%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM236_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 06:21:37 PM UTC 2026 % Result : Theorem 21.38s 3.65s % Output : Proof 32.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : COM236_1 : TPTP v9.3.0. Released v9.3.0. % 0.09/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n009.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Mon May 4 19:19:40 EDT 2026 % 0.15/0.36 % CPUTime : % 0.47/0.62 ________ _____ % 0.47/0.62 ___ __ \_________(_)________________________________ % 0.47/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.47/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.47/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.47/0.62 % 0.47/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.47/0.62 (2023-06-19) % 0.47/0.62 % 0.47/0.62 (c) Philipp Rümmer, 2009-2023 % 0.47/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.47/0.62 Amanda Stjerna. % 0.47/0.62 Free software under BSD-3-Clause. % 0.47/0.62 % 0.47/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.47/0.62 % 0.47/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.63/0.66 Running up to 7 provers in parallel. % 0.63/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.63/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.63/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.63/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.63/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.63/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.63/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.55/1.56 Prover 4: Preprocessing ... % 5.55/1.58 Prover 6: Preprocessing ... % 5.55/1.58 Prover 0: Preprocessing ... % 5.55/1.58 Prover 2: Preprocessing ... % 5.55/1.58 Prover 5: Preprocessing ... % 5.55/1.58 Prover 3: Preprocessing ... % 6.32/1.60 Prover 1: Preprocessing ... % 12.98/2.58 Prover 1: Warning: ignoring some quantifiers % 13.77/2.62 Prover 1: Constructing countermodel ... % 13.77/2.63 Prover 6: Proving ... % 13.77/2.66 Prover 3: Warning: ignoring some quantifiers % 13.77/2.68 Prover 3: Constructing countermodel ... % 14.51/2.71 Prover 5: Proving ... % 14.51/2.78 Prover 4: Warning: ignoring some quantifiers % 15.28/2.83 Prover 0: Proving ... % 15.28/2.83 Prover 4: Constructing countermodel ... % 16.89/3.04 Prover 2: Proving ... % 21.38/3.65 Prover 5: proved (2975ms) % 21.38/3.65 % 21.38/3.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.38/3.65 % 21.38/3.65 Prover 2: stopped % 21.38/3.66 Prover 6: stopped % 21.38/3.66 Prover 3: stopped % 21.38/3.67 Prover 0: stopped % 21.38/3.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.38/3.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.38/3.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.38/3.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.38/3.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.70/3.93 Prover 7: Preprocessing ... % 23.70/3.97 Prover 10: Preprocessing ... % 23.70/3.99 Prover 13: Preprocessing ... % 24.70/4.05 Prover 11: Preprocessing ... % 24.70/4.05 Prover 8: Preprocessing ... % 26.75/4.32 Prover 8: Warning: ignoring some quantifiers % 26.75/4.34 Prover 7: Warning: ignoring some quantifiers % 26.75/4.34 Prover 8: Constructing countermodel ... % 26.75/4.36 Prover 10: Warning: ignoring some quantifiers % 26.75/4.38 Prover 10: Constructing countermodel ... % 26.75/4.38 Prover 7: Constructing countermodel ... % 27.55/4.43 Prover 11: Warning: ignoring some quantifiers % 27.55/4.44 Prover 11: Constructing countermodel ... % 28.31/4.53 Prover 13: Warning: ignoring some quantifiers % 28.31/4.55 Prover 13: Constructing countermodel ... % 31.45/4.96 Prover 10: Found proof (size 38) % 31.45/4.96 Prover 10: proved (1296ms) % 31.45/4.96 Prover 1: stopped % 31.45/4.96 Prover 8: stopped % 31.45/4.96 Prover 4: stopped % 31.45/4.96 Prover 13: stopped % 31.45/4.96 Prover 7: stopped % 31.45/4.96 Prover 11: stopped % 31.45/4.96 % 31.45/4.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 31.45/4.96 % 31.45/4.97 % SZS output start Proof for theBenchmark % 31.45/4.97 Assumptions after simplification: % 31.45/4.97 --------------------------------- % 31.45/4.97 % 31.45/4.97 (Progress-Pred-IH0) % 31.45/5.00 vOptTerm(vnoTerm) & vTerm(vt1) & ? [v0: vOptTerm] : (vreduce(vt1) = v0 & % 31.45/5.00 vOptTerm(v0) & ! [v1: vTy] : ( ~ (v0 = vnoTerm) | ~ vTy(v1) | ~ % 31.45/5.01 vptchecksimple(vt1, v1) | visValue(vt1))) % 31.45/5.01 % 31.45/5.01 (Progress-Pred-Succ-isNV-False-isSomeTerm-True) % 31.45/5.01 vOptTerm(vnoTerm) & vTerm(vt1) & vTerm(vZero) & ? [v0: vTerm] : ? [v1: % 31.45/5.01 vTerm] : ? [v2: vTy] : ? [v3: vOptTerm] : ( ~ (vt1 = vZero) & vreduce(v0) % 31.45/5.01 = vnoTerm & vreduce(vt1) = v3 & vPred(vt1) = v0 & vSucc(v1) = vt1 & vTy(v2) % 31.45/5.01 & vOptTerm(v3) & vTerm(v1) & vTerm(v0) & vptchecksimple(v0, v2) & % 31.45/5.01 visSomeTerm(v3) & ~ visNV(v1) & ~ visValue(v0)) % 31.45/5.01 % 31.45/5.01 (isSomeTerm-0) % 31.45/5.01 vOptTerm(vnoTerm) & ~ visSomeTerm(vnoTerm) % 31.45/5.01 % 31.45/5.01 (isSomeTerm-1) % 31.45/5.01 ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vsomeTerm(v0) = v1) | ~ vTerm(v0) | % 31.45/5.01 visSomeTerm(v1)) % 31.45/5.01 % 31.45/5.01 (reduce-10) % 31.45/5.01 vTerm(vZero) & ! [v0: vTerm] : ! [v1: vTerm] : (v0 = vZero | ~ (vPred(v0) = % 31.45/5.01 v1) | ~ vTerm(v0) | ? [v2: vOptTerm] : ? [v3: vOptTerm] : ? [v4: % 31.45/5.01 vTerm] : ? [v5: vTerm] : ? [v6: vOptTerm] : ? [v7: vTerm] : ? [v8: % 31.45/5.01 vTerm] : (vTerm(v7) & ((v8 = v0 & vSucc(v7) = v0) | (vreduce(v0) = v2 & % 31.45/5.01 vOptTerm(v2) & ( ~ visSomeTerm(v2) | (v6 = v3 & vreduce(v1) = v3 & % 31.45/5.01 vgetTerm(v2) = v4 & vsomeTerm(v5) = v3 & vPred(v4) = v5 & % 31.45/5.01 vOptTerm(v3) & vTerm(v5) & vTerm(v4))))))) % 31.45/5.01 % 31.45/5.01 (reduce-14) % 31.45/5.01 ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | % 31.45/5.01 visNV(v0) | ? [v2: vOptTerm] : ? [v3: vTerm] : ? [v4: vOptTerm] : ? [v5: % 31.45/5.01 vTerm] : ? [v6: vTerm] : ? [v7: vOptTerm] : (vreduce(v1) = v2 & % 31.45/5.01 vOptTerm(v2) & ( ~ visSomeTerm(v2) | (v7 = v4 & vreduce(v3) = v4 & % 31.45/5.01 vgetTerm(v2) = v5 & vsomeTerm(v6) = v4 & vIszero(v5) = v6 & % 31.45/5.01 vIszero(v1) = v3 & vOptTerm(v4) & vTerm(v6) & vTerm(v5) & % 31.45/5.01 vTerm(v3))))) % 31.45/5.01 % 31.45/5.01 (reduce-8) % 31.45/5.01 ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | % 31.45/5.01 visNV(v0) | ? [v2: vOptTerm] : ? [v3: vTerm] : ? [v4: vOptTerm] : ? [v5: % 31.45/5.01 vTerm] : ? [v6: vTerm] : ? [v7: vOptTerm] : (vreduce(v1) = v2 & % 31.45/5.01 vOptTerm(v2) & ( ~ visSomeTerm(v2) | (v7 = v4 & vreduce(v3) = v4 & % 31.45/5.01 vgetTerm(v2) = v5 & vsomeTerm(v6) = v4 & vPred(v5) = v6 & vPred(v1) = % 31.45/5.01 v3 & vOptTerm(v4) & vTerm(v6) & vTerm(v5) & vTerm(v3))))) % 31.45/5.01 % 31.45/5.01 (function-axioms) % 31.45/5.01 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : ! [v4: % 31.45/5.01 vTerm] : (v1 = v0 | ~ (vIfelse(v4, v3, v2) = v1) | ~ (vIfelse(v4, v3, v2) % 31.45/5.01 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] % 31.45/5.01 : (v1 = v0 | ~ (vplusop(v3, v2) = v1) | ~ (vplusop(v3, v2) = v0)) & ! [v0: % 31.45/5.01 vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : (v1 = v0 | ~ % 31.45/5.01 (vPlus(v3, v2) = v1) | ~ (vPlus(v3, v2) = v0)) & ! [v0: vOptTerm] : ! % 31.45/5.01 [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ % 31.45/5.01 (vreduce(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : % 31.45/5.01 (v1 = v0 | ~ (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) & ! [v0: % 31.45/5.01 vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 31.45/5.01 (vsomeTerm(v2) = v1) | ~ (vsomeTerm(v2) = v0)) & ! [v0: vTerm] : ! [v1: % 31.45/5.01 vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vIszero(v2) = v1) | ~ (vIszero(v2) % 31.45/5.01 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 31.45/5.01 (vPred(v2) = v1) | ~ (vPred(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : % 32.20/5.01 ! [v2: vTerm] : (v1 = v0 | ~ (vSucc(v2) = v1) | ~ (vSucc(v2) = v0)) % 32.20/5.01 % 32.20/5.01 Further assumptions not needed in the proof: % 32.20/5.01 -------------------------------------------- % 32.20/5.01 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 32.20/5.01 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 32.20/5.01 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 32.20/5.01 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 32.20/5.01 DIFF-Succ-Plus, DIFF-Succ-Pred, DIFF-True-False, DIFF-True-Ifelse, % 32.20/5.01 DIFF-True-Iszero, DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, % 32.20/5.01 DIFF-True-Zero, DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, % 32.20/5.01 DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, % 32.20/5.01 EQ-Succ, EQ-someTerm, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, % 32.20/5.01 TPred_inv1, TPred_inv2, TSucc, TSucc_inv1, TSucc_inv2, TZero, TZero_inv, Tfalse, % 32.20/5.01 Tif, Tif_inv1, Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, % 32.20/5.01 dom-OptTerm, dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, % 32.20/5.01 isNV-false-INV, isNV-true-INV, isNVisNat, isSomeTerm-false-INV, % 32.20/5.01 isSomeTerm-true-INV, isValue-0, isValue-1, isValue-2, isValue-false-INV, % 32.20/5.01 isValue-true-INV, plusop-0, plusop-1, plusop-2, plusop-INV, reduce-0, reduce-1, % 32.20/5.01 reduce-11, reduce-12, reduce-13, reduce-15, reduce-16, reduce-17, reduce-18, % 32.20/5.01 reduce-19, reduce-2, reduce-20, reduce-21, reduce-22, reduce-23, reduce-3, % 32.20/5.01 reduce-4, reduce-5, reduce-6, reduce-7, reduce-9, reduce-INV % 32.20/5.01 % 32.20/5.01 Those formulas are unsatisfiable: % 32.20/5.01 --------------------------------- % 32.20/5.01 % 32.20/5.01 Begin of proof % 32.20/5.02 | % 32.20/5.02 | ALPHA: (isSomeTerm-0) implies: % 32.20/5.02 | (1) ~ visSomeTerm(vnoTerm) % 32.20/5.03 | % 32.20/5.03 | ALPHA: (reduce-10) implies: % 32.20/5.03 | (2) ! [v0: vTerm] : ! [v1: vTerm] : (v0 = vZero | ~ (vPred(v0) = v1) | % 32.20/5.03 | ~ vTerm(v0) | ? [v2: vOptTerm] : ? [v3: vOptTerm] : ? [v4: vTerm] % 32.20/5.03 | : ? [v5: vTerm] : ? [v6: vOptTerm] : ? [v7: vTerm] : ? [v8: % 32.20/5.03 | vTerm] : (vTerm(v7) & ((v8 = v0 & vSucc(v7) = v0) | (vreduce(v0) = % 32.20/5.03 | v2 & vOptTerm(v2) & ( ~ visSomeTerm(v2) | (v6 = v3 & % 32.20/5.03 | vreduce(v1) = v3 & vgetTerm(v2) = v4 & vsomeTerm(v5) = v3 & % 32.20/5.03 | vPred(v4) = v5 & vOptTerm(v3) & vTerm(v5) & vTerm(v4))))))) % 32.20/5.03 | % 32.20/5.03 | ALPHA: (Progress-Pred-IH0) implies: % 32.20/5.03 | (3) ? [v0: vOptTerm] : (vreduce(vt1) = v0 & vOptTerm(v0) & ! [v1: vTy] : % 32.20/5.03 | ( ~ (v0 = vnoTerm) | ~ vTy(v1) | ~ vptchecksimple(vt1, v1) | % 32.20/5.03 | visValue(vt1))) % 32.20/5.03 | % 32.20/5.03 | ALPHA: (Progress-Pred-Succ-isNV-False-isSomeTerm-True) implies: % 32.20/5.03 | (4) vTerm(vt1) % 32.20/5.03 | (5) ? [v0: vTerm] : ? [v1: vTerm] : ? [v2: vTy] : ? [v3: vOptTerm] : ( % 32.20/5.03 | ~ (vt1 = vZero) & vreduce(v0) = vnoTerm & vreduce(vt1) = v3 & % 32.20/5.03 | vPred(vt1) = v0 & vSucc(v1) = vt1 & vTy(v2) & vOptTerm(v3) & % 32.20/5.03 | vTerm(v1) & vTerm(v0) & vptchecksimple(v0, v2) & visSomeTerm(v3) & ~ % 32.20/5.03 | visNV(v1) & ~ visValue(v0)) % 32.20/5.03 | % 32.20/5.03 | ALPHA: (function-axioms) implies: % 32.20/5.03 | (6) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 32.20/5.03 | (vPred(v2) = v1) | ~ (vPred(v2) = v0)) % 32.20/5.04 | (7) ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 32.20/5.04 | (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) % 32.20/5.04 | % 32.20/5.04 | DELTA: instantiating (3) with fresh symbol all_101_0 gives: % 32.20/5.04 | (8) vreduce(vt1) = all_101_0 & vOptTerm(all_101_0) & ! [v0: vTy] : ( ~ % 32.20/5.04 | (all_101_0 = vnoTerm) | ~ vTy(v0) | ~ vptchecksimple(vt1, v0) | % 32.20/5.04 | visValue(vt1)) % 32.20/5.04 | % 32.20/5.04 | ALPHA: (8) implies: % 32.20/5.04 | (9) vreduce(vt1) = all_101_0 % 32.20/5.04 | % 32.20/5.04 | DELTA: instantiating (5) with fresh symbols all_108_0, all_108_1, all_108_2, % 32.20/5.04 | all_108_3 gives: % 32.20/5.04 | (10) ~ (vt1 = vZero) & vreduce(all_108_3) = vnoTerm & vreduce(vt1) = % 32.20/5.04 | all_108_0 & vPred(vt1) = all_108_3 & vSucc(all_108_2) = vt1 & % 32.20/5.04 | vTy(all_108_1) & vOptTerm(all_108_0) & vTerm(all_108_2) & % 32.20/5.04 | vTerm(all_108_3) & vptchecksimple(all_108_3, all_108_1) & % 32.20/5.04 | visSomeTerm(all_108_0) & ~ visNV(all_108_2) & ~ visValue(all_108_3) % 32.20/5.04 | % 32.20/5.04 | ALPHA: (10) implies: % 32.20/5.04 | (11) ~ (vt1 = vZero) % 32.20/5.04 | (12) ~ visNV(all_108_2) % 32.20/5.04 | (13) visSomeTerm(all_108_0) % 32.20/5.04 | (14) vTerm(all_108_2) % 32.20/5.04 | (15) vSucc(all_108_2) = vt1 % 32.20/5.04 | (16) vPred(vt1) = all_108_3 % 32.20/5.04 | (17) vreduce(vt1) = all_108_0 % 32.20/5.04 | (18) vreduce(all_108_3) = vnoTerm % 32.20/5.04 | % 32.20/5.04 | GROUND_INST: instantiating (7) with all_101_0, all_108_0, vt1, simplifying % 32.20/5.04 | with (9), (17) gives: % 32.20/5.04 | (19) all_108_0 = all_101_0 % 32.20/5.04 | % 32.20/5.04 | REDUCE: (13), (19) imply: % 32.20/5.04 | (20) visSomeTerm(all_101_0) % 32.20/5.04 | % 32.20/5.04 | GROUND_INST: instantiating (reduce-14) with all_108_2, vt1, simplifying with % 32.20/5.04 | (12), (14), (15) gives: % 32.20/5.04 | (21) ? [v0: vOptTerm] : ? [v1: vTerm] : ? [v2: vOptTerm] : ? [v3: % 32.20/5.04 | vTerm] : ? [v4: vTerm] : ? [v5: vOptTerm] : (vreduce(vt1) = v0 & % 32.20/5.04 | vOptTerm(v0) & ( ~ visSomeTerm(v0) | (v5 = v2 & vreduce(v1) = v2 & % 32.20/5.04 | vgetTerm(v0) = v3 & vsomeTerm(v4) = v2 & vIszero(v3) = v4 & % 32.20/5.04 | vIszero(vt1) = v1 & vOptTerm(v2) & vTerm(v4) & vTerm(v3) & % 32.20/5.04 | vTerm(v1)))) % 32.20/5.04 | % 32.20/5.04 | GROUND_INST: instantiating (reduce-8) with all_108_2, vt1, simplifying with % 32.20/5.04 | (12), (14), (15) gives: % 32.20/5.04 | (22) ? [v0: vOptTerm] : ? [v1: vTerm] : ? [v2: vOptTerm] : ? [v3: % 32.20/5.04 | vTerm] : ? [v4: vTerm] : ? [v5: vOptTerm] : (vreduce(vt1) = v0 & % 32.20/5.04 | vOptTerm(v0) & ( ~ visSomeTerm(v0) | (v5 = v2 & vreduce(v1) = v2 & % 32.20/5.04 | vgetTerm(v0) = v3 & vsomeTerm(v4) = v2 & vPred(v3) = v4 & % 32.20/5.04 | vPred(vt1) = v1 & vOptTerm(v2) & vTerm(v4) & vTerm(v3) & % 32.20/5.04 | vTerm(v1)))) % 32.20/5.04 | % 32.20/5.04 | GROUND_INST: instantiating (2) with vt1, all_108_3, simplifying with (4), (16) % 32.20/5.04 | gives: % 32.20/5.05 | (23) vt1 = vZero | ? [v0: vOptTerm] : ? [v1: vOptTerm] : ? [v2: vTerm] : % 32.20/5.05 | ? [v3: vTerm] : ? [v4: vOptTerm] : ? [v5: vTerm] : ? [v6: vTerm] : % 32.20/5.05 | (vTerm(v5) & ((v6 = vt1 & vSucc(v5) = vt1) | (vreduce(vt1) = v0 & % 32.20/5.05 | vOptTerm(v0) & ( ~ visSomeTerm(v0) | (v4 = v1 & % 32.20/5.05 | vreduce(all_108_3) = v1 & vgetTerm(v0) = v2 & vsomeTerm(v3) % 32.20/5.05 | = v1 & vPred(v2) = v3 & vOptTerm(v1) & vTerm(v3) & % 32.20/5.05 | vTerm(v2)))))) % 32.20/5.05 | % 32.20/5.05 | DELTA: instantiating (22) with fresh symbols all_136_0, all_136_1, all_136_2, % 32.20/5.05 | all_136_3, all_136_4, all_136_5 gives: % 32.20/5.05 | (24) vreduce(vt1) = all_136_5 & vOptTerm(all_136_5) & ( ~ % 32.20/5.05 | visSomeTerm(all_136_5) | (all_136_0 = all_136_3 & vreduce(all_136_4) % 32.20/5.05 | = all_136_3 & vgetTerm(all_136_5) = all_136_2 & % 32.20/5.05 | vsomeTerm(all_136_1) = all_136_3 & vPred(all_136_2) = all_136_1 & % 32.20/5.05 | vPred(vt1) = all_136_4 & vOptTerm(all_136_3) & vTerm(all_136_1) & % 32.20/5.05 | vTerm(all_136_2) & vTerm(all_136_4))) % 32.20/5.05 | % 32.20/5.05 | ALPHA: (24) implies: % 32.20/5.05 | (25) vreduce(vt1) = all_136_5 % 32.20/5.05 | (26) ~ visSomeTerm(all_136_5) | (all_136_0 = all_136_3 & % 32.20/5.05 | vreduce(all_136_4) = all_136_3 & vgetTerm(all_136_5) = all_136_2 & % 32.20/5.05 | vsomeTerm(all_136_1) = all_136_3 & vPred(all_136_2) = all_136_1 & % 32.20/5.05 | vPred(vt1) = all_136_4 & vOptTerm(all_136_3) & vTerm(all_136_1) & % 32.20/5.05 | vTerm(all_136_2) & vTerm(all_136_4)) % 32.20/5.05 | % 32.20/5.05 | DELTA: instantiating (21) with fresh symbols all_138_0, all_138_1, all_138_2, % 32.20/5.05 | all_138_3, all_138_4, all_138_5 gives: % 32.20/5.05 | (27) vreduce(vt1) = all_138_5 & vOptTerm(all_138_5) & ( ~ % 32.20/5.05 | visSomeTerm(all_138_5) | (all_138_0 = all_138_3 & vreduce(all_138_4) % 32.20/5.05 | = all_138_3 & vgetTerm(all_138_5) = all_138_2 & % 32.20/5.05 | vsomeTerm(all_138_1) = all_138_3 & vIszero(all_138_2) = all_138_1 % 32.20/5.05 | & vIszero(vt1) = all_138_4 & vOptTerm(all_138_3) & % 32.20/5.05 | vTerm(all_138_1) & vTerm(all_138_2) & vTerm(all_138_4))) % 32.20/5.05 | % 32.20/5.05 | ALPHA: (27) implies: % 32.20/5.05 | (28) vreduce(vt1) = all_138_5 % 32.20/5.05 | % 32.20/5.05 | BETA: splitting (23) gives: % 32.20/5.05 | % 32.20/5.05 | Case 1: % 32.20/5.05 | | % 32.20/5.05 | | (29) vt1 = vZero % 32.20/5.05 | | % 32.20/5.05 | | REDUCE: (11), (29) imply: % 32.20/5.05 | | (30) $false % 32.20/5.05 | | % 32.20/5.05 | | CLOSE: (30) is inconsistent. % 32.20/5.05 | | % 32.20/5.05 | Case 2: % 32.20/5.05 | | % 32.20/5.05 | | % 32.20/5.05 | | GROUND_INST: instantiating (7) with all_101_0, all_138_5, vt1, simplifying % 32.20/5.05 | | with (9), (28) gives: % 32.20/5.05 | | (31) all_138_5 = all_101_0 % 32.20/5.05 | | % 32.20/5.05 | | GROUND_INST: instantiating (7) with all_136_5, all_138_5, vt1, simplifying % 32.20/5.05 | | with (25), (28) gives: % 32.20/5.05 | | (32) all_138_5 = all_136_5 % 32.20/5.05 | | % 32.20/5.05 | | COMBINE_EQS: (31), (32) imply: % 32.20/5.05 | | (33) all_136_5 = all_101_0 % 32.20/5.05 | | % 32.20/5.05 | | BETA: splitting (26) gives: % 32.20/5.05 | | % 32.20/5.05 | | Case 1: % 32.20/5.05 | | | % 32.20/5.05 | | | (34) ~ visSomeTerm(all_136_5) % 32.20/5.05 | | | % 32.20/5.05 | | | REDUCE: (33), (34) imply: % 32.20/5.05 | | | (35) ~ visSomeTerm(all_101_0) % 32.20/5.05 | | | % 32.20/5.05 | | | PRED_UNIFY: (20), (35) imply: % 32.20/5.05 | | | (36) $false % 32.20/5.05 | | | % 32.20/5.05 | | | CLOSE: (36) is inconsistent. % 32.20/5.05 | | | % 32.20/5.05 | | Case 2: % 32.20/5.05 | | | % 32.20/5.05 | | | (37) all_136_0 = all_136_3 & vreduce(all_136_4) = all_136_3 & % 32.20/5.05 | | | vgetTerm(all_136_5) = all_136_2 & vsomeTerm(all_136_1) = all_136_3 % 32.20/5.05 | | | & vPred(all_136_2) = all_136_1 & vPred(vt1) = all_136_4 & % 32.20/5.05 | | | vOptTerm(all_136_3) & vTerm(all_136_1) & vTerm(all_136_2) & % 32.20/5.05 | | | vTerm(all_136_4) % 32.20/5.05 | | | % 32.20/5.05 | | | ALPHA: (37) implies: % 32.20/5.05 | | | (38) vTerm(all_136_1) % 32.20/5.05 | | | (39) vPred(vt1) = all_136_4 % 32.20/5.05 | | | (40) vsomeTerm(all_136_1) = all_136_3 % 32.20/5.05 | | | (41) vreduce(all_136_4) = all_136_3 % 32.20/5.05 | | | % 32.20/5.05 | | | GROUND_INST: instantiating (6) with all_108_3, all_136_4, vt1, simplifying % 32.20/5.05 | | | with (16), (39) gives: % 32.20/5.05 | | | (42) all_136_4 = all_108_3 % 32.20/5.05 | | | % 32.20/5.05 | | | REDUCE: (41), (42) imply: % 32.20/5.05 | | | (43) vreduce(all_108_3) = all_136_3 % 32.20/5.05 | | | % 32.20/5.05 | | | GROUND_INST: instantiating (7) with vnoTerm, all_136_3, all_108_3, % 32.20/5.05 | | | simplifying with (18), (43) gives: % 32.20/5.05 | | | (44) all_136_3 = vnoTerm % 32.20/5.05 | | | % 32.20/5.05 | | | REDUCE: (40), (44) imply: % 32.20/5.05 | | | (45) vsomeTerm(all_136_1) = vnoTerm % 32.20/5.05 | | | % 32.20/5.05 | | | GROUND_INST: instantiating (isSomeTerm-1) with all_136_1, vnoTerm, % 32.20/5.06 | | | simplifying with (1), (38), (45) gives: % 32.20/5.06 | | | (46) $false % 32.20/5.06 | | | % 32.20/5.06 | | | CLOSE: (46) is inconsistent. % 32.20/5.06 | | | % 32.20/5.06 | | End of split % 32.20/5.06 | | % 32.20/5.06 | End of split % 32.20/5.06 | % 32.20/5.06 End of proof % 32.20/5.06 % SZS output end Proof for theBenchmark % 32.20/5.06 % 32.20/5.06 4435ms %------------------------------------------------------------------------------