%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN067+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 05:22:36 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN067+2 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 02:11:32 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(r1_type, type, (
% 0.13/0.40 r1: $i > $o)).
% 0.13/0.40 tff(tptp_fun_Y21_1_type, type, (
% 0.13/0.40 tptp_fun_Y21_1: $i > $i)).
% 0.13/0.40 tff(tptp_fun_Y24_0_type, type, (
% 0.13/0.40 tptp_fun_Y24_0: $i)).
% 0.13/0.40 tff(tptp_fun_Y14_8_type, type, (
% 0.13/0.40 tptp_fun_Y14_8: ( $i * $i ) > $i)).
% 0.13/0.40 tff(r2_type, type, (
% 0.13/0.40 r2: ( $i * $i ) > $o)).
% 0.13/0.40 tff(r4_type, type, (
% 0.13/0.40 r4: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_Y6_9_type, type, (
% 0.13/0.40 tptp_fun_Y6_9: ( $i * $i ) > $i)).
% 0.13/0.40 tff(r3_type, type, (
% 0.13/0.40 r3: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_Y2_7_type, type, (
% 0.13/0.40 tptp_fun_Y2_7: ( $i * $i ) > $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X2: $i, X9: $i] : rewrite((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))) <=> (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))) <=> ![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (^[X2: $i, X9: $i] : rewrite(((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))) <=> (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![X2: $i, X9: $i] : ((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))) <=> ![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (^[X2: $i, X9: $i] : quant_intro(proof_bind(^[Y2: $i] : rewrite((?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))))), (?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,axiom,(![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_2a')).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.40 tff(11,plain,(
% 0.13/0.40 ![X2: $i, X9: $i] : ((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[10])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 ((r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (^[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)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (^[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)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(pull_quant,[status(thm)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,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')).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,(
% 0.13/0.40 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[27])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (((~![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_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(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_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ((~![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_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 ((~![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_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[34, 31, 19])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y14_8(Y24!0, Y24!0)),
% 0.13/0.40 inference(symmetry,[status(thm)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (r1(tptp_fun_Y21_1(Y24!0)) <=> r1(tptp_fun_Y14_8(Y24!0, Y24!0))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (r1(tptp_fun_Y14_8(Y24!0, Y24!0)) <=> r1(tptp_fun_Y21_1(Y24!0))),
% 0.13/0.40 inference(symmetry,[status(thm)],[39])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~r1(tptp_fun_Y14_8(Y24!0, Y24!0))) <=> (~r1(tptp_fun_Y21_1(Y24!0)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.40 tff(47,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')).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.13/0.40 tff(50,plain,(
% 0.13/0.40 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[49])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (~r1(tptp_fun_Y14_8(Y24!0, Y24!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 51, 17])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (~r1(tptp_fun_Y21_1(Y24!0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[55, 41])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (^[Y1: $i] : refl(r1(Y1) <=> r1(Y1))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (![Y1: $i] : r1(Y1) <=> ![Y1: $i] : r1(Y1)),
% 0.13/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 ((~?[Y1: $i] : (~r1(Y1))) <=> (~?[Y1: $i] : (~r1(Y1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 ((~?[Y1: $i] : ![Y2: $i] : ((~r1(Y2)) | (~(Y1 = Y2)))) <=> (~?[Y1: $i] : (~r1(Y1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(61,axiom,(~?[Y1: $i] : ![Y2: $i] : ((~r1(Y2)) | (~(Y1 = Y2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nonzerosexist')).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (~?[Y1: $i] : (~r1(Y1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (~?[Y1: $i] : (~r1(Y1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (~?[Y1: $i] : (~r1(Y1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (~?[Y1: $i] : (~r1(Y1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[64, 59])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (^[Y1: $i] : refl($oeq(r1(Y1), r1(Y1)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(67,plain,(
% 0.13/0.40 ![Y1: $i] : r1(Y1)),
% 0.13/0.40 inference(nnf-neg,[status(sab)],[65, 66])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![Y1: $i] : r1(Y1)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[67, 58])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~![Y1: $i] : r1(Y1)) | r1(tptp_fun_Y21_1(Y24!0))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (r1(tptp_fun_Y21_1(Y24!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[70, 56])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------