%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN608-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:39:40 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN608-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:40:57 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(p2_type, type, (
% 0.11/0.37 p2: ( $i * $i ) > $o)).
% 0.11/0.37 tff(f6_type, type, (
% 0.11/0.37 f6: $i > $i)).
% 0.11/0.37 tff(f7_type, type, (
% 0.11/0.37 f7: $i > $i)).
% 0.11/0.37 tff(f8_type, type, (
% 0.11/0.37 f8: $i > $i)).
% 0.11/0.37 tff(c20_type, type, (
% 0.11/0.37 c20: $i)).
% 0.11/0.37 tff(p5_type, type, (
% 0.11/0.37 p5: ( $i * $i ) > $o)).
% 0.11/0.37 tff(f9_type, type, (
% 0.11/0.37 f9: $i > $i)).
% 0.11/0.37 tff(f10_type, type, (
% 0.11/0.37 f10: ( $i * $i ) > $i)).
% 0.11/0.37 tff(f12_type, type, (
% 0.11/0.37 f12: ( $i * $i ) > $i)).
% 0.11/0.37 tff(c21_type, type, (
% 0.11/0.37 c21: $i)).
% 0.11/0.37 tff(c22_type, type, (
% 0.11/0.37 c22: $i)).
% 0.11/0.37 tff(f14_type, type, (
% 0.11/0.37 f14: ( $i * $i ) > $i)).
% 0.11/0.37 tff(c19_type, type, (
% 0.11/0.37 c19: $i)).
% 0.11/0.37 tff(f4_type, type, (
% 0.11/0.37 f4: $i > $i)).
% 0.11/0.37 tff(f15_type, type, (
% 0.11/0.37 f15: $i > $i)).
% 0.11/0.37 tff(p3_type, type, (
% 0.11/0.37 p3: ( $i * $i ) > $o)).
% 0.11/0.37 tff(p17_type, type, (
% 0.11/0.37 p17: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,assumption,(~p5(f8(c20), f8(c20))), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[X43: $i] : refl(p5(X43, X43) <=> p5(X43, X43))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X43: $i] : p5(X43, X43) <=> ![X43: $i] : p5(X43, X43)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![X43: $i] : p5(X43, X43) <=> ![X43: $i] : p5(X43, X43)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,axiom,(![X43: $i] : p5(X43, X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_3')).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (![X43: $i] : p5(X43, X43)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.37 tff(7,plain,(
% 0.11/0.37 ![X43: $i] : p5(X43, X43)),
% 0.11/0.37 inference(skolemize,[status(sab)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![X43: $i] : p5(X43, X43)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 ((~![X43: $i] : p5(X43, X43)) | p5(f8(c20), f8(c20))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.37 tff(11,plain,(p5(f8(c20), f8(c20))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (^[X47: $i, X46: $i] : refl(((~p5(X46, X47)) | p5(f7(X46), f7(X47))) <=> ((~p5(X46, X47)) | p5(f7(X46), f7(X47))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47))) <=> ![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47))) <=> ![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (^[X47: $i, X46: $i] : rewrite((p5(f7(X46), f7(X47)) | (~p5(X46, X47))) <=> ((~p5(X46, X47)) | p5(f7(X46), f7(X47))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![X47: $i, X46: $i] : (p5(f7(X46), f7(X47)) | (~p5(X46, X47))) <=> ![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.37 tff(17,axiom,(![X47: $i, X46: $i] : (p5(f7(X46), f7(X47)) | (~p5(X46, X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_16')).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.37 tff(20,plain,(
% 0.11/0.37 ![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[19])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (((~![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))) | ((~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20))))) <=> ((~![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))) | (~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ((~![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))) | ((~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 ((~![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))) | (~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 ((~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (p5(f7(f8(c20)), f7(f8(c20)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (^[X14: $i, X15: $i] : refl(((~p5(X14, X15)) | p2(f6(X14), f6(X15))) <=> ((~p5(X14, X15)) | p2(f6(X14), f6(X15))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15))) <=> ![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15))) <=> ![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (^[X14: $i, X15: $i] : rewrite((p2(f6(X14), f6(X15)) | (~p5(X14, X15))) <=> ((~p5(X14, X15)) | p2(f6(X14), f6(X15))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (![X14: $i, X15: $i] : (p2(f6(X14), f6(X15)) | (~p5(X14, X15))) <=> ![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.11/0.38 tff(32,axiom,(![X14: $i, X15: $i] : (p2(f6(X14), f6(X15)) | (~p5(X14, X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_11')).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.11/0.38 tff(35,plain,(
% 0.11/0.38 ![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[34])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (((~![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))) | ((~p5(f7(f8(c20)), f7(f8(c20)))) | p2(f6(f7(f8(c20))), f6(f7(f8(c20)))))) <=> ((~![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))) | (~p5(f7(f8(c20)), f7(f8(c20)))) | p2(f6(f7(f8(c20))), f6(f7(f8(c20)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 ((~![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))) | ((~p5(f7(f8(c20)), f7(f8(c20)))) | p2(f6(f7(f8(c20))), f6(f7(f8(c20)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 ((~![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))) | (~p5(f7(f8(c20)), f7(f8(c20)))) | p2(f6(f7(f8(c20))), f6(f7(f8(c20))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (p2(f6(f7(f8(c20))), f6(f7(f8(c20))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 0.11/0.38 tff(41,assumption,(~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))), introduced(assumption)).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (^[X18: $i] : refl(p3(X18, X18) <=> p3(X18, X18))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (![X18: $i] : p3(X18, X18) <=> ![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![X18: $i] : p3(X18, X18) <=> ![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(45,axiom,(![X18: $i] : p3(X18, X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_4')).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.11/0.38 tff(47,plain,(
% 0.11/0.38 ![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(skolemize,[status(sab)],[46])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 ((~![X18: $i] : p3(X18, X18)) | p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[49, 48, 41])).
% 0.11/0.38 tff(51,plain,(p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(52,assumption,(~p3(f12(c22, c21), f12(c22, c21))), introduced(assumption)).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 ((~![X18: $i] : p3(X18, X18)) | p3(f12(c22, c21), f12(c22, c21))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[53, 48, 52])).
% 0.11/0.38 tff(55,plain,(p3(f12(c22, c21), f12(c22, c21))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (^[X22: $i, X21: $i, X23: $i, X24: $i] : refl(((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24))) <=> ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24))) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24))) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (^[X22: $i, X21: $i, X23: $i, X24: $i] : trans(monotonicity(rewrite((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) <=> ((~p3(X21, X23)) | p3(f10(X21, X22), f10(X23, X24)))), (((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) | (~p3(X22, X24))) <=> (((~p3(X21, X23)) | p3(f10(X21, X22), f10(X23, X24))) | (~p3(X22, X24))))), rewrite((((~p3(X21, X23)) | p3(f10(X21, X22), f10(X23, X24))) | (~p3(X22, X24))) <=> ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))), (((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) | (~p3(X22, X24))) <=> ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) | (~p3(X22, X24))) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.11/0.38 tff(61,axiom,(![X22: $i, X21: $i, X23: $i, X24: $i] : ((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) | (~p3(X22, X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_24')).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.11/0.38 tff(64,plain,(
% 0.11/0.38 ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[63])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f12(c22, c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f12(c22, c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f12(c22, c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f12(c22, c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f12(c22, c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[69, 55, 51])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (^[X17: $i, X16: $i] : refl(((~p3(X16, X17)) | p2(f9(X16), f9(X17))) <=> ((~p3(X16, X17)) | p2(f9(X16), f9(X17))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17))) <=> ![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[71])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17))) <=> ![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (^[X17: $i, X16: $i] : rewrite((p2(f9(X16), f9(X17)) | (~p3(X16, X17))) <=> ((~p3(X16, X17)) | p2(f9(X16), f9(X17))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (![X17: $i, X16: $i] : (p2(f9(X16), f9(X17)) | (~p3(X16, X17))) <=> ![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[74])).
% 0.11/0.38 tff(76,axiom,(![X17: $i, X16: $i] : (p2(f9(X16), f9(X17)) | (~p3(X16, X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_12')).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.11/0.38 tff(79,plain,(
% 0.11/0.38 ![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[78])).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | ((~p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))))) <=> ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | (~p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | ((~p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | (~p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 (p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[83, 80, 70])).
% 0.11/0.38 tff(85,plain,
% 0.11/0.38 (p3(f12(c22, c21), f15(c22)) <=> p3(f12(c22, c21), f15(c22))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(86,axiom,(p3(f12(c22, c21), f15(c22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_6')).
% 0.11/0.39 tff(87,plain,
% 0.11/0.39 (p3(f12(c22, c21), f15(c22))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.11/0.39 tff(88,plain,
% 0.11/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f12(c22, c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f12(c22, c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(89,plain,
% 0.11/0.39 (((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f15(c22))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) <=> ((~p3(f12(c22, c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(90,plain,
% 0.11/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f15(c22))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f12(c22, c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[89])).
% 0.11/0.39 tff(91,plain,
% 0.11/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f15(c22))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f12(c22, c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[90, 88])).
% 0.11/0.39 tff(92,plain,
% 0.11/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(c22, c21), f15(c22))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(93,plain,
% 0.11/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f12(c22, c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.11/0.39 tff(94,plain,
% 0.11/0.39 ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[93, 87, 65])).
% 0.11/0.39 tff(95,plain,
% 0.11/0.39 (p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[94, 51])).
% 0.11/0.39 tff(96,plain,
% 0.11/0.39 (((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | ((~p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22)))))) <=> ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | (~p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(97,plain,
% 0.11/0.39 ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | ((~p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22)))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(98,plain,
% 0.11/0.39 ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | (~p3(f10(f14(f4(f9(c19)), c19), f12(c22, c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.11/0.39 tff(99,plain,
% 0.11/0.39 (p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[98, 80, 95])).
% 0.11/0.39 tff(100,plain,
% 0.11/0.39 (^[X12: $i, X11: $i, X13: $i] : refl(((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13)) <=> ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(101,plain,
% 0.11/0.39 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13)) <=> ![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[100])).
% 0.11/0.39 tff(102,plain,
% 0.11/0.39 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13)) <=> ![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(103,plain,
% 0.11/0.39 (^[X12: $i, X11: $i, X13: $i] : trans(monotonicity(rewrite((p2(X12, X13) | (~p2(X11, X12))) <=> ((~p2(X11, X12)) | p2(X12, X13))), (((p2(X12, X13) | (~p2(X11, X12))) | (~p2(X11, X13))) <=> (((~p2(X11, X12)) | p2(X12, X13)) | (~p2(X11, X13))))), rewrite((((~p2(X11, X12)) | p2(X12, X13)) | (~p2(X11, X13))) <=> ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))), (((p2(X12, X13) | (~p2(X11, X12))) | (~p2(X11, X13))) <=> ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(104,plain,
% 0.11/0.39 (![X12: $i, X11: $i, X13: $i] : ((p2(X12, X13) | (~p2(X11, X12))) | (~p2(X11, X13))) <=> ![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[103])).
% 0.11/0.39 tff(105,axiom,(![X12: $i, X11: $i, X13: $i] : ((p2(X12, X13) | (~p2(X11, X12))) | (~p2(X11, X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_17')).
% 0.11/0.39 tff(106,plain,
% 0.11/0.39 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.11/0.39 tff(107,plain,
% 0.11/0.39 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.11/0.39 tff(108,plain,(
% 0.11/0.39 ![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.11/0.39 inference(skolemize,[status(sab)],[107])).
% 0.11/0.39 tff(109,plain,
% 0.11/0.39 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.11/0.39 tff(110,plain,
% 0.11/0.39 (((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))))) <=> ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(111,plain,
% 0.11/0.39 (((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) <=> ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(112,plain,
% 0.11/0.40 (((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))))) <=> ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.11/0.40 tff(113,plain,
% 0.11/0.40 (((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))))) <=> ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))))),
% 0.11/0.40 inference(transitivity,[status(thm)],[112, 110])).
% 0.11/0.40 tff(114,plain,
% 0.11/0.40 ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(115,plain,
% 0.11/0.40 ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.11/0.40 tff(116,plain,
% 0.11/0.40 (p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[115, 109, 99, 84])).
% 0.11/0.40 tff(117,plain,
% 0.11/0.40 (^[X50: $i] : refl((~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))) <=> (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(118,plain,
% 0.11/0.40 (![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))) <=> ![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[117])).
% 0.11/0.40 tff(119,plain,
% 0.11/0.40 (![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))) <=> ![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(120,axiom,(![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p17_29')).
% 0.11/0.40 tff(121,plain,
% 0.11/0.40 (![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.11/0.40 tff(122,plain,(
% 0.11/0.40 ![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[121])).
% 0.11/0.40 tff(123,plain,
% 0.11/0.40 (![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.11/0.40 tff(124,plain,
% 0.11/0.40 ((~![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(125,plain,
% 0.11/0.40 (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.11/0.40 tff(126,plain,
% 0.11/0.40 (p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20)))) <=> p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(127,axiom,(p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p17_27')).
% 0.11/0.40 tff(128,plain,
% 0.11/0.40 (p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.11/0.40 tff(129,plain,
% 0.11/0.40 (^[X4: $i, X3: $i, X2: $i, X5: $i] : refl(((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) <=> ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(130,plain,
% 0.11/0.40 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) <=> ![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[129])).
% 0.11/0.40 tff(131,plain,
% 0.11/0.40 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) <=> ![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(132,plain,
% 0.11/0.40 (^[X4: $i, X3: $i, X2: $i, X5: $i] : trans(monotonicity(trans(monotonicity(rewrite((p17(X2, X3) | (~p2(X4, X2))) <=> ((~p2(X4, X2)) | p17(X2, X3))), (((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) <=> (((~p2(X4, X2)) | p17(X2, X3)) | (~p2(X5, X3))))), rewrite((((~p2(X4, X2)) | p17(X2, X3)) | (~p2(X5, X3))) <=> ((~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))), (((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) <=> ((~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)))), ((((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) | (~p17(X4, X5))) <=> (((~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) | (~p17(X4, X5))))), rewrite((((~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) | (~p17(X4, X5))) <=> ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))), ((((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) | (~p17(X4, X5))) <=> ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(133,plain,
% 0.11/0.40 (![X4: $i, X3: $i, X2: $i, X5: $i] : (((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) | (~p17(X4, X5))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[132])).
% 0.11/0.40 tff(134,axiom,(![X4: $i, X3: $i, X2: $i, X5: $i] : (((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) | (~p17(X4, X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p17_20')).
% 0.11/0.40 tff(135,plain,
% 0.11/0.40 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.11/0.40 tff(136,plain,
% 0.11/0.40 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.11/0.40 tff(137,plain,(
% 0.11/0.40 ![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.11/0.40 inference(skolemize,[status(sab)],[136])).
% 0.11/0.40 tff(138,plain,
% 0.11/0.40 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.11/0.40 tff(139,plain,
% 0.11/0.40 (((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | (p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(140,plain,
% 0.11/0.40 (((~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20))))) <=> (p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(141,plain,
% 0.11/0.40 (((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | ((~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | (p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20)))))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[140])).
% 0.11/0.40 tff(142,plain,
% 0.11/0.40 (((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | ((~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))))),
% 0.11/0.40 inference(transitivity,[status(thm)],[141, 139])).
% 0.11/0.40 tff(143,plain,
% 0.11/0.40 ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | ((~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(144,plain,
% 0.11/0.40 ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))), f6(f7(f8(c20)))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(c22, c21))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.11/0.40 tff(145,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[144, 138, 128, 125, 116, 40])).
% 0.11/0.40 % SZS output end Proof
% 0.11/0.41 % E exiting
%------------------------------------------------------------------------------