%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN088+3 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.23s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : NUN088+3 : TPTP v9.0.0. Released v7.3.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 02:16:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.40 % SZS status Theorem
% 0.23/0.40 % SZS output start Proof
% 0.23/0.40 tff(r2_type, type, (
% 0.23/0.40 r2: ( $i * $i ) > $o)).
% 0.23/0.40 tff(tptp_fun_Y0_14_type, type, (
% 0.23/0.40 tptp_fun_Y0_14: $i)).
% 0.23/0.40 tff(r1_type, type, (
% 0.23/0.40 r1: $i > $o)).
% 0.23/0.40 tff(1,plain,
% 0.23/0.40 ((~![Y0: $i] : ((~r1(Y0)) | (~r2(Y0, Y0)))) <=> (~![Y0: $i] : ((~r1(Y0)) | (~r2(Y0, Y0))))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(2,plain,
% 0.23/0.40 ((~![Y0: $i] : (![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))) | (~r1(Y0)))) <=> (~![Y0: $i] : ((~r1(Y0)) | (~r2(Y0, Y0))))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(3,axiom,(~![Y0: $i] : (![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))) | (~r1(Y0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zerouneqone2')).
% 0.23/0.40 tff(4,plain,
% 0.23/0.40 (~![Y0: $i] : ((~r1(Y0)) | (~r2(Y0, Y0)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.23/0.40 tff(5,plain,
% 0.23/0.40 (~![Y0: $i] : ((~r1(Y0)) | (~r2(Y0, Y0)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.23/0.40 tff(6,plain,
% 0.23/0.40 (~![Y0: $i] : ((~r1(Y0)) | (~r2(Y0, Y0)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.23/0.40 tff(7,plain,
% 0.23/0.40 (~![Y0: $i] : ((~r1(Y0)) | (~r2(Y0, Y0)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.23/0.40 tff(8,plain,(
% 0.23/0.40 ~((~r1(Y0!14)) | (~r2(Y0!14, Y0!14)))),
% 0.23/0.40 inference(skolemize,[status(sab)],[7])).
% 0.23/0.40 tff(9,plain,
% 0.23/0.40 (r2(Y0!14, Y0!14)),
% 0.23/0.40 inference(or_elim,[status(thm)],[8])).
% 0.23/0.40 tff(10,plain,
% 0.23/0.40 (r1(Y0!14)),
% 0.23/0.40 inference(or_elim,[status(thm)],[8])).
% 0.23/0.40 tff(11,plain,
% 0.23/0.40 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(12,plain,
% 0.23/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.23/0.40 tff(13,plain,
% 0.23/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(14,plain,
% 0.23/0.40 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(15,plain,
% 0.23/0.40 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.23/0.40 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')).
% 0.23/0.40 tff(17,plain,
% 0.23/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.23/0.40 tff(18,plain,
% 0.23/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.23/0.40 tff(19,plain,(
% 0.23/0.40 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.23/0.40 inference(skolemize,[status(sab)],[18])).
% 0.23/0.40 tff(20,plain,
% 0.23/0.40 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.23/0.40 tff(21,plain,
% 0.23/0.40 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y0!14)) | (~r2(Y0!14, Y0!14)))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y0!14)) | (~r2(Y0!14, Y0!14)))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(22,plain,
% 0.23/0.40 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y0!14)) | (~r2(Y0!14, Y0!14)))),
% 0.23/0.40 inference(quant_inst,[status(thm)],[])).
% 0.23/0.40 tff(23,plain,
% 0.23/0.40 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y0!14)) | (~r2(Y0!14, Y0!14))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.40 tff(24,plain,
% 0.23/0.40 ($false),
% 0.23/0.40 inference(unit_resolution,[status(thm)],[23, 20, 10, 9])).
% 0.23/0.40 % SZS output end Proof
% 0.23/0.40 % E exiting
%------------------------------------------------------------------------------