%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN061+1 : TPTP v8.1.2. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 : Fri Sep 1 03:26:24 EDT 2023 % Result : Theorem 3.49s 1.17s % Output : Proof 4.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN061+1 : TPTP v8.1.2. Released v2.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n004.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 18:31:07 EDT 2023 % 0.20/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.53/0.93 Prover 1: Preprocessing ... % 1.53/0.93 Prover 4: Preprocessing ... % 2.10/0.98 Prover 2: Preprocessing ... % 2.10/0.98 Prover 6: Preprocessing ... % 2.10/0.98 Prover 3: Preprocessing ... % 2.10/0.98 Prover 0: Preprocessing ... % 2.10/0.98 Prover 5: Preprocessing ... % 2.61/1.05 Prover 2: Proving ... % 2.61/1.05 Prover 5: Proving ... % 2.61/1.07 Prover 1: Constructing countermodel ... % 2.61/1.07 Prover 6: Proving ... % 2.61/1.07 Prover 4: Constructing countermodel ... % 2.61/1.08 Prover 3: Constructing countermodel ... % 2.61/1.10 Prover 0: Proving ... % 3.08/1.13 Prover 3: gave up % 3.08/1.13 Prover 1: gave up % 3.08/1.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.08/1.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.08/1.15 Prover 7: Preprocessing ... % 3.08/1.16 Prover 8: Preprocessing ... % 3.49/1.17 Prover 2: proved (548ms) % 3.49/1.17 % 3.49/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.49/1.17 % 3.49/1.17 Prover 0: stopped % 3.49/1.18 Prover 5: stopped % 3.49/1.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.49/1.18 Prover 6: stopped % 3.49/1.18 Prover 7: Warning: ignoring some quantifiers % 3.49/1.18 Prover 10: Preprocessing ... % 3.49/1.18 Prover 7: Constructing countermodel ... % 3.49/1.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.49/1.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.49/1.19 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 3.49/1.20 Prover 16: Preprocessing ... % 3.49/1.21 Prover 11: Preprocessing ... % 3.49/1.21 Prover 13: Preprocessing ... % 3.49/1.21 Prover 8: Warning: ignoring some quantifiers % 3.49/1.22 Prover 16: Warning: ignoring some quantifiers % 3.49/1.22 Prover 10: Warning: ignoring some quantifiers % 3.49/1.22 Prover 16: Constructing countermodel ... % 3.49/1.23 Prover 10: Constructing countermodel ... % 3.49/1.23 Prover 13: Warning: ignoring some quantifiers % 3.49/1.23 Prover 7: gave up % 3.49/1.23 Prover 13: Constructing countermodel ... % 3.49/1.23 Prover 8: Constructing countermodel ... % 3.49/1.23 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 3.49/1.24 Prover 10: gave up % 3.49/1.24 Prover 19: Preprocessing ... % 3.49/1.24 Prover 13: gave up % 3.49/1.25 Prover 4: Found proof (size 20) % 3.49/1.25 Prover 4: proved (623ms) % 3.49/1.25 Prover 8: stopped % 3.49/1.25 Prover 16: stopped % 3.49/1.25 Prover 11: Constructing countermodel ... % 4.19/1.26 Prover 11: stopped % 4.19/1.27 Prover 19: Warning: ignoring some quantifiers % 4.19/1.28 Prover 19: Constructing countermodel ... % 4.19/1.28 Prover 19: stopped % 4.19/1.28 % 4.19/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.19/1.28 % 4.19/1.29 % SZS output start Proof for theBenchmark % 4.19/1.29 Assumptions after simplification: % 4.19/1.29 --------------------------------- % 4.19/1.29 % 4.19/1.29 (pel31) % 4.35/1.32 ! [v0: $i] : ( ~ (big_j(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 4.35/1.32 big_i(v0) = v1)) & ! [v0: $i] : ( ~ (big_i(v0) = 0) | ~ $i(v0) | ? [v1: % 4.35/1.32 int] : ( ~ (v1 = 0) & big_j(v0) = v1)) % 4.35/1.32 % 4.35/1.32 (pel31_1) % 4.35/1.33 ! [v0: $i] : ! [v1: any] : ( ~ (big_g(v0) = v1) | ~ $i(v0) | ? [v2: any] : % 4.35/1.33 ? [v3: any] : (big_f(v0) = v2 & big_h(v0) = v3 & ( ~ (v2 = 0) | ( ~ (v3 = % 4.35/1.33 0) & ~ (v1 = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ (big_h(v0) = % 4.35/1.33 v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (big_g(v0) = v3 & % 4.35/1.33 big_f(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ~ (v1 = 0))))) & ! [v0: % 4.35/1.33 $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: int] : ( ~ % 4.35/1.33 (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v1 & big_h(v0) = v2)) % 4.35/1.33 % 4.35/1.33 (pel31_2) % 4.35/1.33 ? [v0: $i] : (big_i(v0) = 0 & big_f(v0) = 0 & $i(v0)) % 4.35/1.33 % 4.35/1.33 (pel31_3) % 4.35/1.33 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_j(v0) = v1) | ~ $i(v0) | % 4.35/1.33 big_h(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_h(v0) = v1) % 4.35/1.33 | ~ $i(v0) | big_j(v0) = 0) % 4.35/1.33 % 4.35/1.33 (function-axioms) % 4.35/1.33 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 4.35/1.33 v0 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0)) & ! [v0: MultipleValueBool] % 4.35/1.33 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_i(v2) = v1) | % 4.35/1.33 ~ (big_i(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 4.35/1.33 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ % 4.35/1.33 (big_g(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 4.35/1.33 : ! [v2: $i] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! % 4.35/1.33 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 4.35/1.33 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0)) % 4.35/1.33 % 4.35/1.33 Those formulas are unsatisfiable: % 4.35/1.33 --------------------------------- % 4.35/1.33 % 4.35/1.33 Begin of proof % 4.35/1.34 | % 4.35/1.34 | ALPHA: (pel31_1) implies: % 4.35/1.34 | (1) ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: % 4.35/1.34 | int] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v1 & big_h(v0) = % 4.35/1.34 | v2)) % 4.35/1.34 | % 4.35/1.34 | ALPHA: (pel31_3) implies: % 4.35/1.34 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_h(v0) = v1) | ~ $i(v0) % 4.35/1.34 | | big_j(v0) = 0) % 4.35/1.34 | % 4.35/1.34 | ALPHA: (pel31) implies: % 4.35/1.34 | (3) ! [v0: $i] : ( ~ (big_i(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 4.35/1.34 | = 0) & big_j(v0) = v1)) % 4.35/1.34 | % 4.35/1.34 | ALPHA: (function-axioms) implies: % 4.35/1.34 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.35/1.34 | (v1 = v0 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0)) % 4.35/1.34 | % 4.35/1.34 | DELTA: instantiating (pel31_2) with fresh symbol all_6_0 gives: % 4.35/1.34 | (5) big_i(all_6_0) = 0 & big_f(all_6_0) = 0 & $i(all_6_0) % 4.35/1.34 | % 4.35/1.34 | ALPHA: (5) implies: % 4.35/1.34 | (6) $i(all_6_0) % 4.35/1.34 | (7) big_f(all_6_0) = 0 % 4.35/1.34 | (8) big_i(all_6_0) = 0 % 4.35/1.34 | % 4.35/1.35 | GROUND_INST: instantiating (1) with all_6_0, simplifying with (6), (7) gives: % 4.35/1.35 | (9) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 4.35/1.35 | big_g(all_6_0) = v0 & big_h(all_6_0) = v1) % 4.35/1.35 | % 4.35/1.35 | GROUND_INST: instantiating (3) with all_6_0, simplifying with (6), (8) gives: % 4.35/1.35 | (10) ? [v0: int] : ( ~ (v0 = 0) & big_j(all_6_0) = v0) % 4.35/1.35 | % 4.35/1.35 | DELTA: instantiating (10) with fresh symbol all_13_0 gives: % 4.35/1.35 | (11) ~ (all_13_0 = 0) & big_j(all_6_0) = all_13_0 % 4.35/1.35 | % 4.35/1.35 | ALPHA: (11) implies: % 4.35/1.35 | (12) ~ (all_13_0 = 0) % 4.35/1.35 | (13) big_j(all_6_0) = all_13_0 % 4.35/1.35 | % 4.35/1.35 | DELTA: instantiating (9) with fresh symbols all_15_0, all_15_1 gives: % 4.35/1.35 | (14) ~ (all_15_0 = 0) & ~ (all_15_1 = 0) & big_g(all_6_0) = all_15_1 & % 4.35/1.35 | big_h(all_6_0) = all_15_0 % 4.35/1.35 | % 4.35/1.35 | ALPHA: (14) implies: % 4.35/1.35 | (15) ~ (all_15_0 = 0) % 4.35/1.35 | (16) big_h(all_6_0) = all_15_0 % 4.35/1.35 | % 4.35/1.35 | GROUND_INST: instantiating (2) with all_6_0, all_15_0, simplifying with (6), % 4.35/1.35 | (16) gives: % 4.35/1.35 | (17) all_15_0 = 0 | big_j(all_6_0) = 0 % 4.35/1.35 | % 4.35/1.35 | BETA: splitting (17) gives: % 4.35/1.35 | % 4.35/1.35 | Case 1: % 4.35/1.35 | | % 4.35/1.35 | | (18) big_j(all_6_0) = 0 % 4.35/1.35 | | % 4.35/1.35 | | GROUND_INST: instantiating (4) with all_13_0, 0, all_6_0, simplifying with % 4.35/1.35 | | (13), (18) gives: % 4.35/1.35 | | (19) all_13_0 = 0 % 4.35/1.35 | | % 4.35/1.35 | | REDUCE: (12), (19) imply: % 4.35/1.35 | | (20) $false % 4.35/1.35 | | % 4.35/1.35 | | CLOSE: (20) is inconsistent. % 4.35/1.35 | | % 4.35/1.35 | Case 2: % 4.35/1.35 | | % 4.35/1.35 | | (21) all_15_0 = 0 % 4.35/1.35 | | % 4.35/1.35 | | REDUCE: (15), (21) imply: % 4.35/1.35 | | (22) $false % 4.35/1.35 | | % 4.35/1.35 | | CLOSE: (22) is inconsistent. % 4.35/1.35 | | % 4.35/1.35 | End of split % 4.35/1.35 | % 4.35/1.35 End of proof % 4.35/1.35 % SZS output end Proof for theBenchmark % 4.35/1.36 % 4.35/1.36 753ms %------------------------------------------------------------------------------