%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM242_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 : n004.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 18.40s 3.26s % Output : Proof 30.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM242_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 : n004.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 19:30:17 EDT 2026 % 0.15/0.33 % CPUTime : % 0.51/0.59 ________ _____ % 0.51/0.59 ___ __ \_________(_)________________________________ % 0.51/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.59 % 0.51/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.59 (2023-06-19) % 0.51/0.59 % 0.51/0.59 (c) Philipp Rümmer, 2009-2023 % 0.51/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.59 Amanda Stjerna. % 0.51/0.59 Free software under BSD-3-Clause. % 0.51/0.59 % 0.51/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.59 % 0.51/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.51/0.60 Running up to 7 provers in parallel. % 0.51/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.51/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.51/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.51/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.97/1.46 Prover 4: Preprocessing ... % 4.97/1.47 Prover 1: Preprocessing ... % 5.68/1.50 Prover 5: Preprocessing ... % 5.68/1.50 Prover 6: Preprocessing ... % 5.68/1.50 Prover 3: Preprocessing ... % 5.68/1.50 Prover 0: Preprocessing ... % 5.68/1.50 Prover 2: Preprocessing ... % 12.40/2.40 Prover 1: Warning: ignoring some quantifiers % 12.40/2.43 Prover 3: Warning: ignoring some quantifiers % 12.40/2.46 Prover 3: Constructing countermodel ... % 12.40/2.48 Prover 1: Constructing countermodel ... % 13.17/2.54 Prover 6: Proving ... % 13.17/2.55 Prover 5: Proving ... % 13.88/2.63 Prover 4: Warning: ignoring some quantifiers % 13.88/2.65 Prover 0: Proving ... % 13.88/2.67 Prover 4: Constructing countermodel ... % 15.35/2.87 Prover 2: Proving ... % 18.40/3.26 Prover 5: proved (2643ms) % 18.40/3.26 % 18.40/3.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.40/3.26 % 18.40/3.27 Prover 3: stopped % 18.40/3.27 Prover 2: stopped % 18.40/3.28 Prover 0: stopped % 18.40/3.28 Prover 6: stopped % 18.40/3.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.40/3.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.40/3.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.40/3.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.40/3.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.38/3.63 Prover 7: Preprocessing ... % 21.38/3.66 Prover 10: Preprocessing ... % 22.15/3.74 Prover 8: Preprocessing ... % 22.15/3.75 Prover 11: Preprocessing ... % 22.15/3.76 Prover 13: Preprocessing ... % 23.75/4.00 Prover 8: Warning: ignoring some quantifiers % 24.70/4.03 Prover 8: Constructing countermodel ... % 24.70/4.03 Prover 7: Warning: ignoring some quantifiers % 24.70/4.09 Prover 7: Constructing countermodel ... % 24.70/4.10 Prover 10: Warning: ignoring some quantifiers % 25.47/4.13 Prover 10: Constructing countermodel ... % 25.47/4.18 Prover 11: Warning: ignoring some quantifiers % 26.07/4.20 Prover 11: Constructing countermodel ... % 26.07/4.30 Prover 13: Warning: ignoring some quantifiers % 26.85/4.31 Prover 13: Constructing countermodel ... % 29.93/4.73 Prover 10: Found proof (size 25) % 29.93/4.73 Prover 10: proved (1457ms) % 29.93/4.73 Prover 13: stopped % 29.93/4.73 Prover 8: stopped % 29.93/4.73 Prover 4: stopped % 29.93/4.73 Prover 1: stopped % 29.93/4.73 Prover 7: stopped % 29.93/4.73 Prover 11: stopped % 29.93/4.73 % 29.93/4.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.93/4.74 % 29.93/4.74 % SZS output start Proof for theBenchmark % 29.93/4.74 Assumptions after simplification: % 29.93/4.74 --------------------------------- % 29.93/4.74 % 29.93/4.75 (Progress-Succ-IH0) % 29.93/4.77 vOptTerm(vnoTerm) & vTerm(vt1) & ? [v0: vOptTerm] : (vreduce(vt1) = v0 & % 29.93/4.77 vOptTerm(v0) & ! [v1: vTy] : ( ~ (v0 = vnoTerm) | ~ vTy(v1) | ~ % 29.93/4.77 vptchecksimple(vt1, v1) | visValue(vt1))) % 29.93/4.77 % 29.93/4.77 (Progress-Succ-isSomeTerm-True) % 29.93/4.77 vOptTerm(vnoTerm) & vTerm(vt1) & ? [v0: vOptTerm] : ? [v1: vTerm] : ? [v2: % 29.93/4.77 vTy] : (vreduce(v1) = vnoTerm & vreduce(vt1) = v0 & vSucc(vt1) = v1 & % 29.93/4.77 vTy(v2) & vOptTerm(v0) & vTerm(v1) & vptchecksimple(v1, v2) & % 29.93/4.77 visSomeTerm(v0) & ~ visValue(v1)) % 29.93/4.77 % 29.93/4.77 (isSomeTerm-0) % 29.93/4.77 vOptTerm(vnoTerm) & ~ visSomeTerm(vnoTerm) % 29.93/4.77 % 29.93/4.77 (isSomeTerm-1) % 29.93/4.77 ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vsomeTerm(v0) = v1) | ~ vTerm(v0) | % 29.93/4.77 visSomeTerm(v1)) % 29.93/4.77 % 29.93/4.77 (reduce-4) % 29.93/4.78 ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | ? % 29.93/4.78 [v2: vOptTerm] : ? [v3: vOptTerm] : ? [v4: vTerm] : ? [v5: vTerm] : ? % 29.93/4.78 [v6: vOptTerm] : (vreduce(v0) = v2 & vOptTerm(v2) & ( ~ visSomeTerm(v2) | % 29.93/4.78 (v6 = v3 & vreduce(v1) = v3 & vgetTerm(v2) = v4 & vsomeTerm(v5) = v3 & % 29.93/4.78 vSucc(v4) = v5 & vOptTerm(v3) & vTerm(v5) & vTerm(v4))))) % 29.93/4.78 % 29.93/4.78 (function-axioms) % 29.93/4.78 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : ! [v4: % 29.93/4.78 vTerm] : (v1 = v0 | ~ (vIfelse(v4, v3, v2) = v1) | ~ (vIfelse(v4, v3, v2) % 29.93/4.78 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] % 29.93/4.78 : (v1 = v0 | ~ (vplusop(v3, v2) = v1) | ~ (vplusop(v3, v2) = v0)) & ! [v0: % 29.93/4.78 vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : (v1 = v0 | ~ % 29.93/4.78 (vPlus(v3, v2) = v1) | ~ (vPlus(v3, v2) = v0)) & ! [v0: vOptTerm] : ! % 29.93/4.78 [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ % 29.93/4.78 (vreduce(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : % 29.93/4.78 (v1 = v0 | ~ (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) & ! [v0: % 29.93/4.78 vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 29.93/4.78 (vsomeTerm(v2) = v1) | ~ (vsomeTerm(v2) = v0)) & ! [v0: vTerm] : ! [v1: % 29.93/4.78 vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vIszero(v2) = v1) | ~ (vIszero(v2) % 29.93/4.78 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 29.93/4.78 (vPred(v2) = v1) | ~ (vPred(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : % 29.93/4.78 ! [v2: vTerm] : (v1 = v0 | ~ (vSucc(v2) = v1) | ~ (vSucc(v2) = v0)) % 29.93/4.78 % 29.93/4.78 Further assumptions not needed in the proof: % 29.93/4.78 -------------------------------------------- % 29.93/4.78 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 29.93/4.78 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 29.93/4.78 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 29.93/4.78 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 29.93/4.78 DIFF-Succ-Plus, DIFF-Succ-Pred, DIFF-True-False, DIFF-True-Ifelse, % 29.93/4.78 DIFF-True-Iszero, DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, % 29.93/4.78 DIFF-True-Zero, DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, % 29.93/4.78 DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, % 29.93/4.78 EQ-Succ, EQ-someTerm, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, % 29.93/4.78 TPred_inv1, TPred_inv2, TSucc, TSucc_inv1, TSucc_inv2, TZero, TZero_inv, Tfalse, % 29.93/4.78 Tif, Tif_inv1, Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, % 29.93/4.78 dom-OptTerm, dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, % 29.93/4.78 isNV-false-INV, isNV-true-INV, isSomeTerm-false-INV, isSomeTerm-true-INV, % 29.93/4.78 isValue-0, isValue-1, isValue-2, isValue-false-INV, isValue-true-INV, plusop-0, % 29.93/4.78 plusop-1, plusop-2, plusop-INV, reduce-0, reduce-1, reduce-10, reduce-11, % 29.93/4.78 reduce-12, reduce-13, reduce-14, reduce-15, reduce-16, reduce-17, reduce-18, % 29.93/4.78 reduce-19, reduce-2, reduce-20, reduce-21, reduce-22, reduce-23, reduce-3, % 29.93/4.78 reduce-5, reduce-6, reduce-7, reduce-8, reduce-9, reduce-INV % 29.93/4.78 % 29.93/4.78 Those formulas are unsatisfiable: % 29.93/4.78 --------------------------------- % 29.93/4.78 % 29.93/4.78 Begin of proof % 29.93/4.78 | % 29.93/4.78 | ALPHA: (isSomeTerm-0) implies: % 29.93/4.79 | (1) ~ visSomeTerm(vnoTerm) % 29.93/4.79 | % 29.93/4.79 | ALPHA: (Progress-Succ-IH0) implies: % 29.93/4.79 | (2) ? [v0: vOptTerm] : (vreduce(vt1) = v0 & vOptTerm(v0) & ! [v1: vTy] : % 29.93/4.79 | ( ~ (v0 = vnoTerm) | ~ vTy(v1) | ~ vptchecksimple(vt1, v1) | % 29.93/4.79 | visValue(vt1))) % 29.93/4.79 | % 29.93/4.79 | ALPHA: (Progress-Succ-isSomeTerm-True) implies: % 29.93/4.79 | (3) vTerm(vt1) % 29.93/4.79 | (4) ? [v0: vOptTerm] : ? [v1: vTerm] : ? [v2: vTy] : (vreduce(v1) = % 29.93/4.79 | vnoTerm & vreduce(vt1) = v0 & vSucc(vt1) = v1 & vTy(v2) & % 29.93/4.79 | vOptTerm(v0) & vTerm(v1) & vptchecksimple(v1, v2) & visSomeTerm(v0) & % 29.93/4.79 | ~ visValue(v1)) % 29.93/4.79 | % 29.93/4.79 | ALPHA: (function-axioms) implies: % 29.93/4.79 | (5) ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 29.93/4.79 | (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) % 29.93/4.79 | % 29.93/4.79 | DELTA: instantiating (2) with fresh symbol all_100_0 gives: % 29.93/4.79 | (6) vreduce(vt1) = all_100_0 & vOptTerm(all_100_0) & ! [v0: vTy] : ( ~ % 29.93/4.79 | (all_100_0 = vnoTerm) | ~ vTy(v0) | ~ vptchecksimple(vt1, v0) | % 29.93/4.79 | visValue(vt1)) % 29.93/4.79 | % 29.93/4.79 | ALPHA: (6) implies: % 29.93/4.79 | (7) vreduce(vt1) = all_100_0 % 29.93/4.79 | % 29.93/4.79 | DELTA: instantiating (4) with fresh symbols all_106_0, all_106_1, all_106_2 % 29.93/4.79 | gives: % 29.93/4.79 | (8) vreduce(all_106_1) = vnoTerm & vreduce(vt1) = all_106_2 & vSucc(vt1) = % 29.93/4.79 | all_106_1 & vTy(all_106_0) & vOptTerm(all_106_2) & vTerm(all_106_1) & % 29.93/4.79 | vptchecksimple(all_106_1, all_106_0) & visSomeTerm(all_106_2) & ~ % 29.93/4.79 | visValue(all_106_1) % 29.93/4.79 | % 29.93/4.79 | ALPHA: (8) implies: % 29.93/4.79 | (9) visSomeTerm(all_106_2) % 29.93/4.79 | (10) vSucc(vt1) = all_106_1 % 29.93/4.79 | (11) vreduce(vt1) = all_106_2 % 29.93/4.79 | (12) vreduce(all_106_1) = vnoTerm % 29.93/4.79 | % 29.93/4.79 | GROUND_INST: instantiating (5) with all_100_0, all_106_2, vt1, simplifying % 29.93/4.79 | with (7), (11) gives: % 29.93/4.79 | (13) all_106_2 = all_100_0 % 29.93/4.79 | % 29.93/4.79 | REDUCE: (9), (13) imply: % 29.93/4.79 | (14) visSomeTerm(all_100_0) % 29.93/4.79 | % 29.93/4.79 | GROUND_INST: instantiating (reduce-4) with vt1, all_106_1, simplifying with % 29.93/4.79 | (3), (10) gives: % 29.93/4.79 | (15) ? [v0: vOptTerm] : ? [v1: vOptTerm] : ? [v2: vTerm] : ? [v3: % 29.93/4.79 | vTerm] : ? [v4: vOptTerm] : (vreduce(vt1) = v0 & vOptTerm(v0) & ( ~ % 29.93/4.79 | visSomeTerm(v0) | (v4 = v1 & vreduce(all_106_1) = v1 & % 29.93/4.79 | vgetTerm(v0) = v2 & vsomeTerm(v3) = v1 & vSucc(v2) = v3 & % 29.93/4.79 | vOptTerm(v1) & vTerm(v3) & vTerm(v2)))) % 29.93/4.79 | % 29.93/4.79 | DELTA: instantiating (15) with fresh symbols all_131_0, all_131_1, all_131_2, % 29.93/4.79 | all_131_3, all_131_4 gives: % 29.93/4.79 | (16) vreduce(vt1) = all_131_4 & vOptTerm(all_131_4) & ( ~ % 29.93/4.79 | visSomeTerm(all_131_4) | (all_131_0 = all_131_3 & vreduce(all_106_1) % 29.93/4.79 | = all_131_3 & vgetTerm(all_131_4) = all_131_2 & % 29.93/4.79 | vsomeTerm(all_131_1) = all_131_3 & vSucc(all_131_2) = all_131_1 & % 29.93/4.79 | vOptTerm(all_131_3) & vTerm(all_131_1) & vTerm(all_131_2))) % 29.93/4.79 | % 29.93/4.79 | ALPHA: (16) implies: % 29.93/4.80 | (17) vreduce(vt1) = all_131_4 % 29.93/4.80 | (18) ~ visSomeTerm(all_131_4) | (all_131_0 = all_131_3 & % 29.93/4.80 | vreduce(all_106_1) = all_131_3 & vgetTerm(all_131_4) = all_131_2 & % 29.93/4.80 | vsomeTerm(all_131_1) = all_131_3 & vSucc(all_131_2) = all_131_1 & % 29.93/4.80 | vOptTerm(all_131_3) & vTerm(all_131_1) & vTerm(all_131_2)) % 29.93/4.80 | % 29.93/4.80 | GROUND_INST: instantiating (5) with all_100_0, all_131_4, vt1, simplifying % 29.93/4.80 | with (7), (17) gives: % 29.93/4.80 | (19) all_131_4 = all_100_0 % 29.93/4.80 | % 29.93/4.80 | BETA: splitting (18) gives: % 29.93/4.80 | % 29.93/4.80 | Case 1: % 30.53/4.80 | | % 30.53/4.80 | | (20) ~ visSomeTerm(all_131_4) % 30.53/4.80 | | % 30.53/4.80 | | REDUCE: (19), (20) imply: % 30.53/4.80 | | (21) ~ visSomeTerm(all_100_0) % 30.53/4.80 | | % 30.53/4.80 | | PRED_UNIFY: (14), (21) imply: % 30.53/4.80 | | (22) $false % 30.53/4.80 | | % 30.53/4.80 | | CLOSE: (22) is inconsistent. % 30.53/4.80 | | % 30.53/4.80 | Case 2: % 30.53/4.80 | | % 30.53/4.80 | | (23) all_131_0 = all_131_3 & vreduce(all_106_1) = all_131_3 & % 30.53/4.80 | | vgetTerm(all_131_4) = all_131_2 & vsomeTerm(all_131_1) = all_131_3 & % 30.53/4.80 | | vSucc(all_131_2) = all_131_1 & vOptTerm(all_131_3) & % 30.53/4.80 | | vTerm(all_131_1) & vTerm(all_131_2) % 30.53/4.80 | | % 30.53/4.80 | | ALPHA: (23) implies: % 30.53/4.80 | | (24) vTerm(all_131_1) % 30.53/4.80 | | (25) vsomeTerm(all_131_1) = all_131_3 % 30.53/4.80 | | (26) vreduce(all_106_1) = all_131_3 % 30.53/4.80 | | % 30.53/4.80 | | GROUND_INST: instantiating (5) with vnoTerm, all_131_3, all_106_1, % 30.53/4.80 | | simplifying with (12), (26) gives: % 30.53/4.80 | | (27) all_131_3 = vnoTerm % 30.53/4.80 | | % 30.53/4.80 | | REDUCE: (25), (27) imply: % 30.53/4.80 | | (28) vsomeTerm(all_131_1) = vnoTerm % 30.53/4.80 | | % 30.53/4.80 | | GROUND_INST: instantiating (isSomeTerm-1) with all_131_1, vnoTerm, % 30.53/4.80 | | simplifying with (1), (24), (28) gives: % 30.53/4.80 | | (29) $false % 30.53/4.80 | | % 30.53/4.80 | | CLOSE: (29) is inconsistent. % 30.53/4.80 | | % 30.53/4.80 | End of split % 30.53/4.80 | % 30.53/4.80 End of proof % 30.53/4.80 % SZS output end Proof for theBenchmark % 30.53/4.80 % 30.53/4.80 4209ms %------------------------------------------------------------------------------