%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV678+1 : TPTP v9.3.0. Released v9.3.0.
% 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 : Tue May 5 06:56:05 PM UTC 2026
% Result : Theorem 2.25s 2.47s
% Output : Proof 2.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV678+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n004.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 08:25:19 EDT 2026
% 0.14/0.33 % CPUTime :
% 2.25/2.47 % SZS status Theorem
% 2.25/2.47 % SZS output start Proof
% 2.25/2.47 tff(cCoq_2eInit_2eDatatypes_2enat___24t_type, type, (
% 2.25/2.47 cCoq_2eInit_2eDatatypes_2enat___24t: $i > $o)).
% 2.25/2.47 tff(cUseAuto_2eP___24a1_type, type, (
% 2.25/2.47 cUseAuto_2eP___24a1: $i > $o)).
% 2.25/2.47 tff(p_type, type, (
% 2.25/2.47 p: $i > $o)).
% 2.25/2.47 tff(cUseAuto_2emyFact_type, type, (
% 2.25/2.47 cUseAuto_2emyFact: $i)).
% 2.25/2.47 tff(tptp_fun_V0__x_301_type, type, (
% 2.25/2.47 tptp_fun_V0__x_301: $i)).
% 2.25/2.47 tff(cCoq_2eInit_2ePeano_2ele___24a2_type, type, (
% 2.25/2.47 cCoq_2eInit_2ePeano_2ele___24a2: ( $i * $i ) > $o)).
% 2.25/2.47 tff(cCoq_2eInit_2eDatatypes_2eS___24a1_type, type, (
% 2.25/2.47 cCoq_2eInit_2eDatatypes_2eS___24a1: $i > $i)).
% 2.25/2.47 tff(cCoq_2eInit_2eDatatypes_2eO_type, type, (
% 2.25/2.47 cCoq_2eInit_2eDatatypes_2eO: $i)).
% 2.25/2.47 tff(1,plain,
% 2.25/2.47 (^[V0__x: $i] : refl((cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x))) <=> (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x))))),
% 2.25/2.47 inference(bind,[status(th)],[])).
% 2.25/2.47 tff(2,plain,
% 2.25/2.47 (![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x))) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))),
% 2.25/2.47 inference(quant_intro,[status(thm)],[1])).
% 2.25/2.47 tff(3,plain,
% 2.25/2.47 (![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x))) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(4,plain,
% 2.25/2.47 ((~(![V0__x: $i] : (cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) => cUseAuto_2eP___24a1(V0__x)) => p(cUseAuto_2emyFact))) <=> (~(p(cUseAuto_2emyFact) | (~![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(5,axiom,(~(![V0__x: $i] : (cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) => cUseAuto_2eP___24a1(V0__x)) => p(cUseAuto_2emyFact))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''_HAMMER_GOAL'')).
% 2.25/2.47 tff(6,plain,
% 2.25/2.47 (~(p(cUseAuto_2emyFact) | (~![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.25/2.47 tff(7,plain,
% 2.25/2.47 (![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))),
% 2.25/2.47 inference(or_elim,[status(thm)],[6])).
% 2.25/2.47 tff(8,plain,
% 2.25/2.47 (![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.25/2.47 tff(9,plain,(
% 2.25/2.47 ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))),
% 2.25/2.47 inference(skolemize,[status(sab)],[8])).
% 2.25/2.47 tff(10,plain,
% 2.25/2.47 (![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.25/2.47 tff(11,plain,
% 2.25/2.47 ((~p(cUseAuto_2emyFact)) <=> (~p(cUseAuto_2emyFact))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(12,plain,
% 2.25/2.47 (~p(cUseAuto_2emyFact)),
% 2.25/2.47 inference(or_elim,[status(thm)],[6])).
% 2.25/2.47 tff(13,plain,
% 2.25/2.47 (~p(cUseAuto_2emyFact)),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[12, 11])).
% 2.25/2.47 tff(14,plain,
% 2.25/2.47 (((~p(cUseAuto_2emyFact)) | ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))) <=> ((~p(cUseAuto_2emyFact)) | ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(15,plain,
% 2.25/2.47 ((((~p(cUseAuto_2emyFact)) | ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))) & (p(cUseAuto_2emyFact) | (~(cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x!301, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))) <=> (((~p(cUseAuto_2emyFact)) | ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))) & (p(cUseAuto_2emyFact) | (~(cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x!301, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[14])).
% 2.25/2.47 tff(16,plain,
% 2.25/2.47 ((p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))) <=> (p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(17,plain,
% 2.25/2.47 ((p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) => (cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) => cUseAuto_2eP___24a1(V0__x)))) <=> (p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(18,axiom,(p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) => (cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) => cUseAuto_2eP___24a1(V0__x)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$_def_UseAuto.myFact'')).
% 2.25/2.47 tff(19,plain,
% 2.25/2.47 (p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[18, 17])).
% 2.25/2.47 tff(20,plain,
% 2.25/2.47 (p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[19, 16])).
% 2.25/2.47 tff(21,plain,
% 2.25/2.47 (p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[20, 16])).
% 2.25/2.47 tff(22,plain,
% 2.25/2.47 (p(cUseAuto_2emyFact) <=> ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[21, 16])).
% 2.25/2.48 tff(23,plain,(
% 2.25/2.48 ((~p(cUseAuto_2emyFact)) | ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))) & (p(cUseAuto_2emyFact) | (~(cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x!301, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))),
% 2.25/2.48 inference(skolemize,[status(sab)],[22])).
% 2.25/2.48 tff(24,plain,
% 2.25/2.48 (((~p(cUseAuto_2emyFact)) | ![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))) & (p(cUseAuto_2emyFact) | (~(cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x!301, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[23, 15])).
% 2.25/2.48 tff(25,plain,
% 2.25/2.48 (p(cUseAuto_2emyFact) | (~(cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x!301, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))),
% 2.25/2.48 inference(and_elim,[status(thm)],[24])).
% 2.25/2.48 tff(26,plain,
% 2.25/2.48 (~(cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x!301, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[25, 13])).
% 2.25/2.48 tff(27,plain,
% 2.25/2.48 ((cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x!301, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))) | cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)),
% 2.25/2.48 inference(tautology,[status(thm)],[])).
% 2.25/2.48 tff(28,plain,
% 2.25/2.48 (cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[27, 26])).
% 2.25/2.48 tff(29,plain,
% 2.25/2.48 ((cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)) | (~cCoq_2eInit_2ePeano_2ele___24a2(V0__x!301, cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))) | (~cUseAuto_2eP___24a1(V0__x!301))),
% 2.25/2.48 inference(tautology,[status(thm)],[])).
% 2.25/2.48 tff(30,plain,
% 2.25/2.48 (~cUseAuto_2eP___24a1(V0__x!301)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[29, 26])).
% 2.25/2.48 tff(31,plain,
% 2.25/2.48 (((~![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))) | (cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)))) <=> ((~![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))) | cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(32,plain,
% 2.25/2.48 ((~![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))) | (cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301)))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(33,plain,
% 2.25/2.48 ((~![V0__x: $i] : (cUseAuto_2eP___24a1(V0__x) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)))) | cUseAuto_2eP___24a1(V0__x!301) | (~cCoq_2eInit_2eDatatypes_2enat___24t(V0__x!301))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[32, 31])).
% 2.25/2.48 tff(34,plain,
% 2.25/2.48 ($false),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[33, 30, 28, 10])).
% 2.54/2.70 % SZS output end Proof
% 2.54/2.71 % E exiting
%------------------------------------------------------------------------------