%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM227_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 : n025.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 13.33s 2.51s % Output : Proof 19.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM227_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n025.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 19:09:28 EDT 2026 % 0.14/0.33 % CPUTime : % 0.52/0.59 ________ _____ % 0.52/0.59 ___ __ \_________(_)________________________________ % 0.52/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.59 % 0.52/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.59 (2023-06-19) % 0.52/0.59 % 0.52/0.59 (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 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.97/1.48 Prover 1: Preprocessing ... % 4.97/1.49 Prover 4: Preprocessing ... % 5.74/1.51 Prover 5: Preprocessing ... % 5.74/1.51 Prover 6: Preprocessing ... % 5.74/1.51 Prover 3: Preprocessing ... % 5.74/1.52 Prover 0: Preprocessing ... % 5.74/1.52 Prover 2: Preprocessing ... % 12.53/2.48 Prover 5: Constructing countermodel ... % 13.33/2.51 Prover 5: proved (1888ms) % 13.33/2.51 % 13.33/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.33/2.51 % 13.33/2.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.33/2.58 Prover 1: Warning: ignoring some quantifiers % 13.33/2.59 Prover 6: Proving ... % 13.33/2.59 Prover 3: Warning: ignoring some quantifiers % 13.33/2.59 Prover 6: stopped % 13.33/2.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.01/2.61 Prover 3: Constructing countermodel ... % 14.01/2.62 Prover 3: stopped % 14.01/2.64 Prover 1: Constructing countermodel ... % 14.01/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.01/2.69 Prover 7: Preprocessing ... % 14.78/2.72 Prover 8: Preprocessing ... % 14.78/2.76 Prover 10: Preprocessing ... % 14.78/2.78 Prover 4: Warning: ignoring some quantifiers % 15.54/2.83 Prover 4: Constructing countermodel ... % 16.33/2.98 Prover 0: Proving ... % 16.33/2.99 Prover 0: stopped % 16.33/3.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.17/3.03 Prover 1: Found proof (size 10) % 17.17/3.03 Prover 1: proved (2417ms) % 17.17/3.03 Prover 4: stopped % 17.95/3.17 Prover 2: Proving ... % 17.95/3.18 Prover 2: stopped % 17.95/3.18 Prover 11: Preprocessing ... % 17.95/3.18 Prover 7: Warning: ignoring some quantifiers % 18.54/3.21 Prover 8: Warning: ignoring some quantifiers % 18.54/3.21 Prover 7: Constructing countermodel ... % 18.54/3.22 Prover 10: Warning: ignoring some quantifiers % 18.54/3.23 Prover 8: Constructing countermodel ... % 18.54/3.24 Prover 7: stopped % 18.54/3.24 Prover 10: Constructing countermodel ... % 18.54/3.25 Prover 11: stopped % 18.54/3.25 Prover 8: stopped % 18.54/3.27 Prover 10: stopped % 18.54/3.27 % 18.54/3.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.54/3.27 % 18.54/3.27 % SZS output start Proof for theBenchmark % 18.54/3.28 Assumptions after simplification: % 18.54/3.28 --------------------------------- % 18.54/3.28 % 18.54/3.28 (Progress-False) % 19.18/3.30 vOptTerm(vnoTerm) & vTerm(vFalse) & ? [v0: any] : ? [v1: vOptTerm] : % 19.18/3.30 (vreduce(vFalse) = v1 & visValue(vFalse) = v0 & vOptTerm(v1) & ? [v2: vTy] : % 19.18/3.30 (v1 = vnoTerm & ~ (v0 = 0) & vptchecksimple(vFalse, v2) = 0 & vTy(v2))) % 19.18/3.30 % 19.18/3.30 (isValue-1) % 19.18/3.30 visValue(vFalse) = 0 & vTerm(vFalse) % 19.18/3.30 % 19.18/3.30 (function-axioms) % 19.18/3.31 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : ! [v4: % 19.18/3.31 vTerm] : (v1 = v0 | ~ (vIfelse(v4, v3, v2) = v1) | ~ (vIfelse(v4, v3, v2) % 19.18/3.31 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 19.18/3.31 vTy] : ! [v3: vTerm] : (v1 = v0 | ~ (vptchecksimple(v3, v2) = v1) | ~ % 19.18/3.31 (vptchecksimple(v3, v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: % 19.18/3.31 vTerm] : ! [v3: vTerm] : (v1 = v0 | ~ (vplusop(v3, v2) = v1) | ~ % 19.18/3.31 (vplusop(v3, v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : % 19.18/3.31 ! [v3: vTerm] : (v1 = v0 | ~ (vPlus(v3, v2) = v1) | ~ (vPlus(v3, v2) = v0)) % 19.18/3.31 & ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 19.18/3.31 (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: MultipleValueBool] : % 19.18/3.31 ! [v1: MultipleValueBool] : ! [v2: vOptTerm] : (v1 = v0 | ~ (visSomeTerm(v2) % 19.18/3.31 = v1) | ~ (visSomeTerm(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.18/3.31 MultipleValueBool] : ! [v2: vTerm] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 19.18/3.31 (visValue(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.18/3.31 MultipleValueBool] : ! [v2: vTerm] : (v1 = v0 | ~ (visNV(v2) = v1) | ~ % 19.18/3.31 (visNV(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : % 19.18/3.31 (v1 = v0 | ~ (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) & ! [v0: % 19.18/3.31 vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 19.18/3.31 (vsomeTerm(v2) = v1) | ~ (vsomeTerm(v2) = v0)) & ! [v0: vTerm] : ! [v1: % 19.18/3.31 vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vIszero(v2) = v1) | ~ (vIszero(v2) % 19.18/3.31 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 19.18/3.31 (vPred(v2) = v1) | ~ (vPred(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : % 19.18/3.31 ! [v2: vTerm] : (v1 = v0 | ~ (vSucc(v2) = v1) | ~ (vSucc(v2) = v0)) % 19.18/3.31 % 19.18/3.31 Further assumptions not needed in the proof: % 19.18/3.31 -------------------------------------------- % 19.18/3.31 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 19.18/3.31 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 19.18/3.31 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 19.18/3.31 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 19.18/3.31 DIFF-Succ-Plus, DIFF-Succ-Pred, DIFF-True-False, DIFF-True-Ifelse, % 19.18/3.31 DIFF-True-Iszero, DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, % 19.18/3.31 DIFF-True-Zero, DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, % 19.18/3.31 DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, % 19.18/3.31 EQ-Succ, EQ-someTerm, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, % 19.18/3.31 TPred_inv1, TPred_inv2, TSucc, TSucc_inv1, TSucc_inv2, TZero, TZero_inv, Tfalse, % 19.18/3.31 Tif, Tif_inv1, Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, % 19.18/3.31 dom-OptTerm, dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, % 19.18/3.31 isNV-false-INV, isNV-true-INV, isSomeTerm-0, isSomeTerm-1, isSomeTerm-false-INV, % 19.18/3.31 isSomeTerm-true-INV, isValue-0, isValue-2, isValue-false-INV, isValue-true-INV, % 19.18/3.31 plusop-0, plusop-1, plusop-2, plusop-INV, reduce-0, reduce-1, reduce-10, % 19.18/3.31 reduce-11, reduce-12, reduce-13, reduce-14, reduce-15, reduce-16, reduce-17, % 19.18/3.31 reduce-18, reduce-19, reduce-2, reduce-20, reduce-21, reduce-22, reduce-23, % 19.18/3.31 reduce-3, reduce-4, reduce-5, reduce-6, reduce-7, reduce-8, reduce-9, reduce-INV % 19.18/3.31 % 19.18/3.31 Those formulas are unsatisfiable: % 19.18/3.31 --------------------------------- % 19.18/3.31 % 19.18/3.31 Begin of proof % 19.18/3.32 | % 19.18/3.32 | ALPHA: (isValue-1) implies: % 19.18/3.32 | (1) visValue(vFalse) = 0 % 19.18/3.32 | % 19.18/3.32 | ALPHA: (Progress-False) implies: % 19.18/3.32 | (2) ? [v0: any] : ? [v1: vOptTerm] : (vreduce(vFalse) = v1 & % 19.18/3.32 | visValue(vFalse) = v0 & vOptTerm(v1) & ? [v2: vTy] : (v1 = vnoTerm & % 19.18/3.32 | ~ (v0 = 0) & vptchecksimple(vFalse, v2) = 0 & vTy(v2))) % 19.18/3.32 | % 19.18/3.32 | ALPHA: (function-axioms) implies: % 19.18/3.32 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 19.18/3.32 | vTerm] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) % 19.18/3.32 | % 19.18/3.32 | DELTA: instantiating (2) with fresh symbols all_103_0, all_103_1 gives: % 19.18/3.32 | (4) vreduce(vFalse) = all_103_0 & visValue(vFalse) = all_103_1 & % 19.18/3.32 | vOptTerm(all_103_0) & ? [v0: vTy] : (all_103_0 = vnoTerm & ~ % 19.18/3.32 | (all_103_1 = 0) & vptchecksimple(vFalse, v0) = 0 & vTy(v0)) % 19.18/3.32 | % 19.18/3.32 | ALPHA: (4) implies: % 19.18/3.32 | (5) visValue(vFalse) = all_103_1 % 19.18/3.32 | (6) ? [v0: vTy] : (all_103_0 = vnoTerm & ~ (all_103_1 = 0) & % 19.18/3.32 | vptchecksimple(vFalse, v0) = 0 & vTy(v0)) % 19.18/3.32 | % 19.18/3.32 | DELTA: instantiating (6) with fresh symbol all_112_0 gives: % 19.18/3.32 | (7) all_103_0 = vnoTerm & ~ (all_103_1 = 0) & vptchecksimple(vFalse, % 19.18/3.32 | all_112_0) = 0 & vTy(all_112_0) % 19.18/3.32 | % 19.18/3.32 | ALPHA: (7) implies: % 19.18/3.32 | (8) ~ (all_103_1 = 0) % 19.18/3.32 | % 19.18/3.32 | GROUND_INST: instantiating (3) with 0, all_103_1, vFalse, simplifying with % 19.18/3.32 | (1), (5) gives: % 19.18/3.33 | (9) all_103_1 = 0 % 19.18/3.33 | % 19.18/3.33 | REDUCE: (8), (9) imply: % 19.18/3.33 | (10) $false % 19.18/3.33 | % 19.18/3.33 | CLOSE: (10) is inconsistent. % 19.18/3.33 | % 19.18/3.33 End of proof % 19.18/3.33 % SZS output end Proof for theBenchmark % 19.18/3.33 % 19.18/3.33 2731ms %------------------------------------------------------------------------------