.04/1.59 ((~hskp26) | c2_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1404, 1402])).
% 2.04/1.59 tff(1406,plain,
% 2.04/1.59 ((~hskp26) | c2_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1405, 1402])).
% 2.04/1.59 tff(1407,plain,
% 2.04/1.59 ((~hskp26) | c2_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1406, 1402])).
% 2.04/1.59 tff(1408,plain,
% 2.04/1.59 ((~hskp26) | c2_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1407, 1402])).
% 2.04/1.59 tff(1409,plain,
% 2.04/1.59 ((~hskp26) | c2_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1408, 1402])).
% 2.04/1.59 tff(1410,plain,
% 2.04/1.59 ((~hskp26) | c2_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1409, 1402])).
% 2.04/1.59 tff(1411,plain,
% 2.04/1.59 ((~hskp26) | c2_1(a1146)),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1410, 1402])).
% 2.04/1.59 tff(1412,plain,
% 2.04/1.59 (c2_1(a1146)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[1411, 1384])).
% 2.04/1.59 tff(1413,plain,
% 2.04/1.59 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1414,plain,
% 2.04/1.59 ((hskp19 | (~ndr1_0) | c0_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146))) <=> (hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1415,plain,
% 2.04/1.59 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146))))),
% 2.04/1.59 inference(monotonicity,[status(thm)],[1414])).
% 2.04/1.59 tff(1416,plain,
% 2.04/1.59 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 2.04/1.59 inference(transitivity,[status(thm)],[1415, 1413])).
% 2.04/1.59 tff(1417,plain,
% 2.04/1.59 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(1418,plain,
% 2.04/1.59 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | c0_1(a1146) | (~ndr1_0) | (~c2_1(a1146)) | (~c3_1(a1146))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 2.04/1.59 tff(1419,plain,
% 2.04/1.59 (hskp19),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[1418, 186, 1412, 1401, 1390, 79])).
% 2.04/1.59 tff(1420,plain,
% 2.04/1.59 (~c2_1(a1113)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[971, 1419])).
% 2.04/1.59 tff(1421,plain,
% 2.04/1.59 (c1_1(a1113)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[982, 1419])).
% 2.04/1.59 tff(1422,plain,
% 2.04/1.59 (c0_1(a1113)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[993, 1419])).
% 2.04/1.59 tff(1423,plain,
% 2.04/1.59 (c3_1(a1113)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[1000, 186, 1422, 1421, 1115, 1420, 12, 11, 67])).
% 2.04/1.59 tff(1424,plain,
% 2.04/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1425,plain,
% 2.04/1.59 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1113)) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080)) <=> (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1426,plain,
% 2.04/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1113)) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 2.04/1.59 inference(monotonicity,[status(thm)],[1425])).
% 2.04/1.59 tff(1427,plain,
% 2.04/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1113)) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.59 inference(transitivity,[status(thm)],[1426, 1424])).
% 2.04/1.59 tff(1428,plain,
% 2.04/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1113)) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | c0_1(a1080))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(1429,plain,
% 2.04/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1080) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 2.04/1.59 tff(1430,plain,
% 2.04/1.59 (c1_1(a1080)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[1429, 186, 1195, 1194, 1201, 1422, 1421, 90, 69, 374, 1423])).
% 2.04/1.59 tff(1431,plain,
% 2.04/1.59 (hskp3),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[1210, 1430, 90])).
% 2.04/1.59 tff(1432,plain,
% 2.04/1.59 (~c3_1(a1083)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[910, 1431])).
% 2.04/1.59 tff(1433,plain,
% 2.04/1.59 (~c2_1(a1083)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[904, 1431])).
% 2.04/1.59 tff(1434,plain,
% 2.04/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1435,plain,
% 2.04/1.59 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1436,plain,
% 2.04/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 2.04/1.59 inference(monotonicity,[status(thm)],[1435])).
% 2.04/1.59 tff(1437,plain,
% 2.04/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.59 inference(transitivity,[status(thm)],[1436, 1434])).
% 2.04/1.59 tff(1438,plain,
% 2.04/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.04/1.59 inference(quant_inst,[status(thm)],[])).
% 2.04/1.59 tff(1439,plain,
% 2.04/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c0_1(a1083)) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 2.04/1.59 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 2.04/1.59 tff(1440,plain,
% 2.04/1.59 (~c0_1(a1083)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[1439, 186, 1422, 1421, 1115, 1420, 12, 11, 1433, 1432, 67])).
% 2.04/1.59 tff(1441,plain,
% 2.04/1.59 (c1_1(a1083)),
% 2.04/1.59 inference(unit_resolution,[status(thm)],[1099, 1431])).
% 2.04/1.59 tff(1442,plain,
% 2.04/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1443,plain,
% 2.04/1.59 ((hskp4 | (~ndr1_0) | c0_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085)))),
% 2.04/1.59 inference(rewrite,[status(thm)],[])).
% 2.04/1.59 tff(1444,plain,
% 2.04/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085))))),
% 2.04/1.60 inference(monotonicity,[status(thm)],[1443])).
% 2.04/1.60 tff(1445,plain,
% 2.04/1.60 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085)))),
% 2.04/1.60 inference(transitivity,[status(thm)],[1444, 1442])).
% 2.04/1.60 tff(1446,plain,
% 2.04/1.60 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.04/1.60 inference(quant_inst,[status(thm)],[])).
% 2.04/1.60 tff(1447,plain,
% 2.04/1.60 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1085) | c1_1(a1085) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c0_1(a1083) | (~c2_1(a1085))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 2.04/1.60 tff(1448,plain,
% 2.04/1.60 (hskp4),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[1447, 186, 1115, 1441, 12, 11, 1432, 1240, 1440])).
% 2.04/1.60 tff(1449,plain,
% 2.04/1.60 (c0_1(a1084)),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[1258, 1448])).
% 2.04/1.60 tff(1450,plain,
% 2.04/1.60 (~c3_1(a1084)),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[1270, 1448])).
% 2.04/1.60 tff(1451,assumption,(~c2_1(a1084)), introduced(assumption)).
% 2.04/1.60 tff(1452,assumption,(~c2_1(a1113)), introduced(assumption)).
% 2.04/1.60 tff(1453,assumption,(c2_1(a1085)), introduced(assumption)).
% 2.04/1.60 tff(1454,assumption,(c1_1(a1113)), introduced(assumption)).
% 2.04/1.60 tff(1455,assumption,(c0_1(a1113)), introduced(assumption)).
% 2.04/1.60 tff(1456,plain,
% 2.04/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(1457,plain,
% 2.04/1.60 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(1458,plain,
% 2.04/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 2.04/1.60 inference(monotonicity,[status(thm)],[1457])).
% 2.04/1.60 tff(1459,plain,
% 2.04/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.60 inference(transitivity,[status(thm)],[1458, 1456])).
% 2.04/1.60 tff(1460,plain,
% 2.04/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1084) | c3_1(a1084) | (~c0_1(a1084)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.04/1.60 inference(quant_inst,[status(thm)],[])).
% 2.04/1.60 tff(1461,plain,
% 2.04/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | c2_1(a1084) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[1460, 1459])).
% 2.04/1.60 tff(1462,plain,
% 2.04/1.60 ($false),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[1461, 207, 1455, 1454, 1453, 1272, 1452, 12, 11, 1313, 67, 1451])).
% 2.04/1.60 tff(1463,plain,(c2_1(a1084) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c2_1(a1085)) | (~c0_1(a1084)) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.04/1.60 tff(1464,plain,
% 2.04/1.60 (c2_1(a1084) | (~c0_1(a1113)) | (~c1_1(a1113)) | (~c2_1(a1085)) | (~c0_1(a1084)) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c3_1(a1084)),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[1463, 186])).
% 2.04/1.60 tff(1465,plain,
% 2.04/1.60 (c2_1(a1084)),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[1464, 1450, 1422, 1421, 1115, 1449, 1420, 12, 11])).
% 2.04/1.60 tff(1466,plain,
% 2.04/1.60 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(1467,plain,
% 2.04/1.60 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[1466])).
% 2.04/1.60 tff(1468,plain,
% 2.04/1.60 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(1469,plain,
% 2.04/1.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 2.04/1.60 inference(bind,[status(th)],[])).
% 2.04/1.60 tff(1470,plain,
% 2.04/1.60 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.04/1.60 inference(quant_intro,[status(thm)],[1469])).
% 2.04/1.60 tff(1471,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 2.04/1.60 tff(1472,plain,
% 2.04/1.60 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 2.04/1.60 tff(1473,plain,
% 2.04/1.60 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[1472, 1468])).
% 2.04/1.60 tff(1474,plain,(
% 2.04/1.60 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.04/1.60 inference(skolemize,[status(sab)],[1473])).
% 2.04/1.60 tff(1475,plain,
% 2.04/1.60 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.04/1.60 inference(modus_ponens,[status(thm)],[1474, 1467])).
% 2.04/1.60 tff(1476,plain,
% 2.04/1.60 (~c1_1(a1084)),
% 2.04/1.60 inference(unit_resolution,[status(thm)],[1264, 1448])).
% 2.04/1.60 tff(1477,plain,
% 2.04/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(1478,plain,
% 2.04/1.60 (((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085)) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.04/1.60 inference(rewrite,[status(thm)],[])).
% 2.04/1.60 tff(1479,plain,
% 2.04/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113))))),
% 2.04/1.61 inference(monotonicity,[status(thm)],[1478])).
% 2.04/1.61 tff(1480,plain,
% 2.04/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.04/1.61 inference(transitivity,[status(thm)],[1479, 1477])).
% 2.04/1.61 tff(1481,plain,
% 2.04/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))),
% 2.04/1.61 inference(quant_inst,[status(thm)],[])).
% 2.04/1.61 tff(1482,plain,
% 2.04/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1113)) | (~c3_1(a1113))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 2.04/1.61 tff(1483,plain,
% 2.04/1.61 (c3_1(a1085)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[1482, 186, 1421, 1441, 1420, 12, 11, 1433, 1432, 476, 1423])).
% 2.04/1.61 tff(1484,plain,
% 2.04/1.61 (hskp11),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[1136, 1483, 57, 1115])).
% 2.04/1.61 tff(1485,plain,
% 2.04/1.61 (~c0_1(a1091)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[710, 1484])).
% 2.04/1.61 tff(1486,plain,
% 2.04/1.61 (c2_1(a1091)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[721, 1484])).
% 2.04/1.61 tff(1487,plain,
% 2.04/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(1488,plain,
% 2.04/1.61 ((hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1084)) | c0_1(a1091) | (~c2_1(a1091)) | (~c1_1(a1091))) <=> (hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(1489,plain,
% 2.04/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1084)) | c0_1(a1091) | (~c2_1(a1091)) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091))))),
% 2.04/1.61 inference(monotonicity,[status(thm)],[1488])).
% 2.04/1.61 tff(1490,plain,
% 2.04/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1084)) | c0_1(a1091) | (~c2_1(a1091)) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091)))),
% 2.04/1.61 inference(transitivity,[status(thm)],[1489, 1487])).
% 2.04/1.61 tff(1491,plain,
% 2.04/1.61 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1084) | c3_1(a1084) | (~c2_1(a1084)) | c0_1(a1091) | (~c2_1(a1091)) | (~c1_1(a1091)))),
% 2.04/1.61 inference(quant_inst,[status(thm)],[])).
% 2.04/1.61 tff(1492,plain,
% 2.04/1.61 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a1091) | c1_1(a1084) | c3_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c1_1(a1091)) | (~c2_1(a1091))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 2.04/1.61 tff(1493,plain,
% 2.04/1.61 (~c1_1(a1091)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[1492, 186, 57, 1486, 1485, 1476, 1450, 1475, 1465])).
% 2.04/1.61 tff(1494,plain,
% 2.04/1.61 (~c3_1(a1091)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[704, 1484])).
% 2.04/1.61 tff(1495,plain,
% 2.04/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(1496,plain,
% 2.04/1.61 (((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1091) | c0_1(a1091) | c3_1(a1091)) <=> (c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(1497,plain,
% 2.04/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1091) | c0_1(a1091) | c3_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113))))),
% 2.04/1.61 inference(monotonicity,[status(thm)],[1496])).
% 2.04/1.61 tff(1498,plain,
% 2.04/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1091) | c0_1(a1091) | c3_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.04/1.61 inference(transitivity,[status(thm)],[1497, 1495])).
% 2.04/1.61 tff(1499,plain,
% 2.04/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1091) | c0_1(a1091) | c3_1(a1091))),
% 2.04/1.61 inference(quant_inst,[status(thm)],[])).
% 2.04/1.61 tff(1500,plain,
% 2.04/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c0_1(a1091) | c3_1(a1091) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1091) | (~c1_1(a1113)) | (~c3_1(a1113))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 2.04/1.61 tff(1501,plain,
% 2.04/1.61 ($false),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[1500, 186, 1421, 1441, 1420, 1485, 1494, 1433, 1432, 476, 1493, 1423])).
% 2.04/1.61 tff(1502,plain,(c0_1(a1080) | hskp9 | c0_1(a1085) | c1_1(a1085) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 2.04/1.61 tff(1503,plain,
% 2.04/1.61 (c0_1(a1080)),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[1502, 69, 12, 11, 57])).
% 2.04/1.61 tff(1504,plain,
% 2.04/1.61 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) <=> (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(1505,plain,
% 2.04/1.61 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[1504])).
% 2.04/1.61 tff(1506,plain,
% 2.04/1.61 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(1507,plain,
% 2.04/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) | hskp17))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(1508,plain,
% 2.04/1.61 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[1507])).
% 2.04/1.61 tff(1509,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 2.04/1.61 tff(1510,plain,
% 2.04/1.61 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 2.04/1.61 tff(1511,plain,
% 2.04/1.61 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[1510, 1506])).
% 2.04/1.61 tff(1512,plain,(
% 2.04/1.61 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.04/1.61 inference(skolemize,[status(sab)],[1511])).
% 2.04/1.61 tff(1513,plain,
% 2.04/1.61 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[1512, 1505])).
% 2.04/1.61 tff(1514,plain,
% 2.04/1.61 (~hskp0),
% 2.04/1.61 inference(unit_resolution,[status(thm)],[34, 1503])).
% 2.04/1.61 tff(1515,assumption,(c1_1(a1092)), introduced(assumption)).
% 2.04/1.61 tff(1516,plain,
% 2.04/1.61 (^[U: $i] : refl((hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(1517,plain,
% 2.04/1.61 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[1516])).
% 2.04/1.61 tff(1518,plain,
% 2.04/1.61 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.61 inference(rewrite,[status(thm)],[])).
% 2.04/1.61 tff(1519,plain,
% 2.04/1.61 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp2) <=> ((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp2) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.04/1.61 inference(bind,[status(th)],[])).
% 2.04/1.61 tff(1520,plain,
% 2.04/1.61 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp2) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.61 inference(quant_intro,[status(thm)],[1519])).
% 2.04/1.61 tff(1521,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 2.04/1.61 tff(1522,plain,
% 2.04/1.61 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 2.04/1.61 tff(1523,plain,
% 2.04/1.61 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.61 inference(modus_ponens,[status(thm)],[1522, 1518])).
% 2.04/1.61 tff(1524,plain,(
% 2.04/1.61 ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.61 inference(skolemize,[status(sab)],[1523])).
% 2.04/1.62 tff(1525,plain,
% 2.04/1.62 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1524, 1517])).
% 2.04/1.62 tff(1526,plain,
% 2.04/1.62 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1527,plain,
% 2.04/1.62 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.62 inference(quant_inst,[status(thm)],[])).
% 2.04/1.62 tff(1528,plain,
% 2.04/1.62 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 2.04/1.62 tff(1529,plain,
% 2.04/1.62 (hskp19 | hskp2 | (~c1_1(a1092))),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[1528, 186, 1195, 1201, 1525])).
% 2.04/1.62 tff(1530,plain,
% 2.04/1.62 (hskp19),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[1529, 68, 1515])).
% 2.04/1.62 tff(1531,plain,
% 2.04/1.62 (~c2_1(a1113)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[971, 1530])).
% 2.04/1.62 tff(1532,plain,
% 2.04/1.62 (c1_1(a1113)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[982, 1530])).
% 2.04/1.62 tff(1533,plain,
% 2.04/1.62 (c0_1(a1113)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[993, 1530])).
% 2.04/1.62 tff(1534,plain,
% 2.04/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1535,plain,
% 2.04/1.62 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1536,plain,
% 2.04/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 2.04/1.62 inference(monotonicity,[status(thm)],[1535])).
% 2.04/1.62 tff(1537,plain,
% 2.04/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(transitivity,[status(thm)],[1536, 1534])).
% 2.04/1.62 tff(1538,plain,
% 2.04/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.04/1.62 inference(quant_inst,[status(thm)],[])).
% 2.04/1.62 tff(1539,plain,
% 2.04/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1113) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c2_1(a1085)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 2.04/1.62 tff(1540,plain,
% 2.04/1.62 (c3_1(a1080)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[1539, 186, 1533, 1532, 1115, 1531, 12, 11, 1503, 69, 67])).
% 2.04/1.62 tff(1541,plain,
% 2.04/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1542,plain,
% 2.04/1.62 ((hskp1 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080))) <=> (hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1543,plain,
% 2.04/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 2.04/1.62 inference(monotonicity,[status(thm)],[1542])).
% 2.04/1.62 tff(1544,plain,
% 2.04/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(transitivity,[status(thm)],[1543, 1541])).
% 2.04/1.62 tff(1545,plain,
% 2.04/1.62 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))),
% 2.04/1.62 inference(quant_inst,[status(thm)],[])).
% 2.04/1.62 tff(1546,plain,
% 2.04/1.62 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1080) | c2_1(a1113) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 2.04/1.62 tff(1547,plain,
% 2.04/1.62 (hskp1),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[1546, 186, 1533, 1532, 912, 1531, 69, 576, 1540])).
% 2.04/1.62 tff(1548,plain,
% 2.04/1.62 (~c1_1(a1081)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[643, 1547])).
% 2.04/1.62 tff(1549,plain,
% 2.04/1.62 (~c0_1(a1081)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[637, 1547])).
% 2.04/1.62 tff(1550,plain,
% 2.04/1.62 (((~hskp1) | c3_1(a1081)) <=> ((~hskp1) | c3_1(a1081))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1551,axiom,((~hskp1) | c3_1(a1081)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 2.04/1.62 tff(1552,plain,
% 2.04/1.62 ((~hskp1) | c3_1(a1081)),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 2.04/1.62 tff(1553,plain,
% 2.04/1.62 ((~hskp1) | c3_1(a1081)),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1552, 1550])).
% 2.04/1.62 tff(1554,plain,
% 2.04/1.62 ((~hskp1) | c3_1(a1081)),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1553, 1550])).
% 2.04/1.62 tff(1555,plain,
% 2.04/1.62 ((~hskp1) | c3_1(a1081)),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1554, 1550])).
% 2.04/1.62 tff(1556,plain,
% 2.04/1.62 ((~hskp1) | c3_1(a1081)),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1555, 1550])).
% 2.04/1.62 tff(1557,plain,
% 2.04/1.62 ((~hskp1) | c3_1(a1081)),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1556, 1550])).
% 2.04/1.62 tff(1558,plain,
% 2.04/1.62 ((~hskp1) | c3_1(a1081)),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1557, 1550])).
% 2.04/1.62 tff(1559,plain,
% 2.04/1.62 ((~hskp1) | c3_1(a1081)),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1558, 1550])).
% 2.04/1.62 tff(1560,plain,
% 2.04/1.62 (c3_1(a1081)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[1559, 1547])).
% 2.04/1.62 tff(1561,plain,
% 2.04/1.62 (hskp11),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[759, 186, 1195, 1194, 1201, 1560, 1549, 1548, 752])).
% 2.04/1.62 tff(1562,plain,
% 2.04/1.62 (~c3_1(a1091)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[704, 1561])).
% 2.04/1.62 tff(1563,plain,
% 2.04/1.62 (~c0_1(a1091)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[710, 1561])).
% 2.04/1.62 tff(1564,plain,
% 2.04/1.62 (c2_1(a1091)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[721, 1561])).
% 2.04/1.62 tff(1565,plain,
% 2.04/1.62 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1566,plain,
% 2.04/1.62 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113))) <=> (hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1567,plain,
% 2.04/1.62 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 2.04/1.62 inference(monotonicity,[status(thm)],[1566])).
% 2.04/1.62 tff(1568,plain,
% 2.04/1.62 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.04/1.62 inference(transitivity,[status(thm)],[1567, 1565])).
% 2.04/1.62 tff(1569,plain,
% 2.04/1.62 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)))),
% 2.04/1.62 inference(quant_inst,[status(thm)],[])).
% 2.04/1.62 tff(1570,plain,
% 2.04/1.62 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 2.04/1.62 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 2.04/1.62 tff(1571,plain,
% 2.04/1.62 (hskp30),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[1570, 186, 57, 1533, 1532, 1531, 102])).
% 2.04/1.62 tff(1572,plain,
% 2.04/1.62 (c3_1(a1109)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[363, 1571])).
% 2.04/1.62 tff(1573,plain,
% 2.04/1.62 (c1_1(a1109)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[312, 1571])).
% 2.04/1.62 tff(1574,plain,
% 2.04/1.62 (c0_1(a1109)),
% 2.04/1.62 inference(unit_resolution,[status(thm)],[352, 1571])).
% 2.04/1.62 tff(1575,plain,
% 2.04/1.62 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.62 tff(1576,plain,
% 2.04/1.62 ((hskp17 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c0_1(a1091) | (~c2_1(a1091)) | c3_1(a1091)) <=> (hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 2.04/1.62 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1577,plain,
% 2.04/1.63 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c0_1(a1091) | (~c2_1(a1091)) | c3_1(a1091))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109))))),
% 2.04/1.63 inference(monotonicity,[status(thm)],[1576])).
% 2.04/1.63 tff(1578,plain,
% 2.04/1.63 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c0_1(a1091) | (~c2_1(a1091)) | c3_1(a1091))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 2.04/1.63 inference(transitivity,[status(thm)],[1577, 1575])).
% 2.04/1.63 tff(1579,plain,
% 2.04/1.63 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c0_1(a1091) | (~c2_1(a1091)) | c3_1(a1091))),
% 2.04/1.63 inference(quant_inst,[status(thm)],[])).
% 2.04/1.63 tff(1580,plain,
% 2.04/1.63 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | c0_1(a1091) | c3_1(a1091) | (~ndr1_0) | (~c2_1(a1091)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109))),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 2.04/1.63 tff(1581,plain,
% 2.04/1.63 (hskp17),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[1580, 186, 1574, 1573, 1572, 1564, 1563, 1562, 1513])).
% 2.04/1.63 tff(1582,plain,
% 2.04/1.63 (((~hskp17) | (~c0_1(a1102))) <=> ((~hskp17) | (~c0_1(a1102)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1583,plain,
% 2.04/1.63 (((~c0_1(a1102)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1102)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1584,axiom,((~c0_1(a1102)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 2.04/1.63 tff(1585,plain,
% 2.04/1.63 ((~hskp17) | (~c0_1(a1102))),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 2.04/1.63 tff(1586,plain,
% 2.04/1.63 ((~hskp17) | (~c0_1(a1102))),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1585, 1582])).
% 2.04/1.63 tff(1587,plain,
% 2.04/1.63 (~c0_1(a1102)),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[1586, 1581])).
% 2.04/1.63 tff(1588,plain,
% 2.04/1.63 (((~hskp17) | c3_1(a1102)) <=> ((~hskp17) | c3_1(a1102))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1589,axiom,((~hskp17) | c3_1(a1102)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 2.04/1.63 tff(1590,plain,
% 2.04/1.63 ((~hskp17) | c3_1(a1102)),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 2.04/1.63 tff(1591,plain,
% 2.04/1.63 ((~hskp17) | c3_1(a1102)),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1590, 1588])).
% 2.04/1.63 tff(1592,plain,
% 2.04/1.63 ((~hskp17) | c3_1(a1102)),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1591, 1588])).
% 2.04/1.63 tff(1593,plain,
% 2.04/1.63 ((~hskp17) | c3_1(a1102)),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1592, 1588])).
% 2.04/1.63 tff(1594,plain,
% 2.04/1.63 ((~hskp17) | c3_1(a1102)),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1593, 1588])).
% 2.04/1.63 tff(1595,plain,
% 2.04/1.63 ((~hskp17) | c3_1(a1102)),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1594, 1588])).
% 2.04/1.63 tff(1596,plain,
% 2.04/1.63 ((~hskp17) | c3_1(a1102)),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1595, 1588])).
% 2.04/1.63 tff(1597,plain,
% 2.04/1.63 ((~hskp17) | c3_1(a1102)),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1596, 1588])).
% 2.04/1.63 tff(1598,plain,
% 2.04/1.63 (c3_1(a1102)),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[1597, 1581])).
% 2.04/1.63 tff(1599,plain,
% 2.04/1.63 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1600,plain,
% 2.04/1.63 ((hskp9 | hskp2 | (~ndr1_0) | c0_1(a1102) | (~c3_1(a1102)) | (~c1_1(a1102))) <=> (hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1601,plain,
% 2.04/1.63 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1102) | (~c3_1(a1102)) | (~c1_1(a1102)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102))))),
% 2.04/1.63 inference(monotonicity,[status(thm)],[1600])).
% 2.04/1.63 tff(1602,plain,
% 2.04/1.63 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1102) | (~c3_1(a1102)) | (~c1_1(a1102)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102)))),
% 2.04/1.63 inference(transitivity,[status(thm)],[1601, 1599])).
% 2.04/1.63 tff(1603,plain,
% 2.04/1.63 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1102) | (~c3_1(a1102)) | (~c1_1(a1102)))),
% 2.04/1.63 inference(quant_inst,[status(thm)],[])).
% 2.04/1.63 tff(1604,plain,
% 2.04/1.63 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c3_1(a1102))),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 2.04/1.63 tff(1605,plain,
% 2.04/1.63 (~c1_1(a1102)),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[1604, 186, 57, 68, 1598, 1587, 438])).
% 2.04/1.63 tff(1606,plain,
% 2.04/1.63 (((~hskp17) | (~c2_1(a1102))) <=> ((~hskp17) | (~c2_1(a1102)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1607,plain,
% 2.04/1.63 (((~c2_1(a1102)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1102)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1608,axiom,((~c2_1(a1102)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 2.04/1.63 tff(1609,plain,
% 2.04/1.63 ((~hskp17) | (~c2_1(a1102))),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 2.04/1.63 tff(1610,plain,
% 2.04/1.63 ((~hskp17) | (~c2_1(a1102))),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1609, 1606])).
% 2.04/1.63 tff(1611,plain,
% 2.04/1.63 (~c2_1(a1102)),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[1610, 1581])).
% 2.04/1.63 tff(1612,plain,
% 2.04/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1613,plain,
% 2.04/1.63 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1102) | c1_1(a1102) | c0_1(a1102)) <=> (c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1614,plain,
% 2.04/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1102) | c1_1(a1102) | c0_1(a1102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 2.04/1.63 inference(monotonicity,[status(thm)],[1613])).
% 2.04/1.63 tff(1615,plain,
% 2.04/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1102) | c1_1(a1102) | c0_1(a1102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.63 inference(transitivity,[status(thm)],[1614, 1612])).
% 2.04/1.63 tff(1616,plain,
% 2.04/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | c2_1(a1102) | c1_1(a1102) | c0_1(a1102))),
% 2.04/1.63 inference(quant_inst,[status(thm)],[])).
% 2.04/1.63 tff(1617,plain,
% 2.04/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1102) | c2_1(a1102) | (~ndr1_0) | c1_1(a1102) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 2.04/1.63 inference(modus_ponens,[status(thm)],[1616, 1615])).
% 2.04/1.63 tff(1618,plain,
% 2.04/1.63 ($false),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[1617, 186, 1574, 1573, 1572, 1195, 1194, 1201, 1587, 1611, 374, 1605])).
% 2.04/1.63 tff(1619,plain,(hskp2 | hskp9 | c1_1(a1080) | c2_1(a1080) | c0_1(a1085) | c1_1(a1085) | (~c1_1(a1092))), inference(lemma,lemma(discharge,[]))).
% 2.04/1.63 tff(1620,plain,
% 2.04/1.63 (hskp2),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[1619, 1200, 912, 69, 12, 11, 57])).
% 2.04/1.63 tff(1621,plain,
% 2.04/1.63 (~c0_1(a1082)),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[621, 1620])).
% 2.04/1.63 tff(1622,plain,
% 2.04/1.63 (~c2_1(a1082)),
% 2.04/1.63 inference(unit_resolution,[status(thm)],[627, 1620])).
% 2.04/1.63 tff(1623,plain,
% 2.04/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1624,plain,
% 2.04/1.63 (((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.63 inference(rewrite,[status(thm)],[])).
% 2.04/1.63 tff(1625,plain,
% 2.04/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))))),
% 2.04/1.63 inference(monotonicity,[status(thm)],[1624])).
% 2.04/1.63 tff(1626,plain,
% 2.04/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.04/1.64 inference(transitivity,[status(thm)],[1625, 1623])).
% 2.04/1.64 tff(1627,plain,
% 2.04/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | (~c3_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 2.04/1.64 inference(quant_inst,[status(thm)],[])).
% 2.04/1.64 tff(1628,plain,
% 2.04/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | c1_1(a1082) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))),
% 2.04/1.64 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 2.04/1.64 tff(1629,plain,
% 2.04/1.64 (c0_1(a1082) | c1_1(a1082)),
% 2.04/1.64 inference(unit_resolution,[status(thm)],[1628, 186, 1195, 1194, 1201, 629, 374, 1200])).
% 2.04/1.64 tff(1630,plain,
% 2.04/1.64 (c1_1(a1082)),
% 2.04/1.64 inference(unit_resolution,[status(thm)],[1629, 631])).
% 2.04/1.64 tff(1631,plain,
% 2.04/1.64 (hskp3 | c0_1(a1082) | (~c1_1(a1082))),
% 2.04/1.64 inference(unit_resolution,[status(thm)],[898, 186, 1115, 12, 11, 629, 22])).
% 2.04/1.64 tff(1632,plain,
% 2.04/1.64 (hskp3),
% 2.04/1.64 inference(unit_resolution,[status(thm)],[1631, 631, 1630])).
% 2.04/1.64 tff(1633,plain,
% 2.04/1.64 (~c3_1(a1083)),
% 2.04/1.64 inference(unit_resolution,[status(thm)],[910, 1632])).
% 2.04/1.64 tff(1634,plain,
% 2.04/1.64 (~c2_1(a1083)),
% 2.04/1.64 inference(unit_resolution,[status(thm)],[904, 1632])).
% 2.04/1.64 tff(1635,plain,
% 2.04/1.64 (c1_1(a1083)),
% 2.04/1.64 inference(unit_resolution,[status(thm)],[1099, 1632])).
% 2.04/1.64 tff(1636,plain,
% 2.04/1.64 (^[U: $i] : refl((hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 2.04/1.64 inference(bind,[status(th)],[])).
% 2.04/1.64 tff(1637,plain,
% 2.04/1.64 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.04/1.64 inference(quant_intro,[status(thm)],[1636])).
% 2.04/1.64 tff(1638,plain,
% 2.04/1.64 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.04/1.64 inference(rewrite,[status(thm)],[])).
% 2.04/1.64 tff(1639,plain,
% 2.04/1.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp16) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp16) <=> (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp16) <=> (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 2.04/1.64 inference(bind,[status(th)],[])).
% 2.04/1.64 tff(1640,plain,
% 2.04/1.64 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp16) <=> ![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.04/1.64 inference(quant_intro,[status(thm)],[1639])).
% 2.04/1.64 tff(1641,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 2.13/1.64 tff(1642,plain,
% 2.13/1.64 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 2.13/1.64 tff(1643,plain,
% 2.13/1.64 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1642, 1638])).
% 2.13/1.64 tff(1644,plain,(
% 2.13/1.64 ![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.13/1.64 inference(skolemize,[status(sab)],[1643])).
% 2.13/1.64 tff(1645,plain,
% 2.13/1.64 (![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1644, 1637])).
% 2.13/1.64 tff(1646,assumption,(~hskp0), introduced(assumption)).
% 2.13/1.64 tff(1647,plain,
% 2.13/1.64 (((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)))) <=> ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1648,plain,
% 2.13/1.64 ((hskp0 | hskp16 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082))) <=> (hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1649,plain,
% 2.13/1.64 (((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082))))),
% 2.13/1.64 inference(monotonicity,[status(thm)],[1648])).
% 2.13/1.64 tff(1650,plain,
% 2.13/1.64 (((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)))),
% 2.13/1.64 inference(transitivity,[status(thm)],[1649, 1647])).
% 2.13/1.64 tff(1651,plain,
% 2.13/1.64 ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp0 | hskp16 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))),
% 2.13/1.64 inference(quant_inst,[status(thm)],[])).
% 2.13/1.64 tff(1652,plain,
% 2.13/1.64 ((~![U: $i] : (hskp0 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp0 | hskp16 | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 2.13/1.64 tff(1653,plain,
% 2.13/1.64 (hskp16 | c0_1(a1082) | (~c1_1(a1082))),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1652, 1646, 186, 629, 1645])).
% 2.13/1.64 tff(1654,plain,
% 2.13/1.64 (hskp16),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1653, 631, 1630])).
% 2.13/1.64 tff(1655,plain,
% 2.13/1.64 (((~hskp16) | (~c3_1(a1100))) <=> ((~hskp16) | (~c3_1(a1100)))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1656,plain,
% 2.13/1.64 (((~c3_1(a1100)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a1100)))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1657,axiom,((~c3_1(a1100)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 2.13/1.64 tff(1658,plain,
% 2.13/1.64 ((~hskp16) | (~c3_1(a1100))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 2.13/1.64 tff(1659,plain,
% 2.13/1.64 ((~hskp16) | (~c3_1(a1100))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1658, 1655])).
% 2.13/1.64 tff(1660,plain,
% 2.13/1.64 (~c3_1(a1100)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1659, 1654])).
% 2.13/1.64 tff(1661,plain,
% 2.13/1.64 (((~hskp16) | (~c0_1(a1100))) <=> ((~hskp16) | (~c0_1(a1100)))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1662,plain,
% 2.13/1.64 (((~c0_1(a1100)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1100)))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1663,axiom,((~c0_1(a1100)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 2.13/1.64 tff(1664,plain,
% 2.13/1.64 ((~hskp16) | (~c0_1(a1100))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 2.13/1.64 tff(1665,plain,
% 2.13/1.64 ((~hskp16) | (~c0_1(a1100))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1664, 1661])).
% 2.13/1.64 tff(1666,plain,
% 2.13/1.64 (~c0_1(a1100)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1665, 1654])).
% 2.13/1.64 tff(1667,plain,
% 2.13/1.64 (((~hskp16) | c1_1(a1100)) <=> ((~hskp16) | c1_1(a1100))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1668,axiom,((~hskp16) | c1_1(a1100)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 2.13/1.64 tff(1669,plain,
% 2.13/1.64 ((~hskp16) | c1_1(a1100)),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 2.13/1.64 tff(1670,plain,
% 2.13/1.64 ((~hskp16) | c1_1(a1100)),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1669, 1667])).
% 2.13/1.64 tff(1671,plain,
% 2.13/1.64 ((~hskp16) | c1_1(a1100)),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1670, 1667])).
% 2.13/1.64 tff(1672,plain,
% 2.13/1.64 ((~hskp16) | c1_1(a1100)),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1671, 1667])).
% 2.13/1.64 tff(1673,plain,
% 2.13/1.64 ((~hskp16) | c1_1(a1100)),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1672, 1667])).
% 2.13/1.64 tff(1674,plain,
% 2.13/1.64 ((~hskp16) | c1_1(a1100)),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1673, 1667])).
% 2.13/1.64 tff(1675,plain,
% 2.13/1.64 ((~hskp16) | c1_1(a1100)),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1674, 1667])).
% 2.13/1.64 tff(1676,plain,
% 2.13/1.64 ((~hskp16) | c1_1(a1100)),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1675, 1667])).
% 2.13/1.64 tff(1677,plain,
% 2.13/1.64 (c1_1(a1100)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1676, 1654])).
% 2.13/1.64 tff(1678,plain,
% 2.13/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1679,plain,
% 2.13/1.64 ((hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)))),
% 2.13/1.64 inference(rewrite,[status(thm)],[])).
% 2.13/1.64 tff(1680,plain,
% 2.13/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100))))),
% 2.13/1.64 inference(monotonicity,[status(thm)],[1679])).
% 2.13/1.64 tff(1681,plain,
% 2.13/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)))),
% 2.13/1.64 inference(transitivity,[status(thm)],[1680, 1678])).
% 2.13/1.64 tff(1682,plain,
% 2.13/1.64 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.13/1.64 inference(quant_inst,[status(thm)],[])).
% 2.13/1.64 tff(1683,plain,
% 2.13/1.64 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100))),
% 2.13/1.64 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 2.13/1.64 tff(1684,plain,
% 2.13/1.64 (hskp4),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1683, 186, 1677, 1115, 1666, 1660, 12, 11, 1240])).
% 2.13/1.64 tff(1685,plain,
% 2.13/1.64 (c0_1(a1084)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1258, 1684])).
% 2.13/1.64 tff(1686,plain,
% 2.13/1.64 (~c1_1(a1084)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1264, 1684])).
% 2.13/1.64 tff(1687,plain,
% 2.13/1.64 (~c3_1(a1084)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1270, 1684])).
% 2.13/1.64 tff(1688,plain,
% 2.13/1.64 ($false),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1371, 1687, 1686, 57, 208, 1685, 1216, 1635, 1214, 1634, 1633, 1140])).
% 2.13/1.64 tff(1689,plain,(c0_1(a1082) | hskp9 | hskp14 | c0_1(a1085) | c1_1(a1085) | hskp0 | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.64 tff(1690,plain,
% 2.13/1.64 ($false),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1689, 1622, 1621, 208, 12, 11, 1514, 57])).
% 2.13/1.64 tff(1691,plain,(hskp14 | c0_1(a1085) | c1_1(a1085) | hskp9 | c1_1(a1080) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.64 tff(1692,plain,
% 2.13/1.64 (hskp14),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1691, 912, 11, 57, 12, 69])).
% 2.13/1.64 tff(1693,plain,
% 2.13/1.64 (~c2_1(a1097)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[282, 1692])).
% 2.13/1.64 tff(1694,plain,
% 2.13/1.64 (c3_1(a1097)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[333, 1692])).
% 2.13/1.64 tff(1695,plain,
% 2.13/1.64 (c1_1(a1097)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[293, 1692])).
% 2.13/1.64 tff(1696,plain,
% 2.13/1.64 (hskp26),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1383, 186, 1195, 1194, 1201, 1695, 1694, 1693, 89])).
% 2.13/1.64 tff(1697,plain,
% 2.13/1.64 (~c0_1(a1146)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1389, 1696])).
% 2.13/1.64 tff(1698,plain,
% 2.13/1.64 (c3_1(a1146)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1400, 1696])).
% 2.13/1.64 tff(1699,plain,
% 2.13/1.64 (c2_1(a1146)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1411, 1696])).
% 2.13/1.64 tff(1700,plain,
% 2.13/1.64 (hskp19),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1418, 186, 1699, 1698, 1697, 79])).
% 2.13/1.64 tff(1701,plain,
% 2.13/1.64 (~c2_1(a1113)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[971, 1700])).
% 2.13/1.64 tff(1702,plain,
% 2.13/1.64 (c1_1(a1113)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[982, 1700])).
% 2.13/1.64 tff(1703,plain,
% 2.13/1.64 (c0_1(a1113)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[993, 1700])).
% 2.13/1.64 tff(1704,plain,
% 2.13/1.64 (c3_1(a1080)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1539, 186, 1703, 1702, 1115, 1701, 12, 11, 1503, 69, 67])).
% 2.13/1.64 tff(1705,plain,
% 2.13/1.64 (hskp1),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1546, 186, 1703, 1702, 912, 1701, 69, 576, 1704])).
% 2.13/1.64 tff(1706,plain,
% 2.13/1.64 (~c1_1(a1081)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[643, 1705])).
% 2.13/1.64 tff(1707,plain,
% 2.13/1.64 (~c0_1(a1081)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[637, 1705])).
% 2.13/1.64 tff(1708,plain,
% 2.13/1.64 (c3_1(a1081)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1559, 1705])).
% 2.13/1.64 tff(1709,plain,
% 2.13/1.64 (hskp11),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[759, 186, 1195, 1194, 1201, 1708, 1707, 1706, 752])).
% 2.13/1.64 tff(1710,plain,
% 2.13/1.64 (~c3_1(a1091)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[704, 1709])).
% 2.13/1.64 tff(1711,plain,
% 2.13/1.64 (~c0_1(a1091)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[710, 1709])).
% 2.13/1.64 tff(1712,plain,
% 2.13/1.64 (c2_1(a1091)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[721, 1709])).
% 2.13/1.64 tff(1713,plain,
% 2.13/1.64 (hskp30),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1570, 186, 57, 1703, 1702, 1701, 102])).
% 2.13/1.64 tff(1714,plain,
% 2.13/1.64 (c3_1(a1109)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[363, 1713])).
% 2.13/1.64 tff(1715,plain,
% 2.13/1.64 (c1_1(a1109)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[312, 1713])).
% 2.13/1.64 tff(1716,plain,
% 2.13/1.64 (c0_1(a1109)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[352, 1713])).
% 2.13/1.64 tff(1717,plain,
% 2.13/1.64 (hskp17),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1580, 186, 1716, 1715, 1714, 1712, 1711, 1710, 1513])).
% 2.13/1.64 tff(1718,plain,
% 2.13/1.64 (~c2_1(a1102)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1610, 1717])).
% 2.13/1.64 tff(1719,plain,
% 2.13/1.64 (~c0_1(a1102)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1586, 1717])).
% 2.13/1.64 tff(1720,plain,
% 2.13/1.64 (c1_1(a1102)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1617, 186, 1716, 1715, 1714, 1195, 1194, 1201, 1719, 1718, 374])).
% 2.13/1.64 tff(1721,plain,
% 2.13/1.64 (c3_1(a1102)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1597, 1717])).
% 2.13/1.64 tff(1722,plain,
% 2.13/1.64 (hskp2 | (~c1_1(a1102))),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1604, 186, 57, 1721, 1719, 438])).
% 2.13/1.64 tff(1723,plain,
% 2.13/1.64 (hskp2),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[1722, 1720])).
% 2.13/1.64 tff(1724,plain,
% 2.13/1.64 (~c0_1(a1082)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[621, 1723])).
% 2.13/1.64 tff(1725,plain,
% 2.13/1.64 (~c3_1(a1082)),
% 2.13/1.64 inference(unit_resolution,[status(thm)],[451, 1723])).
% 2.13/1.64 tff(1726,plain,
% 2.13/1.64 (~c2_1(a1082)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[627, 1723])).
% 2.13/1.65 tff(1727,plain,
% 2.13/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102)))),
% 2.13/1.65 inference(rewrite,[status(thm)],[])).
% 2.13/1.65 tff(1728,plain,
% 2.13/1.65 ((hskp3 | (~ndr1_0) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102)))),
% 2.13/1.65 inference(rewrite,[status(thm)],[])).
% 2.13/1.65 tff(1729,plain,
% 2.13/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102))))),
% 2.13/1.65 inference(monotonicity,[status(thm)],[1728])).
% 2.13/1.65 tff(1730,plain,
% 2.13/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102)))),
% 2.13/1.65 inference(transitivity,[status(thm)],[1729, 1727])).
% 2.13/1.65 tff(1731,plain,
% 2.13/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.13/1.65 inference(quant_inst,[status(thm)],[])).
% 2.13/1.65 tff(1732,plain,
% 2.13/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a1102) | c2_1(a1102) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1102))),
% 2.13/1.65 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 2.13/1.65 tff(1733,plain,
% 2.13/1.65 (hskp3),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1732, 186, 1115, 1719, 1718, 12, 11, 22, 1720])).
% 2.13/1.65 tff(1734,plain,
% 2.13/1.65 (~c2_1(a1083)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[904, 1733])).
% 2.13/1.65 tff(1735,plain,
% 2.13/1.65 (c1_1(a1083)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1099, 1733])).
% 2.13/1.65 tff(1736,plain,
% 2.13/1.65 (~c3_1(a1083)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[910, 1733])).
% 2.13/1.65 tff(1737,plain,
% 2.13/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085)))),
% 2.13/1.65 inference(rewrite,[status(thm)],[])).
% 2.13/1.65 tff(1738,plain,
% 2.13/1.65 (((~ndr1_0) | c2_1(a1083) | (~c1_1(a1083)) | (~c0_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085)))),
% 2.13/1.65 inference(rewrite,[status(thm)],[])).
% 2.13/1.65 tff(1739,plain,
% 2.13/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1083) | (~c1_1(a1083)) | (~c0_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085))))),
% 2.13/1.65 inference(monotonicity,[status(thm)],[1738])).
% 2.13/1.65 tff(1740,plain,
% 2.13/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1083) | (~c1_1(a1083)) | (~c0_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085)))),
% 2.13/1.65 inference(transitivity,[status(thm)],[1739, 1737])).
% 2.13/1.65 tff(1741,plain,
% 2.13/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1083) | (~c1_1(a1083)) | (~c0_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c0_1(a1083)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.13/1.65 inference(quant_inst,[status(thm)],[])).
% 2.13/1.65 tff(1742,plain,
% 2.13/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1085))),
% 2.13/1.65 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 2.13/1.65 tff(1743,plain,
% 2.13/1.65 (~c0_1(a1083)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1742, 207, 1453, 1293, 12, 11, 1003, 1002, 67])).
% 2.13/1.65 tff(1744,plain,
% 2.13/1.65 (hskp4),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1447, 207, 1453, 1293, 12, 11, 1002, 1240, 1743])).
% 2.13/1.65 tff(1745,plain,
% 2.13/1.65 (c0_1(a1084)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1258, 1744])).
% 2.13/1.65 tff(1746,plain,
% 2.13/1.65 (~c3_1(a1084)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1270, 1744])).
% 2.13/1.65 tff(1747,plain,
% 2.13/1.65 (~c1_1(a1084)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1264, 1744])).
% 2.13/1.65 tff(1748,plain,
% 2.13/1.65 (hskp14),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1370, 57, 207, 1747, 1746, 1745, 1294, 1293, 1273, 1003, 1002, 1274])).
% 2.13/1.65 tff(1749,plain,
% 2.13/1.65 (~c2_1(a1097)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[282, 1748])).
% 2.13/1.65 tff(1750,plain,
% 2.13/1.65 (c3_1(a1097)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[333, 1748])).
% 2.13/1.65 tff(1751,plain,
% 2.13/1.65 (c1_1(a1097)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[293, 1748])).
% 2.13/1.65 tff(1752,plain,
% 2.13/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 2.13/1.65 inference(rewrite,[status(thm)],[])).
% 2.13/1.65 tff(1753,plain,
% 2.13/1.65 (((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085)) <=> (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 2.13/1.65 inference(rewrite,[status(thm)],[])).
% 2.13/1.65 tff(1754,plain,
% 2.13/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 2.13/1.65 inference(monotonicity,[status(thm)],[1753])).
% 2.13/1.65 tff(1755,plain,
% 2.13/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 2.13/1.65 inference(transitivity,[status(thm)],[1754, 1752])).
% 2.13/1.65 tff(1756,plain,
% 2.13/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c1_1(a1085) | c0_1(a1085) | c3_1(a1085))),
% 2.13/1.65 inference(quant_inst,[status(thm)],[])).
% 2.13/1.65 tff(1757,plain,
% 2.13/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1097) | c0_1(a1085) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c3_1(a1085) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 2.13/1.65 inference(modus_ponens,[status(thm)],[1756, 1755])).
% 2.13/1.65 tff(1758,plain,
% 2.13/1.65 (c3_1(a1085)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1757, 207, 1751, 1750, 1293, 1749, 12, 11, 1003, 1002, 476])).
% 2.13/1.65 tff(1759,plain,
% 2.13/1.65 (hskp19 | (~c3_1(a1085))),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[964, 207, 1453, 12, 79])).
% 2.13/1.65 tff(1760,plain,
% 2.13/1.65 (hskp19),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1759, 1758])).
% 2.13/1.65 tff(1761,plain,
% 2.13/1.65 (~c2_1(a1113)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[971, 1760])).
% 2.13/1.65 tff(1762,plain,
% 2.13/1.65 (c1_1(a1113)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[982, 1760])).
% 2.13/1.65 tff(1763,plain,
% 2.13/1.65 (c0_1(a1113)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[993, 1760])).
% 2.13/1.65 tff(1764,plain,
% 2.13/1.65 (c3_1(a1113)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1000, 207, 1763, 1762, 1453, 1761, 12, 11, 67])).
% 2.13/1.65 tff(1765,plain,
% 2.13/1.65 (c2_1(a1084)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1463, 1763, 207, 1762, 1453, 1745, 1761, 12, 11, 1746])).
% 2.13/1.65 tff(1766,plain,
% 2.13/1.65 (hskp9 | hskp8),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1156, 207, 1453, 12, 11, 1150])).
% 2.13/1.65 tff(1767,plain,
% 2.13/1.65 (hskp8),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1766, 57])).
% 2.13/1.65 tff(1768,plain,
% 2.13/1.65 (~c2_1(a1088)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1163, 1767])).
% 2.13/1.65 tff(1769,plain,
% 2.13/1.65 (c0_1(a1088)),
% 2.13/1.65 inference(unit_resolution,[status(thm)],[1185, 1767])).
% 2.13/1.65 tff(1770,plain,
% 2.13/1.65 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088)))),
% 2.13/1.65 inference(rewrite,[status(thm)],[])).
% 2.13/1.65 tff(1771,plain,
% 2.13/1.65 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c0_1(a1088))) <=> (hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088)))),
% 2.13/1.65 inference(rewrite,[status(thm)],[])).
% 2.13/1.65 tff(1772,plain,
% 2.13/1.65 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c0_1(a1088)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088))))),
% 2.13/1.65 inference(monotonicity,[status(thm)],[1771])).
% 2.13/1.65 tff(1773,plain,
% 2.13/1.65 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c0_1(a1088)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088)))),
% 2.13/1.66 inference(transitivity,[status(thm)],[1772, 1770])).
% 2.13/1.66 tff(1774,plain,
% 2.13/1.66 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c0_1(a1088)))),
% 2.13/1.66 inference(quant_inst,[status(thm)],[])).
% 2.13/1.66 tff(1775,plain,
% 2.13/1.66 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a1088) | (~ndr1_0) | (~c0_1(a1088)) | (~c1_1(a1088))),
% 2.13/1.66 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 2.13/1.66 tff(1776,plain,
% 2.13/1.66 (hskp30 | (~c1_1(a1088))),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1775, 207, 57, 1769, 1768, 102])).
% 2.13/1.66 tff(1777,plain,
% 2.13/1.66 (~c1_1(a1088)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1776, 648])).
% 2.13/1.66 tff(1778,plain,
% 2.13/1.66 (c3_1(a1088)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1174, 1767])).
% 2.13/1.66 tff(1779,plain,
% 2.13/1.66 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088)))),
% 2.13/1.66 inference(rewrite,[status(thm)],[])).
% 2.13/1.66 tff(1780,plain,
% 2.13/1.66 ((hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1088) | c1_1(a1088) | (~c3_1(a1088))) <=> (hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088)))),
% 2.13/1.66 inference(rewrite,[status(thm)],[])).
% 2.13/1.66 tff(1781,plain,
% 2.13/1.66 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1088) | c1_1(a1088) | (~c3_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088))))),
% 2.13/1.66 inference(monotonicity,[status(thm)],[1780])).
% 2.13/1.66 tff(1782,plain,
% 2.13/1.66 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1088) | c1_1(a1088) | (~c3_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088)))),
% 2.13/1.66 inference(transitivity,[status(thm)],[1781, 1779])).
% 2.13/1.66 tff(1783,plain,
% 2.13/1.66 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1083) | c3_1(a1083) | (~c1_1(a1083)) | c2_1(a1088) | c1_1(a1088) | (~c3_1(a1088)))),
% 2.13/1.66 inference(quant_inst,[status(thm)],[])).
% 2.13/1.66 tff(1784,plain,
% 2.13/1.66 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a1088) | c2_1(a1083) | c3_1(a1083) | (~ndr1_0) | (~c1_1(a1083)) | c1_1(a1088) | (~c3_1(a1088))),
% 2.13/1.66 inference(modus_ponens,[status(thm)],[1783, 1782])).
% 2.13/1.66 tff(1785,plain,
% 2.13/1.66 (hskp23 | c1_1(a1088)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1784, 207, 1778, 1293, 1768, 1003, 1002, 1292])).
% 2.13/1.66 tff(1786,plain,
% 2.13/1.66 (hskp23),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1785, 1777])).
% 2.13/1.66 tff(1787,plain,
% 2.13/1.66 (c2_1(a1122)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1311, 1786])).
% 2.13/1.66 tff(1788,plain,
% 2.13/1.66 (~c3_1(a1122)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1330, 1786])).
% 2.13/1.66 tff(1789,plain,
% 2.13/1.66 (c0_1(a1122)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1324, 1786])).
% 2.13/1.66 tff(1790,plain,
% 2.13/1.66 (hskp14),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1368, 1789, 57, 207, 1788, 1747, 1746, 1787, 1745])).
% 2.13/1.66 tff(1791,plain,
% 2.13/1.66 (~c2_1(a1097)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[282, 1790])).
% 2.13/1.66 tff(1792,plain,
% 2.13/1.66 (c3_1(a1097)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[333, 1790])).
% 2.13/1.66 tff(1793,plain,
% 2.13/1.66 (c1_1(a1097)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[293, 1790])).
% 2.13/1.66 tff(1794,plain,
% 2.13/1.66 (c3_1(a1085)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1757, 207, 1793, 1792, 1293, 1791, 12, 11, 1003, 1002, 476])).
% 2.13/1.66 tff(1795,plain,
% 2.13/1.66 (hskp19),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1759, 1794])).
% 2.13/1.66 tff(1796,plain,
% 2.13/1.66 (~c2_1(a1113)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[971, 1795])).
% 2.13/1.66 tff(1797,plain,
% 2.13/1.66 (c1_1(a1113)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[982, 1795])).
% 2.13/1.66 tff(1798,plain,
% 2.13/1.66 (c0_1(a1113)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[993, 1795])).
% 2.13/1.66 tff(1799,plain,
% 2.13/1.66 ($false),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1570, 207, 648, 57, 1798, 1797, 1796, 102])).
% 2.13/1.66 tff(1800,plain,(hskp30 | (~ndr1_0) | hskp9 | (~c2_1(a1085)) | c0_1(a1085) | (~c1_1(a1083)) | c1_1(a1085) | c2_1(a1083) | c3_1(a1083)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.66 tff(1801,plain,
% 2.13/1.66 (hskp30),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1800, 57, 207, 1453, 12, 1293, 11, 1003, 1002])).
% 2.13/1.66 tff(1802,plain,
% 2.13/1.66 (c3_1(a1109)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[363, 1801])).
% 2.13/1.66 tff(1803,plain,
% 2.13/1.66 (c1_1(a1109)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[312, 1801])).
% 2.13/1.66 tff(1804,plain,
% 2.13/1.66 (c0_1(a1109)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[352, 1801])).
% 2.13/1.66 tff(1805,plain,
% 2.13/1.66 (hskp28),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1192, 207, 57, 1769, 1778, 1768, 323])).
% 2.13/1.66 tff(1806,plain,
% 2.13/1.66 (hskp11),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[772, 1749, 207, 1805, 1804, 629, 630, 646, 645, 1750, 1751, 1803, 1802, 631])).
% 2.13/1.66 tff(1807,plain,
% 2.13/1.66 (~c0_1(a1091)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[710, 1806])).
% 2.13/1.66 tff(1808,plain,
% 2.13/1.66 (c2_1(a1091)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[721, 1806])).
% 2.13/1.66 tff(1809,plain,
% 2.13/1.66 ((~c2_1(a1084)) | (~c1_1(a1091))),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1492, 207, 57, 1808, 1807, 1747, 1746, 1475])).
% 2.13/1.66 tff(1810,plain,
% 2.13/1.66 (~c1_1(a1091)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1809, 1765])).
% 2.13/1.66 tff(1811,plain,
% 2.13/1.66 (~c3_1(a1091)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[704, 1806])).
% 2.13/1.66 tff(1812,plain,
% 2.13/1.66 ($false),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1500, 207, 1762, 1293, 1761, 1807, 1811, 1003, 1002, 476, 1810, 1764])).
% 2.13/1.66 tff(1813,plain,(hskp9 | (~ndr1_0) | (~c1_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c2_1(a1085)) | c0_1(a1085) | c1_1(a1085) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | (~c3_1(a1103)) | c1_1(a1103) | (~c0_1(a1103))), inference(lemma,lemma(discharge,[]))).
% 2.13/1.66 tff(1814,plain,
% 2.13/1.66 (hskp9 | (~c1_1(a1083)) | c2_1(a1083) | c3_1(a1083) | (~c2_1(a1085)) | c0_1(a1085) | c1_1(a1085) | c2_1(a1082) | c3_1(a1082) | c0_1(a1081) | c1_1(a1081) | c0_1(a1082) | (~c3_1(a1103)) | c1_1(a1103) | (~c0_1(a1103))),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1813, 186])).
% 2.13/1.66 tff(1815,plain,
% 2.13/1.66 ($false),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1814, 1736, 1735, 57, 1707, 1115, 12, 11, 1706, 1734, 1726, 1725, 1724, 1216, 1214, 1140])).
% 2.13/1.66 tff(1816,plain,(c1_1(a1080) | hskp9 | c0_1(a1085) | c1_1(a1085) | c2_1(a1080)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.66 tff(1817,plain,
% 2.13/1.66 (c1_1(a1080)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1816, 69, 12, 11, 57])).
% 2.13/1.66 tff(1818,plain,
% 2.13/1.66 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 2.13/1.66 inference(rewrite,[status(thm)],[])).
% 2.13/1.66 tff(1819,plain,
% 2.13/1.66 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080))) <=> (hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 2.13/1.66 inference(rewrite,[status(thm)],[])).
% 2.13/1.66 tff(1820,plain,
% 2.13/1.66 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080))))),
% 2.13/1.66 inference(monotonicity,[status(thm)],[1819])).
% 2.13/1.66 tff(1821,plain,
% 2.13/1.66 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)))),
% 2.13/1.66 inference(transitivity,[status(thm)],[1820, 1818])).
% 2.13/1.66 tff(1822,plain,
% 2.13/1.66 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)))),
% 2.13/1.66 inference(quant_inst,[status(thm)],[])).
% 2.13/1.66 tff(1823,plain,
% 2.13/1.66 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080))),
% 2.13/1.66 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 2.13/1.66 tff(1824,plain,
% 2.13/1.66 (hskp30 | (~c0_1(a1080)) | (~c1_1(a1080))),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1823, 186, 57, 69, 102])).
% 2.13/1.66 tff(1825,plain,
% 2.13/1.66 (hskp30),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[1824, 1817, 1503])).
% 2.13/1.66 tff(1826,plain,
% 2.13/1.66 (c3_1(a1109)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[363, 1825])).
% 2.13/1.66 tff(1827,plain,
% 2.13/1.66 (c1_1(a1109)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[312, 1825])).
% 2.13/1.66 tff(1828,plain,
% 2.13/1.66 (c0_1(a1109)),
% 2.13/1.66 inference(unit_resolution,[status(thm)],[352, 1825])).
% 2.13/1.66 tff(1829,plain,
% 2.13/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.13/1.66 inference(rewrite,[status(thm)],[])).
% 2.13/1.66 tff(1830,plain,
% 2.13/1.66 (((~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.13/1.66 inference(rewrite,[status(thm)],[])).
% 2.13/1.66 tff(1831,plain,
% 2.13/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085))))),
% 2.13/1.66 inference(monotonicity,[status(thm)],[1830])).
% 2.13/1.66 tff(1832,plain,
% 2.13/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085)))),
% 2.13/1.66 inference(transitivity,[status(thm)],[1831, 1829])).
% 2.13/1.66 tff(1833,plain,
% 2.13/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1080) | (~c1_1(a1080)) | (~c0_1(a1080)) | c2_1(a1080) | c3_1(a1080) | (~c0_1(a1080)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.13/1.67 inference(quant_inst,[status(thm)],[])).
% 2.13/1.67 tff(1834,plain,
% 2.13/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1085) | c1_1(a1085) | (~c0_1(a1080)) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | (~c1_1(a1080)) | (~c2_1(a1085))),
% 2.13/1.67 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 2.13/1.67 tff(1835,plain,
% 2.13/1.67 ((~c0_1(a1080)) | c3_1(a1080) | (~c1_1(a1080))),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1834, 186, 1115, 12, 11, 69, 67])).
% 2.13/1.67 tff(1836,plain,
% 2.13/1.67 (c3_1(a1080)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1835, 1817, 1503])).
% 2.13/1.67 tff(1837,plain,
% 2.13/1.67 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.13/1.67 inference(rewrite,[status(thm)],[])).
% 2.13/1.67 tff(1838,plain,
% 2.13/1.67 ((hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080))) <=> (hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.13/1.67 inference(rewrite,[status(thm)],[])).
% 2.13/1.67 tff(1839,plain,
% 2.13/1.67 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 2.13/1.67 inference(monotonicity,[status(thm)],[1838])).
% 2.13/1.67 tff(1840,plain,
% 2.13/1.67 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.13/1.67 inference(transitivity,[status(thm)],[1839, 1837])).
% 2.13/1.67 tff(1841,plain,
% 2.13/1.67 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1080) | (~c3_1(a1080)) | (~c1_1(a1080)))),
% 2.13/1.67 inference(quant_inst,[status(thm)],[])).
% 2.13/1.67 tff(1842,plain,
% 2.13/1.67 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1080)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 2.13/1.67 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 2.13/1.67 tff(1843,plain,
% 2.13/1.67 (hskp26 | (~c3_1(a1080)) | (~c1_1(a1080))),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1842, 186, 1195, 1194, 1201, 69, 89])).
% 2.13/1.67 tff(1844,plain,
% 2.13/1.67 (hskp26),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1843, 1836, 1817])).
% 2.13/1.67 tff(1845,plain,
% 2.13/1.67 (~c0_1(a1146)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1389, 1844])).
% 2.13/1.67 tff(1846,plain,
% 2.13/1.67 (c3_1(a1146)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1400, 1844])).
% 2.13/1.67 tff(1847,plain,
% 2.13/1.67 (c2_1(a1146)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1411, 1844])).
% 2.13/1.67 tff(1848,plain,
% 2.13/1.67 (hskp19),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1418, 186, 1847, 1846, 1845, 79])).
% 2.13/1.67 tff(1849,plain,
% 2.13/1.67 (c1_1(a1113)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[982, 1848])).
% 2.13/1.67 tff(1850,plain,
% 2.13/1.67 (c0_1(a1113)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[993, 1848])).
% 2.13/1.67 tff(1851,plain,
% 2.13/1.67 (~c2_1(a1113)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[971, 1848])).
% 2.13/1.67 tff(1852,assumption,(~c0_1(a1146)), introduced(assumption)).
% 2.13/1.67 tff(1853,assumption,(c3_1(a1146)), introduced(assumption)).
% 2.13/1.67 tff(1854,plain,
% 2.13/1.67 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146)))),
% 2.13/1.67 inference(rewrite,[status(thm)],[])).
% 2.13/1.67 tff(1855,plain,
% 2.13/1.67 ((hskp9 | hskp2 | (~ndr1_0) | c0_1(a1146) | (~c3_1(a1146)) | (~c1_1(a1146))) <=> (hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146)))),
% 2.13/1.67 inference(rewrite,[status(thm)],[])).
% 2.13/1.67 tff(1856,plain,
% 2.13/1.67 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1146) | (~c3_1(a1146)) | (~c1_1(a1146)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146))))),
% 2.13/1.67 inference(monotonicity,[status(thm)],[1855])).
% 2.13/1.67 tff(1857,plain,
% 2.13/1.67 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1146) | (~c3_1(a1146)) | (~c1_1(a1146)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146)))),
% 2.13/1.67 inference(transitivity,[status(thm)],[1856, 1854])).
% 2.13/1.67 tff(1858,plain,
% 2.13/1.67 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1146) | (~c3_1(a1146)) | (~c1_1(a1146)))),
% 2.13/1.67 inference(quant_inst,[status(thm)],[])).
% 2.13/1.67 tff(1859,plain,
% 2.13/1.67 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1146) | (~ndr1_0) | (~c1_1(a1146)) | (~c3_1(a1146))),
% 2.13/1.67 inference(modus_ponens,[status(thm)],[1858, 1857])).
% 2.13/1.67 tff(1860,plain,
% 2.13/1.67 (hskp2 | (~c1_1(a1146))),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1859, 186, 57, 1853, 1852, 438])).
% 2.13/1.67 tff(1861,plain,
% 2.13/1.67 (~c1_1(a1146)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1860, 68])).
% 2.13/1.67 tff(1862,assumption,(c2_1(a1146)), introduced(assumption)).
% 2.13/1.67 tff(1863,plain,
% 2.13/1.67 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146)))),
% 2.13/1.67 inference(rewrite,[status(thm)],[])).
% 2.13/1.67 tff(1864,plain,
% 2.13/1.67 ((hskp11 | hskp9 | (~ndr1_0) | c1_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146))) <=> (hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146)))),
% 2.13/1.67 inference(rewrite,[status(thm)],[])).
% 2.13/1.67 tff(1865,plain,
% 2.13/1.67 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146))))),
% 2.13/1.67 inference(monotonicity,[status(thm)],[1864])).
% 2.13/1.67 tff(1866,plain,
% 2.13/1.67 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146)))),
% 2.13/1.67 inference(transitivity,[status(thm)],[1865, 1863])).
% 2.13/1.67 tff(1867,plain,
% 2.13/1.67 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1146) | (~c2_1(a1146)) | (~c3_1(a1146)))),
% 2.13/1.67 inference(quant_inst,[status(thm)],[])).
% 2.13/1.67 tff(1868,plain,
% 2.13/1.67 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c2_1(a1146)) | c1_1(a1146) | (~c3_1(a1146))),
% 2.13/1.67 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 2.13/1.67 tff(1869,plain,
% 2.13/1.67 (hskp11 | c1_1(a1146)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1868, 186, 57, 1862, 1853, 1129])).
% 2.13/1.67 tff(1870,plain,
% 2.13/1.67 (hskp11),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1869, 1861])).
% 2.13/1.67 tff(1871,plain,
% 2.13/1.67 (~c3_1(a1091)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[704, 1870])).
% 2.13/1.67 tff(1872,plain,
% 2.13/1.67 (~c0_1(a1091)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[710, 1870])).
% 2.13/1.67 tff(1873,plain,
% 2.13/1.67 (c2_1(a1091)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[721, 1870])).
% 2.13/1.67 tff(1874,plain,
% 2.13/1.67 (hskp17),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1580, 186, 411, 410, 409, 1873, 1872, 1871, 1513])).
% 2.13/1.67 tff(1875,plain,
% 2.13/1.67 (~c0_1(a1102)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1586, 1874])).
% 2.13/1.67 tff(1876,plain,
% 2.13/1.67 (c3_1(a1102)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1597, 1874])).
% 2.13/1.67 tff(1877,plain,
% 2.13/1.67 (~c1_1(a1102)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1604, 186, 57, 68, 1876, 1875, 438])).
% 2.13/1.67 tff(1878,plain,
% 2.13/1.67 (~c2_1(a1102)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1610, 1874])).
% 2.13/1.67 tff(1879,assumption,(c3_1(a1092)), introduced(assumption)).
% 2.13/1.67 tff(1880,assumption,(c2_1(a1092)), introduced(assumption)).
% 2.13/1.67 tff(1881,assumption,(c0_1(a1092)), introduced(assumption)).
% 2.13/1.67 tff(1882,plain,
% 2.13/1.67 ($false),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1617, 186, 411, 410, 409, 1881, 1880, 1879, 1875, 1878, 374, 1877])).
% 2.13/1.67 tff(1883,plain,(hskp2 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109)) | (~c0_1(a1092)) | (~c2_1(a1092)) | (~c3_1(a1092)) | hskp9 | (~c2_1(a1146)) | (~c3_1(a1146)) | c0_1(a1146)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.67 tff(1884,plain,
% 2.13/1.67 (hskp2),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1883, 1828, 1827, 1826, 1195, 1194, 1201, 57, 1847, 1846, 1845])).
% 2.13/1.67 tff(1885,plain,
% 2.13/1.67 (~c0_1(a1082)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[621, 1884])).
% 2.13/1.67 tff(1886,plain,
% 2.13/1.67 (~c2_1(a1082)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[627, 1884])).
% 2.13/1.67 tff(1887,plain,
% 2.13/1.67 (c3_1(a1113)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1000, 186, 1455, 1454, 1115, 1452, 12, 11, 67])).
% 2.13/1.67 tff(1888,plain,
% 2.13/1.67 (c0_1(a1082) | c1_1(a1082)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[741, 186, 411, 410, 409, 1195, 1194, 1201, 629, 374])).
% 2.13/1.67 tff(1889,plain,
% 2.13/1.67 (c1_1(a1082)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1888, 631])).
% 2.13/1.67 tff(1890,plain,
% 2.13/1.67 (hskp16),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1653, 631, 1889])).
% 2.13/1.67 tff(1891,plain,
% 2.13/1.67 (~c3_1(a1100)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1659, 1890])).
% 2.13/1.67 tff(1892,plain,
% 2.13/1.67 (~c0_1(a1100)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1665, 1890])).
% 2.13/1.67 tff(1893,plain,
% 2.13/1.67 (c1_1(a1100)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1676, 1890])).
% 2.13/1.67 tff(1894,plain,
% 2.13/1.67 (hskp4),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1683, 186, 1893, 1115, 1892, 1891, 12, 11, 1240])).
% 2.13/1.67 tff(1895,plain,
% 2.13/1.67 (c0_1(a1084)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1258, 1894])).
% 2.13/1.67 tff(1896,plain,
% 2.13/1.67 (~c3_1(a1084)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1270, 1894])).
% 2.13/1.67 tff(1897,plain,
% 2.13/1.67 (c2_1(a1084)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1464, 1896, 1455, 1454, 1115, 1895, 1452, 12, 11])).
% 2.13/1.67 tff(1898,plain,
% 2.13/1.67 (~c1_1(a1084)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1264, 1894])).
% 2.13/1.67 tff(1899,plain,
% 2.13/1.67 (hskp3),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1631, 631, 1889])).
% 2.13/1.67 tff(1900,plain,
% 2.13/1.67 (~c3_1(a1083)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[910, 1899])).
% 2.13/1.67 tff(1901,plain,
% 2.13/1.67 (~c2_1(a1083)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[904, 1899])).
% 2.13/1.67 tff(1902,plain,
% 2.13/1.67 (c1_1(a1083)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1099, 1899])).
% 2.13/1.67 tff(1903,plain,
% 2.13/1.67 (c3_1(a1085)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1482, 186, 1454, 1902, 1452, 12, 11, 1901, 1900, 476, 1887])).
% 2.13/1.67 tff(1904,plain,
% 2.13/1.67 (hskp11),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1136, 1903, 57, 1115])).
% 2.13/1.67 tff(1905,plain,
% 2.13/1.67 (~c0_1(a1091)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[710, 1904])).
% 2.13/1.67 tff(1906,plain,
% 2.13/1.67 (c2_1(a1091)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[721, 1904])).
% 2.13/1.67 tff(1907,plain,
% 2.13/1.67 (~c1_1(a1091)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1492, 186, 57, 1906, 1905, 1898, 1896, 1475, 1897])).
% 2.13/1.67 tff(1908,plain,
% 2.13/1.67 (~c3_1(a1091)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[704, 1904])).
% 2.13/1.67 tff(1909,plain,
% 2.13/1.67 ($false),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1500, 186, 1454, 1902, 1452, 1905, 1908, 1901, 1900, 476, 1907, 1887])).
% 2.13/1.67 tff(1910,plain,(c0_1(a1082) | (~c1_1(a1113)) | c2_1(a1113) | hskp9 | (~c0_1(a1113)) | c0_1(a1085) | c1_1(a1085) | hskp0 | c2_1(a1082) | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109))), inference(lemma,lemma(discharge,[]))).
% 2.13/1.67 tff(1911,plain,
% 2.13/1.67 ($false),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1910, 1886, 1885, 1851, 57, 1850, 12, 11, 1514, 1849, 1828, 1827, 1826])).
% 2.13/1.67 tff(1912,plain,(c2_1(a1080) | hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.67 tff(1913,plain,
% 2.13/1.67 (c2_1(a1080)),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[1912, 57, 12, 11])).
% 2.13/1.67 tff(1914,plain,
% 2.13/1.67 (~hskp0),
% 2.13/1.67 inference(unit_resolution,[status(thm)],[28, 1913])).
% 2.13/1.67 tff(1915,plain,
% 2.13/1.67 (^[U: $i] : refl((hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 2.13/1.67 inference(bind,[status(th)],[])).
% 2.13/1.67 tff(1916,plain,
% 2.13/1.67 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.13/1.67 inference(quant_intro,[status(thm)],[1915])).
% 2.13/1.67 tff(1917,plain,
% 2.13/1.67 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.13/1.67 inference(rewrite,[status(thm)],[])).
% 2.13/1.67 tff(1918,plain,
% 2.13/1.67 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp2) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp2) <=> (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.13/1.67 inference(bind,[status(th)],[])).
% 2.13/1.67 tff(1919,plain,
% 2.13/1.67 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp2) <=> ![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.13/1.67 inference(quant_intro,[status(thm)],[1918])).
% 2.13/1.67 tff(1920,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 2.13/1.67 tff(1921,plain,
% 2.13/1.67 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.13/1.67 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 2.13/1.67 tff(1922,plain,
% 2.13/1.67 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.13/1.67 inference(modus_ponens,[status(thm)],[1921, 1917])).
% 2.13/1.67 tff(1923,plain,(
% 2.13/1.67 ![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.13/1.68 inference(skolemize,[status(sab)],[1922])).
% 2.13/1.68 tff(1924,plain,
% 2.13/1.68 (![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.13/1.68 inference(modus_ponens,[status(thm)],[1923, 1916])).
% 2.13/1.68 tff(1925,plain,
% 2.13/1.68 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.13/1.68 inference(rewrite,[status(thm)],[])).
% 2.13/1.68 tff(1926,plain,
% 2.13/1.68 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.13/1.68 inference(quant_inst,[status(thm)],[])).
% 2.13/1.68 tff(1927,plain,
% 2.13/1.68 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 2.13/1.68 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 2.13/1.68 tff(1928,plain,
% 2.13/1.68 (hskp0 | hskp2 | c1_1(a1092)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1927, 186, 1195, 1194, 1924])).
% 2.13/1.68 tff(1929,plain,
% 2.13/1.68 (c1_1(a1092)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1928, 68, 1914])).
% 2.13/1.68 tff(1930,plain,
% 2.13/1.68 (hskp19),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1529, 1929, 68])).
% 2.13/1.68 tff(1931,plain,
% 2.13/1.68 (~c2_1(a1113)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[971, 1930])).
% 2.13/1.68 tff(1932,plain,
% 2.13/1.68 (c1_1(a1113)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[982, 1930])).
% 2.13/1.68 tff(1933,plain,
% 2.13/1.68 (c0_1(a1113)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[993, 1930])).
% 2.13/1.68 tff(1934,plain,
% 2.13/1.68 (c3_1(a1113)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1000, 186, 1933, 1932, 1115, 1931, 12, 11, 67])).
% 2.13/1.68 tff(1935,plain,
% 2.13/1.68 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.13/1.68 inference(rewrite,[status(thm)],[])).
% 2.13/1.68 tff(1936,plain,
% 2.13/1.68 ((hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113))) <=> (hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.13/1.68 inference(rewrite,[status(thm)],[])).
% 2.13/1.68 tff(1937,plain,
% 2.13/1.68 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 2.13/1.68 inference(monotonicity,[status(thm)],[1936])).
% 2.13/1.68 tff(1938,plain,
% 2.13/1.68 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.13/1.68 inference(transitivity,[status(thm)],[1937, 1935])).
% 2.13/1.68 tff(1939,plain,
% 2.13/1.68 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)))),
% 2.13/1.68 inference(quant_inst,[status(thm)],[])).
% 2.13/1.68 tff(1940,plain,
% 2.13/1.68 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1113) | (~ndr1_0) | (~c1_1(a1113)) | (~c3_1(a1113)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 2.13/1.68 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 2.13/1.68 tff(1941,plain,
% 2.13/1.68 (hskp26),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1940, 186, 1195, 1194, 1201, 1932, 1931, 89, 1934])).
% 2.13/1.68 tff(1942,plain,
% 2.13/1.68 (~c0_1(a1146)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1389, 1941])).
% 2.13/1.68 tff(1943,plain,
% 2.13/1.68 (c3_1(a1146)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1400, 1941])).
% 2.13/1.68 tff(1944,plain,
% 2.13/1.68 (c2_1(a1146)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1411, 1941])).
% 2.13/1.68 tff(1945,plain,
% 2.13/1.68 (hskp30),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1570, 186, 57, 1933, 1932, 1931, 102])).
% 2.13/1.68 tff(1946,plain,
% 2.13/1.68 (c3_1(a1109)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[363, 1945])).
% 2.13/1.68 tff(1947,plain,
% 2.13/1.68 (c0_1(a1109)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[352, 1945])).
% 2.13/1.68 tff(1948,plain,
% 2.13/1.68 (c1_1(a1109)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[312, 1945])).
% 2.13/1.68 tff(1949,plain,
% 2.13/1.68 ($false),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1883, 1948, 1947, 68, 1946, 1195, 1194, 1201, 57, 1944, 1943, 1942])).
% 2.13/1.68 tff(1950,plain,(hskp2 | hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.68 tff(1951,plain,
% 2.13/1.68 (hskp2),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1950, 57, 12, 11])).
% 2.13/1.68 tff(1952,plain,
% 2.13/1.68 (~c0_1(a1082)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[621, 1951])).
% 2.13/1.68 tff(1953,plain,
% 2.13/1.68 (~c2_1(a1082)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[627, 1951])).
% 2.13/1.68 tff(1954,plain,
% 2.13/1.68 (hskp14),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1689, 631, 629, 12, 11, 1914, 57])).
% 2.13/1.68 tff(1955,plain,
% 2.13/1.68 (~c2_1(a1097)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[282, 1954])).
% 2.13/1.68 tff(1956,plain,
% 2.13/1.68 (c3_1(a1097)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[333, 1954])).
% 2.13/1.68 tff(1957,plain,
% 2.13/1.68 (c1_1(a1097)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[293, 1954])).
% 2.13/1.68 tff(1958,plain,
% 2.13/1.68 (hskp26),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1383, 186, 1195, 1194, 1201, 1957, 1956, 1955, 89])).
% 2.13/1.68 tff(1959,plain,
% 2.13/1.68 (~c0_1(a1146)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1389, 1958])).
% 2.13/1.68 tff(1960,plain,
% 2.13/1.68 (c3_1(a1146)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1400, 1958])).
% 2.13/1.68 tff(1961,plain,
% 2.13/1.68 (c2_1(a1146)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1411, 1958])).
% 2.13/1.68 tff(1962,plain,
% 2.13/1.68 (hskp19),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1418, 186, 1961, 1960, 1959, 79])).
% 2.13/1.68 tff(1963,plain,
% 2.13/1.68 (~c2_1(a1113)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[971, 1962])).
% 2.13/1.68 tff(1964,plain,
% 2.13/1.68 (c1_1(a1113)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[982, 1962])).
% 2.13/1.68 tff(1965,plain,
% 2.13/1.68 (c0_1(a1113)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[993, 1962])).
% 2.13/1.68 tff(1966,plain,
% 2.13/1.68 (hskp30),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1570, 186, 57, 1965, 1964, 1963, 102])).
% 2.13/1.68 tff(1967,plain,
% 2.13/1.68 (c3_1(a1109)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[363, 1966])).
% 2.13/1.68 tff(1968,plain,
% 2.13/1.68 (c0_1(a1109)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[352, 1966])).
% 2.13/1.68 tff(1969,plain,
% 2.13/1.68 (c1_1(a1109)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[312, 1966])).
% 2.13/1.68 tff(1970,plain,
% 2.13/1.68 ($false),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1910, 1969, 1968, 629, 57, 631, 12, 11, 1914, 1964, 1965, 1963, 1967])).
% 2.13/1.68 tff(1971,plain,(c0_1(a1082) | c2_1(a1082) | hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.68 tff(1972,plain,
% 2.13/1.68 ($false),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1971, 1953, 1952, 57, 12, 11])).
% 2.13/1.68 tff(1973,plain,(hskp9 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.13/1.68 tff(1974,plain,
% 2.13/1.68 (hskp9),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1973, 12, 11])).
% 2.13/1.68 tff(1975,plain,
% 2.13/1.68 (~c1_1(a1089)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[534, 1974])).
% 2.13/1.68 tff(1976,plain,
% 2.13/1.68 (c3_1(a1089)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[545, 1974])).
% 2.13/1.68 tff(1977,plain,
% 2.13/1.68 (c2_1(a1089)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[556, 1974])).
% 2.13/1.68 tff(1978,plain,
% 2.13/1.68 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 2.13/1.68 inference(rewrite,[status(thm)],[])).
% 2.13/1.68 tff(1979,plain,
% 2.13/1.68 ((hskp21 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089))) <=> (hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 2.13/1.68 inference(rewrite,[status(thm)],[])).
% 2.13/1.68 tff(1980,plain,
% 2.13/1.68 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089))))),
% 2.13/1.68 inference(monotonicity,[status(thm)],[1979])).
% 2.13/1.68 tff(1981,plain,
% 2.13/1.68 (((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 2.13/1.68 inference(transitivity,[status(thm)],[1980, 1978])).
% 2.13/1.68 tff(1982,plain,
% 2.13/1.68 ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp21 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 2.13/1.68 inference(quant_inst,[status(thm)],[])).
% 2.13/1.68 tff(1983,plain,
% 2.13/1.68 ((~![U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp21 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 2.13/1.68 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 2.13/1.68 tff(1984,plain,
% 2.13/1.68 (hskp21),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1983, 186, 1977, 1976, 1975, 56])).
% 2.13/1.68 tff(1985,plain,
% 2.13/1.68 (c1_1(a1120)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1055, 1984])).
% 2.13/1.68 tff(1986,plain,
% 2.13/1.68 (~c3_1(a1120)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1016, 1984])).
% 2.13/1.68 tff(1987,plain,
% 2.13/1.68 (c2_1(a1120)),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[1027, 1984])).
% 2.13/1.68 tff(1988,plain,
% 2.13/1.68 (~hskp18),
% 2.13/1.68 inference(unit_resolution,[status(thm)],[194, 121])).
% 2.13/1.68 tff(1989,plain,
% 2.13/1.68 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 2.13/1.68 inference(bind,[status(th)],[])).
% 2.13/1.68 tff(1990,plain,
% 2.13/1.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.13/1.68 inference(quant_intro,[status(thm)],[1989])).
% 2.13/1.68 tff(1991,plain,
% 2.13/1.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.13/1.68 inference(rewrite,[status(thm)],[])).
% 2.13/1.68 tff(1992,plain,
% 2.13/1.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 2.17/1.68 inference(bind,[status(th)],[])).
% 2.17/1.68 tff(1993,plain,
% 2.17/1.68 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.17/1.68 inference(quant_intro,[status(thm)],[1992])).
% 2.17/1.68 tff(1994,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 2.17/1.68 tff(1995,plain,
% 2.17/1.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 2.17/1.68 tff(1996,plain,
% 2.17/1.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1995, 1991])).
% 2.17/1.68 tff(1997,plain,(
% 2.17/1.68 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.17/1.68 inference(skolemize,[status(sab)],[1996])).
% 2.17/1.68 tff(1998,plain,
% 2.17/1.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1997, 1990])).
% 2.17/1.68 tff(1999,assumption,(~c3_1(a1120)), introduced(assumption)).
% 2.17/1.68 tff(2000,assumption,(c2_1(a1120)), introduced(assumption)).
% 2.17/1.68 tff(2001,assumption,(c1_1(a1120)), introduced(assumption)).
% 2.17/1.68 tff(2002,plain,
% 2.17/1.68 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(2003,plain,
% 2.17/1.68 ((hskp5 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c0_1(a1120)) | c3_1(a1120) | (~c1_1(a1120)) | (~c0_1(a1120))) <=> (hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(2004,plain,
% 2.17/1.68 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c0_1(a1120)) | c3_1(a1120) | (~c1_1(a1120)) | (~c0_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[2003])).
% 2.17/1.69 tff(2005,plain,
% 2.17/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c0_1(a1120)) | c3_1(a1120) | (~c1_1(a1120)) | (~c0_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.69 inference(transitivity,[status(thm)],[2004, 2002])).
% 2.17/1.69 tff(2006,plain,
% 2.17/1.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c0_1(a1120)) | c3_1(a1120) | (~c1_1(a1120)) | (~c0_1(a1120)))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(2007,plain,
% 2.17/1.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1120) | (~ndr1_0) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 2.17/1.69 tff(2008,plain,
% 2.17/1.69 (hskp5 | (~c0_1(a1120))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2007, 186, 2001, 2000, 1999, 1998])).
% 2.17/1.69 tff(2009,plain,
% 2.17/1.69 (~c0_1(a1120)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2008, 121])).
% 2.17/1.69 tff(2010,plain,
% 2.17/1.69 (hskp18 | c0_1(a1120)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1034, 186, 2000, 1999, 260])).
% 2.17/1.69 tff(2011,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2010, 2009, 1988])).
% 2.17/1.69 tff(2012,plain,(hskp5 | (~c2_1(a1120)) | c3_1(a1120) | (~c1_1(a1120))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.69 tff(2013,plain,
% 2.17/1.69 (hskp5),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2012, 1987, 1986, 1985])).
% 2.17/1.69 tff(2014,plain,
% 2.17/1.69 (c2_1(a1085)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[112, 2013])).
% 2.17/1.69 tff(2015,assumption,(~hskp19), introduced(assumption)).
% 2.17/1.69 tff(2016,assumption,(c3_1(a1089)), introduced(assumption)).
% 2.17/1.69 tff(2017,assumption,(c2_1(a1089)), introduced(assumption)).
% 2.17/1.69 tff(2018,plain,
% 2.17/1.69 (((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2019,plain,
% 2.17/1.69 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(2020,plain,
% 2.17/1.69 ((~![U: $i] : (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 2.17/1.69 tff(2021,plain,
% 2.17/1.69 (hskp19 | c0_1(a1089)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2020, 186, 2017, 2016, 79])).
% 2.17/1.69 tff(2022,plain,
% 2.17/1.69 (c0_1(a1089)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2021, 2015])).
% 2.17/1.69 tff(2023,assumption,(~c1_1(a1089)), introduced(assumption)).
% 2.17/1.69 tff(2024,plain,
% 2.17/1.69 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2025,plain,
% 2.17/1.69 ((hskp14 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089))) <=> (hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2026,plain,
% 2.17/1.69 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089))))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[2025])).
% 2.17/1.69 tff(2027,plain,
% 2.17/1.69 (((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.69 inference(transitivity,[status(thm)],[2026, 2024])).
% 2.17/1.69 tff(2028,plain,
% 2.17/1.69 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(2029,plain,
% 2.17/1.69 ((~![U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 2.17/1.69 tff(2030,plain,
% 2.17/1.69 (hskp14 | (~c0_1(a1089))),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2029, 186, 2017, 2023, 205])).
% 2.17/1.69 tff(2031,plain,
% 2.17/1.69 (hskp14),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2030, 2022])).
% 2.17/1.69 tff(2032,plain,
% 2.17/1.69 (~c2_1(a1097)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[282, 2031])).
% 2.17/1.69 tff(2033,plain,
% 2.17/1.69 (c3_1(a1097)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[333, 2031])).
% 2.17/1.69 tff(2034,plain,
% 2.17/1.69 (c1_1(a1097)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[293, 2031])).
% 2.17/1.69 tff(2035,plain,
% 2.17/1.69 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2036,plain,
% 2.17/1.69 ((hskp26 | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097))) <=> (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2037,plain,
% 2.17/1.69 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097))))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[2036])).
% 2.17/1.69 tff(2038,plain,
% 2.17/1.69 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097)))),
% 2.17/1.69 inference(transitivity,[status(thm)],[2037, 2035])).
% 2.17/1.69 tff(2039,plain,
% 2.17/1.69 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1097) | (~c3_1(a1097)) | (~c1_1(a1097)))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(2040,plain,
% 2.17/1.69 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp26 | c2_1(a1097) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | (~c0_1(a1089)) | (~c1_1(a1097)) | (~c3_1(a1097))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 2.17/1.69 tff(2041,plain,
% 2.17/1.69 (hskp26),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2040, 186, 2034, 2033, 2017, 2016, 2032, 89, 2022])).
% 2.17/1.69 tff(2042,plain,
% 2.17/1.69 (~c0_1(a1146)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1389, 2041])).
% 2.17/1.69 tff(2043,plain,
% 2.17/1.69 (c3_1(a1146)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1400, 2041])).
% 2.17/1.69 tff(2044,plain,
% 2.17/1.69 (c2_1(a1146)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1411, 2041])).
% 2.17/1.69 tff(2045,plain,
% 2.17/1.69 ($false),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1418, 186, 2015, 2044, 2043, 2042, 79])).
% 2.17/1.69 tff(2046,plain,(hskp19 | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.69 tff(2047,plain,
% 2.17/1.69 (hskp19),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2046, 1977, 1976, 1975])).
% 2.17/1.69 tff(2048,plain,
% 2.17/1.69 (~c2_1(a1113)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[971, 2047])).
% 2.17/1.69 tff(2049,plain,
% 2.17/1.69 (c1_1(a1113)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[982, 2047])).
% 2.17/1.69 tff(2050,plain,
% 2.17/1.69 (c0_1(a1113)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[993, 2047])).
% 2.17/1.69 tff(2051,plain,
% 2.17/1.69 (c3_1(a1113)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1000, 186, 2050, 2049, 2014, 2048, 12, 11, 67])).
% 2.17/1.69 tff(2052,assumption,(hskp3), introduced(assumption)).
% 2.17/1.69 tff(2053,plain,
% 2.17/1.69 (~c3_1(a1083)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[910, 2052])).
% 2.17/1.69 tff(2054,plain,
% 2.17/1.69 (~c2_1(a1083)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[904, 2052])).
% 2.17/1.69 tff(2055,plain,
% 2.17/1.69 (c1_1(a1083)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1099, 2052])).
% 2.17/1.69 tff(2056,plain,
% 2.17/1.69 (c3_1(a1085)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1482, 186, 2049, 2055, 2048, 12, 11, 2054, 2053, 476, 2051])).
% 2.17/1.69 tff(2057,plain,
% 2.17/1.69 (~c0_1(a1083)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1439, 186, 2050, 2049, 2014, 2048, 12, 11, 2054, 2053, 67])).
% 2.17/1.69 tff(2058,plain,
% 2.17/1.69 (hskp4),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1447, 186, 2014, 2055, 12, 11, 2053, 1240, 2057])).
% 2.17/1.69 tff(2059,plain,
% 2.17/1.69 (~c3_1(a1084)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1270, 2058])).
% 2.17/1.69 tff(2060,plain,
% 2.17/1.69 (c0_1(a1084)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1258, 2058])).
% 2.17/1.69 tff(2061,plain,
% 2.17/1.69 (c2_1(a1084)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[1464, 2060, 2050, 2049, 2014, 2059, 2048, 12, 11])).
% 2.17/1.69 tff(2062,plain,
% 2.17/1.69 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))))),
% 2.17/1.69 inference(bind,[status(th)],[])).
% 2.17/1.69 tff(2063,plain,
% 2.17/1.69 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 2.17/1.69 inference(quant_intro,[status(thm)],[2062])).
% 2.17/1.69 tff(2064,plain,
% 2.17/1.69 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2065,plain,
% 2.17/1.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp31) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))))),
% 2.17/1.69 inference(bind,[status(th)],[])).
% 2.17/1.69 tff(2066,plain,
% 2.17/1.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 2.17/1.69 inference(quant_intro,[status(thm)],[2065])).
% 2.17/1.69 tff(2067,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 2.17/1.69 tff(2068,plain,
% 2.17/1.69 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 2.17/1.69 tff(2069,plain,
% 2.17/1.69 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2068, 2064])).
% 2.17/1.69 tff(2070,plain,(
% 2.17/1.69 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 2.17/1.69 inference(skolemize,[status(sab)],[2069])).
% 2.17/1.69 tff(2071,plain,
% 2.17/1.69 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2070, 2063])).
% 2.17/1.69 tff(2072,plain,
% 2.17/1.69 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2073,plain,
% 2.17/1.69 ((hskp31 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c2_1(a1084)) | c3_1(a1084) | (~c0_1(a1084))) <=> (hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2074,plain,
% 2.17/1.69 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c2_1(a1084)) | c3_1(a1084) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120))))),
% 2.17/1.69 inference(monotonicity,[status(thm)],[2073])).
% 2.17/1.69 tff(2075,plain,
% 2.17/1.69 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c2_1(a1084)) | c3_1(a1084) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.69 inference(transitivity,[status(thm)],[2074, 2072])).
% 2.17/1.69 tff(2076,plain,
% 2.17/1.69 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c3_1(a1120) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c2_1(a1084)) | c3_1(a1084) | (~c0_1(a1084)))),
% 2.17/1.69 inference(quant_inst,[status(thm)],[])).
% 2.17/1.69 tff(2077,plain,
% 2.17/1.69 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(V) | (~c0_1(V)))) | hskp31 | c3_1(a1120) | c3_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)) | (~c1_1(a1120)) | (~c2_1(a1120))),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 2.17/1.69 tff(2078,plain,
% 2.17/1.69 (hskp31),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2077, 186, 1985, 1987, 2060, 1986, 2059, 2071, 2061])).
% 2.17/1.69 tff(2079,plain,
% 2.17/1.69 (((~hskp31) | c2_1(a1148)) <=> ((~hskp31) | c2_1(a1148))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2080,axiom,((~hskp31) | c2_1(a1148)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 2.17/1.69 tff(2081,plain,
% 2.17/1.69 ((~hskp31) | c2_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 2.17/1.69 tff(2082,plain,
% 2.17/1.69 ((~hskp31) | c2_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2081, 2079])).
% 2.17/1.69 tff(2083,plain,
% 2.17/1.69 ((~hskp31) | c2_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2082, 2079])).
% 2.17/1.69 tff(2084,plain,
% 2.17/1.69 ((~hskp31) | c2_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2083, 2079])).
% 2.17/1.69 tff(2085,plain,
% 2.17/1.69 ((~hskp31) | c2_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2084, 2079])).
% 2.17/1.69 tff(2086,plain,
% 2.17/1.69 ((~hskp31) | c2_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2085, 2079])).
% 2.17/1.69 tff(2087,plain,
% 2.17/1.69 ((~hskp31) | c2_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2086, 2079])).
% 2.17/1.69 tff(2088,plain,
% 2.17/1.69 ((~hskp31) | c2_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2087, 2079])).
% 2.17/1.69 tff(2089,plain,
% 2.17/1.69 (c2_1(a1148)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2088, 2078])).
% 2.17/1.69 tff(2090,plain,
% 2.17/1.69 (((~hskp31) | c1_1(a1148)) <=> ((~hskp31) | c1_1(a1148))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2091,axiom,((~hskp31) | c1_1(a1148)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 2.17/1.69 tff(2092,plain,
% 2.17/1.69 ((~hskp31) | c1_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 2.17/1.69 tff(2093,plain,
% 2.17/1.69 ((~hskp31) | c1_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2092, 2090])).
% 2.17/1.69 tff(2094,plain,
% 2.17/1.69 ((~hskp31) | c1_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2093, 2090])).
% 2.17/1.69 tff(2095,plain,
% 2.17/1.69 ((~hskp31) | c1_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2094, 2090])).
% 2.17/1.69 tff(2096,plain,
% 2.17/1.69 ((~hskp31) | c1_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2095, 2090])).
% 2.17/1.69 tff(2097,plain,
% 2.17/1.69 ((~hskp31) | c1_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2096, 2090])).
% 2.17/1.69 tff(2098,plain,
% 2.17/1.69 ((~hskp31) | c1_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2097, 2090])).
% 2.17/1.69 tff(2099,plain,
% 2.17/1.69 ((~hskp31) | c1_1(a1148)),
% 2.17/1.69 inference(modus_ponens,[status(thm)],[2098, 2090])).
% 2.17/1.69 tff(2100,plain,
% 2.17/1.69 (c1_1(a1148)),
% 2.17/1.69 inference(unit_resolution,[status(thm)],[2099, 2078])).
% 2.17/1.69 tff(2101,plain,
% 2.17/1.69 (((~hskp31) | c0_1(a1148)) <=> ((~hskp31) | c0_1(a1148))),
% 2.17/1.69 inference(rewrite,[status(thm)],[])).
% 2.17/1.69 tff(2102,axiom,((~hskp31) | c0_1(a1148)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 2.17/1.70 tff(2103,plain,
% 2.17/1.70 ((~hskp31) | c0_1(a1148)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 2.17/1.70 tff(2104,plain,
% 2.17/1.70 ((~hskp31) | c0_1(a1148)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2103, 2101])).
% 2.17/1.70 tff(2105,plain,
% 2.17/1.70 ((~hskp31) | c0_1(a1148)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2104, 2101])).
% 2.17/1.70 tff(2106,plain,
% 2.17/1.70 ((~hskp31) | c0_1(a1148)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2105, 2101])).
% 2.17/1.70 tff(2107,plain,
% 2.17/1.70 ((~hskp31) | c0_1(a1148)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2106, 2101])).
% 2.17/1.70 tff(2108,plain,
% 2.17/1.70 ((~hskp31) | c0_1(a1148)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2107, 2101])).
% 2.17/1.70 tff(2109,plain,
% 2.17/1.70 ((~hskp31) | c0_1(a1148)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2108, 2101])).
% 2.17/1.70 tff(2110,plain,
% 2.17/1.70 ((~hskp31) | c0_1(a1148)),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2109, 2101])).
% 2.17/1.70 tff(2111,plain,
% 2.17/1.70 (c0_1(a1148)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[2110, 2078])).
% 2.17/1.70 tff(2112,plain,
% 2.17/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(2113,plain,
% 2.17/1.70 ((hskp10 | (~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085))) <=> (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(2114,plain,
% 2.17/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148))))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[2113])).
% 2.17/1.70 tff(2115,plain,
% 2.17/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 2.17/1.70 inference(transitivity,[status(thm)],[2114, 2112])).
% 2.17/1.70 tff(2116,plain,
% 2.17/1.70 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c1_1(a1085) | c0_1(a1085) | (~c3_1(a1085)))),
% 2.17/1.70 inference(quant_inst,[status(thm)],[])).
% 2.17/1.70 tff(2117,plain,
% 2.17/1.70 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 2.17/1.70 tff(2118,plain,
% 2.17/1.70 (hskp10),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[2117, 186, 2111, 2100, 2089, 12, 11, 1045, 2056])).
% 2.17/1.70 tff(2119,plain,
% 2.17/1.70 (~c3_1(a1090)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1068, 2118])).
% 2.17/1.70 tff(2120,plain,
% 2.17/1.70 (~c1_1(a1090)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1074, 2118])).
% 2.17/1.70 tff(2121,plain,
% 2.17/1.70 (~c0_1(a1090)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1080, 2118])).
% 2.17/1.70 tff(2122,plain,
% 2.17/1.70 ($false),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1106, 186, 2049, 2055, 2048, 2121, 2120, 2119, 2054, 2053, 476, 2051])).
% 2.17/1.70 tff(2123,plain,((~hskp3) | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.70 tff(2124,plain,
% 2.17/1.70 (~hskp3),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[2123, 12, 11])).
% 2.17/1.70 tff(2125,plain,
% 2.17/1.70 ($false),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1087, 186, 2124, 2014, 46, 12, 11, 35, 29, 22])).
% 2.17/1.70 tff(2126,plain,((~hskp0) | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.70 tff(2127,plain,
% 2.17/1.70 (~hskp0),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[2126, 12, 11])).
% 2.17/1.70 tff(2128,plain,
% 2.17/1.70 (^[U: $i] : refl((hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 2.17/1.70 inference(bind,[status(th)],[])).
% 2.17/1.70 tff(2129,plain,
% 2.17/1.70 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.17/1.70 inference(quant_intro,[status(thm)],[2128])).
% 2.17/1.70 tff(2130,plain,
% 2.17/1.70 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(2131,plain,
% 2.17/1.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp16) <=> ((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp16) <=> (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 2.17/1.70 inference(bind,[status(th)],[])).
% 2.17/1.70 tff(2132,plain,
% 2.17/1.70 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp16) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.17/1.70 inference(quant_intro,[status(thm)],[2131])).
% 2.17/1.70 tff(2133,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 2.17/1.70 tff(2134,plain,
% 2.17/1.70 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 2.17/1.70 tff(2135,plain,
% 2.17/1.70 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2134, 2130])).
% 2.17/1.70 tff(2136,plain,(
% 2.17/1.70 ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.17/1.70 inference(skolemize,[status(sab)],[2135])).
% 2.17/1.70 tff(2137,plain,
% 2.17/1.70 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2136, 2129])).
% 2.17/1.70 tff(2138,plain,
% 2.17/1.70 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(2139,plain,
% 2.17/1.70 ((hskp0 | hskp2 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089))) <=> (hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(2140,plain,
% 2.17/1.70 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089))))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[2139])).
% 2.17/1.70 tff(2141,plain,
% 2.17/1.70 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.70 inference(transitivity,[status(thm)],[2140, 2138])).
% 2.17/1.70 tff(2142,plain,
% 2.17/1.70 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.70 inference(quant_inst,[status(thm)],[])).
% 2.17/1.70 tff(2143,plain,
% 2.17/1.70 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c0_1(a1089))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 2.17/1.70 tff(2144,plain,
% 2.17/1.70 (hskp0 | hskp2 | (~c0_1(a1089))),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[2143, 186, 1977, 1975, 1924])).
% 2.17/1.70 tff(2145,plain,
% 2.17/1.70 (~c0_1(a1089)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[2144, 68, 2127])).
% 2.17/1.70 tff(2146,assumption,(hskp4), introduced(assumption)).
% 2.17/1.70 tff(2147,plain,
% 2.17/1.70 (c0_1(a1084)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1258, 2146])).
% 2.17/1.70 tff(2148,plain,
% 2.17/1.70 (~c3_1(a1084)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1270, 2146])).
% 2.17/1.70 tff(2149,plain,
% 2.17/1.70 (c2_1(a1084)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1464, 2148, 2050, 2049, 2014, 2147, 2048, 12, 11])).
% 2.17/1.70 tff(2150,plain,
% 2.17/1.70 (~c1_1(a1084)),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[1264, 2146])).
% 2.17/1.70 tff(2151,plain,
% 2.17/1.70 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(2152,plain,
% 2.17/1.70 ((hskp0 | hskp2 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084))) <=> (hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 2.17/1.70 inference(rewrite,[status(thm)],[])).
% 2.17/1.70 tff(2153,plain,
% 2.17/1.70 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084))))),
% 2.17/1.70 inference(monotonicity,[status(thm)],[2152])).
% 2.17/1.70 tff(2154,plain,
% 2.17/1.70 (((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 2.17/1.70 inference(transitivity,[status(thm)],[2153, 2151])).
% 2.17/1.70 tff(2155,plain,
% 2.17/1.70 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp0 | hskp2 | (~ndr1_0) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.17/1.70 inference(quant_inst,[status(thm)],[])).
% 2.17/1.70 tff(2156,plain,
% 2.17/1.70 ((~![U: $i] : (hskp0 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp0 | hskp2 | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)) | (~c2_1(a1084))),
% 2.17/1.70 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 2.17/1.70 tff(2157,plain,
% 2.17/1.70 ($false),
% 2.17/1.70 inference(unit_resolution,[status(thm)],[2156, 1646, 186, 68, 2147, 2150, 1924, 2149])).
% 2.17/1.71 tff(2158,plain,((~hskp4) | hskp0 | hskp2 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.71 tff(2159,plain,
% 2.17/1.71 (~hskp4),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2158, 68, 2127, 12, 11])).
% 2.17/1.71 tff(2160,assumption,(~c0_1(a1089)), introduced(assumption)).
% 2.17/1.71 tff(2161,assumption,(hskp16), introduced(assumption)).
% 2.17/1.71 tff(2162,plain,
% 2.17/1.71 (~c3_1(a1100)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1659, 2161])).
% 2.17/1.71 tff(2163,plain,
% 2.17/1.71 (~c0_1(a1100)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1665, 2161])).
% 2.17/1.71 tff(2164,plain,
% 2.17/1.71 (c1_1(a1100)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1676, 2161])).
% 2.17/1.71 tff(2165,assumption,(~hskp4), introduced(assumption)).
% 2.17/1.71 tff(2166,plain,
% 2.17/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100)))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2167,plain,
% 2.17/1.71 ((hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089))) <=> (hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100)))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2168,plain,
% 2.17/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100))))),
% 2.17/1.71 inference(monotonicity,[status(thm)],[2167])).
% 2.17/1.71 tff(2169,plain,
% 2.17/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100)))),
% 2.17/1.71 inference(transitivity,[status(thm)],[2168, 2166])).
% 2.17/1.71 tff(2170,plain,
% 2.17/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))),
% 2.17/1.71 inference(quant_inst,[status(thm)],[])).
% 2.17/1.71 tff(2171,plain,
% 2.17/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a1100) | c3_1(a1100) | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c2_1(a1089)) | (~c1_1(a1100))),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[2170, 2169])).
% 2.17/1.71 tff(2172,plain,
% 2.17/1.71 ($false),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2171, 186, 2165, 2164, 2017, 2163, 2162, 2023, 1240, 2160])).
% 2.17/1.71 tff(2173,plain,((~hskp16) | hskp4 | (~c2_1(a1089)) | c1_1(a1089) | c0_1(a1089)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.71 tff(2174,plain,
% 2.17/1.71 (~hskp16),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2173, 2159, 1977, 1975, 2145])).
% 2.17/1.71 tff(2175,plain,
% 2.17/1.71 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2176,plain,
% 2.17/1.71 ((hskp16 | hskp4 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120))) <=> (hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2177,plain,
% 2.17/1.71 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120))))),
% 2.17/1.71 inference(monotonicity,[status(thm)],[2176])).
% 2.17/1.71 tff(2178,plain,
% 2.17/1.71 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120)))),
% 2.17/1.71 inference(transitivity,[status(thm)],[2177, 2175])).
% 2.17/1.71 tff(2179,plain,
% 2.17/1.71 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1120) | c3_1(a1120) | (~c2_1(a1120)))),
% 2.17/1.71 inference(quant_inst,[status(thm)],[])).
% 2.17/1.71 tff(2180,plain,
% 2.17/1.71 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c3_1(a1120) | (~ndr1_0) | c0_1(a1120) | (~c2_1(a1120))),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 2.17/1.71 tff(2181,plain,
% 2.17/1.71 (hskp16 | hskp4 | c0_1(a1120)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2180, 186, 1987, 1986, 2137])).
% 2.17/1.71 tff(2182,plain,
% 2.17/1.71 (c0_1(a1120)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2181, 2174, 2159])).
% 2.17/1.71 tff(2183,plain,
% 2.17/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2184,plain,
% 2.17/1.71 ((hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1089) | c0_1(a1089) | (~c3_1(a1089))) <=> (hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2185,plain,
% 2.17/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1089) | c0_1(a1089) | (~c3_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))))),
% 2.17/1.71 inference(monotonicity,[status(thm)],[2184])).
% 2.17/1.71 tff(2186,plain,
% 2.17/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1089) | c0_1(a1089) | (~c3_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120)))),
% 2.17/1.71 inference(transitivity,[status(thm)],[2185, 2183])).
% 2.17/1.71 tff(2187,plain,
% 2.17/1.71 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1120)) | (~c1_1(a1120)) | (~c0_1(a1120)) | c1_1(a1089) | c0_1(a1089) | (~c3_1(a1089)))),
% 2.17/1.71 inference(quant_inst,[status(thm)],[])).
% 2.17/1.71 tff(2188,plain,
% 2.17/1.71 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1089) | (~ndr1_0) | c0_1(a1089) | (~c3_1(a1089)) | (~c1_1(a1120)) | (~c0_1(a1120)) | (~c2_1(a1120))),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 2.17/1.71 tff(2189,plain,
% 2.17/1.71 (hskp10 | c0_1(a1089) | (~c0_1(a1120))),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2188, 186, 1985, 1987, 1976, 1975, 1045])).
% 2.17/1.71 tff(2190,plain,
% 2.17/1.71 (hskp10),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2189, 2182, 2145])).
% 2.17/1.71 tff(2191,plain,
% 2.17/1.71 (~c3_1(a1090)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1068, 2190])).
% 2.17/1.71 tff(2192,plain,
% 2.17/1.71 (~c0_1(a1090)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1080, 2190])).
% 2.17/1.71 tff(2193,plain,
% 2.17/1.71 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090)))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2194,plain,
% 2.17/1.71 ((hskp16 | hskp4 | (~ndr1_0) | c0_1(a1090) | c3_1(a1090) | (~c2_1(a1090))) <=> (hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090)))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2195,plain,
% 2.17/1.71 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1090) | c3_1(a1090) | (~c2_1(a1090)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090))))),
% 2.17/1.71 inference(monotonicity,[status(thm)],[2194])).
% 2.17/1.71 tff(2196,plain,
% 2.17/1.71 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1090) | c3_1(a1090) | (~c2_1(a1090)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090)))),
% 2.17/1.71 inference(transitivity,[status(thm)],[2195, 2193])).
% 2.17/1.71 tff(2197,plain,
% 2.17/1.71 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c0_1(a1090) | c3_1(a1090) | (~c2_1(a1090)))),
% 2.17/1.71 inference(quant_inst,[status(thm)],[])).
% 2.17/1.71 tff(2198,plain,
% 2.17/1.71 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp4 | c0_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c2_1(a1090))),
% 2.17/1.71 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 2.17/1.71 tff(2199,plain,
% 2.17/1.71 (~c2_1(a1090)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[2198, 186, 2174, 2159, 2192, 2191, 2137])).
% 2.17/1.71 tff(2200,plain,
% 2.17/1.71 (~c1_1(a1090)),
% 2.17/1.71 inference(unit_resolution,[status(thm)],[1074, 2190])).
% 2.17/1.71 tff(2201,plain,
% 2.17/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2202,plain,
% 2.17/1.71 (((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090) | c0_1(a1090) | c3_1(a1090) | c2_1(a1090) | c1_1(a1090) | c0_1(a1090)) <=> (c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090))),
% 2.17/1.71 inference(rewrite,[status(thm)],[])).
% 2.17/1.71 tff(2203,plain,
% 2.17/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090) | c0_1(a1090) | c3_1(a1090) | c2_1(a1090) | c1_1(a1090) | c0_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090)))),
% 2.17/1.71 inference(monotonicity,[status(thm)],[2202])).
% 2.17/1.71 tff(2204,plain,
% 2.17/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090) | c0_1(a1090) | c3_1(a1090) | c2_1(a1090) | c1_1(a1090) | c0_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090))),
% 2.17/1.72 inference(transitivity,[status(thm)],[2203, 2201])).
% 2.17/1.72 tff(2205,plain,
% 2.17/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1089) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090) | c0_1(a1090) | c3_1(a1090) | c2_1(a1090) | c1_1(a1090) | c0_1(a1090))),
% 2.17/1.72 inference(quant_inst,[status(thm)],[])).
% 2.17/1.72 tff(2206,plain,
% 2.17/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | c1_1(a1089) | (~ndr1_0) | (~c2_1(a1089)) | (~c3_1(a1089)) | c2_1(a1090)),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 2.17/1.72 tff(2207,plain,
% 2.17/1.72 ($false),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2206, 186, 1977, 1976, 2192, 2200, 2191, 1975, 464, 2199])).
% 2.17/1.72 tff(2208,plain,(hskp2 | c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.72 tff(2209,plain,
% 2.17/1.72 (hskp2),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2208, 12, 11])).
% 2.17/1.72 tff(2210,plain,
% 2.17/1.72 (~c0_1(a1082)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[621, 2209])).
% 2.17/1.72 tff(2211,plain,
% 2.17/1.72 (~c2_1(a1082)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[627, 2209])).
% 2.17/1.72 tff(2212,plain,
% 2.17/1.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 2.17/1.72 inference(bind,[status(th)],[])).
% 2.17/1.72 tff(2213,plain,
% 2.17/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.17/1.72 inference(quant_intro,[status(thm)],[2212])).
% 2.17/1.72 tff(2214,plain,
% 2.17/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.17/1.72 inference(rewrite,[status(thm)],[])).
% 2.17/1.72 tff(2215,plain,
% 2.17/1.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 2.17/1.72 inference(bind,[status(th)],[])).
% 2.17/1.72 tff(2216,plain,
% 2.17/1.72 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.17/1.72 inference(quant_intro,[status(thm)],[2215])).
% 2.17/1.72 tff(2217,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 2.17/1.72 tff(2218,plain,
% 2.17/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 2.17/1.72 tff(2219,plain,
% 2.17/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2218, 2214])).
% 2.17/1.72 tff(2220,plain,(
% 2.17/1.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.17/1.72 inference(skolemize,[status(sab)],[2219])).
% 2.17/1.72 tff(2221,plain,
% 2.17/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2220, 2213])).
% 2.17/1.72 tff(2222,assumption,(~c1_1(a1082)), introduced(assumption)).
% 2.17/1.72 tff(2223,plain,
% 2.17/1.72 (c0_1(a1082) | c3_1(a1082) | c1_1(a1082)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[842, 186, 2017, 2016, 2023, 629, 464])).
% 2.17/1.72 tff(2224,plain,
% 2.17/1.72 (c3_1(a1082)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2223, 2222, 631])).
% 2.17/1.72 tff(2225,plain,
% 2.17/1.72 (^[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)))),
% 2.17/1.72 inference(bind,[status(th)],[])).
% 2.17/1.72 tff(2226,plain,
% 2.17/1.72 (![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))),
% 2.17/1.72 inference(quant_intro,[status(thm)],[2225])).
% 2.17/1.72 tff(2227,plain,
% 2.17/1.72 (![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))),
% 2.17/1.72 inference(rewrite,[status(thm)],[])).
% 2.17/1.72 tff(2228,plain,
% 2.17/1.72 (^[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))))),
% 2.17/1.72 inference(bind,[status(th)],[])).
% 2.17/1.72 tff(2229,plain,
% 2.17/1.72 (![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))),
% 2.17/1.72 inference(quant_intro,[status(thm)],[2228])).
% 2.17/1.72 tff(2230,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 2.17/1.72 tff(2231,plain,
% 2.17/1.72 (![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))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 2.17/1.72 tff(2232,plain,
% 2.17/1.72 (![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))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2231, 2227])).
% 2.17/1.72 tff(2233,plain,(
% 2.17/1.72 ![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))),
% 2.17/1.72 inference(skolemize,[status(sab)],[2232])).
% 2.17/1.72 tff(2234,plain,
% 2.17/1.72 (![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))),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2233, 2226])).
% 2.17/1.72 tff(2235,plain,
% 2.17/1.72 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082))),
% 2.17/1.72 inference(rewrite,[status(thm)],[])).
% 2.17/1.72 tff(2236,plain,
% 2.17/1.72 ((hskp0 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c3_1(a1082)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082)) <=> (hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082))),
% 2.17/1.72 inference(rewrite,[status(thm)],[])).
% 2.17/1.72 tff(2237,plain,
% 2.17/1.72 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c3_1(a1082)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082)))),
% 2.17/1.72 inference(monotonicity,[status(thm)],[2236])).
% 2.17/1.72 tff(2238,plain,
% 2.17/1.72 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c3_1(a1082)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082))),
% 2.17/1.72 inference(transitivity,[status(thm)],[2237, 2235])).
% 2.17/1.72 tff(2239,plain,
% 2.17/1.72 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1082) | c0_1(a1082) | (~c3_1(a1082)) | c2_1(a1082) | c1_1(a1082) | c0_1(a1082))),
% 2.17/1.72 inference(quant_inst,[status(thm)],[])).
% 2.17/1.72 tff(2240,plain,
% 2.17/1.72 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1082) | c2_1(a1082) | (~c3_1(a1082)) | (~ndr1_0) | c1_1(a1082)),
% 2.17/1.72 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 2.17/1.72 tff(2241,plain,
% 2.17/1.72 (hskp0 | c0_1(a1082) | (~c3_1(a1082)) | c1_1(a1082)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2240, 186, 629, 2234])).
% 2.17/1.72 tff(2242,plain,
% 2.17/1.72 ($false),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2241, 2224, 2222, 631, 1646])).
% 2.17/1.72 tff(2243,plain,(c1_1(a1082) | c0_1(a1082) | hskp0 | c2_1(a1082) | (~c2_1(a1089)) | (~c3_1(a1089)) | c1_1(a1089)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.72 tff(2244,plain,
% 2.17/1.72 (c1_1(a1082)),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[2243, 1646, 631, 629, 1977, 1976, 1975])).
% 2.17/1.72 tff(2245,plain,
% 2.17/1.72 (hskp0 | hskp16 | c0_1(a1082) | (~c1_1(a1082))),
% 2.17/1.72 inference(unit_resolution,[status(thm)],[1652, 186, 629, 1645])).
% 2.17/1.73 tff(2246,plain,
% 2.17/1.73 (hskp16),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2245, 2244, 631, 1646])).
% 2.17/1.73 tff(2247,plain,
% 2.17/1.73 (~c0_1(a1100)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1665, 2246])).
% 2.17/1.73 tff(2248,plain,
% 2.17/1.73 (c1_1(a1100)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1676, 2246])).
% 2.17/1.73 tff(2249,plain,
% 2.17/1.73 (~c3_1(a1100)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1659, 2246])).
% 2.17/1.73 tff(2250,plain,
% 2.17/1.73 (hskp4),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1683, 186, 2248, 2014, 2247, 2249, 12, 11, 1240])).
% 2.17/1.73 tff(2251,plain,
% 2.17/1.73 (~c3_1(a1084)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1270, 2250])).
% 2.17/1.73 tff(2252,plain,
% 2.17/1.73 (c0_1(a1084)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1258, 2250])).
% 2.17/1.73 tff(2253,plain,
% 2.17/1.73 (c2_1(a1084)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1464, 2252, 2050, 2049, 2014, 2251, 2048, 12, 11])).
% 2.17/1.73 tff(2254,plain,
% 2.17/1.73 (hskp31),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2077, 186, 1985, 1987, 2252, 1986, 2251, 2071, 2253])).
% 2.17/1.73 tff(2255,plain,
% 2.17/1.73 (c2_1(a1148)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2088, 2254])).
% 2.17/1.73 tff(2256,plain,
% 2.17/1.73 (c1_1(a1148)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2099, 2254])).
% 2.17/1.73 tff(2257,plain,
% 2.17/1.73 (c0_1(a1148)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2110, 2254])).
% 2.17/1.73 tff(2258,plain,
% 2.17/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.73 tff(2259,plain,
% 2.17/1.73 (((~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c0_1(a1100) | (~c2_1(a1100)) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085))) <=> (c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.73 tff(2260,plain,
% 2.17/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c0_1(a1100) | (~c2_1(a1100)) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148))))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[2259])).
% 2.17/1.73 tff(2261,plain,
% 2.17/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c0_1(a1100) | (~c2_1(a1100)) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148)))),
% 2.17/1.73 inference(transitivity,[status(thm)],[2260, 2258])).
% 2.17/1.73 tff(2262,plain,
% 2.17/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1148)) | (~c1_1(a1148)) | (~c0_1(a1148)) | c0_1(a1100) | (~c2_1(a1100)) | (~c1_1(a1100)) | c1_1(a1085) | c0_1(a1085) | (~c2_1(a1085)))),
% 2.17/1.73 inference(quant_inst,[status(thm)],[])).
% 2.17/1.73 tff(2263,plain,
% 2.17/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1100) | c0_1(a1085) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | (~c1_1(a1100)) | (~c2_1(a1100)) | (~c2_1(a1148)) | (~c0_1(a1148)) | (~c1_1(a1148))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 2.17/1.73 tff(2264,plain,
% 2.17/1.73 (~c2_1(a1100)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2263, 186, 2257, 2256, 2255, 2248, 2014, 2247, 12, 11, 2221])).
% 2.17/1.73 tff(2265,plain,
% 2.17/1.73 (hskp3 | c0_1(a1082) | (~c1_1(a1082))),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[898, 186, 2014, 12, 11, 629, 22])).
% 2.17/1.73 tff(2266,plain,
% 2.17/1.73 (hskp3),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2265, 2244, 631])).
% 2.17/1.73 tff(2267,plain,
% 2.17/1.73 (~c3_1(a1083)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[910, 2266])).
% 2.17/1.73 tff(2268,plain,
% 2.17/1.73 (~c2_1(a1083)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[904, 2266])).
% 2.17/1.73 tff(2269,plain,
% 2.17/1.73 (c1_1(a1083)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1099, 2266])).
% 2.17/1.73 tff(2270,plain,
% 2.17/1.73 (c3_1(a1085)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1482, 186, 2049, 2269, 2048, 12, 11, 2268, 2267, 476, 2051])).
% 2.17/1.73 tff(2271,plain,
% 2.17/1.73 (hskp10),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2117, 186, 2257, 2256, 2255, 12, 11, 1045, 2270])).
% 2.17/1.73 tff(2272,plain,
% 2.17/1.73 (~c3_1(a1090)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1068, 2271])).
% 2.17/1.73 tff(2273,plain,
% 2.17/1.73 (~c1_1(a1090)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1074, 2271])).
% 2.17/1.73 tff(2274,plain,
% 2.17/1.73 (~c0_1(a1090)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[1080, 2271])).
% 2.17/1.73 tff(2275,plain,
% 2.17/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.73 tff(2276,plain,
% 2.17/1.73 (((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090)) <=> (c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.73 tff(2277,plain,
% 2.17/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113))))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[2276])).
% 2.17/1.73 tff(2278,plain,
% 2.17/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113)))),
% 2.17/1.73 inference(transitivity,[status(thm)],[2277, 2275])).
% 2.17/1.73 tff(2279,plain,
% 2.17/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c1_1(a1113)) | c2_1(a1100) | c3_1(a1100) | (~c1_1(a1100)) | c1_1(a1090) | c0_1(a1090) | c3_1(a1090))),
% 2.17/1.73 inference(quant_inst,[status(thm)],[])).
% 2.17/1.73 tff(2280,plain,
% 2.17/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1113) | c3_1(a1100) | c0_1(a1090) | c1_1(a1090) | c3_1(a1090) | (~ndr1_0) | (~c1_1(a1100)) | c2_1(a1100) | (~c1_1(a1113)) | (~c3_1(a1113))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 2.17/1.73 tff(2281,plain,
% 2.17/1.73 ($false),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2280, 186, 2049, 2248, 2048, 2249, 2274, 2273, 2272, 476, 2051, 2264])).
% 2.17/1.73 tff(2282,plain,(hskp0 | c0_1(a1085) | c1_1(a1085) | c0_1(a1082) | c2_1(a1082)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.73 tff(2283,plain,
% 2.17/1.73 ($false),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2282, 2211, 2210, 11, 12, 2127])).
% 2.17/1.73 tff(2284,plain,(c0_1(a1085) | c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.73 tff(2285,plain,
% 2.17/1.73 (c0_1(a1085)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2284, 11])).
% 2.17/1.73 tff(2286,plain,
% 2.17/1.73 (~hskp5),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[870, 2285])).
% 2.17/1.73 tff(2287,plain,
% 2.17/1.73 (hskp0),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[116, 2286])).
% 2.17/1.73 tff(2288,plain,
% 2.17/1.73 (~c2_1(a1080)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[28, 2287])).
% 2.17/1.73 tff(2289,plain,
% 2.17/1.73 (~c0_1(a1080)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[34, 2287])).
% 2.17/1.73 tff(2290,plain,
% 2.17/1.73 (c1_1(a1080)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[45, 2287])).
% 2.17/1.73 tff(2291,plain,
% 2.17/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085)))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.73 tff(2292,plain,
% 2.17/1.73 ((hskp5 | (~ndr1_0) | c1_1(a1085) | (~c3_1(a1085)) | (~c0_1(a1085)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085)))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.73 tff(2293,plain,
% 2.17/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1085) | (~c3_1(a1085)) | (~c0_1(a1085)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085))))),
% 2.17/1.73 inference(monotonicity,[status(thm)],[2292])).
% 2.17/1.73 tff(2294,plain,
% 2.17/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1085) | (~c3_1(a1085)) | (~c0_1(a1085)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085)))),
% 2.17/1.73 inference(transitivity,[status(thm)],[2293, 2291])).
% 2.17/1.73 tff(2295,plain,
% 2.17/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1085) | (~c3_1(a1085)) | (~c0_1(a1085)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 2.17/1.73 inference(quant_inst,[status(thm)],[])).
% 2.17/1.73 tff(2296,plain,
% 2.17/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | (~c0_1(a1085)) | c1_1(a1085) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1085))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 2.17/1.73 tff(2297,plain,
% 2.17/1.73 (~c3_1(a1085)),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[2296, 2286, 186, 2290, 2285, 11, 2289, 2288, 10])).
% 2.17/1.73 tff(2298,assumption,(c0_1(a1085)), introduced(assumption)).
% 2.17/1.73 tff(2299,plain,
% 2.17/1.73 (^[U: $i] : refl((hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 2.17/1.73 inference(bind,[status(th)],[])).
% 2.17/1.73 tff(2300,plain,
% 2.17/1.73 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.17/1.73 inference(quant_intro,[status(thm)],[2299])).
% 2.17/1.73 tff(2301,plain,
% 2.17/1.73 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.73 tff(2302,plain,
% 2.17/1.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp5) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp5) <=> (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 2.17/1.73 inference(bind,[status(th)],[])).
% 2.17/1.73 tff(2303,plain,
% 2.17/1.73 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp5) <=> ![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.17/1.73 inference(quant_intro,[status(thm)],[2302])).
% 2.17/1.73 tff(2304,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 2.17/1.73 tff(2305,plain,
% 2.17/1.73 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2304, 2303])).
% 2.17/1.73 tff(2306,plain,
% 2.17/1.73 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2305, 2301])).
% 2.17/1.73 tff(2307,plain,(
% 2.17/1.73 ![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.17/1.73 inference(skolemize,[status(sab)],[2306])).
% 2.17/1.73 tff(2308,plain,
% 2.17/1.73 (![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.17/1.73 inference(modus_ponens,[status(thm)],[2307, 2300])).
% 2.17/1.73 tff(2309,plain,
% 2.17/1.73 (~hskp5),
% 2.17/1.73 inference(unit_resolution,[status(thm)],[870, 2298])).
% 2.17/1.73 tff(2310,plain,
% 2.17/1.73 (((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085))) <=> ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.73 tff(2311,plain,
% 2.17/1.73 ((hskp5 | hskp22 | (~ndr1_0) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085))) <=> (hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085))),
% 2.17/1.73 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2312,plain,
% 2.17/1.74 (((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | (~ndr1_0) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)))) <=> ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085)))),
% 2.17/1.74 inference(monotonicity,[status(thm)],[2311])).
% 2.17/1.74 tff(2313,plain,
% 2.17/1.74 (((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | (~ndr1_0) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)))) <=> ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085))),
% 2.17/1.74 inference(transitivity,[status(thm)],[2312, 2310])).
% 2.17/1.74 tff(2314,plain,
% 2.17/1.74 ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp5 | hskp22 | (~ndr1_0) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)))),
% 2.17/1.74 inference(quant_inst,[status(thm)],[])).
% 2.17/1.74 tff(2315,plain,
% 2.17/1.74 ((~![U: $i] : (hskp5 | hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp5 | hskp22 | c2_1(a1085) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 2.17/1.74 tff(2316,plain,
% 2.17/1.74 (hskp22 | c2_1(a1085) | c3_1(a1085)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2315, 2309, 186, 2298, 2308])).
% 2.17/1.74 tff(2317,plain,
% 2.17/1.74 (hskp22),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2316, 91, 454])).
% 2.17/1.74 tff(2318,plain,
% 2.17/1.74 (((~hskp22) | (~c0_1(a1121))) <=> ((~hskp22) | (~c0_1(a1121)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2319,plain,
% 2.17/1.74 (((~c0_1(a1121)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a1121)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2320,axiom,((~c0_1(a1121)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 2.17/1.74 tff(2321,plain,
% 2.17/1.74 ((~hskp22) | (~c0_1(a1121))),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 2.17/1.74 tff(2322,plain,
% 2.17/1.74 ((~hskp22) | (~c0_1(a1121))),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2321, 2318])).
% 2.17/1.74 tff(2323,plain,
% 2.17/1.74 (~c0_1(a1121)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2322, 2317])).
% 2.17/1.74 tff(2324,plain,
% 2.17/1.74 (((~hskp22) | c3_1(a1121)) <=> ((~hskp22) | c3_1(a1121))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2325,axiom,((~hskp22) | c3_1(a1121)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 2.17/1.74 tff(2326,plain,
% 2.17/1.74 ((~hskp22) | c3_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 2.17/1.74 tff(2327,plain,
% 2.17/1.74 ((~hskp22) | c3_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2326, 2324])).
% 2.17/1.74 tff(2328,plain,
% 2.17/1.74 ((~hskp22) | c3_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2327, 2324])).
% 2.17/1.74 tff(2329,plain,
% 2.17/1.74 ((~hskp22) | c3_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2328, 2324])).
% 2.17/1.74 tff(2330,plain,
% 2.17/1.74 ((~hskp22) | c3_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2329, 2324])).
% 2.17/1.74 tff(2331,plain,
% 2.17/1.74 ((~hskp22) | c3_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2330, 2324])).
% 2.17/1.74 tff(2332,plain,
% 2.17/1.74 ((~hskp22) | c3_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2331, 2324])).
% 2.17/1.74 tff(2333,plain,
% 2.17/1.74 ((~hskp22) | c3_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2332, 2324])).
% 2.17/1.74 tff(2334,plain,
% 2.17/1.74 (c3_1(a1121)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2333, 2317])).
% 2.17/1.74 tff(2335,plain,
% 2.17/1.74 (((~hskp22) | c1_1(a1121)) <=> ((~hskp22) | c1_1(a1121))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2336,axiom,((~hskp22) | c1_1(a1121)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 2.17/1.74 tff(2337,plain,
% 2.17/1.74 ((~hskp22) | c1_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2336, 2335])).
% 2.17/1.74 tff(2338,plain,
% 2.17/1.74 ((~hskp22) | c1_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2337, 2335])).
% 2.17/1.74 tff(2339,plain,
% 2.17/1.74 ((~hskp22) | c1_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2338, 2335])).
% 2.17/1.74 tff(2340,plain,
% 2.17/1.74 ((~hskp22) | c1_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2339, 2335])).
% 2.17/1.74 tff(2341,plain,
% 2.17/1.74 ((~hskp22) | c1_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2340, 2335])).
% 2.17/1.74 tff(2342,plain,
% 2.17/1.74 ((~hskp22) | c1_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2341, 2335])).
% 2.17/1.74 tff(2343,plain,
% 2.17/1.74 ((~hskp22) | c1_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2342, 2335])).
% 2.17/1.74 tff(2344,plain,
% 2.17/1.74 ((~hskp22) | c1_1(a1121)),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2343, 2335])).
% 2.17/1.74 tff(2345,plain,
% 2.17/1.74 (c1_1(a1121)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2344, 2317])).
% 2.17/1.74 tff(2346,assumption,(~c0_1(a1121)), introduced(assumption)).
% 2.17/1.74 tff(2347,assumption,(c3_1(a1121)), introduced(assumption)).
% 2.17/1.74 tff(2348,assumption,(c1_1(a1121)), introduced(assumption)).
% 2.17/1.74 tff(2349,plain,
% 2.17/1.74 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2350,plain,
% 2.17/1.74 ((hskp30 | hskp18 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121))) <=> (hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2351,plain,
% 2.17/1.74 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 2.17/1.74 inference(monotonicity,[status(thm)],[2350])).
% 2.17/1.74 tff(2352,plain,
% 2.17/1.74 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 2.17/1.74 inference(transitivity,[status(thm)],[2351, 2349])).
% 2.17/1.74 tff(2353,plain,
% 2.17/1.74 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))),
% 2.17/1.74 inference(quant_inst,[status(thm)],[])).
% 2.17/1.74 tff(2354,plain,
% 2.17/1.74 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp18 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 2.17/1.74 tff(2355,plain,
% 2.17/1.74 (hskp30),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2354, 186, 1988, 2348, 2347, 2346, 499])).
% 2.17/1.74 tff(2356,plain,
% 2.17/1.74 (c3_1(a1109)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[363, 2355])).
% 2.17/1.74 tff(2357,plain,
% 2.17/1.74 (c0_1(a1109)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[352, 2355])).
% 2.17/1.74 tff(2358,plain,
% 2.17/1.74 (c1_1(a1109)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[312, 2355])).
% 2.17/1.74 tff(2359,plain,
% 2.17/1.74 (hskp28),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[832, 57, 2358, 2357, 2356, 121])).
% 2.17/1.74 tff(2360,plain,
% 2.17/1.74 (c3_1(a1092)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[385, 2359])).
% 2.17/1.74 tff(2361,plain,
% 2.17/1.74 (c2_1(a1092)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[396, 2359])).
% 2.17/1.74 tff(2362,plain,
% 2.17/1.74 (~hskp11),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[1116, 1988])).
% 2.17/1.74 tff(2363,plain,
% 2.17/1.74 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2364,plain,
% 2.17/1.74 ((hskp11 | hskp9 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c3_1(a1092))) <=> (hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2365,plain,
% 2.17/1.74 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c3_1(a1092)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092))))),
% 2.17/1.74 inference(monotonicity,[status(thm)],[2364])).
% 2.17/1.74 tff(2366,plain,
% 2.17/1.74 (((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c3_1(a1092)))) <=> ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092)))),
% 2.17/1.74 inference(transitivity,[status(thm)],[2365, 2363])).
% 2.17/1.74 tff(2367,plain,
% 2.17/1.74 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp9 | (~ndr1_0) | c1_1(a1092) | (~c2_1(a1092)) | (~c3_1(a1092)))),
% 2.17/1.74 inference(quant_inst,[status(thm)],[])).
% 2.17/1.74 tff(2368,plain,
% 2.17/1.74 ((~![U: $i] : (hskp11 | hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp9 | (~ndr1_0) | (~c3_1(a1092)) | c1_1(a1092) | (~c2_1(a1092))),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 2.17/1.74 tff(2369,plain,
% 2.17/1.74 (c1_1(a1092)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2368, 186, 2362, 57, 2361, 2360, 1129])).
% 2.17/1.74 tff(2370,plain,
% 2.17/1.74 (c0_1(a1092)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[407, 2359])).
% 2.17/1.74 tff(2371,plain,
% 2.17/1.74 (((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))) <=> ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2372,plain,
% 2.17/1.74 ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092)))),
% 2.17/1.74 inference(quant_inst,[status(thm)],[])).
% 2.17/1.74 tff(2373,plain,
% 2.17/1.74 ((~![U: $i] : (hskp5 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp13 | (~ndr1_0) | (~c2_1(a1092)) | (~c1_1(a1092)) | (~c0_1(a1092))),
% 2.17/1.74 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 2.17/1.74 tff(2374,plain,
% 2.17/1.74 (hskp13 | (~c1_1(a1092))),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2373, 121, 186, 2370, 2361, 786])).
% 2.17/1.74 tff(2375,plain,
% 2.17/1.74 (hskp13),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[2374, 2369])).
% 2.17/1.74 tff(2376,plain,
% 2.17/1.74 (~c1_1(a1095)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[805, 2375])).
% 2.17/1.74 tff(2377,plain,
% 2.17/1.74 (c3_1(a1095)),
% 2.17/1.74 inference(unit_resolution,[status(thm)],[823, 2375])).
% 2.17/1.74 tff(2378,plain,
% 2.17/1.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2379,plain,
% 2.17/1.74 ((hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1095) | c0_1(a1095) | (~c3_1(a1095))) <=> (hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.17/1.74 inference(rewrite,[status(thm)],[])).
% 2.17/1.74 tff(2380,plain,
% 2.17/1.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1095) | c0_1(a1095) | (~c3_1(a1095)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))))),
% 2.17/1.74 inference(monotonicity,[status(thm)],[2379])).
% 2.17/1.74 tff(2381,plain,
% 2.17/1.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1095) | c0_1(a1095) | (~c3_1(a1095)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092)))),
% 2.17/1.75 inference(transitivity,[status(thm)],[2380, 2378])).
% 2.17/1.75 tff(2382,plain,
% 2.17/1.75 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a1092)) | (~c3_1(a1092)) | (~c0_1(a1092)) | c1_1(a1095) | c0_1(a1095) | (~c3_1(a1095)))),
% 2.17/1.75 inference(quant_inst,[status(thm)],[])).
% 2.17/1.75 tff(2383,plain,
% 2.17/1.75 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a1095) | (~ndr1_0) | c0_1(a1095) | (~c3_1(a1095)) | (~c3_1(a1092)) | (~c2_1(a1092)) | (~c0_1(a1092))),
% 2.17/1.75 inference(modus_ponens,[status(thm)],[2382, 2381])).
% 2.17/1.75 tff(2384,plain,
% 2.17/1.75 (c0_1(a1095)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2383, 186, 2362, 2370, 2361, 2360, 2377, 2376, 752])).
% 2.17/1.75 tff(2385,plain,
% 2.17/1.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 2.17/1.75 inference(rewrite,[status(thm)],[])).
% 2.17/1.75 tff(2386,plain,
% 2.17/1.75 ((hskp9 | hskp2 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121))) <=> (hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 2.17/1.75 inference(rewrite,[status(thm)],[])).
% 2.17/1.75 tff(2387,plain,
% 2.17/1.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 2.17/1.75 inference(monotonicity,[status(thm)],[2386])).
% 2.17/1.75 tff(2388,plain,
% 2.17/1.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 2.17/1.75 inference(transitivity,[status(thm)],[2387, 2385])).
% 2.17/1.75 tff(2389,plain,
% 2.17/1.75 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))),
% 2.17/1.75 inference(quant_inst,[status(thm)],[])).
% 2.17/1.75 tff(2390,plain,
% 2.17/1.75 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp2 | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 2.17/1.75 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 2.17/1.75 tff(2391,plain,
% 2.17/1.75 (hskp9 | hskp2),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2390, 186, 2348, 2347, 2346, 438])).
% 2.17/1.75 tff(2392,plain,
% 2.17/1.75 (hskp2),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2391, 57])).
% 2.17/1.75 tff(2393,plain,
% 2.17/1.75 (~c2_1(a1082)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[627, 2392])).
% 2.17/1.75 tff(2394,plain,
% 2.17/1.75 (~c0_1(a1082)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[621, 2392])).
% 2.17/1.75 tff(2395,plain,
% 2.17/1.75 (c1_1(a1082)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[741, 186, 2357, 2358, 2356, 2370, 2361, 2360, 2394, 2393, 374])).
% 2.17/1.75 tff(2396,plain,
% 2.17/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 2.17/1.75 inference(rewrite,[status(thm)],[])).
% 2.17/1.75 tff(2397,plain,
% 2.17/1.75 ((hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082))) <=> (hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 2.17/1.75 inference(rewrite,[status(thm)],[])).
% 2.17/1.75 tff(2398,plain,
% 2.17/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095))))),
% 2.17/1.75 inference(monotonicity,[status(thm)],[2397])).
% 2.17/1.75 tff(2399,plain,
% 2.17/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 2.17/1.75 inference(transitivity,[status(thm)],[2398, 2396])).
% 2.17/1.75 tff(2400,plain,
% 2.17/1.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1082) | c0_1(a1082) | (~c1_1(a1082)))),
% 2.17/1.75 inference(quant_inst,[status(thm)],[])).
% 2.17/1.75 tff(2401,plain,
% 2.17/1.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1082) | c2_1(a1082) | (~ndr1_0) | (~c1_1(a1082)) | (~c0_1(a1095)) | (~c3_1(a1095))),
% 2.17/1.75 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 2.17/1.75 tff(2402,plain,
% 2.17/1.75 ($false),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2401, 121, 186, 2377, 2376, 2394, 2393, 10, 2395, 2384])).
% 2.17/1.75 tff(2403,plain,(hskp9 | hskp5 | (~c1_1(a1121)) | (~c3_1(a1121)) | c0_1(a1121)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.75 tff(2404,plain,
% 2.17/1.75 (hskp9),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2403, 2345, 2309, 2334, 2323])).
% 2.17/1.75 tff(2405,plain,
% 2.17/1.75 (~c1_1(a1089)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[534, 2404])).
% 2.17/1.75 tff(2406,plain,
% 2.17/1.75 (~hskp18),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[194, 2309])).
% 2.17/1.75 tff(2407,plain,
% 2.17/1.75 (hskp30),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2354, 186, 2406, 2345, 2334, 2323, 499])).
% 2.17/1.75 tff(2408,plain,
% 2.17/1.75 (c3_1(a1109)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[363, 2407])).
% 2.17/1.75 tff(2409,plain,
% 2.17/1.75 (c1_1(a1109)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[312, 2407])).
% 2.17/1.75 tff(2410,plain,
% 2.17/1.75 (c0_1(a1109)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[352, 2407])).
% 2.17/1.75 tff(2411,assumption,(hskp9), introduced(assumption)).
% 2.17/1.75 tff(2412,plain,
% 2.17/1.75 (~c1_1(a1089)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[534, 2411])).
% 2.17/1.75 tff(2413,plain,
% 2.17/1.75 (c2_1(a1089)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[556, 2411])).
% 2.17/1.75 tff(2414,plain,
% 2.17/1.75 (c3_1(a1089)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[545, 2411])).
% 2.17/1.75 tff(2415,plain,
% 2.17/1.75 ($false),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2046, 2414, 2413, 2015, 2412])).
% 2.17/1.75 tff(2416,plain,((~hskp9) | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.17/1.75 tff(2417,plain,
% 2.17/1.75 (~hskp9),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2416, 2015])).
% 2.17/1.75 tff(2418,plain,
% 2.17/1.75 (hskp28),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[832, 2417, 410, 411, 409, 121])).
% 2.17/1.75 tff(2419,plain,
% 2.17/1.75 (c3_1(a1092)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[385, 2418])).
% 2.17/1.75 tff(2420,plain,
% 2.17/1.75 (c2_1(a1092)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[396, 2418])).
% 2.17/1.75 tff(2421,plain,
% 2.17/1.75 (c1_1(a1092)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2368, 186, 2362, 2417, 2420, 2419, 1129])).
% 2.17/1.75 tff(2422,plain,
% 2.17/1.75 (c0_1(a1092)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[407, 2418])).
% 2.17/1.75 tff(2423,plain,
% 2.17/1.75 (hskp13 | (~c1_1(a1092))),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2373, 121, 186, 2422, 2420, 786])).
% 2.17/1.75 tff(2424,plain,
% 2.17/1.75 (hskp13),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2423, 2421])).
% 2.17/1.75 tff(2425,plain,
% 2.17/1.75 (~c1_1(a1095)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[805, 2424])).
% 2.17/1.75 tff(2426,plain,
% 2.17/1.75 (c3_1(a1095)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[823, 2424])).
% 2.17/1.75 tff(2427,plain,
% 2.17/1.75 (c0_1(a1095)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2383, 186, 2362, 2422, 2420, 2419, 2426, 2425, 752])).
% 2.17/1.75 tff(2428,plain,
% 2.17/1.75 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 2.17/1.75 inference(rewrite,[status(thm)],[])).
% 2.17/1.75 tff(2429,plain,
% 2.17/1.75 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109)))),
% 2.17/1.75 inference(quant_inst,[status(thm)],[])).
% 2.17/1.75 tff(2430,plain,
% 2.17/1.75 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a1109)) | (~c1_1(a1109)) | (~c0_1(a1109))),
% 2.17/1.75 inference(modus_ponens,[status(thm)],[2429, 2428])).
% 2.17/1.75 tff(2431,plain,
% 2.17/1.75 (hskp19 | hskp2),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2430, 186, 411, 410, 409, 1525])).
% 2.17/1.75 tff(2432,plain,
% 2.17/1.75 (hskp2),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2431, 2015])).
% 2.17/1.75 tff(2433,plain,
% 2.17/1.75 (~c2_1(a1082)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[627, 2432])).
% 2.17/1.75 tff(2434,plain,
% 2.17/1.75 (~c0_1(a1082)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[621, 2432])).
% 2.17/1.75 tff(2435,plain,
% 2.17/1.75 (c1_1(a1082)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[741, 186, 411, 410, 409, 2422, 2420, 2419, 2434, 2433, 374])).
% 2.17/1.75 tff(2436,plain,
% 2.17/1.75 ($false),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2401, 121, 186, 2426, 2425, 2434, 2433, 10, 2435, 2427])).
% 2.17/1.75 tff(2437,plain,(hskp19 | hskp5 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.75 tff(2438,plain,
% 2.17/1.75 (hskp19),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[2437, 2410, 2309, 2409, 2408])).
% 2.17/1.75 tff(2439,plain,
% 2.17/1.75 (~c2_1(a1113)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[971, 2438])).
% 2.17/1.75 tff(2440,plain,
% 2.17/1.75 (c2_1(a1089)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[556, 2404])).
% 2.17/1.75 tff(2441,plain,
% 2.17/1.75 (c1_1(a1113)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[982, 2438])).
% 2.17/1.75 tff(2442,plain,
% 2.17/1.75 (c0_1(a1113)),
% 2.17/1.75 inference(unit_resolution,[status(thm)],[993, 2438])).
% 2.17/1.75 tff(2443,plain,
% 2.17/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.17/1.75 inference(rewrite,[status(thm)],[])).
% 2.17/1.75 tff(2444,plain,
% 2.17/1.75 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089))) <=> (c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.17/1.75 inference(rewrite,[status(thm)],[])).
% 2.17/1.75 tff(2445,plain,
% 2.17/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113))))),
% 2.17/1.76 inference(monotonicity,[status(thm)],[2444])).
% 2.17/1.76 tff(2446,plain,
% 2.17/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113)))),
% 2.17/1.76 inference(transitivity,[status(thm)],[2445, 2443])).
% 2.17/1.76 tff(2447,plain,
% 2.17/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c2_1(a1085) | c3_1(a1085) | (~c0_1(a1085)) | c1_1(a1089) | c0_1(a1089) | (~c2_1(a1089)))),
% 2.17/1.76 inference(quant_inst,[status(thm)],[])).
% 2.17/1.76 tff(2448,plain,
% 2.17/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1085) | c2_1(a1113) | c1_1(a1089) | (~c0_1(a1085)) | (~ndr1_0) | c3_1(a1085) | c0_1(a1089) | (~c2_1(a1089)) | (~c0_1(a1113)) | (~c1_1(a1113))),
% 2.17/1.76 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 2.17/1.76 tff(2449,plain,
% 2.17/1.76 (c0_1(a1089)),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[2448, 186, 2442, 2441, 2440, 91, 2439, 2405, 2298, 67, 454])).
% 2.17/1.76 tff(2450,plain,
% 2.17/1.76 (hskp0),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[116, 2309])).
% 2.17/1.76 tff(2451,plain,
% 2.17/1.76 (~c2_1(a1080)),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[28, 2450])).
% 2.17/1.76 tff(2452,plain,
% 2.17/1.76 (~c0_1(a1080)),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[34, 2450])).
% 2.17/1.76 tff(2453,plain,
% 2.17/1.76 (c1_1(a1080)),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[45, 2450])).
% 2.17/1.76 tff(2454,plain,
% 2.17/1.76 (c3_1(a1089)),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[545, 2404])).
% 2.17/1.76 tff(2455,plain,
% 2.17/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.76 inference(rewrite,[status(thm)],[])).
% 2.17/1.76 tff(2456,plain,
% 2.17/1.76 ((hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.76 inference(rewrite,[status(thm)],[])).
% 2.17/1.76 tff(2457,plain,
% 2.17/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089))))),
% 2.17/1.76 inference(monotonicity,[status(thm)],[2456])).
% 2.17/1.76 tff(2458,plain,
% 2.17/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089)))),
% 2.17/1.76 inference(transitivity,[status(thm)],[2457, 2455])).
% 2.17/1.76 tff(2459,plain,
% 2.17/1.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1089) | (~c3_1(a1089)) | (~c0_1(a1089)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 2.17/1.76 inference(quant_inst,[status(thm)],[])).
% 2.17/1.76 tff(2460,plain,
% 2.17/1.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1089) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c3_1(a1089)) | (~c0_1(a1089))),
% 2.17/1.76 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 2.17/1.76 tff(2461,plain,
% 2.17/1.76 ($false),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[2460, 2309, 186, 2454, 2453, 2405, 2452, 2451, 10, 2449])).
% 2.17/1.76 tff(2462,plain,(c2_1(a1085) | (~c0_1(a1085)) | c3_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.76 tff(2463,plain,
% 2.17/1.76 (c2_1(a1085)),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[2462, 2285, 2297])).
% 2.17/1.76 tff(2464,plain,
% 2.17/1.76 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)))),
% 2.17/1.76 inference(bind,[status(th)],[])).
% 2.17/1.76 tff(2465,plain,
% 2.17/1.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.17/1.76 inference(quant_intro,[status(thm)],[2464])).
% 2.17/1.76 tff(2466,plain,
% 2.17/1.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.17/1.76 inference(rewrite,[status(thm)],[])).
% 2.17/1.76 tff(2467,plain,
% 2.17/1.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))))),
% 2.17/1.76 inference(bind,[status(th)],[])).
% 2.17/1.76 tff(2468,plain,
% 2.17/1.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.17/1.76 inference(quant_intro,[status(thm)],[2467])).
% 2.17/1.76 tff(2469,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 2.17/1.76 tff(2470,plain,
% 2.17/1.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.17/1.76 inference(modus_ponens,[status(thm)],[2469, 2468])).
% 2.17/1.76 tff(2471,plain,
% 2.17/1.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.17/1.76 inference(modus_ponens,[status(thm)],[2470, 2466])).
% 2.17/1.76 tff(2472,plain,(
% 2.17/1.76 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.17/1.76 inference(skolemize,[status(sab)],[2471])).
% 2.17/1.76 tff(2473,plain,
% 2.17/1.76 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))),
% 2.17/1.76 inference(modus_ponens,[status(thm)],[2472, 2465])).
% 2.17/1.76 tff(2474,plain,
% 2.17/1.76 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 2.17/1.76 inference(rewrite,[status(thm)],[])).
% 2.17/1.76 tff(2475,plain,
% 2.17/1.76 ((hskp17 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c0_1(a1085)) | c1_1(a1085) | (~c2_1(a1085)) | c3_1(a1085)) <=> (hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 2.17/1.76 inference(rewrite,[status(thm)],[])).
% 2.17/1.76 tff(2476,plain,
% 2.17/1.76 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c0_1(a1085)) | c1_1(a1085) | (~c2_1(a1085)) | c3_1(a1085))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)))),
% 2.17/1.76 inference(monotonicity,[status(thm)],[2475])).
% 2.17/1.76 tff(2477,plain,
% 2.17/1.76 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c0_1(a1085)) | c1_1(a1085) | (~c2_1(a1085)) | c3_1(a1085))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085))),
% 2.17/1.76 inference(transitivity,[status(thm)],[2476, 2474])).
% 2.17/1.76 tff(2478,plain,
% 2.17/1.76 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | (hskp17 | (~ndr1_0) | c1_1(a1085) | (~c2_1(a1085)) | (~c0_1(a1085)) | c1_1(a1085) | (~c2_1(a1085)) | c3_1(a1085))),
% 2.17/1.76 inference(quant_inst,[status(thm)],[])).
% 2.17/1.76 tff(2479,plain,
% 2.17/1.76 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | c3_1(V))) | hskp17 | (~c0_1(a1085)) | c1_1(a1085) | (~ndr1_0) | (~c2_1(a1085)) | c3_1(a1085)),
% 2.17/1.76 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 2.17/1.76 tff(2480,plain,
% 2.17/1.76 (hskp17 | (~c0_1(a1085)) | (~c2_1(a1085)) | c3_1(a1085)),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[2479, 186, 11, 2473])).
% 2.17/1.76 tff(2481,plain,
% 2.17/1.76 (hskp17),
% 2.17/1.76 inference(unit_resolution,[status(thm)],[2480, 2463, 2285, 2297])).
% 2.17/1.76 tff(2482,plain,
% 2.25/1.76 (~c2_1(a1102)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[1610, 2481])).
% 2.25/1.76 tff(2483,plain,
% 2.25/1.76 (~c0_1(a1102)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[1586, 2481])).
% 2.25/1.76 tff(2484,plain,
% 2.25/1.76 (hskp14),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[276, 1988, 132, 124, 123])).
% 2.25/1.76 tff(2485,plain,
% 2.25/1.76 (~c2_1(a1097)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[282, 2484])).
% 2.25/1.76 tff(2486,plain,
% 2.25/1.76 (c3_1(a1097)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[333, 2484])).
% 2.25/1.76 tff(2487,plain,
% 2.25/1.76 (c1_1(a1097)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[293, 2484])).
% 2.25/1.76 tff(2488,plain,
% 2.25/1.76 (hskp30 | hskp9 | (~c0_1(a1097))),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[300, 186, 763, 761, 102])).
% 2.25/1.76 tff(2489,plain,
% 2.25/1.76 (~c0_1(a1097)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2488, 648, 57])).
% 2.25/1.76 tff(2490,plain,
% 2.25/1.76 (hskp30 | c0_1(a1097)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[590, 186, 267, 763, 762, 499])).
% 2.25/1.76 tff(2491,plain,
% 2.25/1.76 ($false),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2490, 2489, 648])).
% 2.25/1.76 tff(2492,plain,(hskp30 | hskp18 | (~c1_1(a1097)) | (~c3_1(a1097)) | hskp9 | c2_1(a1097)), inference(lemma,lemma(discharge,[]))).
% 2.25/1.76 tff(2493,plain,
% 2.25/1.76 (hskp30),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2492, 57, 2487, 2486, 1988, 2485])).
% 2.25/1.76 tff(2494,plain,
% 2.25/1.76 (c3_1(a1109)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[363, 2493])).
% 2.25/1.76 tff(2495,plain,
% 2.25/1.76 (c0_1(a1109)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[352, 2493])).
% 2.25/1.76 tff(2496,plain,
% 2.25/1.76 (c1_1(a1109)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[312, 2493])).
% 2.25/1.76 tff(2497,plain,
% 2.25/1.76 (hskp28),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[832, 2496, 57, 2495, 2494, 121])).
% 2.25/1.76 tff(2498,plain,
% 2.25/1.76 (c3_1(a1092)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[385, 2497])).
% 2.25/1.76 tff(2499,plain,
% 2.25/1.76 (c2_1(a1092)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[396, 2497])).
% 2.25/1.76 tff(2500,plain,
% 2.25/1.76 (c1_1(a1092)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2368, 186, 2362, 57, 2499, 2498, 1129])).
% 2.25/1.76 tff(2501,plain,
% 2.25/1.76 (c0_1(a1092)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[407, 2497])).
% 2.25/1.76 tff(2502,plain,
% 2.25/1.76 (hskp13 | (~c1_1(a1092))),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2373, 121, 186, 2501, 2499, 786])).
% 2.25/1.76 tff(2503,plain,
% 2.25/1.76 (hskp13),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2502, 2500])).
% 2.25/1.76 tff(2504,plain,
% 2.25/1.76 (~c1_1(a1095)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[805, 2503])).
% 2.25/1.76 tff(2505,plain,
% 2.25/1.76 (c3_1(a1095)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[823, 2503])).
% 2.25/1.76 tff(2506,plain,
% 2.25/1.76 (c0_1(a1095)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2383, 186, 2362, 2501, 2499, 2498, 2505, 2504, 752])).
% 2.25/1.76 tff(2507,assumption,(~c2_1(a1102)), introduced(assumption)).
% 2.25/1.76 tff(2508,assumption,(~c0_1(a1102)), introduced(assumption)).
% 2.25/1.76 tff(2509,plain,
% 2.25/1.76 (c1_1(a1102)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[1617, 186, 2495, 2496, 2494, 2501, 2499, 2498, 2508, 2507, 374])).
% 2.25/1.76 tff(2510,plain,
% 2.25/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102)))),
% 2.25/1.76 inference(rewrite,[status(thm)],[])).
% 2.25/1.76 tff(2511,plain,
% 2.25/1.76 ((hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102))) <=> (hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102)))),
% 2.25/1.76 inference(rewrite,[status(thm)],[])).
% 2.25/1.76 tff(2512,plain,
% 2.25/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102))))),
% 2.25/1.76 inference(monotonicity,[status(thm)],[2511])).
% 2.25/1.76 tff(2513,plain,
% 2.25/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102)))),
% 2.25/1.76 inference(transitivity,[status(thm)],[2512, 2510])).
% 2.25/1.76 tff(2514,plain,
% 2.25/1.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1102) | c0_1(a1102) | (~c1_1(a1102)))),
% 2.25/1.76 inference(quant_inst,[status(thm)],[])).
% 2.25/1.76 tff(2515,plain,
% 2.25/1.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a1102) | c2_1(a1102) | c1_1(a1095) | (~ndr1_0) | (~c0_1(a1095)) | (~c3_1(a1095)) | (~c1_1(a1102))),
% 2.25/1.76 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 2.25/1.76 tff(2516,plain,
% 2.25/1.76 ($false),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2515, 121, 186, 2505, 2508, 2507, 2504, 10, 2509, 2506])).
% 2.25/1.76 tff(2517,plain,(hskp9 | hskp5 | c0_1(a1102) | c2_1(a1102)), inference(lemma,lemma(discharge,[]))).
% 2.25/1.76 tff(2518,plain,
% 2.25/1.76 (hskp9),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2517, 2286, 2483, 2482])).
% 2.25/1.76 tff(2519,plain,
% 2.25/1.76 (~c1_1(a1089)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[534, 2518])).
% 2.25/1.76 tff(2520,plain,
% 2.25/1.76 (c3_1(a1089)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[545, 2518])).
% 2.25/1.76 tff(2521,plain,
% 2.25/1.76 (~c0_1(a1089)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2460, 2286, 186, 2520, 2290, 2519, 2289, 2288, 10])).
% 2.25/1.76 tff(2522,plain,
% 2.25/1.76 (c2_1(a1089)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[556, 2518])).
% 2.25/1.76 tff(2523,plain,
% 2.25/1.76 ($false),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[856, 2286, 186, 2522, 2520, 2519, 671, 2521])).
% 2.25/1.76 tff(2524,plain,(c1_1(a1085)), inference(lemma,lemma(discharge,[]))).
% 2.25/1.76 tff(2525,plain,
% 2.25/1.76 (~hskp5),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[864, 2524])).
% 2.25/1.76 tff(2526,plain,
% 2.25/1.76 (hskp0),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[116, 2525])).
% 2.25/1.76 tff(2527,plain,
% 2.25/1.76 (~c2_1(a1080)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[28, 2526])).
% 2.25/1.76 tff(2528,plain,
% 2.25/1.76 (~c0_1(a1080)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[34, 2526])).
% 2.25/1.76 tff(2529,plain,
% 2.25/1.76 (c1_1(a1080)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[45, 2526])).
% 2.25/1.76 tff(2530,plain,
% 2.25/1.76 (~hskp18),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[194, 2525])).
% 2.25/1.76 tff(2531,plain,
% 2.25/1.76 (hskp14),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[276, 2530, 2529, 2528, 2527])).
% 2.25/1.76 tff(2532,plain,
% 2.25/1.76 (~c2_1(a1097)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[282, 2531])).
% 2.25/1.76 tff(2533,plain,
% 2.25/1.76 (c3_1(a1097)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[333, 2531])).
% 2.25/1.76 tff(2534,plain,
% 2.25/1.76 (c1_1(a1097)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[293, 2531])).
% 2.25/1.76 tff(2535,plain,
% 2.25/1.76 (hskp30 | hskp9),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2492, 2534, 2533, 2530, 2532])).
% 2.25/1.76 tff(2536,plain,
% 2.25/1.76 (hskp30),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2535, 57])).
% 2.25/1.76 tff(2537,plain,
% 2.25/1.76 (c3_1(a1109)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[363, 2536])).
% 2.25/1.76 tff(2538,plain,
% 2.25/1.76 (c0_1(a1109)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[352, 2536])).
% 2.25/1.76 tff(2539,plain,
% 2.25/1.76 (c1_1(a1109)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[312, 2536])).
% 2.25/1.76 tff(2540,plain,
% 2.25/1.76 (hskp28 | hskp9 | (~c0_1(a1109)) | (~c1_1(a1109)) | (~c3_1(a1109))),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[832, 2525])).
% 2.25/1.76 tff(2541,plain,
% 2.25/1.76 (hskp28),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[2540, 2539, 57, 2538, 2537])).
% 2.25/1.76 tff(2542,plain,
% 2.25/1.76 (c3_1(a1092)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[385, 2541])).
% 2.25/1.76 tff(2543,plain,
% 2.25/1.76 (c2_1(a1092)),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[396, 2541])).
% 2.25/1.76 tff(2544,plain,
% 2.25/1.76 (~hskp11),
% 2.25/1.76 inference(unit_resolution,[status(thm)],[1116, 2530])).
% 2.27/1.78 tff(2545,plain,
% 2.27/1.78 (c1_1(a1092)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[2368, 186, 2544, 57, 2543, 2542, 1129])).
% 2.27/1.78 tff(2546,plain,
% 2.27/1.78 (c0_1(a1092)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[407, 2541])).
% 2.27/1.78 tff(2547,plain,
% 2.27/1.78 (hskp13 | (~c1_1(a1092))),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[2373, 2525, 186, 2546, 2543, 786])).
% 2.27/1.78 tff(2548,plain,
% 2.27/1.78 (hskp13),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[2547, 2545])).
% 2.27/1.78 tff(2549,plain,
% 2.27/1.78 (~c1_1(a1095)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[805, 2548])).
% 2.27/1.78 tff(2550,plain,
% 2.27/1.78 (c3_1(a1095)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[823, 2548])).
% 2.27/1.78 tff(2551,plain,
% 2.27/1.78 (c0_1(a1095)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[2383, 186, 2544, 2546, 2543, 2542, 2550, 2549, 752])).
% 2.27/1.78 tff(2552,plain,
% 2.27/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 2.27/1.78 inference(rewrite,[status(thm)],[])).
% 2.27/1.78 tff(2553,plain,
% 2.27/1.78 ((hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080))) <=> (hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 2.27/1.78 inference(rewrite,[status(thm)],[])).
% 2.27/1.78 tff(2554,plain,
% 2.27/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095))))),
% 2.27/1.78 inference(monotonicity,[status(thm)],[2553])).
% 2.27/1.78 tff(2555,plain,
% 2.27/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095)))),
% 2.27/1.78 inference(transitivity,[status(thm)],[2554, 2552])).
% 2.27/1.78 tff(2556,plain,
% 2.27/1.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a1095) | (~c3_1(a1095)) | (~c0_1(a1095)) | c2_1(a1080) | c0_1(a1080) | (~c1_1(a1080)))),
% 2.27/1.78 inference(quant_inst,[status(thm)],[])).
% 2.27/1.78 tff(2557,plain,
% 2.27/1.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c1_1(a1095) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c1_1(a1080)) | (~c0_1(a1095)) | (~c3_1(a1095))),
% 2.27/1.78 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 2.27/1.78 tff(2558,plain,
% 2.27/1.78 ($false),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[2557, 2525, 186, 2550, 2529, 2549, 2528, 2527, 10, 2551])).
% 2.27/1.78 tff(2559,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 2.27/1.78 tff(2560,plain,
% 2.27/1.78 (~c1_1(a1089)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[534, 2559])).
% 2.27/1.78 tff(2561,plain,
% 2.27/1.78 (c3_1(a1089)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[545, 2559])).
% 2.27/1.78 tff(2562,plain,
% 2.27/1.78 (~c0_1(a1089)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[2460, 2525, 186, 2561, 2529, 2560, 2528, 2527, 10])).
% 2.27/1.78 tff(2563,plain,
% 2.27/1.78 (c2_1(a1089)),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[556, 2559])).
% 2.27/1.78 tff(2564,plain,
% 2.27/1.78 ($false),
% 2.27/1.78 inference(unit_resolution,[status(thm)],[856, 2525, 186, 2563, 2561, 2560, 671, 2562])).
% 2.27/1.78 % SZS output end Proof
%------------------------------------------------------------------------------