%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM228_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.20s 0.42s
% Output : Proof 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM228_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.14/0.33 % Computer : n014.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % 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 : Mon May 4 19:11:23 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(visSomeTerm_type, type, (
% 0.20/0.42 visSomeTerm: vOptTerm > $o)).
% 0.20/0.42 tff(vreduce_type, type, (
% 0.20/0.42 vreduce: vTerm > vOptTerm)).
% 0.20/0.42 tff(vt1_type, type, (
% 0.20/0.42 vt1: vTerm)).
% 0.20/0.42 tff(visValue_type, type, (
% 0.20/0.42 visValue: vTerm > $o)).
% 0.20/0.42 tff(vIfelse_type, type, (
% 0.20/0.42 vIfelse: ( vTerm * vTerm * vTerm ) > vTerm)).
% 0.20/0.42 tff(vt3_type, type, (
% 0.20/0.42 vt3: vTerm)).
% 0.20/0.42 tff(vt2_type, type, (
% 0.20/0.42 vt2: vTerm)).
% 0.20/0.42 tff(vptchecksimple_type, type, (
% 0.20/0.42 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.20/0.42 tff(tptp_fun_VT_62_type, type, (
% 0.20/0.42 tptp_fun_VT_62: vTy)).
% 0.20/0.42 tff(vFalse_type, type, (
% 0.20/0.42 vFalse: vTerm)).
% 0.20/0.42 tff(vTrue_type, type, (
% 0.20/0.42 vTrue: vTerm)).
% 0.20/0.42 tff(vnoTerm_type, type, (
% 0.20/0.42 vnoTerm: vOptTerm)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 ((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))) <=> (~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 ((~![VT: vTy] : (((((~(vt1 = vTrue)) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)))) <=> (~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(3,axiom,(~![VT: vTy] : (((((~(vt1 = vTrue)) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Progress-Ifelse-t1'')).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.42 tff(8,plain,(
% 0.20/0.42 ~((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[7])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 ((~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62) & (~visValue(vIfelse(vt1, vt2, vt3)))),
% 0.20/0.42 inference(or_elim,[status(thm)],[8])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (~visValue(vIfelse(vt1, vt2, vt3))),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62)),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (~(vt1 = vFalse)),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (~(vt1 = vTrue)),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm),
% 0.20/0.42 inference(or_elim,[status(thm)],[8])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (^[VT: vTy] : refl(((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))) <=> ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (^[VT: vTy] : trans(monotonicity(trans(monotonicity(rewrite(((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))) <=> (~(visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))), ((~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))) <=> (~(~(visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))))), rewrite((~(~(visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))) <=> (visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))), ((~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))) <=> (visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))), (((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))))), rewrite(((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))), (((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))) <=> ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))) <=> ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (^[VT: vTy] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) <=> ((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)))), (((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) <=> (((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))), rewrite((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) <=> ((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT))), (((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) <=> ((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))), ((((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) <=> (((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))))), rewrite((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) <=> ((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))), ((((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) <=> ((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))), (((((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))) <=> (((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))))), rewrite((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))), (((((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (![VT: vTy] : ((((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))) <=> ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.43 tff(22,axiom,(![VT: vTy] : ((((((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Progress-Ifelse-t1-isSomeTerm-False'')).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.43 tff(25,plain,(
% 0.20/0.43 ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~((~visSomeTerm(vreduce(vt1))) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[24])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) | ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62)))) <=> ((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) | (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 ((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) | ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) | (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | visSomeTerm(vreduce(vt1)) | (vt1 = vFalse) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (visSomeTerm(vreduce(vt1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[30, 27, 14, 13, 12, 11, 10])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (^[VT: vTy] : refl(((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))) <=> ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (^[VT: vTy] : trans(monotonicity(trans(monotonicity(rewrite((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))) <=> (~((vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))), ((~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))) <=> (~(~((vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))))), rewrite((~(~((vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))) <=> ((vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))), ((~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))) <=> ((vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT))))), (((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | ((vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))))), rewrite(((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | ((vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))), (((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))) <=> ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))) <=> ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (^[VT: vTy] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) <=> (visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)))), ((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) <=> ((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))), rewrite(((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) <=> (visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT))), ((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) <=> (visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))), (((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) <=> ((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))))), rewrite(((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) <=> (visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))), (((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) <=> (visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))))), ((((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))) <=> ((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))))), rewrite(((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))), ((((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))) <=> ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (![VT: vTy] : (((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm))) <=> ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.44 tff(39,axiom,(![VT: vTy] : (((((visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue))) & (~(vt1 = vFalse))) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT)) & (~visValue(vIfelse(vt1, vt2, vt3)))) => (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Progress-Ifelse-t1-isSomeTerm-True'')).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.30/0.46 tff(41,plain,
% 0.30/0.46 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.30/0.46 tff(42,plain,(
% 0.30/0.46 ![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (~(visSomeTerm(vreduce(vt1)) & (~(vt1 = vTrue)) & (~(vt1 = vFalse)) & vptchecksimple(vIfelse(vt1, vt2, vt3), VT) & (~visValue(vIfelse(vt1, vt2, vt3))))))),
% 0.30/0.46 inference(skolemize,[status(sab)],[41])).
% 0.30/0.46 tff(43,plain,
% 0.30/0.46 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.30/0.46 tff(44,plain,
% 0.30/0.46 (![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.30/0.46 tff(45,plain,
% 0.30/0.46 (((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) | ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62)))) <=> ((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) | (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62)))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(46,plain,
% 0.30/0.46 ((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) | ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62)))),
% 0.30/0.46 inference(quant_inst,[status(thm)],[])).
% 0.30/0.46 tff(47,plain,
% 0.30/0.46 ((~![VT: vTy] : ((~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT)))) | (~(vreduce(vIfelse(vt1, vt2, vt3)) = vnoTerm)) | (vt1 = vFalse) | (~visSomeTerm(vreduce(vt1))) | (vt1 = vTrue) | visValue(vIfelse(vt1, vt2, vt3)) | (~vptchecksimple(vIfelse(vt1, vt2, vt3), VT!62))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.30/0.46 tff(48,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[47, 44, 14, 13, 12, 11, 10, 31])).
% 0.30/0.46 % SZS output end Proof
% 0.30/0.46 % E exiting
%------------------------------------------------------------------------------