%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM231_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 : n010.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 06:21:36 PM UTC 2026 % Result : Theorem 55.00s 7.79s % Output : Proof 95.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : COM231_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.33 % Computer : n010.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Mon May 4 19:13:21 EDT 2026 % 0.15/0.33 % CPUTime : % 0.52/0.60 ________ _____ % 0.52/0.60 ___ __ \_________(_)________________________________ % 0.52/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.60 % 0.52/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.60 (2023-06-19) % 0.52/0.60 % 0.52/0.60 (c) Philipp Rümmer, 2009-2023 % 0.52/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.60 Amanda Stjerna. % 0.52/0.60 Free software under BSD-3-Clause. % 0.52/0.60 % 0.52/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.60 % 0.52/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.52/0.61 Running up to 7 provers in parallel. % 0.52/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.50/1.48 Prover 1: Preprocessing ... % 6.27/1.50 Prover 4: Preprocessing ... % 6.27/1.52 Prover 6: Preprocessing ... % 6.27/1.52 Prover 3: Preprocessing ... % 6.27/1.52 Prover 2: Preprocessing ... % 6.27/1.52 Prover 5: Preprocessing ... % 6.27/1.55 Prover 0: Preprocessing ... % 12.41/2.37 Prover 1: Warning: ignoring some quantifiers % 13.17/2.43 Prover 3: Warning: ignoring some quantifiers % 13.17/2.45 Prover 1: Constructing countermodel ... % 13.17/2.46 Prover 3: Constructing countermodel ... % 13.17/2.49 Prover 6: Proving ... % 13.97/2.57 Prover 5: Proving ... % 14.74/2.62 Prover 4: Warning: ignoring some quantifiers % 15.52/2.71 Prover 4: Constructing countermodel ... % 15.52/2.76 Prover 0: Proving ... % 17.08/2.99 Prover 2: Proving ... % 55.00/7.79 Prover 2: proved (7163ms) % 55.00/7.79 % 55.00/7.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 55.00/7.79 % 55.00/7.79 Prover 5: stopped % 55.00/7.80 Prover 6: stopped % 55.83/7.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 55.83/7.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 55.83/7.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 55.83/7.81 Prover 0: stopped % 55.83/7.81 Prover 3: stopped % 55.83/7.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 55.83/7.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 57.47/8.05 Prover 7: Preprocessing ... % 57.47/8.06 Prover 10: Preprocessing ... % 57.47/8.10 Prover 8: Preprocessing ... % 57.47/8.11 Prover 11: Preprocessing ... % 57.47/8.11 Prover 13: Preprocessing ... % 58.94/8.28 Prover 8: Warning: ignoring some quantifiers % 58.94/8.29 Prover 8: Constructing countermodel ... % 59.72/8.34 Prover 7: Warning: ignoring some quantifiers % 59.72/8.35 Prover 7: Constructing countermodel ... % 59.72/8.38 Prover 10: Warning: ignoring some quantifiers % 59.72/8.39 Prover 11: Warning: ignoring some quantifiers % 60.51/8.40 Prover 10: Constructing countermodel ... % 60.51/8.40 Prover 11: Constructing countermodel ... % 60.51/8.43 Prover 13: Warning: ignoring some quantifiers % 60.51/8.46 Prover 13: Constructing countermodel ... % 91.30/12.32 Prover 13: stopped % 91.30/12.32 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 92.08/12.45 Prover 16: Preprocessing ... % 93.67/12.65 Prover 16: Warning: ignoring some quantifiers % 93.67/12.66 Prover 16: Constructing countermodel ... % 94.44/12.74 Prover 10: Found proof (size 37) % 94.44/12.74 Prover 10: proved (4936ms) % 94.44/12.74 Prover 16: stopped % 94.44/12.75 Prover 7: stopped % 94.44/12.75 Prover 11: stopped % 94.44/12.75 Prover 8: stopped % 94.44/12.75 Prover 1: stopped % 94.44/12.76 Prover 4: stopped % 94.44/12.76 % 94.44/12.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 94.44/12.76 % 94.44/12.76 % SZS output start Proof for theBenchmark % 94.44/12.77 Assumptions after simplification: % 94.44/12.77 --------------------------------- % 94.44/12.77 % 94.44/12.77 (Progress-Iszero-IH0) % 94.44/12.79 vOptTerm(vnoTerm) & vTerm(vt1) & ? [v0: vOptTerm] : (vreduce(vt1) = v0 & % 94.44/12.79 vOptTerm(v0) & ! [v1: vTy] : ( ~ (v0 = vnoTerm) | ~ vTy(v1) | ~ % 94.44/12.79 vptchecksimple(vt1, v1) | visValue(vt1))) % 94.44/12.79 % 94.44/12.79 (Progress-Iszero-t1-isSomeTerm-True) % 94.44/12.79 vOptTerm(vnoTerm) & vTerm(vt1) & vTerm(vZero) & ? [v0: vOptTerm] : ? [v1: % 94.44/12.80 vTerm] : ? [v2: vTy] : ( ~ (vt1 = vZero) & vreduce(v1) = vnoTerm & % 94.44/12.80 vreduce(vt1) = v0 & vIszero(vt1) = v1 & vTy(v2) & vOptTerm(v0) & vTerm(v1) & % 94.44/12.80 vptchecksimple(v1, v2) & visSomeTerm(v0) & ~ visValue(v1) & ! [v3: vTerm] % 94.44/12.80 : ( ~ (vSucc(v3) = vt1) | ~ vTerm(v3))) % 94.44/12.80 % 94.44/12.80 (isSomeTerm-0) % 94.44/12.80 vOptTerm(vnoTerm) & ~ visSomeTerm(vnoTerm) % 94.44/12.80 % 94.44/12.80 (isSomeTerm-1) % 94.44/12.80 ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vsomeTerm(v0) = v1) | ~ vTerm(v0) | % 94.44/12.80 visSomeTerm(v1)) % 94.44/12.80 % 94.44/12.80 (reduce-16) % 95.07/12.80 vTerm(vZero) & ! [v0: vTerm] : ! [v1: vTerm] : (v0 = vZero | ~ (vIszero(v0) % 95.07/12.80 = v1) | ~ vTerm(v0) | ? [v2: vOptTerm] : ? [v3: vOptTerm] : ? [v4: % 95.07/12.80 vTerm] : ? [v5: vTerm] : ? [v6: vOptTerm] : ? [v7: vTerm] : ? [v8: % 95.07/12.80 vTerm] : (vTerm(v7) & ((v8 = v0 & vSucc(v7) = v0) | (vreduce(v0) = v2 & % 95.07/12.80 vOptTerm(v2) & ( ~ visSomeTerm(v2) | (v6 = v3 & vreduce(v1) = v3 & % 95.07/12.80 vgetTerm(v2) = v4 & vsomeTerm(v5) = v3 & vIszero(v4) = v5 & % 95.07/12.80 vOptTerm(v3) & vTerm(v5) & vTerm(v4))))))) % 95.07/12.80 % 95.07/12.80 (function-axioms) % 95.07/12.80 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : ! [v4: % 95.07/12.80 vTerm] : (v1 = v0 | ~ (vIfelse(v4, v3, v2) = v1) | ~ (vIfelse(v4, v3, v2) % 95.07/12.80 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] % 95.07/12.80 : (v1 = v0 | ~ (vplusop(v3, v2) = v1) | ~ (vplusop(v3, v2) = v0)) & ! [v0: % 95.07/12.80 vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : (v1 = v0 | ~ % 95.07/12.80 (vPlus(v3, v2) = v1) | ~ (vPlus(v3, v2) = v0)) & ! [v0: vOptTerm] : ! % 95.07/12.80 [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ % 95.07/12.80 (vreduce(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : % 95.07/12.80 (v1 = v0 | ~ (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) & ! [v0: % 95.07/12.80 vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 95.07/12.80 (vsomeTerm(v2) = v1) | ~ (vsomeTerm(v2) = v0)) & ! [v0: vTerm] : ! [v1: % 95.07/12.80 vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vIszero(v2) = v1) | ~ (vIszero(v2) % 95.07/12.80 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 95.07/12.80 (vPred(v2) = v1) | ~ (vPred(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : % 95.07/12.80 ! [v2: vTerm] : (v1 = v0 | ~ (vSucc(v2) = v1) | ~ (vSucc(v2) = v0)) % 95.07/12.80 % 95.07/12.80 Further assumptions not needed in the proof: % 95.07/12.80 -------------------------------------------- % 95.07/12.80 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 95.07/12.80 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 95.07/12.81 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 95.07/12.81 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 95.07/12.81 DIFF-Succ-Plus, DIFF-Succ-Pred, DIFF-True-False, DIFF-True-Ifelse, % 95.07/12.81 DIFF-True-Iszero, DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, % 95.07/12.81 DIFF-True-Zero, DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, % 95.07/12.81 DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, % 95.07/12.81 EQ-Succ, EQ-someTerm, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, % 95.07/12.81 TPred_inv1, TPred_inv2, TSucc, TSucc_inv1, TSucc_inv2, TZero, TZero_inv, Tfalse, % 95.07/12.81 Tif, Tif_inv1, Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, % 95.07/12.81 dom-OptTerm, dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, % 95.07/12.81 isNV-false-INV, isNV-true-INV, isSomeTerm-false-INV, isSomeTerm-true-INV, % 95.07/12.81 isValue-0, isValue-1, isValue-2, isValue-false-INV, isValue-true-INV, plusop-0, % 95.07/12.81 plusop-1, plusop-2, plusop-INV, reduce-0, reduce-1, reduce-10, reduce-11, % 95.07/12.81 reduce-12, reduce-13, reduce-14, reduce-15, reduce-17, reduce-18, reduce-19, % 95.07/12.81 reduce-2, reduce-20, reduce-21, reduce-22, reduce-23, reduce-3, reduce-4, % 95.07/12.81 reduce-5, reduce-6, reduce-7, reduce-8, reduce-9, reduce-INV % 95.07/12.81 % 95.07/12.81 Those formulas are unsatisfiable: % 95.07/12.81 --------------------------------- % 95.07/12.81 % 95.07/12.81 Begin of proof % 95.07/12.81 | % 95.07/12.81 | ALPHA: (isSomeTerm-0) implies: % 95.07/12.81 | (1) ~ visSomeTerm(vnoTerm) % 95.07/12.81 | % 95.07/12.81 | ALPHA: (reduce-16) implies: % 95.07/12.81 | (2) ! [v0: vTerm] : ! [v1: vTerm] : (v0 = vZero | ~ (vIszero(v0) = v1) | % 95.07/12.81 | ~ vTerm(v0) | ? [v2: vOptTerm] : ? [v3: vOptTerm] : ? [v4: vTerm] % 95.07/12.81 | : ? [v5: vTerm] : ? [v6: vOptTerm] : ? [v7: vTerm] : ? [v8: % 95.07/12.81 | vTerm] : (vTerm(v7) & ((v8 = v0 & vSucc(v7) = v0) | (vreduce(v0) = % 95.07/12.81 | v2 & vOptTerm(v2) & ( ~ visSomeTerm(v2) | (v6 = v3 & % 95.07/12.81 | vreduce(v1) = v3 & vgetTerm(v2) = v4 & vsomeTerm(v5) = v3 & % 95.07/12.81 | vIszero(v4) = v5 & vOptTerm(v3) & vTerm(v5) & % 95.07/12.81 | vTerm(v4))))))) % 95.07/12.81 | % 95.07/12.81 | ALPHA: (Progress-Iszero-IH0) implies: % 95.07/12.81 | (3) ? [v0: vOptTerm] : (vreduce(vt1) = v0 & vOptTerm(v0) & ! [v1: vTy] : % 95.07/12.81 | ( ~ (v0 = vnoTerm) | ~ vTy(v1) | ~ vptchecksimple(vt1, v1) | % 95.07/12.81 | visValue(vt1))) % 95.07/12.81 | % 95.07/12.81 | ALPHA: (Progress-Iszero-t1-isSomeTerm-True) implies: % 95.07/12.81 | (4) vTerm(vt1) % 95.07/12.81 | (5) ? [v0: vOptTerm] : ? [v1: vTerm] : ? [v2: vTy] : ( ~ (vt1 = vZero) & % 95.07/12.81 | vreduce(v1) = vnoTerm & vreduce(vt1) = v0 & vIszero(vt1) = v1 & % 95.07/12.81 | vTy(v2) & vOptTerm(v0) & vTerm(v1) & vptchecksimple(v1, v2) & % 95.07/12.81 | visSomeTerm(v0) & ~ visValue(v1) & ! [v3: vTerm] : ( ~ (vSucc(v3) = % 95.07/12.81 | vt1) | ~ vTerm(v3))) % 95.07/12.81 | % 95.07/12.81 | ALPHA: (function-axioms) implies: % 95.07/12.81 | (6) ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 95.07/12.81 | (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) % 95.07/12.81 | % 95.07/12.81 | DELTA: instantiating (3) with fresh symbol all_100_0 gives: % 95.07/12.81 | (7) vreduce(vt1) = all_100_0 & vOptTerm(all_100_0) & ! [v0: vTy] : ( ~ % 95.07/12.81 | (all_100_0 = vnoTerm) | ~ vTy(v0) | ~ vptchecksimple(vt1, v0) | % 95.07/12.81 | visValue(vt1)) % 95.07/12.81 | % 95.07/12.81 | ALPHA: (7) implies: % 95.07/12.81 | (8) vreduce(vt1) = all_100_0 % 95.07/12.81 | % 95.07/12.81 | DELTA: instantiating (5) with fresh symbols all_107_0, all_107_1, all_107_2 % 95.07/12.81 | gives: % 95.07/12.82 | (9) ~ (vt1 = vZero) & vreduce(all_107_1) = vnoTerm & vreduce(vt1) = % 95.07/12.82 | all_107_2 & vIszero(vt1) = all_107_1 & vTy(all_107_0) & % 95.07/12.82 | vOptTerm(all_107_2) & vTerm(all_107_1) & vptchecksimple(all_107_1, % 95.07/12.82 | all_107_0) & visSomeTerm(all_107_2) & ~ visValue(all_107_1) & ! % 95.07/12.82 | [v0: vTerm] : ( ~ (vSucc(v0) = vt1) | ~ vTerm(v0)) % 95.07/12.82 | % 95.07/12.82 | ALPHA: (9) implies: % 95.07/12.82 | (10) ~ (vt1 = vZero) % 95.07/12.82 | (11) visSomeTerm(all_107_2) % 95.07/12.82 | (12) vIszero(vt1) = all_107_1 % 95.07/12.82 | (13) vreduce(vt1) = all_107_2 % 95.07/12.82 | (14) vreduce(all_107_1) = vnoTerm % 95.07/12.82 | (15) ! [v0: vTerm] : ( ~ (vSucc(v0) = vt1) | ~ vTerm(v0)) % 95.07/12.82 | % 95.07/12.82 | GROUND_INST: instantiating (6) with all_100_0, all_107_2, vt1, simplifying % 95.07/12.82 | with (8), (13) gives: % 95.07/12.82 | (16) all_107_2 = all_100_0 % 95.07/12.82 | % 95.07/12.82 | REDUCE: (11), (16) imply: % 95.07/12.82 | (17) visSomeTerm(all_100_0) % 95.07/12.82 | % 95.07/12.82 | GROUND_INST: instantiating (2) with vt1, all_107_1, simplifying with (4), (12) % 95.07/12.82 | gives: % 95.07/12.82 | (18) vt1 = vZero | ? [v0: vOptTerm] : ? [v1: vOptTerm] : ? [v2: vTerm] : % 95.07/12.82 | ? [v3: vTerm] : ? [v4: vOptTerm] : ? [v5: vTerm] : ? [v6: vTerm] : % 95.07/12.82 | (vTerm(v5) & ((v6 = vt1 & vSucc(v5) = vt1) | (vreduce(vt1) = v0 & % 95.07/12.82 | vOptTerm(v0) & ( ~ visSomeTerm(v0) | (v4 = v1 & % 95.07/12.82 | vreduce(all_107_1) = v1 & vgetTerm(v0) = v2 & vsomeTerm(v3) % 95.07/12.82 | = v1 & vIszero(v2) = v3 & vOptTerm(v1) & vTerm(v3) & % 95.07/12.82 | vTerm(v2)))))) % 95.07/12.82 | % 95.07/12.82 | BETA: splitting (18) gives: % 95.07/12.82 | % 95.07/12.82 | Case 1: % 95.07/12.82 | | % 95.07/12.82 | | (19) vt1 = vZero % 95.07/12.82 | | % 95.07/12.82 | | REDUCE: (10), (19) imply: % 95.07/12.82 | | (20) $false % 95.07/12.82 | | % 95.07/12.82 | | CLOSE: (20) is inconsistent. % 95.07/12.82 | | % 95.07/12.82 | Case 2: % 95.07/12.82 | | % 95.07/12.82 | | (21) ? [v0: vOptTerm] : ? [v1: vOptTerm] : ? [v2: vTerm] : ? [v3: % 95.07/12.82 | | vTerm] : ? [v4: vOptTerm] : ? [v5: vTerm] : ? [v6: vTerm] : % 95.07/12.82 | | (vTerm(v5) & ((v6 = vt1 & vSucc(v5) = vt1) | (vreduce(vt1) = v0 & % 95.07/12.82 | | vOptTerm(v0) & ( ~ visSomeTerm(v0) | (v4 = v1 & % 95.07/12.82 | | vreduce(all_107_1) = v1 & vgetTerm(v0) = v2 & % 95.07/12.82 | | vsomeTerm(v3) = v1 & vIszero(v2) = v3 & vOptTerm(v1) & % 95.07/12.82 | | vTerm(v3) & vTerm(v2)))))) % 95.07/12.82 | | % 95.07/12.82 | | DELTA: instantiating (21) with fresh symbols all_143_0, all_143_1, % 95.07/12.82 | | all_143_2, all_143_3, all_143_4, all_143_5, all_143_6 gives: % 95.07/12.82 | | (22) vTerm(all_143_1) & ((all_143_0 = vt1 & vSucc(all_143_1) = vt1) | % 95.07/12.82 | | (vreduce(vt1) = all_143_6 & vOptTerm(all_143_6) & ( ~ % 95.07/12.82 | | visSomeTerm(all_143_6) | (all_143_2 = all_143_5 & % 95.07/12.82 | | vreduce(all_107_1) = all_143_5 & vgetTerm(all_143_6) = % 95.07/12.82 | | all_143_4 & vsomeTerm(all_143_3) = all_143_5 & % 95.07/12.82 | | vIszero(all_143_4) = all_143_3 & vOptTerm(all_143_5) & % 95.07/12.82 | | vTerm(all_143_3) & vTerm(all_143_4))))) % 95.07/12.82 | | % 95.07/12.82 | | ALPHA: (22) implies: % 95.07/12.82 | | (23) vTerm(all_143_1) % 95.07/12.83 | | (24) (all_143_0 = vt1 & vSucc(all_143_1) = vt1) | (vreduce(vt1) = % 95.07/12.83 | | all_143_6 & vOptTerm(all_143_6) & ( ~ visSomeTerm(all_143_6) | % 95.07/12.83 | | (all_143_2 = all_143_5 & vreduce(all_107_1) = all_143_5 & % 95.07/12.83 | | vgetTerm(all_143_6) = all_143_4 & vsomeTerm(all_143_3) = % 95.07/12.83 | | all_143_5 & vIszero(all_143_4) = all_143_3 & % 95.07/12.83 | | vOptTerm(all_143_5) & vTerm(all_143_3) & vTerm(all_143_4)))) % 95.07/12.83 | | % 95.07/12.83 | | BETA: splitting (24) gives: % 95.07/12.83 | | % 95.07/12.83 | | Case 1: % 95.07/12.83 | | | % 95.07/12.83 | | | (25) all_143_0 = vt1 & vSucc(all_143_1) = vt1 % 95.07/12.83 | | | % 95.07/12.83 | | | ALPHA: (25) implies: % 95.07/12.83 | | | (26) vSucc(all_143_1) = vt1 % 95.07/12.83 | | | % 95.07/12.83 | | | GROUND_INST: instantiating (15) with all_143_1, simplifying with (23), % 95.07/12.83 | | | (26) gives: % 95.07/12.83 | | | (27) $false % 95.07/12.83 | | | % 95.07/12.83 | | | CLOSE: (27) is inconsistent. % 95.07/12.83 | | | % 95.07/12.83 | | Case 2: % 95.07/12.83 | | | % 95.07/12.83 | | | (28) vreduce(vt1) = all_143_6 & vOptTerm(all_143_6) & ( ~ % 95.07/12.83 | | | visSomeTerm(all_143_6) | (all_143_2 = all_143_5 & % 95.07/12.83 | | | vreduce(all_107_1) = all_143_5 & vgetTerm(all_143_6) = % 95.07/12.83 | | | all_143_4 & vsomeTerm(all_143_3) = all_143_5 & % 95.07/12.83 | | | vIszero(all_143_4) = all_143_3 & vOptTerm(all_143_5) & % 95.07/12.83 | | | vTerm(all_143_3) & vTerm(all_143_4))) % 95.07/12.83 | | | % 95.07/12.83 | | | ALPHA: (28) implies: % 95.07/12.83 | | | (29) vreduce(vt1) = all_143_6 % 95.07/12.83 | | | (30) ~ visSomeTerm(all_143_6) | (all_143_2 = all_143_5 & % 95.07/12.83 | | | vreduce(all_107_1) = all_143_5 & vgetTerm(all_143_6) = all_143_4 % 95.07/12.83 | | | & vsomeTerm(all_143_3) = all_143_5 & vIszero(all_143_4) = % 95.07/12.83 | | | all_143_3 & vOptTerm(all_143_5) & vTerm(all_143_3) & % 95.07/12.83 | | | vTerm(all_143_4)) % 95.07/12.83 | | | % 95.07/12.83 | | | GROUND_INST: instantiating (6) with all_100_0, all_143_6, vt1, simplifying % 95.07/12.83 | | | with (8), (29) gives: % 95.07/12.83 | | | (31) all_143_6 = all_100_0 % 95.07/12.83 | | | % 95.07/12.83 | | | BETA: splitting (30) gives: % 95.07/12.83 | | | % 95.07/12.83 | | | Case 1: % 95.07/12.83 | | | | % 95.07/12.83 | | | | (32) ~ visSomeTerm(all_143_6) % 95.07/12.83 | | | | % 95.07/12.83 | | | | REDUCE: (31), (32) imply: % 95.07/12.83 | | | | (33) ~ visSomeTerm(all_100_0) % 95.07/12.83 | | | | % 95.07/12.83 | | | | PRED_UNIFY: (17), (33) imply: % 95.07/12.83 | | | | (34) $false % 95.07/12.83 | | | | % 95.07/12.83 | | | | CLOSE: (34) is inconsistent. % 95.07/12.83 | | | | % 95.07/12.83 | | | Case 2: % 95.07/12.83 | | | | % 95.07/12.83 | | | | (35) all_143_2 = all_143_5 & vreduce(all_107_1) = all_143_5 & % 95.07/12.83 | | | | vgetTerm(all_143_6) = all_143_4 & vsomeTerm(all_143_3) = % 95.07/12.83 | | | | all_143_5 & vIszero(all_143_4) = all_143_3 & vOptTerm(all_143_5) % 95.07/12.83 | | | | & vTerm(all_143_3) & vTerm(all_143_4) % 95.07/12.83 | | | | % 95.07/12.83 | | | | ALPHA: (35) implies: % 95.07/12.83 | | | | (36) vTerm(all_143_3) % 95.07/12.83 | | | | (37) vsomeTerm(all_143_3) = all_143_5 % 95.07/12.83 | | | | (38) vreduce(all_107_1) = all_143_5 % 95.07/12.83 | | | | % 95.07/12.83 | | | | GROUND_INST: instantiating (6) with vnoTerm, all_143_5, all_107_1, % 95.07/12.83 | | | | simplifying with (14), (38) gives: % 95.07/12.83 | | | | (39) all_143_5 = vnoTerm % 95.07/12.83 | | | | % 95.07/12.83 | | | | REDUCE: (37), (39) imply: % 95.07/12.83 | | | | (40) vsomeTerm(all_143_3) = vnoTerm % 95.07/12.83 | | | | % 95.07/12.83 | | | | GROUND_INST: instantiating (isSomeTerm-1) with all_143_3, vnoTerm, % 95.07/12.83 | | | | simplifying with (1), (36), (40) gives: % 95.07/12.83 | | | | (41) $false % 95.07/12.83 | | | | % 95.07/12.83 | | | | CLOSE: (41) is inconsistent. % 95.07/12.83 | | | | % 95.07/12.83 | | | End of split % 95.07/12.83 | | | % 95.07/12.83 | | End of split % 95.07/12.83 | | % 95.07/12.83 | End of split % 95.07/12.83 | % 95.07/12.83 End of proof % 95.07/12.83 % SZS output end Proof for theBenchmark % 95.07/12.83 % 95.07/12.83 12232ms %------------------------------------------------------------------------------