%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN062+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:22:35 AM UTC 2025
% Result : Theorem 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUN062+2 : TPTP v9.0.0. Released v7.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 02:11:17 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 tff(r3_type, type, (
% 0.22/0.43 r3: ( $i * $i * $i ) > $o)).
% 0.22/0.43 tff(tptp_fun_Y7_6_type, type, (
% 0.22/0.43 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_X1_14_type, type, (
% 0.22/0.43 tptp_fun_X1_14: $i)).
% 0.22/0.43 tff(tptp_fun_Y21_1_type, type, (
% 0.22/0.43 tptp_fun_Y21_1: $i > $i)).
% 0.22/0.43 tff(tptp_fun_Y24_0_type, type, (
% 0.22/0.43 tptp_fun_Y24_0: $i)).
% 0.22/0.43 tff(r2_type, type, (
% 0.22/0.43 r2: ( $i * $i ) > $o)).
% 0.22/0.43 tff(tptp_fun_Y4_4_type, type, (
% 0.22/0.43 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_Y15_5_type, type, (
% 0.22/0.43 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.22/0.43 tff(r1_type, type, (
% 0.22/0.43 r1: $i > $o)).
% 0.22/0.43 tff(1,plain,
% 0.22/0.43 (^[X1: $i, X8: $i] : rewrite((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))) <=> (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(2,plain,
% 0.22/0.43 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))) <=> ![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.43 tff(3,plain,
% 0.22/0.43 (^[X1: $i, X8: $i] : rewrite(((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))) <=> (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(4,plain,
% 0.22/0.43 (![X1: $i, X8: $i] : ((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))) <=> ![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.43 tff(5,plain,
% 0.22/0.43 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(6,plain,
% 0.22/0.43 (^[X1: $i, X8: $i] : quant_intro(proof_bind(^[Y4: $i] : rewrite((?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))))), (?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(7,plain,
% 0.22/0.43 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.43 tff(8,axiom,(![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1a')).
% 0.22/0.43 tff(9,plain,
% 0.22/0.43 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.43 tff(10,plain,
% 0.22/0.44 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.22/0.44 tff(11,plain,(
% 0.22/0.44 ![X1: $i, X8: $i] : ((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[10])).
% 0.22/0.44 tff(12,plain,
% 0.22/0.44 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.22/0.44 tff(13,plain,
% 0.22/0.44 (![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.22/0.44 tff(14,plain,
% 0.22/0.44 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r3(X1!14, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), X1!14), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14)))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(15,plain,
% 0.22/0.44 (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r3(X1!14, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), X1!14), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.22/0.44 tff(16,plain,
% 0.22/0.44 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r3(X1!14, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), X1!14), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), X1!14))) | (~r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14)))) | r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(17,plain,
% 0.22/0.44 (r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.22/0.44 tff(18,plain,
% 0.22/0.44 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(19,plain,
% 0.22/0.44 (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[18, 13])).
% 0.22/0.44 tff(20,plain,
% 0.22/0.44 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(21,plain,
% 0.22/0.44 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.22/0.44 tff(22,plain,
% 0.22/0.44 ((r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(23,plain,
% 0.22/0.44 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.22/0.44 tff(24,plain,
% 0.22/0.44 (^[X11: $i, X12: $i] : refl(((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(25,plain,
% 0.22/0.44 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[24])).
% 0.22/0.44 tff(26,plain,
% 0.22/0.44 (^[X11: $i, X12: $i] : rewrite((((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(27,plain,
% 0.22/0.44 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.44 tff(28,plain,
% 0.22/0.44 (![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.22/0.44 inference(pull_quant,[status(thm)],[])).
% 0.22/0.44 tff(29,plain,
% 0.22/0.44 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21))) <=> ![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(30,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.22/0.44 tff(31,plain,
% 0.22/0.44 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.22/0.44 tff(32,plain,(
% 0.22/0.44 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[31])).
% 0.22/0.44 tff(33,plain,
% 0.22/0.44 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.22/0.44 tff(35,plain,
% 0.22/0.44 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[34, 25])).
% 0.22/0.44 tff(36,plain,
% 0.22/0.44 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(37,plain,
% 0.22/0.44 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(38,plain,
% 0.22/0.44 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.22/0.44 tff(39,plain,
% 0.22/0.44 (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[38, 35, 23])).
% 0.22/0.44 tff(40,plain,
% 0.22/0.44 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(41,plain,
% 0.22/0.44 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.22/0.44 tff(42,plain,
% 0.22/0.44 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 0.22/0.44 inference(symmetry,[status(thm)],[41])).
% 0.22/0.44 tff(43,plain,
% 0.22/0.44 (r1(tptp_fun_Y21_1(Y24!0)) <=> r1(tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[42])).
% 0.22/0.44 tff(44,plain,
% 0.22/0.44 (r1(tptp_fun_Y15_5(Y24!0, Y24!0)) <=> r1(tptp_fun_Y21_1(Y24!0))),
% 0.22/0.44 inference(symmetry,[status(thm)],[43])).
% 0.22/0.44 tff(45,plain,
% 0.22/0.44 ((~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) <=> (~r1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[44])).
% 0.22/0.44 tff(46,plain,
% 0.22/0.44 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(47,plain,
% 0.22/0.44 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.44 tff(48,plain,
% 0.22/0.44 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(49,plain,
% 0.22/0.44 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(50,plain,
% 0.22/0.44 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.22/0.44 tff(51,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.22/0.44 tff(52,plain,
% 0.22/0.44 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.44 tff(53,plain,
% 0.22/0.44 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.22/0.44 tff(54,plain,(
% 0.22/0.44 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[53])).
% 0.22/0.44 tff(55,plain,
% 0.22/0.44 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.22/0.44 tff(56,plain,
% 0.22/0.44 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(57,plain,
% 0.22/0.44 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(58,plain,
% 0.22/0.44 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.22/0.45 tff(59,plain,
% 0.22/0.45 (~r1(tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[58, 55, 21])).
% 0.22/0.45 tff(60,plain,
% 0.22/0.45 (~r1(tptp_fun_Y21_1(Y24!0))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[59, 45])).
% 0.22/0.45 tff(61,plain,
% 0.22/0.45 (^[Y2: $i, Y1: $i] : refl((r1(Y1) | (~r3(X1!14, Y1, Y2))) <=> (r1(Y1) | (~r3(X1!14, Y1, Y2))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(62,plain,
% 0.22/0.45 (![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2))) <=> ![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.22/0.45 tff(63,plain,
% 0.22/0.45 (^[Y2: $i, Y1: $i] : trans(monotonicity(rewrite(((~r1(Y1)) & r3(X1!14, Y1, Y2)) <=> (~(r1(Y1) | (~r3(X1!14, Y1, Y2))))), ((~((~r1(Y1)) & r3(X1!14, Y1, Y2))) <=> (~(~(r1(Y1) | (~r3(X1!14, Y1, Y2))))))), rewrite((~(~(r1(Y1) | (~r3(X1!14, Y1, Y2))))) <=> (r1(Y1) | (~r3(X1!14, Y1, Y2)))), ((~((~r1(Y1)) & r3(X1!14, Y1, Y2))) <=> (r1(Y1) | (~r3(X1!14, Y1, Y2)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(64,plain,
% 0.22/0.45 (![Y2: $i, Y1: $i] : (~((~r1(Y1)) & r3(X1!14, Y1, Y2))) <=> ![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.22/0.45 tff(65,plain,
% 0.22/0.45 ((~![X1: $i] : ?[Y2: $i, Y1: $i] : ((~r1(Y1)) & r3(X1, Y1, Y2))) <=> (~![X1: $i] : ?[Y2: $i, Y1: $i] : ((~r1(Y1)) & r3(X1, Y1, Y2)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(66,plain,
% 0.22/0.45 ((~![X1: $i] : ?[Y2: $i, Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))) & ?[Y3: $i] : (r3(X1, Y1, Y3) & (Y3 = Y2)))) <=> (~![X1: $i] : ?[Y2: $i, Y1: $i] : ((~r1(Y1)) & r3(X1, Y1, Y2)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(67,axiom,(~![X1: $i] : ?[Y2: $i, Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))) & ?[Y3: $i] : (r3(X1, Y1, Y3) & (Y3 = Y2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','infiniteNumbers')).
% 0.22/0.45 tff(68,plain,
% 0.22/0.45 (~![X1: $i] : ?[Y2: $i, Y1: $i] : ((~r1(Y1)) & r3(X1, Y1, Y2))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.22/0.45 tff(69,plain,
% 0.22/0.45 (~![X1: $i] : ?[Y2: $i, Y1: $i] : ((~r1(Y1)) & r3(X1, Y1, Y2))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.22/0.45 tff(70,plain,
% 0.22/0.45 (~![X1: $i] : ?[Y2: $i, Y1: $i] : ((~r1(Y1)) & r3(X1, Y1, Y2))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.22/0.45 tff(71,plain,
% 0.22/0.45 (~![X1: $i] : ?[Y2: $i, Y1: $i] : ((~r1(Y1)) & r3(X1, Y1, Y2))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[70, 65])).
% 0.22/0.45 tff(72,plain,(
% 0.22/0.45 $oeq((~?[Y2: $i, Y1: $i] : ((~r1(Y1)) & r3(X1!14, Y1, Y2))), ![Y2: $i, Y1: $i] : (~((~r1(Y1)) & r3(X1!14, Y1, Y2))))),
% 0.22/0.45 inference(transitivity,[status(sab)],[71])).
% 0.22/0.45 tff(73,plain,
% 0.22/0.45 (![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[72, 64])).
% 0.22/0.45 tff(74,plain,
% 0.22/0.45 (![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[73, 62])).
% 0.22/0.45 tff(75,plain,
% 0.22/0.45 (((~![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2)))) | (r1(tptp_fun_Y21_1(Y24!0)) | (~r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14))))) <=> ((~![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2)))) | r1(tptp_fun_Y21_1(Y24!0)) | (~r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(76,plain,
% 0.22/0.45 ((~![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2)))) | (r1(tptp_fun_Y21_1(Y24!0)) | (~r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(77,plain,
% 0.22/0.45 ((~![Y2: $i, Y1: $i] : (r1(Y1) | (~r3(X1!14, Y1, Y2)))) | r1(tptp_fun_Y21_1(Y24!0)) | (~r3(X1!14, tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), X1!14)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.22/0.45 tff(78,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[77, 74, 60, 17])).
% 0.22/0.45 % SZS output end Proof
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------