%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM836+1 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 : Thu Aug 31 11:50:17 EDT 2023 % Result : Theorem 6.84s 1.77s % Output : Proof 8.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM836+1 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n026.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 08:52:32 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.67 Running up to 7 provers in parallel. % 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.68/1.17 Prover 4: Preprocessing ... % 2.68/1.17 Prover 1: Preprocessing ... % 3.10/1.22 Prover 2: Preprocessing ... % 3.10/1.22 Prover 3: Preprocessing ... % 3.10/1.22 Prover 5: Preprocessing ... % 3.10/1.22 Prover 6: Preprocessing ... % 3.10/1.23 Prover 0: Preprocessing ... % 5.54/1.57 Prover 1: Warning: ignoring some quantifiers % 5.54/1.57 Prover 4: Warning: ignoring some quantifiers % 5.54/1.59 Prover 1: Constructing countermodel ... % 5.54/1.59 Prover 4: Constructing countermodel ... % 5.54/1.59 Prover 6: Proving ... % 5.54/1.60 Prover 3: Warning: ignoring some quantifiers % 5.54/1.61 Prover 3: Constructing countermodel ... % 5.91/1.61 Prover 5: Proving ... % 5.91/1.62 Prover 0: Proving ... % 5.91/1.65 Prover 2: Proving ... % 6.84/1.77 Prover 0: proved (1085ms) % 6.84/1.77 % 6.84/1.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.84/1.77 % 6.84/1.77 Prover 3: stopped % 6.84/1.78 Prover 2: stopped % 6.84/1.78 Prover 5: stopped % 7.21/1.80 Prover 6: stopped % 7.21/1.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.21/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.21/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.21/1.80 Prover 4: Found proof (size 21) % 7.21/1.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.21/1.80 Prover 4: proved (1106ms) % 7.21/1.80 Prover 1: stopped % 7.21/1.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.21/1.81 Prover 7: Preprocessing ... % 7.21/1.82 Prover 10: Preprocessing ... % 7.21/1.82 Prover 8: Preprocessing ... % 7.21/1.83 Prover 11: Preprocessing ... % 7.21/1.84 Prover 7: stopped % 7.21/1.84 Prover 13: Preprocessing ... % 7.65/1.85 Prover 10: stopped % 7.72/1.86 Prover 11: stopped % 7.72/1.87 Prover 13: stopped % 7.72/1.90 Prover 8: Warning: ignoring some quantifiers % 8.00/1.91 Prover 8: Constructing countermodel ... % 8.00/1.92 Prover 8: stopped % 8.00/1.92 % 8.00/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.00/1.92 % 8.00/1.93 % SZS output start Proof for theBenchmark % 8.00/1.93 Assumptions after simplification: % 8.00/1.93 --------------------------------- % 8.00/1.93 % 8.00/1.93 (ass(cond(61, 0), 0)) % 8.20/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v1, v0) = v2) | ~ $i(v1) % 8.20/1.96 | ~ $i(v0) | (vplus(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : % 8.20/1.96 ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (vplus(v1, v0) % 8.20/1.96 = v2 & $i(v2))) % 8.20/1.96 % 8.20/1.96 (ass(cond(goal(88), 0), 2)) % 8.20/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vplus(v1, v3) = % 8.20/1.96 v0) | ~ (vplus(v0, v2) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.20/1.96 $i(v0)) % 8.20/1.96 % 8.20/1.96 (def(cond(conseq(axiom(3)), 11), 1)) % 8.20/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 8.20/1.96 (vplus(v0, v3) = v1) | ~ (greater(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | % 8.20/1.96 ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ % 8.20/1.96 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 8.20/1.96 % 8.20/1.96 (def(cond(conseq(axiom(3)), 12), 1)) % 8.20/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 8.20/1.96 (less(v1, v0) = v2) | ~ (vplus(v1, v3) = v0) | ~ $i(v3) | ~ $i(v1) | ~ % 8.20/1.96 $i(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (less(v1, v0) = 0) | ~ $i(v1) | % 8.20/1.96 ~ $i(v0) | ? [v2: $i] : (vplus(v1, v2) = v0 & $i(v2))) % 8.20/1.96 % 8.20/1.96 (dis(ex(cond(conseq(131), 0), 0))) % 8.20/1.96 $i(vd204) & $i(vd203) & ? [v0: any] : (greater(vd203, vd204) = v0 & ( ~ (v0 = % 8.20/1.96 0) | ~ (vd204 = vd203))) % 8.20/1.96 % 8.20/1.96 (dis(ex(cond(conseq(131), 0), 1))) % 8.20/1.97 less(vd203, vd204) = 0 & greater(vd203, vd204) = 0 & $i(vd204) & $i(vd203) % 8.20/1.97 % 8.20/1.97 (function-axioms) % 8.20/1.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.20/1.97 [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! % 8.20/1.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, % 8.20/1.97 v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.20/1.97 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.20/1.97 (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.20/1.97 $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = % 8.20/1.97 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) % 8.20/1.97 = v1) | ~ (vsucc(v2) = v0)) % 8.20/1.97 % 8.20/1.97 Further assumptions not needed in the proof: % 8.20/1.97 -------------------------------------------- % 8.20/1.97 ass(cond(12, 0), 0), ass(cond(20, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), % 8.20/1.97 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(73, 0), 0), ass(cond(81, % 8.20/1.97 0), 0), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), 1), % 8.20/1.97 ass(cond(goal(88), 0), 3), qu(antec(axiom(3)), imp(antec(axiom(3)))), % 8.20/1.97 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 8.20/1.97 holds(definiens(29), 44, 0))), qu(restrictor(axiom(1)), % 8.20/1.97 holds(scope(axiom(1)), 2, 0)) % 8.20/1.97 % 8.20/1.97 Those formulas are unsatisfiable: % 8.20/1.97 --------------------------------- % 8.20/1.97 % 8.20/1.97 Begin of proof % 8.20/1.97 | % 8.20/1.97 | ALPHA: (dis(ex(cond(conseq(131), 0), 0))) implies: % 8.20/1.97 | (1) ? [v0: any] : (greater(vd203, vd204) = v0 & ( ~ (v0 = 0) | ~ (vd204 = % 8.20/1.97 | vd203))) % 8.20/1.97 | % 8.20/1.97 | ALPHA: (def(cond(conseq(axiom(3)), 12), 1)) implies: % 8.20/1.97 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (less(v1, v0) = 0) | ~ $i(v1) | ~ % 8.20/1.97 | $i(v0) | ? [v2: $i] : (vplus(v1, v2) = v0 & $i(v2))) % 8.20/1.97 | % 8.20/1.97 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies: % 8.20/1.97 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~ % 8.20/1.97 | $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 8.20/1.97 | % 8.20/1.97 | ALPHA: (ass(cond(61, 0), 0)) implies: % 8.20/1.98 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v1, v0) = v2) | ~ % 8.20/1.98 | $i(v1) | ~ $i(v0) | (vplus(v0, v1) = v2 & $i(v2))) % 8.20/1.98 | % 8.20/1.98 | ALPHA: (dis(ex(cond(conseq(131), 0), 1))) implies: % 8.20/1.98 | (5) $i(vd203) % 8.20/1.98 | (6) $i(vd204) % 8.20/1.98 | (7) greater(vd203, vd204) = 0 % 8.20/1.98 | (8) less(vd203, vd204) = 0 % 8.20/1.98 | % 8.20/1.98 | ALPHA: (function-axioms) implies: % 8.20/1.98 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.20/1.98 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 8.20/1.98 | v2) = v0)) % 8.20/1.98 | % 8.20/1.98 | DELTA: instantiating (1) with fresh symbol all_20_0 gives: % 8.20/1.98 | (10) greater(vd203, vd204) = all_20_0 & ( ~ (all_20_0 = 0) | ~ (vd204 = % 8.20/1.98 | vd203)) % 8.20/1.98 | % 8.20/1.98 | ALPHA: (10) implies: % 8.20/1.98 | (11) greater(vd203, vd204) = all_20_0 % 8.20/1.98 | % 8.20/1.98 | GROUND_INST: instantiating (9) with 0, all_20_0, vd204, vd203, simplifying % 8.20/1.98 | with (7), (11) gives: % 8.20/1.98 | (12) all_20_0 = 0 % 8.20/1.98 | % 8.20/1.98 | GROUND_INST: instantiating (3) with vd204, vd203, simplifying with (5), (6), % 8.20/1.98 | (7) gives: % 8.20/1.98 | (13) ? [v0: $i] : (vplus(vd204, v0) = vd203 & $i(v0)) % 8.20/1.98 | % 8.20/1.98 | GROUND_INST: instantiating (2) with vd204, vd203, simplifying with (5), (6), % 8.20/1.98 | (8) gives: % 8.20/1.98 | (14) ? [v0: $i] : (vplus(vd203, v0) = vd204 & $i(v0)) % 8.20/1.98 | % 8.20/1.98 | DELTA: instantiating (14) with fresh symbol all_38_0 gives: % 8.20/1.98 | (15) vplus(vd203, all_38_0) = vd204 & $i(all_38_0) % 8.20/1.98 | % 8.20/1.98 | ALPHA: (15) implies: % 8.20/1.98 | (16) $i(all_38_0) % 8.20/1.98 | (17) vplus(vd203, all_38_0) = vd204 % 8.20/1.98 | % 8.20/1.98 | DELTA: instantiating (13) with fresh symbol all_40_0 gives: % 8.20/1.98 | (18) vplus(vd204, all_40_0) = vd203 & $i(all_40_0) % 8.20/1.98 | % 8.20/1.98 | ALPHA: (18) implies: % 8.20/1.98 | (19) $i(all_40_0) % 8.20/1.98 | (20) vplus(vd204, all_40_0) = vd203 % 8.20/1.98 | % 8.20/1.98 | GROUND_INST: instantiating (4) with all_38_0, vd203, vd204, simplifying with % 8.20/1.98 | (5), (16), (17) gives: % 8.20/1.98 | (21) vplus(all_38_0, vd203) = vd204 & $i(vd204) % 8.20/1.98 | % 8.20/1.99 | GROUND_INST: instantiating (ass(cond(goal(88), 0), 2)) with vd203, vd204, % 8.20/1.99 | all_38_0, all_40_0, simplifying with (5), (6), (16), (17), (19), % 8.20/1.99 | (20) gives: % 8.20/1.99 | (22) $false % 8.20/1.99 | % 8.20/1.99 | CLOSE: (22) is inconsistent. % 8.20/1.99 | % 8.20/1.99 End of proof % 8.20/1.99 % SZS output end Proof for theBenchmark % 8.20/1.99 % 8.20/1.99 1333ms %------------------------------------------------------------------------------