%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN070+2 : TPTP v9.0.0. Released v7.3.0.
% 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 05:22:37 AM UTC 2025
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN070+2 : TPTP v9.0.0. Released v7.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 02:13:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(r3_type, type, (
% 0.19/0.41 r3: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y21_1_type, type, (
% 0.19/0.41 tptp_fun_Y21_1: $i > $i)).
% 0.19/0.41 tff(tptp_fun_Y24_0_type, type, (
% 0.19/0.41 tptp_fun_Y24_0: $i)).
% 0.19/0.41 tff(tptp_fun_Y16_10_type, type, (
% 0.19/0.41 tptp_fun_Y16_10: $i > $i)).
% 0.19/0.41 tff(r1_type, type, (
% 0.19/0.41 r1: $i > $o)).
% 0.19/0.41 tff(r2_type, type, (
% 0.19/0.41 r2: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y15_5_type, type, (
% 0.19/0.41 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y7_6_type, type, (
% 0.19/0.41 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y4_4_type, type, (
% 0.19/0.41 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[X4: $i] : rewrite((r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4)) <=> (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4)) <=> ![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (^[X4: $i] : trans(der(?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ?[Y9: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))), elim_unused(?[Y9: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))), (?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.41 tff(6,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,(
% 0.19/0.41 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.19/0.41 inference(skolemize,[status(sab)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 ((~![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))) | (~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.41 tff(24,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/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1a')).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.41 tff(27,plain,(
% 0.19/0.41 ![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))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[26])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 ((~![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)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (~((~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))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (((~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))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((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)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (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))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (^[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)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (![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))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (^[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)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (![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))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(pull_quant,[status(thm)],[])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(42,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.42 tff(44,plain,(
% 0.19/0.42 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[43])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[45, 39])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[46, 37])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (((~![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))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 ((~![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))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((~![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)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (~((~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))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[50, 47, 35])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (((~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))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 0.19/0.42 inference(symmetry,[status(thm)],[53])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (r2(Y24!0, tptp_fun_Y21_1(Y24!0)) <=> r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) <=> r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.42 inference(symmetry,[status(thm)],[55])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[33, 56])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (^[X19: $i] : trans(monotonicity(rewrite((r1(X19) & (X19 = Y24!0)) <=> (~((~r1(X19)) | (~(X19 = Y24!0))))), rewrite(((~r1(X19)) & (~(X19 = Y24!0))) <=> (~(r1(X19) | (X19 = Y24!0)))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))), rewrite(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (^[Y24: $i] : quant_intro(proof_bind(^[X19: $i] : rewrite((((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))))), (![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.42 tff(65,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.42 tff(68,plain,(
% 0.19/0.42 $oeq(![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))), ![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))))),
% 0.19/0.42 inference(transitivity,[status(sab)],[67])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ((~$true) <=> $false),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 ((r1(Y24!0) | $true) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((Y24!0 = Y24!0) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.19/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[78, 73])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[82, 73])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.19/0.42 inference(transitivity,[status(thm)],[84, 81])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.19/0.42 inference(transitivity,[status(thm)],[86, 80])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[87, 79])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.19/0.42 inference(transitivity,[status(thm)],[88, 72])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.19/0.42 inference(transitivity,[status(thm)],[90, 71])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (r1(Y24!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 70])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (^[Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : trans(monotonicity(rewrite((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) <=> ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y5)) | (~r2(Y5, Y2)))), (((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> (((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y5)) | (~r2(Y5, Y2))) | ((~r1(Y6)) | (~r2(Y6, Y1)))))), rewrite((((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y5)) | (~r2(Y5, Y2))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))), (((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (^[Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : refl(((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (![Y1: $i] : ![Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(pull_quant,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (^[Y1: $i] : pull_quant((![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (![Y1: $i] : (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i] : ![Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (![Y1: $i] : (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (![Y1: $i] : (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[102, 98])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (^[Y1: $i] : rewrite((![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i] : (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (^[Y1: $i] : rewrite((![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y2, Y4, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1)))) <=> (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (![Y1: $i] : (![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y2, Y4, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1)))) <=> ![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 ((~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))) <=> (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 ((~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y3: $i] : ((Y1 = Y3) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y3))))) <=> (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(111,axiom,(~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y3: $i] : ((Y1 = Y3) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','onepluszeroeqone')).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[112, 109])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[114, 109])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (^[Y1: $i] : nnf_neg(nnf_neg(proof_bind(^[Y2: $i] : nnf_neg(nnf_neg(proof_bind(^[Y4: $i] : refl($oeq((~(r1(Y4) & r3(Y2, Y4, Y1))), (~(r1(Y4) & r3(Y2, Y4, Y1)))))), $oeq((~?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1))), ![Y4: $i] : (~(r1(Y4) & r3(Y2, Y4, Y1))))), nnf_neg(proof_bind(^[Y5: $i] : refl($oeq((~(r1(Y5) & r2(Y5, Y2))), (~(r1(Y5) & r2(Y5, Y2)))))), $oeq((~?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))), ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2))))), $oeq((~(?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2)))), (![Y4: $i] : (~(r1(Y4) & r3(Y2, Y4, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2))))))), $oeq((~?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2)))), ![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y2, Y4, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))))), nnf_neg(proof_bind(^[Y6: $i] : refl($oeq((~(r1(Y6) & r2(Y6, Y1))), (~(r1(Y6) & r2(Y6, Y1)))))), $oeq((~?[Y6: $i] : (r1(Y6) & r2(Y6, Y1))), ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1))))), $oeq((~(?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y2, Y4, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))), (![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y2, Y4, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(117,plain,(
% 0.19/0.43 ![Y1: $i] : (![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y2, Y4, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1))))),
% 0.19/0.43 inference(nnf-neg,[status(sab)],[115, 116])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[117, 108])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y2, Y4, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[118, 106])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[119, 96])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))))) <=> ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(Y24!0)) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0)))) <=> ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(Y24!0)) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))))) <=> ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(Y24!0)) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))))) <=> ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[123, 121])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(Y24!0)) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y2, Y4, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[126, 120, 94, 57, 16, 14])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------