%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM231_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 06:23:02 PM UTC 2026
% Result : Theorem 43.23s 43.45s
% Output : Proof 43.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : COM231_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.08 % Command : run_E %s %d THM
% 0.09/0.27 % Computer : n031.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Mon May 4 19:15:10 EDT 2026
% 0.09/0.27 % CPUTime :
% 43.23/43.45 % SZS status Theorem
% 43.23/43.45 % SZS output start Proof
% 43.23/43.45 tff(vsomeTerm_type, type, (
% 43.23/43.45 vsomeTerm: vTerm > vOptTerm)).
% 43.23/43.45 tff(vIszero_type, type, (
% 43.23/43.45 vIszero: vTerm > vTerm)).
% 43.23/43.45 tff(vgetTerm_type, type, (
% 43.23/43.45 vgetTerm: vOptTerm > vTerm)).
% 43.23/43.45 tff(vreduce_type, type, (
% 43.23/43.45 vreduce: vTerm > vOptTerm)).
% 43.23/43.45 tff(vt1_type, type, (
% 43.23/43.45 vt1: vTerm)).
% 43.23/43.45 tff(vnoTerm_type, type, (
% 43.23/43.45 vnoTerm: vOptTerm)).
% 43.23/43.45 tff(vSucc_type, type, (
% 43.23/43.45 vSucc: vTerm > vTerm)).
% 43.23/43.45 tff(tptp_fun_Vnv00_15_type, type, (
% 43.23/43.45 tptp_fun_Vnv00_15: vTerm > vTerm)).
% 43.23/43.45 tff(visValue_type, type, (
% 43.23/43.45 visValue: vTerm > $o)).
% 43.23/43.45 tff(vptchecksimple_type, type, (
% 43.23/43.45 vptchecksimple: ( vTerm * vTy ) > $o)).
% 43.23/43.45 tff(tptp_fun_VT_62_type, type, (
% 43.23/43.45 tptp_fun_VT_62: vTy)).
% 43.23/43.45 tff(vZero_type, type, (
% 43.23/43.45 vZero: vTerm)).
% 43.23/43.45 tff(visSomeTerm_type, type, (
% 43.23/43.45 visSomeTerm: vOptTerm > $o)).
% 43.23/43.45 tff(1,assumption,(vt1 = vSucc(tptp_fun_Vnv00_15(vt1))), introduced(assumption)).
% 43.23/43.45 tff(2,plain,
% 43.23/43.45 (^[Vnv00: vTerm] : refl((~(vt1 = vSucc(Vnv00))) <=> (~(vt1 = vSucc(Vnv00))))),
% 43.23/43.45 inference(bind,[status(th)],[])).
% 43.23/43.45 tff(3,plain,
% 43.23/43.45 (![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) <=> ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00)))),
% 43.23/43.45 inference(quant_intro,[status(thm)],[2])).
% 43.23/43.45 tff(4,plain,
% 43.23/43.45 (((vreduce(vIszero(vt1)) = vnoTerm) & (visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1))))) <=> ((vreduce(vIszero(vt1)) = vnoTerm) & visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1))))),
% 43.23/43.45 inference(rewrite,[status(thm)],[])).
% 43.23/43.45 tff(5,plain,
% 43.23/43.45 ((visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1)))) <=> (visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1))))),
% 43.23/43.45 inference(rewrite,[status(thm)],[])).
% 43.23/43.45 tff(6,plain,
% 43.23/43.45 (((vreduce(vIszero(vt1)) = vnoTerm) & (visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1))))) <=> ((vreduce(vIszero(vt1)) = vnoTerm) & (visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1)))))),
% 43.23/43.45 inference(monotonicity,[status(thm)],[5])).
% 43.23/43.45 tff(7,plain,
% 43.23/43.45 (((vreduce(vIszero(vt1)) = vnoTerm) & (visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1))))) <=> ((vreduce(vIszero(vt1)) = vnoTerm) & visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1))))),
% 43.23/43.45 inference(transitivity,[status(thm)],[6, 4])).
% 43.23/43.45 tff(8,plain,
% 43.23/43.45 ((~![VT: vTy] : ((~(vreduce(vIszero(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT) & (~visValue(vIszero(vt1))))))) <=> (~![VT: vTy] : ((~(vreduce(vIszero(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT) & (~visValue(vIszero(vt1)))))))),
% 43.23/43.45 inference(rewrite,[status(thm)],[])).
% 43.23/43.45 tff(9,plain,
% 43.23/43.45 ((~![VT: vTy] : (((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero))) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00)))) & vptchecksimple(vIszero(vt1), VT)) & (~visValue(vIszero(vt1)))) => (~(vreduce(vIszero(vt1)) = vnoTerm)))) <=> (~![VT: vTy] : ((~(vreduce(vIszero(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT) & (~visValue(vIszero(vt1)))))))),
% 43.23/43.45 inference(rewrite,[status(thm)],[])).
% 43.23/43.45 tff(10,axiom,(~![VT: vTy] : (((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero))) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00)))) & vptchecksimple(vIszero(vt1), VT)) & (~visValue(vIszero(vt1)))) => (~(vreduce(vIszero(vt1)) = vnoTerm)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Progress-Iszero-t1-isSomeTerm-True'')).
% 43.23/43.45 tff(11,plain,
% 43.23/43.45 (~![VT: vTy] : ((~(vreduce(vIszero(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT) & (~visValue(vIszero(vt1))))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[10, 9])).
% 43.23/43.45 tff(12,plain,
% 43.23/43.45 (~![VT: vTy] : ((~(vreduce(vIszero(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT) & (~visValue(vIszero(vt1))))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[11, 8])).
% 43.23/43.45 tff(13,plain,
% 43.23/43.45 (~![VT: vTy] : ((~(vreduce(vIszero(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT) & (~visValue(vIszero(vt1))))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[12, 8])).
% 43.23/43.45 tff(14,plain,
% 43.23/43.45 (~![VT: vTy] : ((~(vreduce(vIszero(vt1)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT) & (~visValue(vIszero(vt1))))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[13, 8])).
% 43.23/43.45 tff(15,plain,
% 43.23/43.45 ((vreduce(vIszero(vt1)) = vnoTerm) & visSomeTerm(vreduce(vt1)) & (~(vt1 = vZero)) & ![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00))) & vptchecksimple(vIszero(vt1), VT!62) & (~visValue(vIszero(vt1)))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[14, 7])).
% 43.23/43.45 tff(16,plain,
% 43.23/43.45 (![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00)))),
% 43.23/43.45 inference(and_elim,[status(thm)],[15])).
% 43.23/43.45 tff(17,plain,
% 43.23/43.45 (![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00)))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[16, 3])).
% 43.23/43.45 tff(18,plain,
% 43.23/43.45 ((~![Vnv00: vTerm] : (~(vt1 = vSucc(Vnv00)))) | (~(vt1 = vSucc(tptp_fun_Vnv00_15(vt1))))),
% 43.23/43.45 inference(quant_inst,[status(thm)],[])).
% 43.23/43.45 tff(19,plain,
% 43.23/43.45 ($false),
% 43.23/43.45 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 43.23/43.45 tff(20,plain,(~(vt1 = vSucc(tptp_fun_Vnv00_15(vt1)))), inference(lemma,lemma(discharge,[]))).
% 43.23/43.45 tff(21,plain,
% 43.23/43.45 (~(vt1 = vZero)),
% 43.23/43.45 inference(and_elim,[status(thm)],[15])).
% 43.23/43.45 tff(22,plain,
% 43.23/43.45 (visSomeTerm(vreduce(vt1))),
% 43.23/43.45 inference(and_elim,[status(thm)],[15])).
% 43.23/43.45 tff(23,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1)))) <=> ![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))),
% 43.23/43.45 inference(rewrite,[status(thm)],[])).
% 43.23/43.45 tff(24,plain,
% 43.23/43.45 (^[Vt1: vTerm] : refl(((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1)))) <=> ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1)))))),
% 43.23/43.45 inference(bind,[status(th)],[])).
% 43.23/43.45 tff(25,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1)))) <=> ![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))),
% 43.23/43.45 inference(quant_intro,[status(thm)],[24])).
% 43.23/43.45 tff(26,plain,
% 43.23/43.45 (^[Vt1: vTerm] : trans(monotonicity(rewrite(((Vt1 = vZero) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))) | (~visSomeTerm(vreduce(Vt1)))) <=> ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))), ((((Vt1 = vZero) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))) | (~visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> (((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))))), rewrite((((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))), ((((Vt1 = vZero) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))) | (~visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))))),
% 43.23/43.45 inference(bind,[status(th)],[])).
% 43.23/43.45 tff(27,plain,
% 43.23/43.45 (![Vt1: vTerm] : (((Vt1 = vZero) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))) | (~visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))),
% 43.23/43.45 inference(quant_intro,[status(thm)],[26])).
% 43.23/43.45 tff(28,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((~((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))))),
% 43.23/43.45 inference(rewrite,[status(thm)],[])).
% 43.23/43.45 tff(29,plain,
% 43.23/43.45 (^[Vt1: vTerm] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) <=> ((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))))), ((((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) & visSomeTerm(vreduce(Vt1))) <=> (((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) & visSomeTerm(vreduce(Vt1))))), rewrite((((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) & visSomeTerm(vreduce(Vt1))) <=> ((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1)))), ((((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) & visSomeTerm(vreduce(Vt1))) <=> ((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1))))), (((((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) & visSomeTerm(vreduce(Vt1))) => (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> (((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1))) => (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))))), rewrite((((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1))) => (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> ((~((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))))), (((((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) & visSomeTerm(vreduce(Vt1))) => (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> ((~((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))))))),
% 43.23/43.45 inference(bind,[status(th)],[])).
% 43.23/43.45 tff(30,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) & visSomeTerm(vreduce(Vt1))) => (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))))),
% 43.23/43.45 inference(quant_intro,[status(thm)],[29])).
% 43.23/43.45 tff(31,axiom,(![Vt1: vTerm] : ((((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00)))) & visSomeTerm(vreduce(Vt1))) => (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''reduce-16'')).
% 43.23/43.45 tff(32,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((~((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 43.23/43.45 tff(33,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((~((~(Vt1 = vZero)) & ![Vnv00: vTerm] : (~(Vt1 = vSucc(Vnv00))) & visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[32, 28])).
% 43.23/43.45 tff(34,plain,(
% 43.23/43.45 ![Vt1: vTerm] : (((Vt1 = vZero) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))) | (~visSomeTerm(vreduce(Vt1)))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))))),
% 43.23/43.45 inference(skolemize,[status(sab)],[33])).
% 43.23/43.45 tff(35,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[34, 27])).
% 43.23/43.45 tff(36,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[35, 25])).
% 43.23/43.45 tff(37,plain,
% 43.23/43.45 (![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[36, 23])).
% 43.23/43.45 tff(38,plain,
% 43.23/43.45 (((~![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))) | ((vt1 = vZero) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1))))) | (vt1 = vSucc(tptp_fun_Vnv00_15(vt1))))) <=> ((~![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))) | (vt1 = vZero) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1))))) | (vt1 = vSucc(tptp_fun_Vnv00_15(vt1))))),
% 43.23/43.45 inference(rewrite,[status(thm)],[])).
% 43.23/43.45 tff(39,plain,
% 43.23/43.45 ((~![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))) | ((vt1 = vZero) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1))))) | (vt1 = vSucc(tptp_fun_Vnv00_15(vt1))))),
% 43.23/43.45 inference(quant_inst,[status(thm)],[])).
% 43.23/43.45 tff(40,plain,
% 43.23/43.45 ((~![Vt1: vTerm] : ((Vt1 = vZero) | (~visSomeTerm(vreduce(Vt1))) | (vreduce(vIszero(Vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(Vt1))))) | (Vt1 = vSucc(tptp_fun_Vnv00_15(Vt1))))) | (vt1 = vZero) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1))))) | (vt1 = vSucc(tptp_fun_Vnv00_15(vt1)))),
% 43.23/43.45 inference(modus_ponens,[status(thm)],[39, 38])).
% 43.23/43.45 tff(41,plain,
% 43.23/43.45 ((vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1))))) | (vt1 = vSucc(tptp_fun_Vnv00_15(vt1)))),
% 43.23/43.45 inference(unit_resolution,[status(thm)],[40, 37, 22, 21])).
% 43.23/43.45 tff(42,plain,
% 43.23/43.45 (vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1))))),
% 43.23/43.45 inference(unit_resolution,[status(thm)],[41, 20])).
% 43.23/43.45 tff(43,plain,
% 43.23/43.45 (vreduce(vIszero(vt1)) = vnoTerm),
% 43.23/43.45 inference(and_elim,[status(thm)],[15])).
% 43.23/43.45 tff(44,plain,
% 43.23/43.45 (vnoTerm = vreduce(vIszero(vt1))),
% 43.23/43.45 inference(symmetry,[status(thm)],[43])).
% 43.23/43.45 tff(45,plain,
% 43.23/43.45 (vnoTerm = vsomeTerm(vIszero(vgetTerm(vreduce(vt1))))),
% 43.23/43.45 inference(transitivity,[status(thm)],[44, 42])).
% 43.23/43.45 tff(46,plain,
% 43.23/43.45 (^[VTerm0: vTerm] : refl((~(vnoTerm = vsomeTerm(VTerm0))) <=> (~(vnoTerm = vsomeTerm(VTerm0))))),
% 43.23/43.45 inference(bind,[status(th)],[])).
% 43.23/43.45 tff(47,plain,
% 43.23/43.45 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 43.23/43.45 inference(quant_intro,[status(thm)],[46])).
% 43.23/43.45 tff(48,plain,
% 43.23/43.45 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0))) <=> ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 43.23/43.47 inference(rewrite,[status(thm)],[])).
% 43.23/43.47 tff(49,axiom,(![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''DIFF-noTerm-someTerm'')).
% 43.23/43.47 tff(50,plain,
% 43.23/43.47 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 43.23/43.47 inference(modus_ponens,[status(thm)],[49, 48])).
% 43.23/43.47 tff(51,plain,(
% 43.23/43.47 ![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 43.23/43.47 inference(skolemize,[status(sab)],[50])).
% 43.23/43.47 tff(52,plain,
% 43.23/43.47 (![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))),
% 43.23/43.47 inference(modus_ponens,[status(thm)],[51, 47])).
% 43.23/43.47 tff(53,plain,
% 43.23/43.47 ((~![VTerm0: vTerm] : (~(vnoTerm = vsomeTerm(VTerm0)))) | (~(vnoTerm = vsomeTerm(vIszero(vgetTerm(vreduce(vt1))))))),
% 43.23/43.47 inference(quant_inst,[status(thm)],[])).
% 43.23/43.47 tff(54,plain,
% 43.23/43.47 ($false),
% 43.23/43.47 inference(unit_resolution,[status(thm)],[53, 52, 45])).
% 43.23/43.47 % SZS output end Proof
% 43.23/43.48 % E exiting
%------------------------------------------------------------------------------