%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM212_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 : n015.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 06:21:35 PM UTC 2026 % Result : Theorem 21.10s 3.50s % Output : Proof 26.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM212_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.34 % Computer : n015.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Mon May 4 18:45:01 EDT 2026 % 0.15/0.34 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.63 Running up to 7 provers in parallel. % 0.70/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.94/1.50 Prover 4: Preprocessing ... % 5.94/1.50 Prover 1: Preprocessing ... % 5.94/1.52 Prover 0: Preprocessing ... % 5.94/1.52 Prover 5: Preprocessing ... % 5.94/1.52 Prover 6: Preprocessing ... % 5.94/1.52 Prover 2: Preprocessing ... % 5.94/1.52 Prover 3: Preprocessing ... % 12.75/2.46 Prover 1: Warning: ignoring some quantifiers % 13.54/2.53 Prover 1: Constructing countermodel ... % 13.54/2.56 Prover 3: Warning: ignoring some quantifiers % 13.54/2.58 Prover 6: Proving ... % 13.54/2.59 Prover 3: Constructing countermodel ... % 15.04/2.70 Prover 5: Proving ... % 15.04/2.73 Prover 4: Warning: ignoring some quantifiers % 15.04/2.77 Prover 4: Constructing countermodel ... % 15.04/2.78 Prover 0: Proving ... % 17.41/3.03 Prover 2: Proving ... % 21.10/3.50 Prover 0: proved (2862ms) % 21.10/3.50 % 21.10/3.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.10/3.50 % 21.10/3.50 Prover 3: stopped % 21.10/3.51 Prover 2: stopped % 21.10/3.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.10/3.52 Prover 6: stopped % 21.10/3.52 Prover 5: stopped % 21.10/3.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.10/3.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.10/3.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.10/3.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.65/3.73 Prover 13: Preprocessing ... % 22.65/3.76 Prover 8: Preprocessing ... % 22.65/3.78 Prover 11: Preprocessing ... % 23.41/3.83 Prover 7: Preprocessing ... % 23.41/3.83 Prover 10: Preprocessing ... % 25.04/4.02 Prover 4: Found proof (size 16) % 25.04/4.03 Prover 4: proved (3385ms) % 25.04/4.03 Prover 1: stopped % 25.04/4.03 Prover 8: Warning: ignoring some quantifiers % 25.04/4.04 Prover 8: Constructing countermodel ... % 25.04/4.06 Prover 8: stopped % 25.04/4.09 Prover 10: Warning: ignoring some quantifiers % 25.04/4.11 Prover 10: Constructing countermodel ... % 25.79/4.12 Prover 10: stopped % 25.79/4.15 Prover 13: Warning: ignoring some quantifiers % 25.79/4.16 Prover 7: Warning: ignoring some quantifiers % 25.79/4.16 Prover 13: Constructing countermodel ... % 25.79/4.17 Prover 11: Warning: ignoring some quantifiers % 25.79/4.17 Prover 7: Constructing countermodel ... % 25.79/4.18 Prover 13: stopped % 25.79/4.18 Prover 11: Constructing countermodel ... % 25.79/4.18 Prover 7: stopped % 25.79/4.19 Prover 11: stopped % 25.79/4.19 % 25.79/4.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 25.79/4.19 % 25.79/4.20 % SZS output start Proof for theBenchmark % 26.26/4.20 Assumptions after simplification: % 26.26/4.20 --------------------------------- % 26.26/4.20 % 26.26/4.20 (DIFF-False-Succ) % 26.26/4.22 vTerm(vFalse) & ! [v0: vTerm] : ( ~ (vSucc(v0) = vFalse) | ~ vTerm(v0)) % 26.26/4.22 % 26.26/4.22 (DIFF-False-Zero) % 26.26/4.22 ~ (vFalse = vZero) & vTerm(vFalse) & vTerm(vZero) % 26.26/4.22 % 26.26/4.22 (isNV-true-INV) % 26.26/4.22 vTerm(vZero) & ! [v0: vTerm] : (v0 = vZero | ~ (visNV(v0) = 0) | ~ % 26.26/4.22 vTerm(v0) | ? [v1: vTerm] : (visNV(v1) = 0 & vSucc(v1) = v0 & vTerm(v1))) % 26.26/4.22 % 26.26/4.22 (isNVisNat-False) % 26.26/4.23 vTy(vNat) & vTerm(vFalse) & ? [v0: int] : ( ~ (v0 = 0) & % 26.26/4.23 vptchecksimple(vFalse, vNat) = v0 & visNV(vFalse) = 0) % 26.26/4.23 % 26.26/4.23 Further assumptions not needed in the proof: % 26.26/4.23 -------------------------------------------- % 26.26/4.23 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 26.26/4.23 DIFF-False-Pred, DIFF-Ifelse-Iszero, DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, % 26.26/4.23 DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, DIFF-Iszero-Plus, DIFF-Pred-Iszero, % 26.26/4.23 DIFF-Pred-Plus, DIFF-Succ-Iszero, DIFF-Succ-Plus, DIFF-Succ-Pred, % 26.26/4.23 DIFF-True-False, DIFF-True-Ifelse, DIFF-True-Iszero, DIFF-True-Plus, % 26.26/4.23 DIFF-True-Pred, DIFF-True-Succ, DIFF-True-Zero, DIFF-Zero-Iszero, % 26.26/4.23 DIFF-Zero-Plus, DIFF-Zero-Pred, DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, % 26.26/4.23 EQ-Iszero, EQ-Plus, EQ-Pred, EQ-Succ, EQ-someTerm, TPlus, TPlus_inv0, % 26.26/4.23 TPlus_inv1, TPlus_inv2, TPred, TPred_inv1, TPred_inv2, TSucc, TSucc_inv1, % 26.26/4.23 TSucc_inv2, TZero, TZero_inv, Tfalse, Tif, Tif_inv1, Tif_inv2, Tif_inv3, % 26.26/4.23 Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, dom-OptTerm, dom-Term, dom-Ty, % 26.26/4.23 getTerm-0, isNV-0, isNV-1, isNV-2, isNV-false-INV, isSomeTerm-0, isSomeTerm-1, % 26.26/4.23 isSomeTerm-false-INV, isSomeTerm-true-INV, isValue-0, isValue-1, isValue-2, % 26.26/4.23 isValue-false-INV, isValue-true-INV, plusop-0, plusop-1, plusop-2, plusop-INV, % 26.26/4.23 reduce-0, reduce-1, reduce-10, reduce-11, reduce-12, reduce-13, reduce-14, % 26.26/4.23 reduce-15, reduce-16, reduce-17, reduce-18, reduce-19, reduce-2, reduce-20, % 26.26/4.23 reduce-21, reduce-22, reduce-23, reduce-3, reduce-4, reduce-5, reduce-6, % 26.26/4.23 reduce-7, reduce-8, reduce-9, reduce-INV % 26.26/4.23 % 26.26/4.23 Those formulas are unsatisfiable: % 26.26/4.23 --------------------------------- % 26.26/4.23 % 26.26/4.23 Begin of proof % 26.26/4.23 | % 26.26/4.23 | ALPHA: (DIFF-False-Zero) implies: % 26.26/4.23 | (1) ~ (vFalse = vZero) % 26.26/4.23 | % 26.26/4.23 | ALPHA: (DIFF-False-Succ) implies: % 26.26/4.23 | (2) ! [v0: vTerm] : ( ~ (vSucc(v0) = vFalse) | ~ vTerm(v0)) % 26.26/4.23 | % 26.26/4.23 | ALPHA: (isNV-true-INV) implies: % 26.26/4.23 | (3) ! [v0: vTerm] : (v0 = vZero | ~ (visNV(v0) = 0) | ~ vTerm(v0) | ? % 26.26/4.23 | [v1: vTerm] : (visNV(v1) = 0 & vSucc(v1) = v0 & vTerm(v1))) % 26.26/4.23 | % 26.26/4.23 | ALPHA: (isNVisNat-False) implies: % 26.26/4.23 | (4) vTerm(vFalse) % 26.26/4.23 | (5) ? [v0: int] : ( ~ (v0 = 0) & vptchecksimple(vFalse, vNat) = v0 & % 26.26/4.23 | visNV(vFalse) = 0) % 26.26/4.23 | % 26.26/4.23 | DELTA: instantiating (5) with fresh symbol all_98_0 gives: % 26.26/4.23 | (6) ~ (all_98_0 = 0) & vptchecksimple(vFalse, vNat) = all_98_0 & % 26.26/4.23 | visNV(vFalse) = 0 % 26.26/4.23 | % 26.26/4.23 | ALPHA: (6) implies: % 26.26/4.23 | (7) visNV(vFalse) = 0 % 26.26/4.23 | % 26.26/4.23 | GROUND_INST: instantiating (3) with vFalse, simplifying with (4), (7) gives: % 26.26/4.24 | (8) vFalse = vZero | ? [v0: vTerm] : (visNV(v0) = 0 & vSucc(v0) = vFalse & % 26.26/4.24 | vTerm(v0)) % 26.26/4.24 | % 26.26/4.24 | BETA: splitting (8) gives: % 26.26/4.24 | % 26.26/4.24 | Case 1: % 26.26/4.24 | | % 26.26/4.24 | | (9) vFalse = vZero % 26.26/4.24 | | % 26.26/4.24 | | REDUCE: (1), (9) imply: % 26.26/4.24 | | (10) $false % 26.26/4.24 | | % 26.26/4.24 | | CLOSE: (10) is inconsistent. % 26.26/4.24 | | % 26.26/4.24 | Case 2: % 26.26/4.24 | | % 26.26/4.24 | | (11) ? [v0: vTerm] : (visNV(v0) = 0 & vSucc(v0) = vFalse & vTerm(v0)) % 26.26/4.24 | | % 26.26/4.24 | | DELTA: instantiating (11) with fresh symbol all_182_0 gives: % 26.26/4.24 | | (12) visNV(all_182_0) = 0 & vSucc(all_182_0) = vFalse & vTerm(all_182_0) % 26.26/4.24 | | % 26.26/4.24 | | ALPHA: (12) implies: % 26.26/4.24 | | (13) vTerm(all_182_0) % 26.26/4.24 | | (14) vSucc(all_182_0) = vFalse % 26.26/4.24 | | % 26.26/4.24 | | GROUND_INST: instantiating (2) with all_182_0, simplifying with (13), (14) % 26.26/4.24 | | gives: % 26.26/4.24 | | (15) $false % 26.26/4.24 | | % 26.26/4.24 | | CLOSE: (15) is inconsistent. % 26.26/4.24 | | % 26.26/4.24 | End of split % 26.26/4.24 | % 26.26/4.24 End of proof % 26.26/4.24 % SZS output end Proof for theBenchmark % 26.26/4.24 % 26.26/4.24 3641ms %------------------------------------------------------------------------------