%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM242_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n031.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 06:23:03 PM UTC 2026
% Result : Theorem 0.16s 0.53s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : COM242_1 : TPTP v9.3.0. Released v9.3.0.
% 0.03/0.21 % Command : run_E %s %d THM
% 0.14/0.43 % Computer : n031.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8042.1875MB
% 0.14/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Mon May 4 19:33:25 EDT 2026
% 0.14/0.44 % CPUTime :
% 0.16/0.53 % SZS status Theorem
% 0.16/0.53 % SZS output start Proof
% 0.16/0.53 tff(vsomeTerm_type, type, (
% 0.16/0.53 vsomeTerm: vTerm > vOptTerm)).
% 0.16/0.53 tff(vSucc_type, type, (
% 0.16/0.53 vSucc: vTerm > vTerm)).
% 0.16/0.53 tff(vgetTerm_type, type, (
% 0.16/0.53 vgetTerm: vOptTerm > vTerm)).
% 0.16/0.53 tff(vreduce_type, type, (
% 0.16/0.53 vreduce: vTerm > vOptTerm)).
% 0.16/0.53 tff(vt1_type, type, (
% 0.16/0.53 vt1: vTerm)).
% 0.16/0.53 tff(vnoTerm_type, type, (
% 0.16/0.53 vnoTerm: vOptTerm)).
% 0.16/0.53 tff(visSomeTerm_type, type, (
% 0.16/0.53 visSomeTerm: vOptTerm > $o)).
% 0.16/0.53 tff(visValue_type, type, (
% 0.16/0.53 visValue: vTerm > $o)).
% 0.16/0.53 tff(vptchecksimple_type, type, (
% 0.16/0.53 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.16/0.53 tff(tptp_fun_VT_62_type, type, (
% 0.16/0.53 tptp_fun_VT_62: vTy)).
% 0.16/0.53 tff(1,plain,
% 0.16/0.53 ((~![VT: vTy] : ((~(vreduce(vSucc(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (~visValue(vSucc(vt1))))))) <=> (~![VT: vTy] : ((~(vreduce(vSucc(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (~visValue(vSucc(vt1)))))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(2,plain,
% 0.16/0.53 ((~![VT: vTy] : (((visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT)) & (~visValue(vSucc(vt1)))) => (~(vreduce(vSucc(vt1)) = vnoTerm)))) <=> (~![VT: vTy] : ((~(vreduce(vSucc(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (~visValue(vSucc(vt1)))))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(3,axiom,(~![VT: vTy] : (((visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT)) & (~visValue(vSucc(vt1)))) => (~(vreduce(vSucc(vt1)) = vnoTerm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Progress-Succ-isSomeTerm-True'')).
% 0.16/0.53 tff(4,plain,
% 0.16/0.53 (~![VT: vTy] : ((~(vreduce(vSucc(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (~visValue(vSucc(vt1))))))),
% 0.16/0.53 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.16/0.53 tff(5,plain,
% 0.16/0.53 (~![VT: vTy] : ((~(vreduce(vSucc(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (~visValue(vSucc(vt1))))))),
% 0.16/0.53 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.16/0.53 tff(6,plain,
% 0.16/0.53 (~![VT: vTy] : ((~(vreduce(vSucc(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (~visValue(vSucc(vt1))))))),
% 0.16/0.53 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.16/0.53 tff(7,plain,
% 0.16/0.53 (~![VT: vTy] : ((~(vreduce(vSucc(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (~visValue(vSucc(vt1))))))),
% 0.16/0.53 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.16/0.53 tff(8,plain,(
% 0.16/0.53 ~((~(vreduce(vSucc(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT!62) & (~visValue(vSucc(vt1))))))),
% 0.16/0.53 inference(skolemize,[status(sab)],[7])).
% 0.16/0.53 tff(9,plain,
% 0.16/0.53 (visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT!62) & (~visValue(vSucc(vt1)))),
% 0.16/0.53 inference(or_elim,[status(thm)],[8])).
% 0.16/0.53 tff(10,plain,
% 0.16/0.53 (visSomeTerm(vreduce(vt1))),
% 0.16/0.53 inference(and_elim,[status(thm)],[9])).
% 0.16/0.53 tff(11,plain,
% 0.16/0.53 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(12,plain,
% 0.16/0.53 (^[Vt1: vTerm] : refl(((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))))),
% 0.16/0.53 inference(bind,[status(th)],[])).
% 0.16/0.53 tff(13,plain,
% 0.16/0.53 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.53 inference(quant_intro,[status(thm)],[12])).
% 0.16/0.53 tff(14,plain,
% 0.16/0.53 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(15,plain,
% 0.16/0.53 (^[Vt1: vTerm] : rewrite((visSomeTerm(vreduce(Vt1)) => (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))))),
% 0.16/0.54 inference(bind,[status(th)],[])).
% 0.16/0.54 tff(16,plain,
% 0.16/0.54 (![Vt1: vTerm] : (visSomeTerm(vreduce(Vt1)) => (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.54 inference(quant_intro,[status(thm)],[15])).
% 0.16/0.54 tff(17,axiom,(![Vt1: vTerm] : (visSomeTerm(vreduce(Vt1)) => (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduce-4'')).
% 0.16/0.54 tff(18,plain,
% 0.16/0.54 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.54 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.16/0.54 tff(19,plain,
% 0.16/0.54 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.54 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.16/0.54 tff(20,plain,(
% 0.16/0.54 ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.54 inference(skolemize,[status(sab)],[19])).
% 0.16/0.54 tff(21,plain,
% 0.16/0.54 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.54 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.16/0.54 tff(22,plain,
% 0.16/0.54 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.16/0.54 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.16/0.54 tff(23,plain,
% 0.16/0.54 (((~![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))) | ((~visSomeTerm(vreduce(vt1))) | (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))))) <=> ((~![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))))),
% 0.16/0.54 inference(rewrite,[status(thm)],[])).
% 0.16/0.54 tff(24,plain,
% 0.16/0.54 ((~![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))) | ((~visSomeTerm(vreduce(vt1))) | (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))))),
% 0.16/0.54 inference(quant_inst,[status(thm)],[])).
% 0.16/0.54 tff(25,plain,
% 0.16/0.54 ((~![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1)))))),
% 0.16/0.54 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.16/0.54 tff(26,plain,
% 0.16/0.54 (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))),
% 0.16/0.54 inference(unit_resolution,[status(thm)],[25, 22, 10])).
% 0.16/0.54 tff(27,plain,
% 0.16/0.54 (vreduce(vSucc(vt1)) = vnoTerm),
% 0.16/0.54 inference(or_elim,[status(thm)],[8])).
% 0.16/0.54 tff(28,plain,
% 0.16/0.54 (vnoTerm = vreduce(vSucc(vt1))),
% 0.16/0.54 inference(symmetry,[status(thm)],[27])).
% 0.16/0.54 tff(29,plain,
% 0.16/0.54 (vnoTerm = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))),
% 0.16/0.54 inference(transitivity,[status(thm)],[28, 26])).
% 0.16/0.54 tff(30,plain,
% 0.16/0.54 (^[VTerm0: vTerm] : refl((~(vnoTerm = vsomeTerm(VTerm0))) <=> (~(vnoTerm = vsomeTerm(VTerm0))))),
% 0.16/0.54 inference(bind,[status(th)],[])).
% 0.16/0.54 tff(31,plain,
% 0.16/0.54 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.16/0.54 inference(quant_intro,[status(thm)],[30])).
% 0.16/0.54 tff(32,plain,
% 0.16/0.54 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.16/0.54 inference(rewrite,[status(thm)],[])).
% 0.16/0.54 tff(33,axiom,(![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''DIFF-noTerm-someTerm'')).
% 0.16/0.54 tff(34,plain,
% 0.16/0.54 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.16/0.54 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.16/0.54 tff(35,plain,(
% 0.16/0.54 ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.16/0.54 inference(skolemize,[status(sab)],[34])).
% 0.16/0.54 tff(36,plain,
% 0.16/0.54 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 0.16/0.54 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.16/0.54 tff(37,plain,
% 0.16/0.54 ((~![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))) | (~(vnoTerm = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))))),
% 0.16/0.54 inference(quant_inst,[status(thm)],[])).
% 0.16/0.54 tff(38,plain,
% 0.16/0.54 ($false),
% 0.16/0.54 inference(unit_resolution,[status(thm)],[37, 36, 29])).
% 0.16/0.54 % SZS output end Proof
% 0.16/0.54 % E exiting
%------------------------------------------------------------------------------