%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM214_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 : n027.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 23.31s 3.75s % Output : Proof 35.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : COM214_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.07 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.07/0.26 % Computer : n027.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Mon May 4 18:48:49 EDT 2026 % 0.07/0.26 % CPUTime : % 0.37/0.49 ________ _____ % 0.37/0.49 ___ __ \_________(_)________________________________ % 0.37/0.49 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.37/0.49 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.37/0.49 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.37/0.49 % 0.37/0.49 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.37/0.49 (2023-06-19) % 0.37/0.49 % 0.37/0.49 (c) Philipp Rümmer, 2009-2023 % 0.37/0.49 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.37/0.49 Amanda Stjerna. % 0.37/0.49 Free software under BSD-3-Clause. % 0.37/0.49 % 0.37/0.49 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.37/0.49 % 0.37/0.49 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.37/0.50 Running up to 7 provers in parallel. % 0.37/0.51 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.37/0.51 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.37/0.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.37/0.51 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.37/0.51 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.37/0.51 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.37/0.51 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.80/1.44 Prover 1: Preprocessing ... % 5.80/1.45 Prover 4: Preprocessing ... % 5.80/1.48 Prover 3: Preprocessing ... % 5.80/1.48 Prover 6: Preprocessing ... % 5.80/1.48 Prover 0: Preprocessing ... % 5.80/1.48 Prover 5: Preprocessing ... % 5.80/1.48 Prover 2: Preprocessing ... % 14.92/2.62 Prover 1: Warning: ignoring some quantifiers % 14.92/2.70 Prover 3: Warning: ignoring some quantifiers % 15.70/2.71 Prover 1: Constructing countermodel ... % 15.70/2.72 Prover 3: Constructing countermodel ... % 15.70/2.77 Prover 6: Proving ... % 17.24/2.93 Prover 4: Warning: ignoring some quantifiers % 17.24/2.99 Prover 5: Proving ... % 18.24/3.05 Prover 4: Constructing countermodel ... % 18.24/3.05 Prover 0: Proving ... % 20.24/3.37 Prover 2: Proving ... % 23.31/3.74 Prover 5: proved (3231ms) % 23.31/3.75 % 23.31/3.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.31/3.75 % 23.31/3.75 Prover 0: stopped % 23.31/3.75 Prover 6: stopped % 23.31/3.75 Prover 3: stopped % 23.31/3.76 Prover 2: stopped % 23.31/3.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.31/3.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.31/3.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.31/3.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.31/3.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 25.84/4.07 Prover 13: Preprocessing ... % 25.84/4.10 Prover 11: Preprocessing ... % 25.84/4.12 Prover 8: Preprocessing ... % 26.65/4.14 Prover 10: Preprocessing ... % 26.65/4.16 Prover 7: Preprocessing ... % 29.35/4.54 Prover 8: Warning: ignoring some quantifiers % 30.12/4.60 Prover 8: Constructing countermodel ... % 30.12/4.60 Prover 7: Warning: ignoring some quantifiers % 30.12/4.64 Prover 10: Warning: ignoring some quantifiers % 30.12/4.66 Prover 10: Constructing countermodel ... % 30.12/4.66 Prover 7: Constructing countermodel ... % 30.12/4.67 Prover 13: Warning: ignoring some quantifiers % 30.92/4.71 Prover 13: Constructing countermodel ... % 31.64/4.81 Prover 11: Warning: ignoring some quantifiers % 31.64/4.83 Prover 11: Constructing countermodel ... % 35.53/5.31 Prover 7: Found proof (size 21) % 35.53/5.31 Prover 7: proved (1560ms) % 35.53/5.31 Prover 1: stopped % 35.53/5.31 Prover 11: stopped % 35.53/5.31 Prover 8: stopped % 35.53/5.31 Prover 10: stopped % 35.53/5.31 Prover 13: stopped % 35.53/5.31 Prover 4: stopped % 35.53/5.31 % 35.53/5.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 35.53/5.31 % 35.53/5.32 % SZS output start Proof for theBenchmark % 35.53/5.33 Assumptions after simplification: % 35.53/5.33 --------------------------------- % 35.53/5.33 % 35.53/5.34 (DIFF-False-Succ) % 35.53/5.36 vTerm(vFalse) & ! [v0: vTerm] : ( ~ (vSucc(v0) = vFalse) | ~ vTerm(v0)) % 35.53/5.36 % 35.53/5.36 (DIFF-False-Zero) % 35.53/5.36 ~ (vFalse = vZero) & vTerm(vFalse) & vTerm(vZero) % 35.53/5.36 % 35.53/5.36 (PlusPreservation-False) % 35.53/5.37 vTy(vNat) & vTerm(vFalse) & ? [v0: vTerm] : ? [v1: vTerm] : (vplusop(v0, % 35.53/5.37 vFalse) = v1 & vTerm(v1) & vTerm(v0) & vptchecksimple(v0, vNat) & % 35.53/5.37 vptchecksimple(vFalse, vNat) & ~ vptchecksimple(v1, vNat)) % 35.53/5.37 % 35.53/5.37 (plusop-2) % 35.53/5.37 vTerm(vZero) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v2 = v0 | % 35.53/5.37 v0 = vZero | ~ (vplusop(v1, v0) = v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? % 35.53/5.37 [v3: vTerm] : (vSucc(v3) = v0 & vTerm(v3))) % 35.53/5.37 % 35.53/5.37 Further assumptions not needed in the proof: % 35.53/5.37 -------------------------------------------- % 35.53/5.37 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 35.53/5.37 DIFF-False-Pred, DIFF-Ifelse-Iszero, DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, % 35.53/5.37 DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, DIFF-Iszero-Plus, DIFF-Pred-Iszero, % 35.53/5.37 DIFF-Pred-Plus, DIFF-Succ-Iszero, DIFF-Succ-Plus, DIFF-Succ-Pred, % 35.53/5.37 DIFF-True-False, DIFF-True-Ifelse, DIFF-True-Iszero, DIFF-True-Plus, % 35.53/5.37 DIFF-True-Pred, DIFF-True-Succ, DIFF-True-Zero, DIFF-Zero-Iszero, % 35.53/5.37 DIFF-Zero-Plus, DIFF-Zero-Pred, DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, % 35.53/5.37 EQ-Iszero, EQ-Plus, EQ-Pred, EQ-Succ, EQ-someTerm, TPlus, TPlus_inv0, % 35.53/5.37 TPlus_inv1, TPlus_inv2, TPred, TPred_inv1, TPred_inv2, TSucc, TSucc_inv1, % 35.53/5.37 TSucc_inv2, TZero, TZero_inv, Tfalse, Tif, Tif_inv1, Tif_inv2, Tif_inv3, % 35.53/5.37 Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, dom-OptTerm, dom-Term, dom-Ty, % 35.53/5.37 getTerm-0, isNV-0, isNV-1, isNV-2, isNV-false-INV, isNV-true-INV, isSomeTerm-0, % 35.53/5.37 isSomeTerm-1, isSomeTerm-false-INV, isSomeTerm-true-INV, isValue-0, isValue-1, % 35.53/5.37 isValue-2, isValue-false-INV, isValue-true-INV, plusop-0, plusop-1, plusop-INV, % 35.53/5.37 reduce-0, reduce-1, reduce-10, reduce-11, reduce-12, reduce-13, reduce-14, % 35.53/5.37 reduce-15, reduce-16, reduce-17, reduce-18, reduce-19, reduce-2, reduce-20, % 35.53/5.37 reduce-21, reduce-22, reduce-23, reduce-3, reduce-4, reduce-5, reduce-6, % 35.53/5.37 reduce-7, reduce-8, reduce-9, reduce-INV % 35.53/5.37 % 35.53/5.37 Those formulas are unsatisfiable: % 35.53/5.37 --------------------------------- % 35.53/5.37 % 35.53/5.37 Begin of proof % 35.53/5.37 | % 35.53/5.37 | ALPHA: (DIFF-False-Zero) implies: % 35.53/5.37 | (1) ~ (vFalse = vZero) % 35.53/5.37 | % 35.53/5.37 | ALPHA: (DIFF-False-Succ) implies: % 35.53/5.37 | (2) ! [v0: vTerm] : ( ~ (vSucc(v0) = vFalse) | ~ vTerm(v0)) % 35.53/5.37 | % 35.53/5.37 | ALPHA: (plusop-2) implies: % 35.53/5.38 | (3) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v2 = v0 | v0 = % 35.53/5.38 | vZero | ~ (vplusop(v1, v0) = v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? % 35.53/5.38 | [v3: vTerm] : (vSucc(v3) = v0 & vTerm(v3))) % 35.53/5.38 | % 35.53/5.38 | ALPHA: (PlusPreservation-False) implies: % 35.53/5.38 | (4) vTerm(vFalse) % 35.53/5.38 | (5) ? [v0: vTerm] : ? [v1: vTerm] : (vplusop(v0, vFalse) = v1 & vTerm(v1) % 35.53/5.38 | & vTerm(v0) & vptchecksimple(v0, vNat) & vptchecksimple(vFalse, vNat) % 35.53/5.38 | & ~ vptchecksimple(v1, vNat)) % 35.53/5.38 | % 35.53/5.38 | DELTA: instantiating (5) with fresh symbols all_100_0, all_100_1 gives: % 35.53/5.38 | (6) vplusop(all_100_1, vFalse) = all_100_0 & vTerm(all_100_0) & % 35.53/5.38 | vTerm(all_100_1) & vptchecksimple(all_100_1, vNat) & % 35.53/5.38 | vptchecksimple(vFalse, vNat) & ~ vptchecksimple(all_100_0, vNat) % 35.53/5.38 | % 35.53/5.38 | ALPHA: (6) implies: % 35.53/5.38 | (7) ~ vptchecksimple(all_100_0, vNat) % 35.53/5.38 | (8) vptchecksimple(vFalse, vNat) % 35.53/5.38 | (9) vTerm(all_100_1) % 35.53/5.38 | (10) vplusop(all_100_1, vFalse) = all_100_0 % 35.53/5.38 | % 35.53/5.38 | PRED_UNIFY: (7), (8) imply: % 35.53/5.38 | (11) ~ (all_100_0 = vFalse) % 35.53/5.38 | % 35.53/5.38 | GROUND_INST: instantiating (3) with vFalse, all_100_1, all_100_0, simplifying % 35.53/5.38 | with (4), (9), (10) gives: % 35.53/5.38 | (12) all_100_0 = vFalse | vFalse = vZero | ? [v0: vTerm] : (vSucc(v0) = % 35.53/5.38 | vFalse & vTerm(v0)) % 35.53/5.38 | % 35.53/5.38 | BETA: splitting (12) gives: % 35.53/5.38 | % 35.53/5.38 | Case 1: % 35.53/5.38 | | % 35.53/5.39 | | (13) vFalse = vZero % 35.53/5.39 | | % 35.53/5.39 | | REDUCE: (1), (13) imply: % 35.53/5.39 | | (14) $false % 35.53/5.39 | | % 35.53/5.39 | | CLOSE: (14) is inconsistent. % 35.53/5.39 | | % 35.53/5.39 | Case 2: % 35.53/5.39 | | % 35.53/5.39 | | (15) all_100_0 = vFalse | ? [v0: vTerm] : (vSucc(v0) = vFalse & % 35.53/5.39 | | vTerm(v0)) % 35.53/5.39 | | % 35.53/5.39 | | BETA: splitting (15) gives: % 35.53/5.39 | | % 35.53/5.39 | | Case 1: % 35.53/5.39 | | | % 35.53/5.39 | | | (16) all_100_0 = vFalse % 35.53/5.39 | | | % 35.53/5.39 | | | REDUCE: (11), (16) imply: % 35.53/5.39 | | | (17) $false % 35.53/5.39 | | | % 35.53/5.39 | | | CLOSE: (17) is inconsistent. % 35.53/5.39 | | | % 35.53/5.39 | | Case 2: % 35.53/5.39 | | | % 35.53/5.39 | | | (18) ? [v0: vTerm] : (vSucc(v0) = vFalse & vTerm(v0)) % 35.53/5.39 | | | % 35.53/5.39 | | | DELTA: instantiating (18) with fresh symbol all_151_0 gives: % 35.53/5.39 | | | (19) vSucc(all_151_0) = vFalse & vTerm(all_151_0) % 35.53/5.39 | | | % 35.53/5.39 | | | ALPHA: (19) implies: % 35.53/5.39 | | | (20) vTerm(all_151_0) % 35.53/5.39 | | | (21) vSucc(all_151_0) = vFalse % 35.53/5.39 | | | % 35.53/5.39 | | | GROUND_INST: instantiating (2) with all_151_0, simplifying with (20), (21) % 35.53/5.39 | | | gives: % 35.53/5.39 | | | (22) $false % 35.53/5.39 | | | % 35.53/5.39 | | | CLOSE: (22) is inconsistent. % 35.53/5.39 | | | % 35.53/5.39 | | End of split % 35.53/5.39 | | % 35.53/5.39 | End of split % 35.53/5.39 | % 35.53/5.39 End of proof % 35.53/5.39 % SZS output end Proof for theBenchmark % 35.53/5.39 % 35.53/5.39 4896ms %------------------------------------------------------------------------------