%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO611-1 : TPTP v9.0.0. Released v7.1.0.
% 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 05:41:58 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO611-1 : TPTP v9.0.0. Released v7.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:16:37 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(le_type, type, (
% 0.20/0.37 le: ( $i * $i ) > $o)).
% 0.20/0.37 tff(s_type, type, (
% 0.20/0.37 s: $i > $i)).
% 0.20/0.37 tff(elem_0_type, type, (
% 0.20/0.37 elem_0: $i)).
% 0.20/0.37 tff(eq_type, type, (
% 0.20/0.37 eq: ( $i * $i ) > $o)).
% 0.20/0.37 tff(a0_type, type, (
% 0.20/0.37 a0: $i)).
% 0.20/0.37 tff(f_type, type, (
% 0.20/0.37 f: $i > $i)).
% 0.20/0.37 tff(1,assumption,(~eq(f(s(elem!0)), a0)), introduced(assumption)).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (^[A: $i] : refl(eq(f(A), a0) <=> eq(f(A), a0))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (![A: $i] : eq(f(A), a0) <=> ![A: $i] : eq(f(A), a0)),
% 0.20/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![A: $i] : eq(f(A), a0) <=> ![A: $i] : eq(f(A), a0)),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(5,axiom,(![A: $i] : eq(f(A), a0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_04')).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (![A: $i] : eq(f(A), a0)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.37 tff(7,plain,(
% 0.20/0.37 ![A: $i] : eq(f(A), a0)),
% 0.20/0.37 inference(skolemize,[status(sab)],[6])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (![A: $i] : eq(f(A), a0)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 ((~![A: $i] : eq(f(A), a0)) | eq(f(s(elem!0)), a0)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.37 tff(11,plain,(eq(f(s(elem!0)), a0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 ((~![A: $i] : eq(f(A), a0)) | eq(f(elem!0), a0)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (eq(f(elem!0), a0)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[12, 8])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (^[A0: $i, A1: $i] : refl(((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (^[A0: $i, A1: $i] : trans(monotonicity(rewrite(((~eq(f(A0), a0)) | (~eq(f(A1), a0))) <=> ((~eq(f(A1), a0)) | (~eq(f(A0), a0)))), ((((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> (((~eq(f(A1), a0)) | (~eq(f(A0), a0))) | (~le(s(A0), A1))))), rewrite((((~eq(f(A1), a0)) | (~eq(f(A0), a0))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))), ((((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![A0: $i, A1: $i] : (((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.37 tff(19,axiom,(![A0: $i, A1: $i] : (((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_05')).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.37 tff(22,plain,(
% 0.20/0.37 ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[21])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~le(s(elem!0), s(elem!0))) | (~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0))) <=> ((~le(s(elem!0), s(elem!0))) | (~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~le(s(elem!0), s(elem!0))) | (~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~le(s(elem!0), s(elem!0))) | (~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 23, 13])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (~le(s(elem!0), s(elem!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[30, 11])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (^[A: $i] : refl(le(A, A) <=> le(A, A))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![A: $i] : le(A, A) <=> ![A: $i] : le(A, A)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![A: $i] : le(A, A) <=> ![A: $i] : le(A, A)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(35,axiom,(![A: $i] : le(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_01')).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![A: $i] : le(A, A)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.38 tff(37,plain,(
% 0.20/0.38 ![A: $i] : le(A, A)),
% 0.20/0.38 inference(skolemize,[status(sab)],[36])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (![A: $i] : le(A, A)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~![A: $i] : le(A, A)) | le(s(elem!0), s(elem!0))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[39, 38, 31])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------