%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN623-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:42 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN623-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:40:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(p16_type, type, (
% 0.20/0.41 p16: ( $i * $i ) > $o)).
% 0.20/0.41 tff(f9_type, type, (
% 0.20/0.41 f9: ( $i * $i ) > $i)).
% 0.20/0.41 tff(c25_type, type, (
% 0.20/0.41 c25: $i)).
% 0.20/0.41 tff(f11_type, type, (
% 0.20/0.41 f11: ( $i * $i ) > $i)).
% 0.20/0.41 tff(c24_type, type, (
% 0.20/0.41 c24: $i)).
% 0.20/0.41 tff(c29_type, type, (
% 0.20/0.41 c29: $i)).
% 0.20/0.41 tff(f4_type, type, (
% 0.20/0.41 f4: ( $i * $i ) > $i)).
% 0.20/0.41 tff(f13_type, type, (
% 0.20/0.41 f13: ( $i * $i ) > $i)).
% 0.20/0.41 tff(f15_type, type, (
% 0.20/0.41 f15: ( $i * $i ) > $i)).
% 0.20/0.41 tff(c28_type, type, (
% 0.20/0.41 c28: $i)).
% 0.20/0.41 tff(c21_type, type, (
% 0.20/0.41 c21: $i)).
% 0.20/0.41 tff(c20_type, type, (
% 0.20/0.41 c20: $i)).
% 0.20/0.41 tff(p3_type, type, (
% 0.20/0.41 p3: ( $i * $i ) > $o)).
% 0.20/0.41 tff(c22_type, type, (
% 0.20/0.41 c22: $i)).
% 0.20/0.41 tff(c23_type, type, (
% 0.20/0.41 c23: $i)).
% 0.20/0.41 tff(p8_type, type, (
% 0.20/0.41 p8: ( $i * $i ) > $o)).
% 0.20/0.41 tff(p2_type, type, (
% 0.20/0.41 p2: ( $i * $i ) > $o)).
% 0.20/0.41 tff(p18_type, type, (
% 0.20/0.41 p18: ( $i * $i ) > $o)).
% 0.20/0.41 tff(c26_type, type, (
% 0.20/0.41 c26: $i)).
% 0.20/0.41 tff(c19_type, type, (
% 0.20/0.41 c19: $i)).
% 0.20/0.41 tff(f6_type, type, (
% 0.20/0.41 f6: ( $i * $i ) > $i)).
% 0.20/0.41 tff(c27_type, type, (
% 0.20/0.41 c27: $i)).
% 0.20/0.41 tff(1,assumption,(~p3(c22, c22)), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[X37: $i] : refl(p3(X37, X37) <=> p3(X37, X37))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![X37: $i] : p3(X37, X37) <=> ![X37: $i] : p3(X37, X37)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![X37: $i] : p3(X37, X37) <=> ![X37: $i] : p3(X37, X37)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(5,axiom,(![X37: $i] : p3(X37, X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_5')).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![X37: $i] : p3(X37, X37)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.42 tff(7,plain,(
% 0.20/0.42 ![X37: $i] : p3(X37, X37)),
% 0.20/0.42 inference(skolemize,[status(sab)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![X37: $i] : p3(X37, X37)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 ((~![X37: $i] : p3(X37, X37)) | p3(c22, c22)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.42 tff(11,plain,(p3(c22, c22)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (^[X39: $i, X38: $i, X37: $i] : refl(((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39)) <=> ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39)) <=> ![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39)) <=> ![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (^[X39: $i, X38: $i, X37: $i] : trans(monotonicity(rewrite((p3(X38, X39) | (~p3(X37, X38))) <=> ((~p3(X37, X38)) | p3(X38, X39))), (((p3(X38, X39) | (~p3(X37, X38))) | (~p3(X37, X39))) <=> (((~p3(X37, X38)) | p3(X38, X39)) | (~p3(X37, X39))))), rewrite((((~p3(X37, X38)) | p3(X38, X39)) | (~p3(X37, X39))) <=> ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))), (((p3(X38, X39) | (~p3(X37, X38))) | (~p3(X37, X39))) <=> ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i] : ((p3(X38, X39) | (~p3(X37, X38))) | (~p3(X37, X39))) <=> ![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.42 tff(17,axiom,(![X39: $i, X38: $i, X37: $i] : ((p3(X38, X39) | (~p3(X37, X38))) | (~p3(X37, X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_20')).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.42 tff(20,plain,(
% 0.20/0.42 ![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))),
% 0.20/0.42 inference(skolemize,[status(sab)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (p3(c22, c23) <=> p3(c22, c23)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,axiom,(p3(c22, c23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_11')).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (p3(c22, c23)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (((~![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))) | ((~p3(c22, c22)) | (~p3(c22, c23)) | p3(c23, c22))) <=> ((~![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))) | (~p3(c22, c22)) | (~p3(c22, c23)) | p3(c23, c22))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 ((~![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))) | ((~p3(c22, c22)) | (~p3(c22, c23)) | p3(c23, c22))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 ((~![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))) | (~p3(c22, c22)) | (~p3(c22, c23)) | p3(c23, c22)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (p3(c23, c22)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[27, 24, 21, 11])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (p3(c23, f4(c24, c20)) <=> p3(c23, f4(c24, c20))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(30,axiom,(p3(c23, f4(c24, c20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_14')).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (p3(c23, f4(c24, c20))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (((~![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))) | ((~p3(c23, c22)) | (~p3(c23, f4(c24, c20))) | p3(f4(c24, c20), c22))) <=> ((~![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))) | (~p3(c23, c22)) | (~p3(c23, f4(c24, c20))) | p3(f4(c24, c20), c22))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))) | ((~p3(c23, c22)) | (~p3(c23, f4(c24, c20))) | p3(f4(c24, c20), c22))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~![X39: $i, X38: $i, X37: $i] : ((~p3(X37, X39)) | (~p3(X37, X38)) | p3(X38, X39))) | (~p3(c23, c22)) | (~p3(c23, f4(c24, c20))) | p3(f4(c24, c20), c22)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (p3(f4(c24, c20), c22)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 31, 21, 28])).
% 0.20/0.42 tff(36,assumption,(p16(f4(c24, c20), c21)), introduced(assumption)).
% 0.20/0.42 tff(37,assumption,(~p8(c21, c21)), introduced(assumption)).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (^[X58: $i] : refl(p8(X58, X58) <=> p8(X58, X58))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![X58: $i] : p8(X58, X58) <=> ![X58: $i] : p8(X58, X58)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![X58: $i] : p8(X58, X58) <=> ![X58: $i] : p8(X58, X58)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(41,axiom,(![X58: $i] : p8(X58, X58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_2')).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![X58: $i] : p8(X58, X58)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,(
% 0.20/0.42 ![X58: $i] : p8(X58, X58)),
% 0.20/0.42 inference(skolemize,[status(sab)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![X58: $i] : p8(X58, X58)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![X58: $i] : p8(X58, X58)) | p8(c21, c21)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 44, 37])).
% 0.20/0.42 tff(47,plain,(p8(c21, c21)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (^[X14: $i, X13: $i, X16: $i, X15: $i] : refl(((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14)) <=> ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14)) <=> ![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14)) <=> ![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (^[X14: $i, X13: $i, X16: $i, X15: $i] : trans(monotonicity(trans(monotonicity(rewrite((p16(X13, X14) | (~p3(X15, X13))) <=> ((~p3(X15, X13)) | p16(X13, X14))), (((p16(X13, X14) | (~p3(X15, X13))) | (~p8(X16, X14))) <=> (((~p3(X15, X13)) | p16(X13, X14)) | (~p8(X16, X14))))), rewrite((((~p3(X15, X13)) | p16(X13, X14)) | (~p8(X16, X14))) <=> ((~p3(X15, X13)) | (~p8(X16, X14)) | p16(X13, X14))), (((p16(X13, X14) | (~p3(X15, X13))) | (~p8(X16, X14))) <=> ((~p3(X15, X13)) | (~p8(X16, X14)) | p16(X13, X14)))), ((((p16(X13, X14) | (~p3(X15, X13))) | (~p8(X16, X14))) | (~p16(X15, X16))) <=> (((~p3(X15, X13)) | (~p8(X16, X14)) | p16(X13, X14)) | (~p16(X15, X16))))), rewrite((((~p3(X15, X13)) | (~p8(X16, X14)) | p16(X13, X14)) | (~p16(X15, X16))) <=> ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))), ((((p16(X13, X14) | (~p3(X15, X13))) | (~p8(X16, X14))) | (~p16(X15, X16))) <=> ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![X14: $i, X13: $i, X16: $i, X15: $i] : (((p16(X13, X14) | (~p3(X15, X13))) | (~p8(X16, X14))) | (~p16(X15, X16))) <=> ![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.42 tff(53,axiom,(![X14: $i, X13: $i, X16: $i, X15: $i] : (((p16(X13, X14) | (~p3(X15, X13))) | (~p8(X16, X14))) | (~p16(X15, X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p16_26')).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.42 tff(56,plain,(
% 0.20/0.42 ![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))),
% 0.20/0.42 inference(skolemize,[status(sab)],[55])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~p16(c22, c21)) <=> (~p16(c22, c21))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,axiom,(~p16(c22, c21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p16_13')).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (~p16(c22, c21)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (((~![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))) | (p16(c22, c21) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | (~p3(f4(c24, c20), c22)))) <=> ((~![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))) | p16(c22, c21) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | (~p3(f4(c24, c20), c22)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((~p3(f4(c24, c20), c22)) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | p16(c22, c21)) <=> (p16(c22, c21) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | (~p3(f4(c24, c20), c22)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (((~![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))) | ((~p3(f4(c24, c20), c22)) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | p16(c22, c21))) <=> ((~![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))) | (p16(c22, c21) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | (~p3(f4(c24, c20), c22))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (((~![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))) | ((~p3(f4(c24, c20), c22)) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | p16(c22, c21))) <=> ((~![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))) | p16(c22, c21) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | (~p3(f4(c24, c20), c22)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 ((~![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))) | ((~p3(f4(c24, c20), c22)) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | p16(c22, c21))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((~![X14: $i, X13: $i, X16: $i, X15: $i] : ((~p3(X15, X13)) | (~p16(X15, X16)) | (~p8(X16, X14)) | p16(X13, X14))) | p16(c22, c21) | (~p16(f4(c24, c20), c21)) | (~p8(c21, c21)) | (~p3(f4(c24, c20), c22))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[66, 60, 57, 47, 36, 35])).
% 0.20/0.42 tff(68,plain,(~p16(f4(c24, c20), c21)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (^[X17: $i, X18: $i, X20: $i, X19: $i] : refl(((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)) <=> ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)) <=> ![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)) <=> ![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (^[X17: $i, X18: $i, X20: $i, X19: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p16(f4(X17, X18), X19) | (~p2(X17, X20))) <=> ((~p2(X17, X20)) | p16(f4(X17, X18), X19))), (((p16(f4(X17, X18), X19) | (~p2(X17, X20))) | (~p18(c26, X20))) <=> (((~p2(X17, X20)) | p16(f4(X17, X18), X19)) | (~p18(c26, X20))))), rewrite((((~p2(X17, X20)) | p16(f4(X17, X18), X19)) | (~p18(c26, X20))) <=> ((~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))), (((p16(f4(X17, X18), X19) | (~p2(X17, X20))) | (~p18(c26, X20))) <=> ((~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)))), ((((p16(f4(X17, X18), X19) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) <=> (((~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)) | (~p16(f4(c19, X18), X19))))), rewrite((((~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)) | (~p16(f4(c19, X18), X19))) <=> ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))), ((((p16(f4(X17, X18), X19) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) <=> ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)))), (((((p16(f4(X17, X18), X19) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) | (~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) <=> (((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)) | (~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))))), rewrite((((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19)) | (~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) <=> ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))), (((((p16(f4(X17, X18), X19) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) | (~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) <=> ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((((p16(f4(X17, X18), X19) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) | (~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) <=> ![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.43 tff(74,axiom,(![X17: $i, X18: $i, X20: $i, X19: $i] : ((((p16(f4(X17, X18), X19) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) | (~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p16_34')).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.43 tff(77,plain,(
% 0.20/0.43 ![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))),
% 0.20/0.43 inference(skolemize,[status(sab)],[76])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (p16(f4(c19, c20), c21) <=> p16(f4(c19, c20), c21)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(80,axiom,(p16(f4(c19, c20), c21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p16_15')).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (p16(f4(c19, c20), c21)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (p2(c24, c25) <=> p2(c24, c25)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(83,axiom,(p2(c24, c25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_12')).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (p2(c24, c25)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (p18(c26, c25) <=> p18(c26, c25)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(86,axiom,(p18(c26, c25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p18_10')).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (p18(c26, c25)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))) | ((~p2(c24, c25)) | (~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)))) <=> ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))) | (~p2(c24, c25)) | (~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (((~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | (~p18(c26, c25)) | (~p2(c24, c25)) | p16(f4(c24, c20), c21)) <=> ((~p2(c24, c25)) | (~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))) | ((~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | (~p18(c26, c25)) | (~p2(c24, c25)) | p16(f4(c24, c20), c21))) <=> ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))) | ((~p2(c24, c25)) | (~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))) | ((~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | (~p18(c26, c25)) | (~p2(c24, c25)) | p16(f4(c24, c20), c21))) <=> ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))) | (~p2(c24, c25)) | (~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[90, 88])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))) | ((~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | (~p18(c26, c25)) | (~p2(c24, c25)) | p16(f4(c24, c20), c21))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(X20, f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19))) | (~p2(c24, c25)) | (~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (~p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[93, 87, 84, 81, 78, 68])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (^[X17: $i, X18: $i, X20: $i, X19: $i] : refl(((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) <=> ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) <=> ![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) <=> ![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (^[X17: $i, X18: $i, X20: $i, X19: $i] : trans(monotonicity(trans(monotonicity(rewrite(((p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p2(X17, X20))) <=> ((~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))), ((((p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p2(X17, X20))) | (~p18(c26, X20))) <=> (((~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p18(c26, X20))))), rewrite((((~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p18(c26, X20))) <=> ((~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))), ((((p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p2(X17, X20))) | (~p18(c26, X20))) <=> ((~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))))), (((((p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) <=> (((~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19))))), rewrite((((~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p16(f4(c19, X18), X19))) <=> ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))), (((((p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) <=> ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((((p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19))) <=> ![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.43 tff(100,axiom,(![X17: $i, X18: $i, X20: $i, X19: $i] : ((((p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20))) | (~p2(X17, X20))) | (~p18(c26, X20))) | (~p16(f4(c19, X18), X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p16_35')).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.44 tff(103,plain,(
% 0.20/0.44 ![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[102])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) | ((~p2(c24, c25)) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))) <=> ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) | (~p2(c24, c25)) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (((~p16(f4(c19, c20), c21)) | (~p18(c26, c25)) | (~p2(c24, c25)) | p16(f4(c24, c20), c21) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) <=> ((~p2(c24, c25)) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) | ((~p16(f4(c19, c20), c21)) | (~p18(c26, c25)) | (~p2(c24, c25)) | p16(f4(c24, c20), c21) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))) <=> ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) | ((~p2(c24, c25)) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) | ((~p16(f4(c19, c20), c21)) | (~p18(c26, c25)) | (~p2(c24, c25)) | p16(f4(c24, c20), c21) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))) <=> ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) | (~p2(c24, c25)) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[107, 105])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) | ((~p16(f4(c19, c20), c21)) | (~p18(c26, c25)) | (~p2(c24, c25)) | p16(f4(c24, c20), c21) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~![X17: $i, X18: $i, X20: $i, X19: $i] : ((~p16(f4(c19, X18), X19)) | (~p18(c26, X20)) | (~p2(X17, X20)) | p16(f4(X17, X18), X19) | p16(f4(f6(c27, X20), f13(f15(c28, X17), X20)), f9(f11(c29, X17), X20)))) | (~p2(c24, c25)) | (~p16(f4(c19, c20), c21)) | p16(f4(c24, c20), c21) | (~p18(c26, c25)) | p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[110, 87, 84, 81, 104, 68])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (^[X22: $i, X21: $i] : refl(((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22)) <=> ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22)) <=> ![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22)) <=> ![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (^[X22: $i, X21: $i] : rewrite((p16(f4(c25, X21), X22) | (~p16(f4(f6(c27, c25), X21), X22))) <=> ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (![X22: $i, X21: $i] : (p16(f4(c25, X21), X22) | (~p16(f4(f6(c27, c25), X21), X22))) <=> ![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.45 tff(117,axiom,(![X22: $i, X21: $i] : (p16(f4(c25, X21), X22) | (~p16(f4(f6(c27, c25), X21), X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p16_25')).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.20/0.45 tff(120,plain,(
% 0.20/0.45 ![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))),
% 0.20/0.45 inference(skolemize,[status(sab)],[119])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (((~![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))) | ((~p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))) <=> ((~![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))) | (~p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))) | ((~p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ((~![X22: $i, X21: $i] : ((~p16(f4(f6(c27, c25), X21), X22)) | p16(f4(c25, X21), X22))) | (~p16(f4(f6(c27, c25), f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))) | p16(f4(c25, f13(f15(c28, c24), c25)), f9(f11(c29, c24), c25))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[124, 121, 111, 94])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------