%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN089+1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:22:40 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUN089+1 : TPTP v9.0.0. Released v7.3.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Jun 20 02:15:40 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(id_type, type, (
% 0.12/0.39 id: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_Y1_20_type, type, (
% 0.12/0.39 tptp_fun_Y1_20: $i)).
% 0.12/0.39 tff(tptp_fun_Y4_23_type, type, (
% 0.12/0.39 tptp_fun_Y4_23: $i)).
% 0.12/0.39 tff(r1_type, type, (
% 0.12/0.39 r1: $i > $o)).
% 0.12/0.39 tff(r2_type, type, (
% 0.12/0.39 r2: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_Y2_21_type, type, (
% 0.12/0.39 tptp_fun_Y2_21: $i)).
% 0.12/0.39 tff(tptp_fun_Y3_22_type, type, (
% 0.12/0.39 tptp_fun_Y3_22: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (((r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))) <=> (r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21)))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))) <=> (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (((r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))) <=> ((r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (((r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))) <=> (r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21)))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[3, 1])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 ((~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))) <=> (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 ((~![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~r2(Y2, Y1))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))) <=> (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(7,axiom,(~![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~r2(Y2, Y1))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zerounidtwo')).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21)))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (id(Y4!23, Y1!20)),
% 0.12/0.39 inference(or_elim,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (^[X21: $i, X22: $i] : refl(((~id(X21, X22)) | id(X22, X21)) <=> ((~id(X21, X22)) | id(X22, X21)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21)) <=> ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21)) <=> ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(18,axiom,(![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_6')).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,(
% 0.12/0.39 ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.12/0.39 inference(skolemize,[status(sab)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y4!23))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(Y4!23, Y1!20)) | id(Y1!20, Y4!23))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y4!23))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(Y4!23, Y1!20)) | id(Y1!20, Y4!23)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (id(Y1!20, Y4!23)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (^[X23: $i, X24: $i, X25: $i] : rewrite((((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25))) <=> ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![X23: $i, X24: $i, X25: $i] : (((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.39 tff(30,axiom,(![X23: $i, X24: $i, X25: $i] : (((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_7')).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.39 tff(33,plain,(
% 0.12/0.39 ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (((~id(Y4!23, Y1!20)) | id(Y1!20, Y1!20) | (~id(Y1!20, Y4!23))) <=> ((~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y1!20) | (~id(Y1!20, Y4!23)))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[36])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y1!20) | (~id(Y1!20, Y4!23)))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20))),
% 0.12/0.40 inference(transitivity,[status(thm)],[37, 35])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y1!20) | (~id(Y1!20, Y4!23)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (id(Y1!20, Y1!20)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[40, 34, 14, 25])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (r2(Y2!21, Y1!20)),
% 0.12/0.40 inference(and_elim,[status(thm)],[12])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (^[X7: $i, Y10: $i] : refl(((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (^[X7: $i, Y10: $i] : rewrite(((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[46, 44])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_7a')).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.12/0.40 tff(54,plain,(
% 0.12/0.40 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~id(Y20, Y1!20)) | (~r1(Y20)))) <=> ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~id(Y20, Y1!20)) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[57])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~id(Y20, Y1!20)) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[58, 56])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~id(Y20, Y1!20)) | (~r1(Y20))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[61, 55, 42])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (r1(Y4!23)),
% 0.12/0.40 inference(or_elim,[status(thm)],[13])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 ((r1(Y1!20) | r1(Y4!23)) | (~r1(Y4!23))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (r1(Y1!20) | r1(Y4!23)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (^[X26: $i, X27: $i] : refl(((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (^[X26: $i, X27: $i] : trans(monotonicity(rewrite((r1(X26) & r1(X27)) <=> (~((~r1(X27)) | (~r1(X26))))), rewrite(((~r1(X26)) & (~r1(X27))) <=> (~(r1(X27) | r1(X26)))), (((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))))), rewrite(((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))), (((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (^[X26: $i, X27: $i] : rewrite((((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27))) <=> ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (![X26: $i, X27: $i] : (((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.12/0.40 tff(73,axiom,(![X26: $i, X27: $i] : (((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_8')).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.12/0.40 tff(76,plain,(
% 0.12/0.40 ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[75])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(Y4!23, Y1!20)) | (~((~r1(Y1!20)) | (~r1(Y4!23)))) | (~(r1(Y1!20) | r1(Y4!23))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(Y4!23, Y1!20)) | (~((~r1(Y1!20)) | (~r1(Y4!23)))) | (~(r1(Y1!20) | r1(Y4!23))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(Y4!23, Y1!20)) | (~((~r1(Y1!20)) | (~r1(Y4!23)))) | (~(r1(Y1!20) | r1(Y4!23))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(Y4!23, Y1!20)) | (~((~r1(Y1!20)) | (~r1(Y4!23)))) | (~(r1(Y1!20) | r1(Y4!23)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (~((~r1(Y1!20)) | (~r1(Y4!23)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[81, 78, 14, 65])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (((~r1(Y1!20)) | (~r1(Y4!23))) | r1(Y1!20)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (r1(Y1!20)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))) | ((~r1(Y1!20)) | (~id(Y1!20, Y1!20)))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))) | (~r1(Y1!20)) | (~id(Y1!20, Y1!20)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))) | ((~r1(Y1!20)) | (~id(Y1!20, Y1!20)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))) | (~r1(Y1!20)) | (~id(Y1!20, Y1!20))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[87, 84, 62, 41])).
% 0.12/0.40 % SZS output end Proof
% 0.12/0.41 % E exiting
%------------------------------------------------------------------------------