%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM243_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 : n007.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 14.76s 3.03s % Output : Proof 21.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.28 % Problem : COM243_1 : TPTP v9.3.0. Released v9.3.0. % 0.11/0.29 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.52 % Computer : n007.cluster.edu % 0.15/0.52 % Model : x86_64 x86_64 % 0.15/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.52 % Memory : 8042.1875MB % 0.15/0.52 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.52 % CPULimit : 300 % 0.15/0.52 % WCLimit : 300 % 0.15/0.52 % DateTime : Mon May 4 19:31:09 EDT 2026 % 0.15/0.52 % CPUTime : % 0.41/0.79 ________ _____ % 0.41/0.79 ___ __ \_________(_)________________________________ % 0.41/0.79 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.41/0.79 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.41/0.79 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.41/0.79 % 0.41/0.79 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.41/0.79 (2023-06-19) % 0.41/0.79 % 0.41/0.79 (c) Philipp Rümmer, 2009-2023 % 0.41/0.79 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.41/0.79 Amanda Stjerna. % 0.41/0.79 Free software under BSD-3-Clause. % 0.41/0.79 % 0.41/0.79 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.41/0.79 % 0.41/0.79 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.64/0.81 Running up to 7 provers in parallel. % 0.64/0.82 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.82 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.82 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.82 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.82 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.82 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.82 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.08/1.66 Prover 1: Preprocessing ... % 5.08/1.66 Prover 4: Preprocessing ... % 5.08/1.70 Prover 5: Preprocessing ... % 5.08/1.70 Prover 0: Preprocessing ... % 5.08/1.70 Prover 3: Preprocessing ... % 5.08/1.70 Prover 2: Preprocessing ... % 5.08/1.70 Prover 6: Preprocessing ... % 14.76/2.92 Prover 1: Warning: ignoring some quantifiers % 14.76/2.93 Prover 5: Constructing countermodel ... % 14.76/2.94 Prover 3: Warning: ignoring some quantifiers % 14.76/2.96 Prover 3: Constructing countermodel ... % 14.76/2.97 Prover 6: Proving ... % 14.76/3.01 Prover 1: Constructing countermodel ... % 14.76/3.02 Prover 5: proved (2193ms) % 14.76/3.03 % 14.76/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.76/3.03 % 15.77/3.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.77/3.04 Prover 6: stopped % 15.77/3.05 Prover 3: stopped % 15.77/3.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.77/3.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.70/3.34 Prover 8: Preprocessing ... % 17.70/3.36 Prover 4: Warning: ignoring some quantifiers % 17.70/3.38 Prover 0: Proving ... % 17.70/3.39 Prover 7: Preprocessing ... % 17.70/3.39 Prover 10: Preprocessing ... % 17.70/3.39 Prover 0: stopped % 17.70/3.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.47/3.43 Prover 4: Constructing countermodel ... % 18.47/3.48 Prover 1: Found proof (size 10) % 18.47/3.48 Prover 1: proved (2672ms) % 19.24/3.52 Prover 4: stopped % 19.24/3.57 Prover 10: stopped % 19.24/3.58 Prover 7: stopped % 20.03/3.62 Prover 11: Preprocessing ... % 20.73/3.70 Prover 2: Proving ... % 20.73/3.71 Prover 2: stopped % 20.73/3.74 Prover 11: stopped % 21.27/3.82 Prover 8: Warning: ignoring some quantifiers % 21.27/3.85 Prover 8: Constructing countermodel ... % 21.27/3.89 Prover 8: stopped % 21.27/3.89 % 21.27/3.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.27/3.89 % 21.27/3.89 % SZS output start Proof for theBenchmark % 21.74/3.90 Assumptions after simplification: % 21.74/3.90 --------------------------------- % 21.74/3.90 % 21.74/3.90 (Progress-True) % 21.74/3.93 vOptTerm(vnoTerm) & vTerm(vTrue) & ? [v0: any] : ? [v1: vOptTerm] : % 21.74/3.93 (vreduce(vTrue) = v1 & visValue(vTrue) = v0 & vOptTerm(v1) & ? [v2: vTy] : % 21.74/3.93 (v1 = vnoTerm & ~ (v0 = 0) & vptchecksimple(vTrue, v2) = 0 & vTy(v2))) % 21.74/3.93 % 21.74/3.93 (isValue-0) % 21.74/3.94 visValue(vTrue) = 0 & vTerm(vTrue) % 21.74/3.94 % 21.74/3.94 (function-axioms) % 21.74/3.95 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : ! [v4: % 21.74/3.95 vTerm] : (v1 = v0 | ~ (vIfelse(v4, v3, v2) = v1) | ~ (vIfelse(v4, v3, v2) % 21.74/3.95 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.74/3.95 vTy] : ! [v3: vTerm] : (v1 = v0 | ~ (vptchecksimple(v3, v2) = v1) | ~ % 21.74/3.95 (vptchecksimple(v3, v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: % 21.74/3.95 vTerm] : ! [v3: vTerm] : (v1 = v0 | ~ (vplusop(v3, v2) = v1) | ~ % 21.74/3.95 (vplusop(v3, v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : % 21.74/3.95 ! [v3: vTerm] : (v1 = v0 | ~ (vPlus(v3, v2) = v1) | ~ (vPlus(v3, v2) = v0)) % 21.74/3.95 & ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 21.74/3.95 (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: MultipleValueBool] : % 21.74/3.95 ! [v1: MultipleValueBool] : ! [v2: vOptTerm] : (v1 = v0 | ~ (visSomeTerm(v2) % 21.74/3.95 = v1) | ~ (visSomeTerm(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.74/3.95 MultipleValueBool] : ! [v2: vTerm] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 21.74/3.95 (visValue(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.74/3.95 MultipleValueBool] : ! [v2: vTerm] : (v1 = v0 | ~ (visNV(v2) = v1) | ~ % 21.74/3.95 (visNV(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : % 21.74/3.95 (v1 = v0 | ~ (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) & ! [v0: % 21.74/3.95 vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 21.74/3.95 (vsomeTerm(v2) = v1) | ~ (vsomeTerm(v2) = v0)) & ! [v0: vTerm] : ! [v1: % 21.74/3.95 vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vIszero(v2) = v1) | ~ (vIszero(v2) % 21.74/3.95 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 21.74/3.95 (vPred(v2) = v1) | ~ (vPred(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : % 21.74/3.95 ! [v2: vTerm] : (v1 = v0 | ~ (vSucc(v2) = v1) | ~ (vSucc(v2) = v0)) % 21.74/3.95 % 21.74/3.95 Further assumptions not needed in the proof: % 21.74/3.95 -------------------------------------------- % 21.74/3.95 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 21.74/3.95 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 21.74/3.95 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 21.74/3.95 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 21.74/3.95 DIFF-Succ-Plus, DIFF-Succ-Pred, DIFF-True-False, DIFF-True-Ifelse, % 21.74/3.95 DIFF-True-Iszero, DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, % 21.74/3.95 DIFF-True-Zero, DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, % 21.74/3.95 DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, % 21.74/3.95 EQ-Succ, EQ-someTerm, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, % 21.74/3.95 TPred_inv1, TPred_inv2, TSucc, TSucc_inv1, TSucc_inv2, TZero, TZero_inv, Tfalse, % 21.74/3.95 Tif, Tif_inv1, Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, % 21.74/3.95 dom-OptTerm, dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, % 21.74/3.95 isNV-false-INV, isNV-true-INV, isSomeTerm-0, isSomeTerm-1, isSomeTerm-false-INV, % 21.74/3.95 isSomeTerm-true-INV, isValue-1, isValue-2, isValue-false-INV, isValue-true-INV, % 21.74/3.95 plusop-0, plusop-1, plusop-2, plusop-INV, reduce-0, reduce-1, reduce-10, % 21.74/3.95 reduce-11, reduce-12, reduce-13, reduce-14, reduce-15, reduce-16, reduce-17, % 21.74/3.95 reduce-18, reduce-19, reduce-2, reduce-20, reduce-21, reduce-22, reduce-23, % 21.74/3.95 reduce-3, reduce-4, reduce-5, reduce-6, reduce-7, reduce-8, reduce-9, reduce-INV % 21.74/3.95 % 21.74/3.95 Those formulas are unsatisfiable: % 21.74/3.95 --------------------------------- % 21.74/3.95 % 21.74/3.95 Begin of proof % 21.74/3.95 | % 21.74/3.95 | ALPHA: (isValue-0) implies: % 21.74/3.95 | (1) visValue(vTrue) = 0 % 21.74/3.95 | % 21.74/3.95 | ALPHA: (Progress-True) implies: % 21.74/3.96 | (2) ? [v0: any] : ? [v1: vOptTerm] : (vreduce(vTrue) = v1 & % 21.74/3.96 | visValue(vTrue) = v0 & vOptTerm(v1) & ? [v2: vTy] : (v1 = vnoTerm & % 21.74/3.96 | ~ (v0 = 0) & vptchecksimple(vTrue, v2) = 0 & vTy(v2))) % 21.74/3.96 | % 21.74/3.96 | ALPHA: (function-axioms) implies: % 21.74/3.96 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.74/3.96 | vTerm] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) % 21.74/3.96 | % 21.74/3.96 | DELTA: instantiating (2) with fresh symbols all_103_0, all_103_1 gives: % 21.74/3.96 | (4) vreduce(vTrue) = all_103_0 & visValue(vTrue) = all_103_1 & % 21.74/3.96 | vOptTerm(all_103_0) & ? [v0: vTy] : (all_103_0 = vnoTerm & ~ % 21.74/3.96 | (all_103_1 = 0) & vptchecksimple(vTrue, v0) = 0 & vTy(v0)) % 21.74/3.96 | % 21.74/3.96 | ALPHA: (4) implies: % 21.74/3.96 | (5) visValue(vTrue) = all_103_1 % 21.74/3.96 | (6) ? [v0: vTy] : (all_103_0 = vnoTerm & ~ (all_103_1 = 0) & % 21.74/3.96 | vptchecksimple(vTrue, v0) = 0 & vTy(v0)) % 21.74/3.96 | % 21.74/3.96 | DELTA: instantiating (6) with fresh symbol all_112_0 gives: % 21.74/3.96 | (7) all_103_0 = vnoTerm & ~ (all_103_1 = 0) & vptchecksimple(vTrue, % 21.74/3.96 | all_112_0) = 0 & vTy(all_112_0) % 21.74/3.96 | % 21.74/3.96 | ALPHA: (7) implies: % 21.74/3.96 | (8) ~ (all_103_1 = 0) % 21.74/3.96 | % 21.74/3.96 | GROUND_INST: instantiating (3) with 0, all_103_1, vTrue, simplifying with (1), % 21.74/3.96 | (5) gives: % 21.74/3.96 | (9) all_103_1 = 0 % 21.74/3.96 | % 21.74/3.96 | REDUCE: (8), (9) imply: % 21.74/3.96 | (10) $false % 21.74/3.97 | % 21.74/3.97 | CLOSE: (10) is inconsistent. % 21.74/3.97 | % 21.74/3.97 End of proof % 21.74/3.97 % SZS output end Proof for theBenchmark % 21.74/3.97 % 21.74/3.97 3172ms %------------------------------------------------------------------------------