%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN089+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:40 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUN089+2 : TPTP v9.0.0. Released v7.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:16:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(r2_type, type, (
% 0.12/0.37 r2: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_Y1_14_type, type, (
% 0.12/0.37 tptp_fun_Y1_14: $i)).
% 0.12/0.37 tff(tptp_fun_Y2_15_type, type, (
% 0.12/0.37 tptp_fun_Y2_15: $i)).
% 0.12/0.37 tff(tptp_fun_Y3_16_type, type, (
% 0.12/0.37 tptp_fun_Y3_16: $i)).
% 0.12/0.37 tff(r1_type, type, (
% 0.12/0.37 r1: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((r1(Y1!14) & (r2(Y2!15, Y1!14) & (~((~r1(Y3!16)) | (~r2(Y3!16, Y2!15)))))) <=> (r1(Y1!14) & r2(Y2!15, Y1!14) & (~((~r1(Y3!16)) | (~r2(Y3!16, Y2!15)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))))) <=> (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((~![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~r2(Y2, Y1))) | ![Y4: $i] : ((~(Y4 = Y1)) | (~r1(Y4))))) <=> (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(~![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~r2(Y2, Y1))) | ![Y4: $i] : ((~(Y4 = Y1)) | (~r1(Y4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','zerouneqtwo')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (r1(Y1!14) & r2(Y2!15, Y1!14) & (~((~r1(Y3!16)) | (~r2(Y3!16, Y2!15))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (r2(Y2!15, Y1!14)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (r1(Y1!14)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.37 tff(17,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')).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.37 tff(20,plain,(
% 0.12/0.37 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y1!14)) | (~r2(Y2!15, Y1!14)))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y1!14)) | (~r2(Y2!15, Y1!14)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y1!14)) | (~r2(Y2!15, Y1!14)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y1!14)) | (~r2(Y2!15, Y1!14))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[24, 21, 11, 10])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------