%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN553-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.12s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN553-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:37:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(p2_type, type, (
% 0.12/0.37 p2: ( $i * $i ) > $o)).
% 0.12/0.37 tff(f8_type, type, (
% 0.12/0.37 f8: ( $i * $i ) > $i)).
% 0.12/0.37 tff(c4_type, type, (
% 0.12/0.37 c4: $i)).
% 0.12/0.37 tff(f9_type, type, (
% 0.12/0.37 f9: $i > $i)).
% 0.12/0.37 tff(c3_type, type, (
% 0.12/0.37 c3: $i)).
% 0.12/0.37 tff(1,assumption,(~p2(f9(c4), f9(c4))), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[X0: $i] : refl(p2(X0, X0) <=> p2(X0, X0))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(![X0: $i] : p2(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_1')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![X0: $i] : p2(X0, X0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,(
% 0.12/0.37 ![X0: $i] : p2(X0, X0)),
% 0.12/0.37 inference(skolemize,[status(sab)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![X0: $i] : p2(X0, X0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 ((~![X0: $i] : p2(X0, X0)) | p2(f9(c4), f9(c4))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.37 tff(11,plain,(p2(f9(c4), f9(c4))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (^[X12: $i, X11: $i] : refl(p2(f8(X11, X12), f8(X12, X11)) <=> p2(f8(X11, X12), f8(X12, X11)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11)) <=> ![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11)) <=> ![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,axiom,(![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_5')).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.37 tff(17,plain,(
% 0.12/0.37 ![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))),
% 0.12/0.37 inference(skolemize,[status(sab)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ((~![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))) | p2(f8(c4, f9(c3)), f8(f9(c3), c4))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (p2(f8(c4, f9(c3)), f8(f9(c3), c4))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (^[X6: $i, X4: $i, X7: $i, X5: $i] : refl(((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7))) <=> ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7))) <=> ![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7))) <=> ![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (^[X6: $i, X4: $i, X7: $i, X5: $i] : trans(monotonicity(rewrite((p2(f8(X4, X5), f8(X6, X7)) | (~p2(X4, X6))) <=> ((~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))), (((p2(f8(X4, X5), f8(X6, X7)) | (~p2(X4, X6))) | (~p2(X5, X7))) <=> (((~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7))) | (~p2(X5, X7))))), rewrite((((~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7))) | (~p2(X5, X7))) <=> ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))), (((p2(f8(X4, X5), f8(X6, X7)) | (~p2(X4, X6))) | (~p2(X5, X7))) <=> ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((p2(f8(X4, X5), f8(X6, X7)) | (~p2(X4, X6))) | (~p2(X5, X7))) <=> ![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,axiom,(![X6: $i, X4: $i, X7: $i, X5: $i] : ((p2(f8(X4, X5), f8(X6, X7)) | (~p2(X4, X6))) | (~p2(X5, X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_8')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.38 tff(29,plain,(
% 0.12/0.38 ![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))) | ((~p2(f9(c4), f9(c4))) | (~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4))))) <=> ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))) | (~p2(f9(c4), f9(c4))) | (~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (((~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | (~p2(f9(c4), f9(c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))) <=> ((~p2(f9(c4), f9(c4))) | (~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))) | ((~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | (~p2(f9(c4), f9(c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4))))) <=> ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))) | ((~p2(f9(c4), f9(c4))) | (~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))) | ((~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | (~p2(f9(c4), f9(c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4))))) <=> ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))) | (~p2(f9(c4), f9(c4))) | (~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[33, 31])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))) | ((~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | (~p2(f9(c4), f9(c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((~![X6: $i, X4: $i, X7: $i, X5: $i] : ((~p2(X5, X7)) | (~p2(X4, X6)) | p2(f8(X4, X5), f8(X6, X7)))) | (~p2(f9(c4), f9(c4))) | (~p2(f8(c4, f9(c3)), f8(f9(c3), c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~p2(f9(c4), f9(c4))) | p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 30, 20])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 11])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (^[X9: $i, X10: $i, X8: $i] : refl(p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10)) <=> p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10)) <=> ![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10)) <=> ![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(42,axiom,(![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_7')).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.38 tff(44,plain,(
% 0.20/0.38 ![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))),
% 0.20/0.38 inference(skolemize,[status(sab)],[43])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 ((~![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))) | p2(f8(c4, f8(f9(c3), f9(c4))), f8(f8(c4, f9(c3)), f9(c4)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (p2(f8(c4, f8(f9(c3), f9(c4))), f8(f8(c4, f9(c3)), f9(c4)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 ((~![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))) | p2(f8(f8(c4, f9(c3)), f9(c4)), f8(f9(c4), f8(c4, f9(c3))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 (p2(f8(f8(c4, f9(c3)), f9(c4)), f8(f9(c4), f8(c4, f9(c3))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[48, 18])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2)) <=> ![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2)) <=> ![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p2(X1, X2) | (~p2(X1, X3))) <=> ((~p2(X1, X3)) | p2(X1, X2))), (((p2(X1, X2) | (~p2(X1, X3))) | (~p2(X3, X2))) <=> (((~p2(X1, X3)) | p2(X1, X2)) | (~p2(X3, X2))))), rewrite((((~p2(X1, X3)) | p2(X1, X2)) | (~p2(X3, X2))) <=> ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))), (((p2(X1, X2) | (~p2(X1, X3))) | (~p2(X3, X2))) <=> ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (![X3: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X1, X3))) | (~p2(X3, X2))) <=> ![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.38 tff(54,axiom,(![X3: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X1, X3))) | (~p2(X3, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_6')).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.38 tff(57,plain,(
% 0.20/0.38 ![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))),
% 0.20/0.38 inference(skolemize,[status(sab)],[56])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(f8(c4, f9(c3)), f9(c4)), f8(f9(c4), f8(c4, f9(c3))))) | (~p2(f8(c4, f8(f9(c3), f9(c4))), f8(f8(c4, f9(c3)), f9(c4)))) | p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3)))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(f8(c4, f9(c3)), f9(c4)), f8(f9(c4), f8(c4, f9(c3))))) | (~p2(f8(c4, f8(f9(c3), f9(c4))), f8(f8(c4, f9(c3)), f9(c4)))) | p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(f8(c4, f9(c3)), f9(c4)), f8(f9(c4), f8(c4, f9(c3))))) | (~p2(f8(c4, f8(f9(c3), f9(c4))), f8(f8(c4, f9(c3)), f9(c4)))) | p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(f8(c4, f9(c3)), f9(c4)), f8(f9(c4), f8(c4, f9(c3))))) | (~p2(f8(c4, f8(f9(c3), f9(c4))), f8(f8(c4, f9(c3)), f9(c4)))) | p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[61, 58, 49, 47])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((~![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))) | p2(f8(f8(f9(c3), f9(c4)), c4), f8(c4, f8(f9(c3), f9(c4))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (p2(f8(f8(f9(c3), f9(c4)), c4), f8(c4, f8(f9(c3), f9(c4))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[63, 18])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~![X9: $i, X10: $i, X8: $i] : p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))) | p2(f8(f9(c3), f8(f9(c4), c4)), f8(f8(f9(c3), f9(c4)), c4))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (p2(f8(f9(c3), f8(f9(c4), c4)), f8(f8(f9(c3), f9(c4)), c4))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[65, 45])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((~![X12: $i, X11: $i] : p2(f8(X11, X12), f8(X12, X11))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(f9(c4), c4)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(f9(c4), c4)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[67, 18])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(f9(c3), f8(f9(c4), c4)), f8(f8(f9(c3), f9(c4)), c4))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(f9(c4), c4)))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(f9(c3), f8(f9(c4), c4)), f8(f8(f9(c3), f9(c4)), c4))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(f9(c4), c4)))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(f9(c3), f8(f9(c4), c4)), f8(f8(f9(c3), f9(c4)), c4))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(f9(c4), c4)))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(f9(c3), f8(f9(c4), c4)), f8(f8(f9(c3), f9(c4)), c4))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(f9(c4), c4)))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 58, 68, 66])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(f8(f9(c3), f9(c4)), c4), f8(c4, f8(f9(c3), f9(c4))))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4)))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(f8(f9(c3), f9(c4)), c4), f8(c4, f8(f9(c3), f9(c4))))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(f8(f9(c3), f9(c4)), c4), f8(c4, f8(f9(c3), f9(c4))))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(f8(f9(c3), f9(c4)), c4), f8(c4, f8(f9(c3), f9(c4))))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(f9(c3), f9(c4)), c4))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[75, 58, 72, 64])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3))))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4))))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3)))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3))))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4))))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3))))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4))))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(c4, f8(f9(c3), f9(c4))), f8(f9(c4), f8(c4, f9(c3))))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(c4, f8(f9(c3), f9(c4))))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[79, 58, 76, 62])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 ((~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))) <=> (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(82,axiom,(~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p2_9')).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3))))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3))))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | ((~p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3))))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((~![X3: $i, X2: $i, X1: $i] : ((~p2(X3, X2)) | (~p2(X1, X3)) | p2(X1, X2))) | (~p2(f8(f9(c4), f8(c4, f9(c3))), f8(f9(c4), f8(f9(c3), c4)))) | (~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(c4, f9(c3))))) | p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[86, 58, 83, 80, 38])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------