%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN555-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN555-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:38:50 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(p4_type, type, (
% 0.13/0.39 p4: ( $i * $i ) > $o)).
% 0.13/0.39 tff(f5_type, type, (
% 0.13/0.39 f5: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(c9_type, type, (
% 0.13/0.39 c9: $i)).
% 0.13/0.39 tff(c10_type, type, (
% 0.13/0.39 c10: $i)).
% 0.13/0.39 tff(c7_type, type, (
% 0.13/0.39 c7: $i)).
% 0.13/0.39 tff(f6_type, type, (
% 0.13/0.39 f6: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(c8_type, type, (
% 0.13/0.39 c8: $i)).
% 0.13/0.39 tff(p3_type, type, (
% 0.13/0.39 p3: ( $i * $i ) > $o)).
% 0.13/0.39 tff(p2_type, type, (
% 0.13/0.39 p2: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(~p4(c8, c8)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[X12: $i] : refl(p4(X12, X12) <=> p4(X12, X12))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![X12: $i] : p4(X12, X12) <=> ![X12: $i] : p4(X12, X12)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![X12: $i] : p4(X12, X12) <=> ![X12: $i] : p4(X12, X12)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,axiom,(![X12: $i] : p4(X12, X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_2')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![X12: $i] : p4(X12, X12)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,(
% 0.13/0.39 ![X12: $i] : p4(X12, X12)),
% 0.13/0.39 inference(skolemize,[status(sab)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![X12: $i] : p4(X12, X12)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 ((~![X12: $i] : p4(X12, X12)) | p4(c8, c8)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.13/0.39 tff(11,plain,(p4(c8, c8)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (^[X24: $i] : refl(p4(f5(c7, X24, c8), f5(c7, X24, c9)) <=> p4(f5(c7, X24, c8), f5(c7, X24, c9)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9)) <=> ![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9)) <=> ![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,axiom,(![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_6')).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,(
% 0.13/0.39 ![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9))),
% 0.13/0.39 inference(skolemize,[status(sab)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ((~![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9))) | p4(f5(c7, c10, c8), f5(c7, c10, c9))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (p4(f5(c7, c10, c8), f5(c7, c10, c9))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (^[X14: $i, X12: $i, X13: $i] : refl(((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14)) <=> ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (^[X14: $i, X12: $i, X13: $i] : trans(monotonicity(rewrite((p4(X13, X14) | (~p4(X12, X13))) <=> ((~p4(X12, X13)) | p4(X13, X14))), (((p4(X13, X14) | (~p4(X12, X13))) | (~p4(X12, X14))) <=> (((~p4(X12, X13)) | p4(X13, X14)) | (~p4(X12, X14))))), rewrite((((~p4(X12, X13)) | p4(X13, X14)) | (~p4(X12, X14))) <=> ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))), (((p4(X13, X14) | (~p4(X12, X13))) | (~p4(X12, X14))) <=> ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![X14: $i, X12: $i, X13: $i] : ((p4(X13, X14) | (~p4(X12, X13))) | (~p4(X12, X14))) <=> ![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.39 tff(26,axiom,(![X14: $i, X12: $i, X13: $i] : ((p4(X13, X14) | (~p4(X12, X13))) | (~p4(X12, X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_8')).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.39 tff(29,plain,(
% 0.13/0.39 ![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 0.13/0.39 inference(skolemize,[status(sab)],[28])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (p4(f5(c7, c10, c9), f5(c7, c10, c9)) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | p4(f5(c7, c10, c9), f5(c7, c10, c9)) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (((~p4(f5(c7, c10, c8), f5(c7, c10, c9))) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9))) | p4(f5(c7, c10, c9), f5(c7, c10, c9))) <=> (p4(f5(c7, c10, c9), f5(c7, c10, c9)) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, c10, c8), f5(c7, c10, c9))) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9))) | p4(f5(c7, c10, c9), f5(c7, c10, c9)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (p4(f5(c7, c10, c9), f5(c7, c10, c9)) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9)))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, c10, c8), f5(c7, c10, c9))) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9))) | p4(f5(c7, c10, c9), f5(c7, c10, c9)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | p4(f5(c7, c10, c9), f5(c7, c10, c9)) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[33, 31])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, c10, c8), f5(c7, c10, c9))) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9))) | p4(f5(c7, c10, c9), f5(c7, c10, c9)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | p4(f5(c7, c10, c9), f5(c7, c10, c9)) | (~p4(f5(c7, c10, c8), f5(c7, c10, c9)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (p4(f5(c7, c10, c9), f5(c7, c10, c9))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[36, 30, 20])).
% 0.13/0.39 tff(38,assumption,(~p3(c10, c10)), introduced(assumption)).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (^[X3: $i] : refl(p3(X3, X3) <=> p3(X3, X3))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![X3: $i] : p3(X3, X3) <=> ![X3: $i] : p3(X3, X3)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![X3: $i] : p3(X3, X3) <=> ![X3: $i] : p3(X3, X3)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,axiom,(![X3: $i] : p3(X3, X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_3')).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (![X3: $i] : p3(X3, X3)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,(
% 0.13/0.39 ![X3: $i] : p3(X3, X3)),
% 0.13/0.39 inference(skolemize,[status(sab)],[43])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![X3: $i] : p3(X3, X3)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 ((~![X3: $i] : p3(X3, X3)) | p3(c10, c10)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[46, 45, 38])).
% 0.13/0.39 tff(48,plain,(p3(c10, c10)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (^[X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : refl(((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))) <=> ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))) <=> ![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))) <=> ![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (^[X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p3(f6(X6, X7, X8), f6(X9, X10, X11)) | (~p4(X8, X11))) <=> ((~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))), (((p3(f6(X6, X7, X8), f6(X9, X10, X11)) | (~p4(X8, X11))) | (~p4(X7, X10))) <=> (((~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))) | (~p4(X7, X10))))), rewrite((((~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))) | (~p4(X7, X10))) <=> ((~p4(X7, X10)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))), (((p3(f6(X6, X7, X8), f6(X9, X10, X11)) | (~p4(X8, X11))) | (~p4(X7, X10))) <=> ((~p4(X7, X10)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))))), ((((p3(f6(X6, X7, X8), f6(X9, X10, X11)) | (~p4(X8, X11))) | (~p4(X7, X10))) | (~p3(X6, X9))) <=> (((~p4(X7, X10)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))) | (~p3(X6, X9))))), rewrite((((~p4(X7, X10)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11))) | (~p3(X6, X9))) <=> ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))), ((((p3(f6(X6, X7, X8), f6(X9, X10, X11)) | (~p4(X8, X11))) | (~p4(X7, X10))) | (~p3(X6, X9))) <=> ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : (((p3(f6(X6, X7, X8), f6(X9, X10, X11)) | (~p4(X8, X11))) | (~p4(X7, X10))) | (~p3(X6, X9))) <=> ![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.13/0.39 tff(54,axiom,(![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : (((p3(f6(X6, X7, X8), f6(X9, X10, X11)) | (~p4(X8, X11))) | (~p4(X7, X10))) | (~p3(X6, X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_10')).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.13/0.39 tff(57,plain,(
% 0.13/0.39 ![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[56])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (((~![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))) | ((~p3(c10, c10)) | (~p4(c8, c8)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8)))) <=> ((~![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))) | (~p3(c10, c10)) | (~p4(c8, c8)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (((~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | (~p3(c10, c10)) | (~p4(c8, c8)) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) <=> ((~p3(c10, c10)) | (~p4(c8, c8)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (((~![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))) | ((~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | (~p3(c10, c10)) | (~p4(c8, c8)) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8)))) <=> ((~![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))) | ((~p3(c10, c10)) | (~p4(c8, c8)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[60])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (((~![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))) | ((~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | (~p3(c10, c10)) | (~p4(c8, c8)) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8)))) <=> ((~![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))) | (~p3(c10, c10)) | (~p4(c8, c8)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[61, 59])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 ((~![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))) | ((~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | (~p3(c10, c10)) | (~p4(c8, c8)) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 ((~![X9: $i, X11: $i, X6: $i, X10: $i, X7: $i, X8: $i] : ((~p4(X7, X10)) | (~p3(X6, X9)) | (~p4(X8, X11)) | p3(f6(X6, X7, X8), f6(X9, X10, X11)))) | (~p3(c10, c10)) | (~p4(c8, c8)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[64, 58, 48, 37, 11])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (p4(f5(c7, c10, c9), c9) <=> p4(f5(c7, c10, c9), c9)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(67,axiom,(p4(f5(c7, c10, c9), c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_4')).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (p4(f5(c7, c10, c9), c9)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, c10, c9), c9)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p4(c9, f5(c7, c10, c9)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f5(c7, c10, c9), c9)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p4(c9, f5(c7, c10, c9)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (((~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | (~p4(f5(c7, c10, c9), c9)) | p4(c9, f5(c7, c10, c9))) <=> ((~p4(f5(c7, c10, c9), c9)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p4(c9, f5(c7, c10, c9)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | (~p4(f5(c7, c10, c9), c9)) | p4(c9, f5(c7, c10, c9)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, c10, c9), c9)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p4(c9, f5(c7, c10, c9))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | (~p4(f5(c7, c10, c9), c9)) | p4(c9, f5(c7, c10, c9)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f5(c7, c10, c9), c9)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p4(c9, f5(c7, c10, c9)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[71, 69])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | (~p4(f5(c7, c10, c9), c9)) | p4(c9, f5(c7, c10, c9)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f5(c7, c10, c9), c9)) | (~p4(f5(c7, c10, c9), f5(c7, c10, c9))) | p4(c9, f5(c7, c10, c9))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (p4(c9, f5(c7, c10, c9))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[74, 68, 30, 37])).
% 0.13/0.40 tff(76,assumption,(~p2(c7, c7)), introduced(assumption)).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (^[X0: $i] : refl(p2(X0, X0) <=> p2(X0, X0))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.13/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(80,axiom,(![X0: $i] : p2(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_1')).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 (![X0: $i] : p2(X0, X0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.13/0.40 tff(82,plain,(
% 0.13/0.40 ![X0: $i] : p2(X0, X0)),
% 0.13/0.40 inference(skolemize,[status(sab)],[81])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 (![X0: $i] : p2(X0, X0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 ((~![X0: $i] : p2(X0, X0)) | p2(c7, c7)),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[84, 83, 76])).
% 0.13/0.40 tff(86,plain,(p2(c7, c7)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 (^[X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : refl(((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))) <=> ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))) <=> ![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[87])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))) <=> ![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 (^[X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : trans(monotonicity(trans(monotonicity(rewrite((p4(f5(X15, X16, X17), f5(X18, X19, X20)) | (~p3(X16, X19))) <=> ((~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))), (((p4(f5(X15, X16, X17), f5(X18, X19, X20)) | (~p3(X16, X19))) | (~p4(X17, X20))) <=> (((~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))) | (~p4(X17, X20))))), rewrite((((~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))) | (~p4(X17, X20))) <=> ((~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))), (((p4(f5(X15, X16, X17), f5(X18, X19, X20)) | (~p3(X16, X19))) | (~p4(X17, X20))) <=> ((~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))))), ((((p4(f5(X15, X16, X17), f5(X18, X19, X20)) | (~p3(X16, X19))) | (~p4(X17, X20))) | (~p2(X15, X18))) <=> (((~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))) | (~p2(X15, X18))))), rewrite((((~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20))) | (~p2(X15, X18))) <=> ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))), ((((p4(f5(X15, X16, X17), f5(X18, X19, X20)) | (~p3(X16, X19))) | (~p4(X17, X20))) | (~p2(X15, X18))) <=> ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : (((p4(f5(X15, X16, X17), f5(X18, X19, X20)) | (~p3(X16, X19))) | (~p4(X17, X20))) | (~p2(X15, X18))) <=> ![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.13/0.41 tff(92,axiom,(![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : (((p4(f5(X15, X16, X17), f5(X18, X19, X20)) | (~p3(X16, X19))) | (~p4(X17, X20))) | (~p2(X15, X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_11')).
% 0.13/0.41 tff(93,plain,
% 0.13/0.41 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.13/0.41 tff(94,plain,
% 0.13/0.41 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.13/0.41 tff(95,plain,(
% 0.13/0.41 ![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[94])).
% 0.13/0.41 tff(96,plain,
% 0.13/0.41 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.13/0.41 tff(97,plain,
% 0.13/0.41 (((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p2(c7, c7)) | (~p4(c9, f5(c7, c10, c9))) | (~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9))))) <=> ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | (~p2(c7, c7)) | (~p4(c9, f5(c7, c10, c9))) | (~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(98,plain,
% 0.13/0.41 ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p2(c7, c7)) | (~p4(c9, f5(c7, c10, c9))) | (~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(99,plain,
% 0.13/0.41 ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | (~p2(c7, c7)) | (~p4(c9, f5(c7, c10, c9))) | (~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.13/0.41 tff(100,plain,
% 0.21/0.41 (p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[99, 96, 86, 75, 65])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 ((~![X24: $i] : p4(f5(c7, X24, c8), f5(c7, X24, c9))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c9))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c9))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[101, 18])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 (((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p2(c7, c7)) | (~p4(c8, c8)) | (~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))) <=> ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | (~p2(c7, c7)) | (~p4(c8, c8)) | (~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p2(c7, c7)) | (~p4(c8, c8)) | (~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | (~p2(c7, c7)) | (~p4(c8, c8)) | (~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 ((~p3(f6(c10, f5(c7, c10, c9), c8), f6(c10, f5(c7, c10, c9), c8))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[105, 96, 86, 11])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[106, 65])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c9))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c9))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c9))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c8), f5(c7, f6(c10, f5(c7, c10, c9), c8), c9))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[110, 30, 107, 102])).
% 0.21/0.42 tff(112,assumption,(~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))), introduced(assumption)).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p4(f5(c7, c10, c9), c9)) | (~p2(c7, c7)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9)))) <=> ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | (~p4(f5(c7, c10, c9), c9)) | (~p2(c7, c7)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (((~p2(c7, c7)) | (~p4(f5(c7, c10, c9), c9)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) <=> ((~p4(f5(c7, c10, c9), c9)) | (~p2(c7, c7)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p2(c7, c7)) | (~p4(f5(c7, c10, c9), c9)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9)))) <=> ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p4(f5(c7, c10, c9), c9)) | (~p2(c7, c7)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p2(c7, c7)) | (~p4(f5(c7, c10, c9), c9)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9)))) <=> ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | (~p4(f5(c7, c10, c9), c9)) | (~p2(c7, c7)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | ((~p2(c7, c7)) | (~p4(f5(c7, c10, c9), c9)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p2(X15, X18)) | (~p4(X17, X20)) | (~p3(X16, X19)) | p4(f5(X15, X16, X17), f5(X18, X19, X20)))) | (~p4(f5(c7, c10, c9), c9)) | (~p2(c7, c7)) | (~p3(c10, c10)) | p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[118, 68, 96, 86, 48, 112])).
% 0.21/0.42 tff(120,plain,(p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (^[X22: $i, X21: $i, X23: $i] : refl(((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22)) <=> ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22)) <=> ![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[121])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22)) <=> ![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (^[X22: $i, X21: $i, X23: $i] : trans(monotonicity(rewrite((p4(f5(c7, X21, X22), X22) | (~p4(f5(c7, X21, X23), X23))) <=> ((~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))), (((p4(f5(c7, X21, X22), X22) | (~p4(f5(c7, X21, X23), X23))) | (~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22)))) <=> (((~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22)) | (~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22)))))), rewrite((((~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22)) | (~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22)))) <=> ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))), (((p4(f5(c7, X21, X22), X22) | (~p4(f5(c7, X21, X23), X23))) | (~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22)))) <=> ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (![X22: $i, X21: $i, X23: $i] : ((p4(f5(c7, X21, X22), X22) | (~p4(f5(c7, X21, X23), X23))) | (~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22)))) <=> ![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[124])).
% 0.21/0.42 tff(126,axiom,(![X22: $i, X21: $i, X23: $i] : ((p4(f5(c7, X21, X22), X22) | (~p4(f5(c7, X21, X23), X23))) | (~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_12')).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.21/0.42 tff(129,plain,(
% 0.21/0.42 ![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))),
% 0.21/0.42 inference(skolemize,[status(sab)],[128])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 (![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 ((~p4(f5(c7, c10, c8), c8)) <=> (~p4(f5(c7, c10, c8), c8))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(132,axiom,(~p4(f5(c7, c10, c8), c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p4_5')).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 (~p4(f5(c7, c10, c8), c8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 (((~![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))) | (p4(f5(c7, c10, c8), c8) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))))) <=> ((~![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))) | p4(f5(c7, c10, c8), c8) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 (((~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | p4(f5(c7, c10, c8), c8)) <=> (p4(f5(c7, c10, c8), c8) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (((~![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))) | ((~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | p4(f5(c7, c10, c8), c8))) <=> ((~![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))) | (p4(f5(c7, c10, c8), c8) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[135])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (((~![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))) | ((~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | p4(f5(c7, c10, c8), c8))) <=> ((~![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))) | p4(f5(c7, c10, c8), c8) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[136, 134])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 ((~![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))) | ((~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | p4(f5(c7, c10, c8), c8))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 ((~![X22: $i, X21: $i, X23: $i] : ((~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))) | (~p4(f5(c7, X21, X23), X23)) | p4(f5(c7, X21, X22), X22))) | p4(f5(c7, c10, c8), c8) | (~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 ((~p4(f5(c7, c10, f5(c7, c10, c9)), f5(c7, c10, c9))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[139, 133, 130])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[140, 120])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))) | (~p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), c9), f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)))) | p4(f5(c7, f6(c10, f5(c7, c10, c9), c8), f5(c7, c10, c9)), f5(c7, f6(c10, f5(c7, c10, c9), c8), c8))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[144, 30, 141, 111, 100])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------