%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN088+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:22:39 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN088+2 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:16:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(r2_type, type, (
% 0.12/0.38 r2: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_Y1_14_type, type, (
% 0.12/0.38 tptp_fun_Y1_14: $i)).
% 0.12/0.38 tff(tptp_fun_Y3_15_type, type, (
% 0.12/0.38 tptp_fun_Y3_15: $i)).
% 0.12/0.38 tff(r1_type, type, (
% 0.12/0.38 r1: $i > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~![Y1: $i] : ((~r1(Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))) <=> (~![Y1: $i] : ((~r1(Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))) <=> (~![Y1: $i] : ((~r1(Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zerouneqone')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (~![Y1: $i] : ((~r1(Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![Y1: $i] : ((~r1(Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![Y1: $i] : ((~r1(Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![Y1: $i] : ((~r1(Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~((~r1(Y3!15)) | (~r2(Y3!15, Y1!14)))),
% 0.12/0.38 inference(and_elim,[status(thm)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (r2(Y3!15, Y1!14)),
% 0.12/0.38 inference(or_elim,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (r1(Y1!14)),
% 0.12/0.38 inference(and_elim,[status(thm)],[7])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.38 tff(16,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.38 tff(19,plain,(
% 0.12/0.38 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y1!14)) | (~r2(Y3!15, Y1!14)))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y1!14)) | (~r2(Y3!15, Y1!14)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y1!14)) | (~r2(Y3!15, Y1!14)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y1!14)) | (~r2(Y3!15, Y1!14))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[23, 20, 10, 9])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------