%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN556-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:34 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN556-1 : TPTP v9.0.0. Released v2.5.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:38:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(p3_type, type, (
% 0.19/0.39 p3: ( $i * $i ) > $o)).
% 0.19/0.39 tff(c9_type, type, (
% 0.19/0.39 c9: $i)).
% 0.19/0.39 tff(f4_type, type, (
% 0.19/0.39 f4: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(c11_type, type, (
% 0.19/0.39 c11: $i)).
% 0.19/0.39 tff(f5_type, type, (
% 0.19/0.39 f5: ( $i * $i ) > $i)).
% 0.19/0.39 tff(f6_type, type, (
% 0.19/0.39 f6: $i > $i)).
% 0.19/0.39 tff(f7_type, type, (
% 0.19/0.39 f7: $i > $i)).
% 0.19/0.39 tff(c12_type, type, (
% 0.19/0.39 c12: $i)).
% 0.19/0.39 tff(f8_type, type, (
% 0.19/0.39 f8: ( $i * $i ) > $i)).
% 0.19/0.39 tff(c13_type, type, (
% 0.19/0.39 c13: $i)).
% 0.19/0.39 tff(c10_type, type, (
% 0.19/0.39 c10: $i)).
% 0.19/0.39 tff(p2_type, type, (
% 0.19/0.39 p2: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,assumption,(~p3(c11, c11)), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[X15: $i] : refl(p3(X15, X15) <=> p3(X15, X15))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![X15: $i] : p3(X15, X15) <=> ![X15: $i] : p3(X15, X15)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![X15: $i] : p3(X15, X15) <=> ![X15: $i] : p3(X15, X15)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(5,axiom,(![X15: $i] : p3(X15, X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_2')).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![X15: $i] : p3(X15, X15)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.39 tff(7,plain,(
% 0.19/0.39 ![X15: $i] : p3(X15, X15)),
% 0.19/0.39 inference(skolemize,[status(sab)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![X15: $i] : p3(X15, X15)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ((~![X15: $i] : p3(X15, X15)) | p3(c11, c11)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.39 tff(11,plain,(p3(c11, c11)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(12,assumption,(~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c10), f6(f7(c12))))), introduced(assumption)).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (^[X0: $i] : refl(p2(X0, X0) <=> p2(X0, X0))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,axiom,(![X0: $i] : p2(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_1')).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![X0: $i] : p2(X0, X0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,(
% 0.19/0.39 ![X0: $i] : p2(X0, X0)),
% 0.19/0.39 inference(skolemize,[status(sab)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![X0: $i] : p2(X0, X0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~![X0: $i] : p2(X0, X0)) | p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c10), f6(f7(c12))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.19/0.39 tff(22,plain,(p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c10), f6(f7(c12))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(23,assumption,(~p2(c10, c10)), introduced(assumption)).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~![X0: $i] : p2(X0, X0)) | p2(c10, c10)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[24, 19, 23])).
% 0.19/0.39 tff(26,plain,(p2(c10, c10)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : refl(((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))) <=> ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))) <=> ![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))) <=> ![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (^[X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : trans(monotonicity(trans(monotonicity(rewrite((p3(f4(X18, X19, X20), f4(X21, X22, X23)) | (~p2(X19, X22))) <=> ((~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))), (((p3(f4(X18, X19, X20), f4(X21, X22, X23)) | (~p2(X19, X22))) | (~p3(X20, X23))) <=> (((~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))) | (~p3(X20, X23))))), rewrite((((~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))) | (~p3(X20, X23))) <=> ((~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))), (((p3(f4(X18, X19, X20), f4(X21, X22, X23)) | (~p2(X19, X22))) | (~p3(X20, X23))) <=> ((~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))))), ((((p3(f4(X18, X19, X20), f4(X21, X22, X23)) | (~p2(X19, X22))) | (~p3(X20, X23))) | (~p2(X18, X21))) <=> (((~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))) | (~p2(X18, X21))))), rewrite((((~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23))) | (~p2(X18, X21))) <=> ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))), ((((p3(f4(X18, X19, X20), f4(X21, X22, X23)) | (~p2(X19, X22))) | (~p3(X20, X23))) | (~p2(X18, X21))) <=> ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : (((p3(f4(X18, X19, X20), f4(X21, X22, X23)) | (~p2(X19, X22))) | (~p3(X20, X23))) | (~p2(X18, X21))) <=> ![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.39 tff(32,axiom,(![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : (((p3(f4(X18, X19, X20), f4(X21, X22, X23)) | (~p2(X19, X22))) | (~p3(X20, X23))) | (~p2(X18, X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_12')).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.39 tff(35,plain,(
% 0.19/0.39 ![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[34])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))) | ((~p2(c10, c10)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c10), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))) <=> ((~![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))) | (~p2(c10, c10)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c10), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))) | ((~p2(c10, c10)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c10), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))) | (~p2(c10, c10)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c10), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~p2(c10, c10)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c10), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 26, 22, 11])).
% 0.19/0.39 tff(42,assumption,(~p2(c12, c12)), introduced(assumption)).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((~![X0: $i] : p2(X0, X0)) | p2(c12, c12)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[43, 19, 42])).
% 0.19/0.39 tff(45,plain,(p2(c12, c12)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (^[X9: $i, X10: $i] : refl(((~p2(X9, X10)) | p2(f7(X9), f7(X10))) <=> ((~p2(X9, X10)) | p2(f7(X9), f7(X10))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10))) <=> ![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10))) <=> ![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (^[X9: $i, X10: $i] : rewrite((p2(f7(X9), f7(X10)) | (~p2(X9, X10))) <=> ((~p2(X9, X10)) | p2(f7(X9), f7(X10))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (![X9: $i, X10: $i] : (p2(f7(X9), f7(X10)) | (~p2(X9, X10))) <=> ![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.39 tff(51,axiom,(![X9: $i, X10: $i] : (p2(f7(X9), f7(X10)) | (~p2(X9, X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.39 tff(54,plain,(
% 0.19/0.39 ![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))) | ((~p2(c12, c12)) | p2(f7(c12), f7(c12)))) <=> ((~![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))) | (~p2(c12, c12)) | p2(f7(c12), f7(c12)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))) | ((~p2(c12, c12)) | p2(f7(c12), f7(c12)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~![X9: $i, X10: $i] : ((~p2(X9, X10)) | p2(f7(X9), f7(X10)))) | (~p2(c12, c12)) | p2(f7(c12), f7(c12))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((~p2(c12, c12)) | p2(f7(c12), f7(c12))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (p2(f7(c12), f7(c12))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[59, 45])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (^[X7: $i, X8: $i] : refl(((~p2(X7, X8)) | p2(f6(X7), f6(X8))) <=> ((~p2(X7, X8)) | p2(f6(X7), f6(X8))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (^[X7: $i, X8: $i] : rewrite((p2(f6(X7), f6(X8)) | (~p2(X7, X8))) <=> ((~p2(X7, X8)) | p2(f6(X7), f6(X8))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (![X7: $i, X8: $i] : (p2(f6(X7), f6(X8)) | (~p2(X7, X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.39 tff(66,axiom,(![X7: $i, X8: $i] : (p2(f6(X7), f6(X8)) | (~p2(X7, X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_5')).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.39 tff(69,plain,(
% 0.19/0.39 ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[68])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))) | ((~p2(f7(c12), f7(c12))) | p2(f6(f7(c12)), f6(f7(c12))))) <=> ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))) | (~p2(f7(c12), f7(c12))) | p2(f6(f7(c12)), f6(f7(c12))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))) | ((~p2(f7(c12), f7(c12))) | p2(f6(f7(c12)), f6(f7(c12))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f6(X7), f6(X8)))) | (~p2(f7(c12), f7(c12))) | p2(f6(f7(c12)), f6(f7(c12)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 ((~p2(f7(c12), f7(c12))) | p2(f6(f7(c12)), f6(f7(c12)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (p2(f6(f7(c12)), f6(f7(c12)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[74, 60])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (^[X14: $i, X12: $i, X11: $i, X13: $i] : refl(((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14))) <=> ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (^[X14: $i, X12: $i, X11: $i, X13: $i] : trans(monotonicity(rewrite((p2(f8(X11, X12), f8(X13, X14)) | (~p2(X12, X14))) <=> ((~p2(X12, X14)) | p2(f8(X11, X12), f8(X13, X14)))), (((p2(f8(X11, X12), f8(X13, X14)) | (~p2(X12, X14))) | (~p3(X11, X13))) <=> (((~p2(X12, X14)) | p2(f8(X11, X12), f8(X13, X14))) | (~p3(X11, X13))))), rewrite((((~p2(X12, X14)) | p2(f8(X11, X12), f8(X13, X14))) | (~p3(X11, X13))) <=> ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))), (((p2(f8(X11, X12), f8(X13, X14)) | (~p2(X12, X14))) | (~p3(X11, X13))) <=> ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((p2(f8(X11, X12), f8(X13, X14)) | (~p2(X12, X14))) | (~p3(X11, X13))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.39 tff(81,axiom,(![X14: $i, X12: $i, X11: $i, X13: $i] : ((p2(f8(X11, X12), f8(X13, X14)) | (~p2(X12, X14))) | (~p3(X11, X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_11')).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.40 tff(84,plain,(
% 0.19/0.40 ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[83])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (p2(c10, c13) <=> p2(c10, c13)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,axiom,(p2(c10, c13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_3')).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (p2(c10, c13)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))) | ((~p2(c10, c13)) | (~p3(c11, c11)) | p2(f8(c11, c10), f8(c11, c13)))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))) | (~p2(c10, c13)) | (~p3(c11, c11)) | p2(f8(c11, c10), f8(c11, c13)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))) | ((~p2(c10, c13)) | (~p3(c11, c11)) | p2(f8(c11, c10), f8(c11, c13)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X12, X14)) | (~p3(X11, X13)) | p2(f8(X11, X12), f8(X13, X14)))) | (~p2(c10, c13)) | (~p3(c11, c11)) | p2(f8(c11, c10), f8(c11, c13))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~p3(c11, c11)) | p2(f8(c11, c10), f8(c11, c13))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[91, 88, 85])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (p2(f8(c11, c10), f8(c11, c13))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 11])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(rewrite((p2(f5(X3, X4), f5(X5, X6)) | (~p2(X3, X5))) <=> ((~p2(X3, X5)) | p2(f5(X3, X4), f5(X5, X6)))), (((p2(f5(X3, X4), f5(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> (((~p2(X3, X5)) | p2(f5(X3, X4), f5(X5, X6))) | (~p2(X4, X6))))), rewrite((((~p2(X3, X5)) | p2(f5(X3, X4), f5(X5, X6))) | (~p2(X4, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))), (((p2(f5(X3, X4), f5(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((p2(f5(X3, X4), f5(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.40 tff(99,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((p2(f5(X3, X4), f5(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_10')).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.19/0.40 tff(102,plain,(
% 0.19/0.40 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[101])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))) | ((~p2(f8(c11, c10), f8(c11, c13))) | (~p2(f6(f7(c12)), f6(f7(c12)))) | p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12)))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))) | (~p2(f8(c11, c10), f8(c11, c13))) | (~p2(f6(f7(c12)), f6(f7(c12)))) | p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))) | ((~p2(f8(c11, c10), f8(c11, c13))) | (~p2(f6(f7(c12)), f6(f7(c12)))) | p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f5(X3, X4), f5(X5, X6)))) | (~p2(f8(c11, c10), f8(c11, c13))) | (~p2(f6(f7(c12)), f6(f7(c12)))) | p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ((~p2(f8(c11, c10), f8(c11, c13))) | (~p2(f6(f7(c12)), f6(f7(c12)))) | p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[107, 93, 75])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (((~![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))) | ((~p2(c10, c13)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)))) <=> ((~![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))) | (~p2(c10, c13)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 ((~![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))) | ((~p2(c10, c13)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~![X22: $i, X21: $i, X18: $i, X20: $i, X23: $i, X19: $i] : ((~p2(X18, X21)) | (~p3(X20, X23)) | (~p2(X19, X22)) | p3(f4(X18, X19, X20), f4(X21, X22, X23)))) | (~p2(c10, c13)) | (~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 ((~p3(c11, c11)) | (~p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12))))) | p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[111, 88, 36])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[112, 108, 11])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (^[X17: $i, X16: $i, X15: $i] : refl(((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17)) <=> ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17)) <=> ![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17)) <=> ![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (^[X17: $i, X16: $i, X15: $i] : trans(monotonicity(rewrite((p3(X16, X17) | (~p3(X15, X16))) <=> ((~p3(X15, X16)) | p3(X16, X17))), (((p3(X16, X17) | (~p3(X15, X16))) | (~p3(X15, X17))) <=> (((~p3(X15, X16)) | p3(X16, X17)) | (~p3(X15, X17))))), rewrite((((~p3(X15, X16)) | p3(X16, X17)) | (~p3(X15, X17))) <=> ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))), (((p3(X16, X17) | (~p3(X15, X16))) | (~p3(X15, X17))) <=> ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((p3(X16, X17) | (~p3(X15, X16))) | (~p3(X15, X17))) <=> ![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.41 tff(119,axiom,(![X17: $i, X16: $i, X15: $i] : ((p3(X16, X17) | (~p3(X15, X16))) | (~p3(X15, X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_7')).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.41 tff(122,plain,(
% 0.19/0.41 ![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))),
% 0.19/0.41 inference(skolemize,[status(sab)],[121])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | ((~p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))) | p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))) <=> ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | (~p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))) | p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | ((~p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))) | p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | (~p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))) | p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[126, 123, 113, 41])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 ((~p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) <=> (~p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(129,axiom,(~p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p3_9')).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (~p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | (p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)))) <=> ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (((~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)) | p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) <=> (p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | ((~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)) | p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))) <=> ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | (p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[132])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | ((~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)) | p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))) <=> ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[133, 131])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | ((~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)) | p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))) | (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (~p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[136, 123, 130, 127])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)) <=> p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(139,axiom,(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_8')).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 (((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | ((~p3(c9, c9)) | (~p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))) | p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9))) <=> ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | (~p3(c9, c9)) | (~p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))) | p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | ((~p3(c9, c9)) | (~p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))) | p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 ((~![X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X15, X16)) | p3(X16, X17))) | (~p3(c9, c9)) | (~p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))) | p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (~p3(c9, c9)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[143, 123, 140, 137])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 ((~![X15: $i] : p3(X15, X15)) | p3(c9, c9)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[145, 8, 144])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------