%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM240_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 06:23:02 PM UTC 2026
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM240_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 19:27:34 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % SZS output start Proof
% 0.18/0.41 tff(vsomeTerm_type, type, (
% 0.18/0.41 vsomeTerm: vTerm > vOptTerm)).
% 0.18/0.41 tff(vZero_type, type, (
% 0.18/0.41 vZero: vTerm)).
% 0.18/0.41 tff(vnoTerm_type, type, (
% 0.18/0.41 vnoTerm: vOptTerm)).
% 0.18/0.41 tff(vreduce_type, type, (
% 0.18/0.41 vreduce: vTerm > vOptTerm)).
% 0.18/0.41 tff(vPred_type, type, (
% 0.18/0.41 vPred: vTerm > vTerm)).
% 0.18/0.41 tff(vt1_type, type, (
% 0.18/0.41 vt1: vTerm)).
% 0.18/0.41 tff(visValue_type, type, (
% 0.18/0.41 visValue: vTerm > $o)).
% 0.18/0.41 tff(vptchecksimple_type, type, (
% 0.18/0.41 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.18/0.41 tff(tptp_fun_VT_62_type, type, (
% 0.18/0.41 tptp_fun_VT_62: vTy)).
% 0.18/0.41 tff(1,plain,
% 0.18/0.41 ((vreduce(vPred(vZero)) = vsomeTerm(vZero)) <=> (vreduce(vPred(vZero)) = vsomeTerm(vZero))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(2,axiom,(vreduce(vPred(vZero)) = vsomeTerm(vZero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduce-6'')).
% 0.18/0.41 tff(3,plain,
% 0.18/0.41 (vreduce(vPred(vZero)) = vsomeTerm(vZero)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.18/0.41 tff(4,plain,
% 0.18/0.41 ((~![VT: vTy] : ((~(vreduce(vPred(vt1)) = vnoTerm)) | (~((vt1 = vZero) & vptchecksimple(vPred(vt1), VT) & (~visValue(vPred(vt1))))))) <=> (~![VT: vTy] : ((~(vreduce(vPred(vt1)) = vnoTerm)) | (~((vt1 = vZero) & vptchecksimple(vPred(vt1), VT) & (~visValue(vPred(vt1)))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(5,plain,
% 0.18/0.41 ((~![VT: vTy] : ((((vt1 = vZero) & vptchecksimple(vPred(vt1), VT)) & (~visValue(vPred(vt1)))) => (~(vreduce(vPred(vt1)) = vnoTerm)))) <=> (~![VT: vTy] : ((~(vreduce(vPred(vt1)) = vnoTerm)) | (~((vt1 = vZero) & vptchecksimple(vPred(vt1), VT) & (~visValue(vPred(vt1)))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(6,axiom,(~![VT: vTy] : ((((vt1 = vZero) & vptchecksimple(vPred(vt1), VT)) & (~visValue(vPred(vt1)))) => (~(vreduce(vPred(vt1)) = vnoTerm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Progress-Pred-Zero'')).
% 0.18/0.41 tff(7,plain,
% 0.18/0.41 (~![VT: vTy] : ((~(vreduce(vPred(vt1)) = vnoTerm)) | (~((vt1 = vZero) & vptchecksimple(vPred(vt1), VT) & (~visValue(vPred(vt1))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.41 tff(8,plain,
% 0.18/0.41 (~![VT: vTy] : ((~(vreduce(vPred(vt1)) = vnoTerm)) | (~((vt1 = vZero) & vptchecksimple(vPred(vt1), VT) & (~visValue(vPred(vt1))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.18/0.41 tff(9,plain,
% 0.18/0.41 (~![VT: vTy] : ((~(vreduce(vPred(vt1)) = vnoTerm)) | (~((vt1 = vZero) & vptchecksimple(vPred(vt1), VT) & (~visValue(vPred(vt1))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.41 tff(10,plain,
% 0.18/0.41 (~![VT: vTy] : ((~(vreduce(vPred(vt1)) = vnoTerm)) | (~((vt1 = vZero) & vptchecksimple(vPred(vt1), VT) & (~visValue(vPred(vt1))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.18/0.41 tff(11,plain,(
% 0.18/0.41 ~((~(vreduce(vPred(vt1)) = vnoTerm)) | (~((vt1 = vZero) & vptchecksimple(vPred(vt1), VT!62) & (~visValue(vPred(vt1))))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[10])).
% 0.18/0.41 tff(12,plain,
% 0.18/0.41 ((vt1 = vZero) & vptchecksimple(vPred(vt1), VT!62) & (~visValue(vPred(vt1)))),
% 0.18/0.41 inference(or_elim,[status(thm)],[11])).
% 0.18/0.41 tff(13,plain,
% 0.18/0.41 (vt1 = vZero),
% 0.18/0.41 inference(and_elim,[status(thm)],[12])).
% 0.18/0.41 tff(14,plain,
% 0.18/0.41 (vPred(vt1) = vPred(vZero)),
% 0.18/0.41 inference(monotonicity,[status(thm)],[13])).
% 0.18/0.41 tff(15,plain,
% 0.18/0.41 (vreduce(vPred(vt1)) = vreduce(vPred(vZero))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[14])).
% 0.18/0.41 tff(16,plain,
% 0.18/0.41 (vreduce(vPred(vt1)) = vnoTerm),
% 0.18/0.41 inference(or_elim,[status(thm)],[11])).
% 0.18/0.41 tff(17,plain,
% 0.18/0.41 (vnoTerm = vreduce(vPred(vt1))),
% 0.18/0.41 inference(symmetry,[status(thm)],[16])).
% 0.18/0.41 tff(18,plain,
% 0.18/0.41 (vnoTerm = vsomeTerm(vZero)),
% 0.18/0.41 inference(transitivity,[status(thm)],[17, 15, 3])).
% 0.18/0.41 tff(19,plain,
% 0.18/0.41 (^[VTerm0: vTerm] : refl((~(vnoTerm = vsomeTerm(VTerm0))) <=> (~(vnoTerm = vsomeTerm(VTerm0))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(20,plain,
% 0.18/0.41 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.41 tff(21,plain,
% 0.18/0.41 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(22,axiom,(![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-noTerm-someTerm'')).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.42 tff(24,plain,(
% 0.18/0.42 ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[23])).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 ((~![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))) | (~(vnoTerm = vsomeTerm(vZero)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[26, 25, 18])).
% 0.18/0.42 % SZS output end Proof
% 0.18/0.42 % E exiting
%------------------------------------------------------------------------------