%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM213_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 : n018.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 22.63s 3.86s % Output : Proof 33.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM213_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n018.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon May 4 18:46:17 EDT 2026 % 0.16/0.34 % CPUTime : % 0.65/0.64 ________ _____ % 0.65/0.64 ___ __ \_________(_)________________________________ % 0.65/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.65/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.65/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.65/0.64 % 0.65/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.65/0.64 (2023-06-19) % 0.65/0.64 % 0.65/0.64 (c) Philipp Rümmer, 2009-2023 % 0.65/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.65/0.64 Amanda Stjerna. % 0.65/0.64 Free software under BSD-3-Clause. % 0.65/0.64 % 0.65/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.64 % 0.65/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.65 Running up to 7 provers in parallel. % 0.65/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.65/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.65/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.65/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.65/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.65/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.65/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.32/1.56 Prover 4: Preprocessing ... % 5.32/1.57 Prover 1: Preprocessing ... % 5.32/1.59 Prover 6: Preprocessing ... % 5.32/1.59 Prover 0: Preprocessing ... % 5.32/1.59 Prover 2: Preprocessing ... % 5.32/1.59 Prover 5: Preprocessing ... % 5.32/1.59 Prover 3: Preprocessing ... % 13.49/2.60 Prover 1: Warning: ignoring some quantifiers % 13.49/2.66 Prover 3: Warning: ignoring some quantifiers % 13.49/2.68 Prover 1: Constructing countermodel ... % 13.49/2.68 Prover 3: Constructing countermodel ... % 14.28/2.71 Prover 6: Proving ... % 15.75/2.90 Prover 4: Warning: ignoring some quantifiers % 15.75/2.92 Prover 5: Proving ... % 15.75/2.94 Prover 4: Constructing countermodel ... % 16.62/3.06 Prover 0: Proving ... % 17.98/3.28 Prover 2: Proving ... % 22.63/3.86 Prover 5: proved (3189ms) % 22.63/3.86 % 22.63/3.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.63/3.86 % 22.63/3.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.63/3.86 Prover 0: stopped % 22.63/3.87 Prover 3: stopped % 22.63/3.87 Prover 6: stopped % 22.63/3.88 Prover 2: stopped % 22.63/3.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.63/3.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.63/3.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.63/3.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.34/4.30 Prover 11: Preprocessing ... % 26.34/4.31 Prover 10: Preprocessing ... % 26.34/4.38 Prover 13: Preprocessing ... % 26.34/4.38 Prover 7: Preprocessing ... % 26.34/4.38 Prover 8: Preprocessing ... % 29.44/4.72 Prover 8: Warning: ignoring some quantifiers % 29.44/4.74 Prover 8: Constructing countermodel ... % 29.44/4.74 Prover 7: Warning: ignoring some quantifiers % 29.44/4.75 Prover 10: Warning: ignoring some quantifiers % 29.44/4.77 Prover 7: Constructing countermodel ... % 29.44/4.77 Prover 10: Constructing countermodel ... % 30.23/4.84 Prover 13: Warning: ignoring some quantifiers % 30.23/4.86 Prover 11: Warning: ignoring some quantifiers % 30.23/4.87 Prover 11: Constructing countermodel ... % 30.23/4.87 Prover 13: Constructing countermodel ... % 33.36/5.21 Prover 7: Found proof (size 16) % 33.36/5.21 Prover 7: proved (1351ms) % 33.36/5.22 Prover 1: stopped % 33.36/5.22 Prover 11: stopped % 33.36/5.22 Prover 10: stopped % 33.36/5.22 Prover 4: stopped % 33.36/5.22 Prover 13: stopped % 33.36/5.22 Prover 8: stopped % 33.36/5.22 % 33.36/5.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 33.36/5.22 % 33.36/5.23 % SZS output start Proof for theBenchmark % 33.36/5.23 Assumptions after simplification: % 33.36/5.23 --------------------------------- % 33.36/5.23 % 33.36/5.23 (DIFF-Succ-Pred) % 33.36/5.25 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vPred(v1) = v2) | ~ % 33.36/5.25 (vSucc(v0) = v2) | ~ vTerm(v1) | ~ vTerm(v0)) % 33.36/5.25 % 33.36/5.25 (TZero) % 33.36/5.25 vTy(vNat) & vTerm(vZero) & vptchecksimple(vZero, vNat) % 33.36/5.25 % 33.36/5.25 (isNV-true-INV) % 33.36/5.26 vTerm(vZero) & ! [v0: vTerm] : (v0 = vZero | ~ vTerm(v0) | ~ visNV(v0) | ? % 33.36/5.26 [v1: vTerm] : (vSucc(v1) = v0 & vTerm(v1) & visNV(v1))) % 33.36/5.26 % 33.36/5.26 (isNVisNat-Pred) % 33.36/5.26 vTy(vNat) & vTerm(vt1) & ? [v0: vTerm] : (vPred(vt1) = v0 & vTerm(v0) & % 33.36/5.26 visNV(v0) & ~ vptchecksimple(v0, vNat)) % 33.36/5.26 % 33.36/5.26 Further assumptions not needed in the proof: % 33.36/5.26 -------------------------------------------- % 33.36/5.26 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 33.36/5.26 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 33.36/5.26 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 33.36/5.26 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 33.36/5.26 DIFF-Succ-Plus, DIFF-True-False, DIFF-True-Ifelse, DIFF-True-Iszero, % 33.36/5.26 DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, DIFF-True-Zero, % 33.36/5.26 DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, DIFF-Zero-Succ, % 33.36/5.26 DIFF-noTerm-someTerm, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, EQ-Succ, % 33.36/5.26 EQ-someTerm, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, TPred_inv1, % 33.36/5.26 TPred_inv2, TSucc, TSucc_inv1, TSucc_inv2, TZero_inv, Tfalse, Tif, Tif_inv1, % 33.36/5.26 Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, dom-OptTerm, % 33.36/5.26 dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, isNV-false-INV, % 33.36/5.26 isNVisNat-Pred-IH0, isSomeTerm-0, isSomeTerm-1, isSomeTerm-false-INV, % 33.36/5.26 isSomeTerm-true-INV, isValue-0, isValue-1, isValue-2, isValue-false-INV, % 33.36/5.26 isValue-true-INV, plusop-0, plusop-1, plusop-2, plusop-INV, reduce-0, reduce-1, % 33.36/5.26 reduce-10, reduce-11, reduce-12, reduce-13, reduce-14, reduce-15, reduce-16, % 33.36/5.26 reduce-17, reduce-18, reduce-19, reduce-2, reduce-20, reduce-21, reduce-22, % 33.36/5.26 reduce-23, reduce-3, reduce-4, reduce-5, reduce-6, reduce-7, reduce-8, reduce-9, % 33.36/5.26 reduce-INV % 33.36/5.26 % 33.36/5.26 Those formulas are unsatisfiable: % 33.36/5.26 --------------------------------- % 33.36/5.26 % 33.36/5.26 Begin of proof % 33.36/5.26 | % 33.36/5.26 | ALPHA: (isNV-true-INV) implies: % 33.36/5.26 | (1) ! [v0: vTerm] : (v0 = vZero | ~ vTerm(v0) | ~ visNV(v0) | ? [v1: % 33.36/5.26 | vTerm] : (vSucc(v1) = v0 & vTerm(v1) & visNV(v1))) % 33.36/5.26 | % 33.36/5.26 | ALPHA: (TZero) implies: % 33.36/5.26 | (2) vptchecksimple(vZero, vNat) % 33.36/5.26 | % 33.36/5.26 | ALPHA: (isNVisNat-Pred) implies: % 33.36/5.26 | (3) vTerm(vt1) % 33.36/5.26 | (4) ? [v0: vTerm] : (vPred(vt1) = v0 & vTerm(v0) & visNV(v0) & ~ % 33.36/5.26 | vptchecksimple(v0, vNat)) % 33.36/5.26 | % 33.36/5.26 | DELTA: instantiating (4) with fresh symbol all_94_0 gives: % 33.36/5.26 | (5) vPred(vt1) = all_94_0 & vTerm(all_94_0) & visNV(all_94_0) & ~ % 33.36/5.26 | vptchecksimple(all_94_0, vNat) % 33.36/5.26 | % 33.36/5.26 | ALPHA: (5) implies: % 33.36/5.26 | (6) ~ vptchecksimple(all_94_0, vNat) % 33.36/5.26 | (7) visNV(all_94_0) % 33.36/5.26 | (8) vTerm(all_94_0) % 33.36/5.26 | (9) vPred(vt1) = all_94_0 % 33.36/5.26 | % 33.36/5.26 | PRED_UNIFY: (2), (6) imply: % 33.36/5.26 | (10) ~ (all_94_0 = vZero) % 33.36/5.26 | % 33.36/5.26 | GROUND_INST: instantiating (1) with all_94_0, simplifying with (7), (8) gives: % 33.36/5.27 | (11) all_94_0 = vZero | ? [v0: vTerm] : (vSucc(v0) = all_94_0 & vTerm(v0) % 33.36/5.27 | & visNV(v0)) % 33.36/5.27 | % 33.36/5.27 | BETA: splitting (11) gives: % 33.36/5.27 | % 33.36/5.27 | Case 1: % 33.36/5.27 | | % 33.36/5.27 | | (12) all_94_0 = vZero % 33.36/5.27 | | % 33.36/5.27 | | REDUCE: (10), (12) imply: % 33.36/5.27 | | (13) $false % 33.36/5.27 | | % 33.36/5.27 | | CLOSE: (13) is inconsistent. % 33.36/5.27 | | % 33.36/5.27 | Case 2: % 33.36/5.27 | | % 33.36/5.27 | | (14) ? [v0: vTerm] : (vSucc(v0) = all_94_0 & vTerm(v0) & visNV(v0)) % 33.36/5.27 | | % 33.36/5.27 | | DELTA: instantiating (14) with fresh symbol all_150_0 gives: % 33.36/5.27 | | (15) vSucc(all_150_0) = all_94_0 & vTerm(all_150_0) & visNV(all_150_0) % 33.36/5.27 | | % 33.36/5.27 | | ALPHA: (15) implies: % 33.36/5.27 | | (16) vTerm(all_150_0) % 33.36/5.27 | | (17) vSucc(all_150_0) = all_94_0 % 33.36/5.27 | | % 33.36/5.27 | | GROUND_INST: instantiating (DIFF-Succ-Pred) with all_150_0, vt1, all_94_0, % 33.36/5.27 | | simplifying with (3), (9), (16), (17) gives: % 33.36/5.27 | | (18) $false % 33.36/5.27 | | % 33.36/5.27 | | CLOSE: (18) is inconsistent. % 33.36/5.27 | | % 33.36/5.27 | End of split % 33.36/5.27 | % 33.36/5.27 End of proof % 33.36/5.27 % SZS output end Proof for theBenchmark % 33.36/5.27 % 33.36/5.27 4631ms %------------------------------------------------------------------------------