%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO632-1 : TPTP v9.0.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:42:00 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO632-1 : TPTP v9.0.0. Released v7.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:22:42 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(tptp_fun__E__type, type, (
% 0.11/0.36 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.11/0.36 tff(s_type, type, (
% 0.11/0.36 s: $i > $i)).
% 0.11/0.36 tff(tptp_fun__0__type, type, (
% 0.11/0.36 tptp_fun__0_: $i)).
% 0.11/0.36 tff(f_type, type, (
% 0.11/0.36 f: $i > $i)).
% 0.11/0.36 tff(tptp_fun__AP__type, type, (
% 0.11/0.36 tptp_fun__AP_: ( $i * $i ) > $i)).
% 0.11/0.36 tff(elem_0_type, type, (
% 0.11/0.36 elem_0: $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[K: $i] : refl(tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|) <=> tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|) <=> ![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|)),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|) <=> ![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,axiom,(![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2_02')).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.36 tff(6,plain,(
% 0.11/0.36 ![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|)),
% 0.11/0.36 inference(skolemize,[status(sab)],[5])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 ((~![K: $i] : tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), K)), |'0'|)) | tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), |'0'|)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), |'0'|)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (^[B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|)))) <=> ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|)))) <=> ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(13,axiom,(![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1_04')).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.36 tff(15,plain,(
% 0.11/0.36 ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[14])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))) | ((~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), s(|'0'|))))) <=> ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), s(|'0'|))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))) | ((~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), s(|'0'|))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_0), |'0'|)) | (~tptp_fun__E_(f(B_0), s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), s(|'0'|)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (~tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), s(|'0'|))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (^[B: $i] : refl(tptp_fun__E_(f(B), s(|'0'|)) <=> tptp_fun__E_(f(B), s(|'0'|)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![B: $i] : tptp_fun__E_(f(B), s(|'0'|)) <=> ![B: $i] : tptp_fun__E_(f(B), s(|'0'|))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![B: $i] : tptp_fun__E_(f(B), s(|'0'|)) <=> ![B: $i] : tptp_fun__E_(f(B), s(|'0'|))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(24,axiom,(![B: $i] : tptp_fun__E_(f(B), s(|'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_0_03')).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (![B: $i] : tptp_fun__E_(f(B), s(|'0'|))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.36 tff(26,plain,(
% 0.11/0.36 ![B: $i] : tptp_fun__E_(f(B), s(|'0'|))),
% 0.11/0.36 inference(skolemize,[status(sab)],[25])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (![B: $i] : tptp_fun__E_(f(B), s(|'0'|))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 ((~![B: $i] : tptp_fun__E_(f(B), s(|'0'|))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(|'0'|)), elem!0)), s(|'0'|))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[28, 27, 20])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------