%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP019+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 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 05:11:30 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP019+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Thu Jun 19 18:18:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(ap_type, type, (
% 0.12/0.39 ap: ( $i * $i ) > $i)).
% 0.12/0.39 tff(c_2Enum_2E0_type, type, (
% 0.12/0.39 c_2Enum_2E0: $i)).
% 0.12/0.39 tff(c_2Ecomplex_2Ecomplex__of__num_type, type, (
% 0.12/0.39 c_2Ecomplex_2Ecomplex__of__num: $i)).
% 0.12/0.39 tff(tptp_fun_V0z_3_type, type, (
% 0.12/0.39 tptp_fun_V0z_3: $i)).
% 0.12/0.39 tff(c_2Ecomplex_2Ecomplex__inv_type, type, (
% 0.12/0.39 c_2Ecomplex_2Ecomplex__inv: $i)).
% 0.12/0.39 tff(mem_type, type, (
% 0.12/0.39 mem: ( $i * $i ) > $o)).
% 0.12/0.39 tff(ty_2Epair_2Eprod_type, type, (
% 0.12/0.39 ty_2Epair_2Eprod: ( $i * $i ) > $i)).
% 0.12/0.39 tff(ty_2Erealax_2Ereal_type, type, (
% 0.12/0.39 ty_2Erealax_2Ereal: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((~((V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) <=> (~((V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~![V0z: $i] : ((V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))) <=> (~![V0z: $i] : ((V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 ((~![V0z: $i] : (mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => ((~(V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) => (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))))) <=> (~![V0z: $i] : ((V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(~![V0z: $i] : (mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => ((~(V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) => (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (~![V0z: $i] : ((V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (~![V0z: $i] : ((V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (~![V0z: $i] : ((V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~![V0z: $i] : ((V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.39 tff(9,plain,(
% 0.12/0.39 ~((V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~((V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (~mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~(V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))),
% 0.12/0.39 inference(or_elim,[status(thm)],[10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((~((ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))) | (~(ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))) | (V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~((ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[13, 12, 11])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))),
% 0.12/0.39 inference(or_elim,[status(thm)],[10])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (^[V0z: $i] : refl(((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))) <=> ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))) <=> ![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))) <=> ![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (^[V0z: $i] : rewrite((mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))) <=> ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![V0z: $i] : (mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))) <=> ![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.39 tff(21,axiom,(![V0z: $i] : (mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal)) => ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0')).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.12/0.39 tff(24,plain,(
% 0.12/0.39 ![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (((~![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))) | ((~mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))) <=> ((~![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))) | (~mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))) | ((~mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 ((~![V0z: $i] : ((~mem(V0z, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0))))) | (~mem(V0z!3, ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal))) | ((ap(c_2Ecomplex_2Ecomplex__inv, V0z!3) = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)) <=> (V0z!3 = ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[28, 25, 15, 14])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------