%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU155+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 17:42:50 EDT 2023 % Result : Theorem 4.61s 1.37s % Output : Proof 5.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU155+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Aug 24 01:10:13 EDT 2023 % 0.13/0.35 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.13/0.97 Prover 4: Preprocessing ... % 2.13/0.98 Prover 1: Preprocessing ... % 2.37/1.02 Prover 6: Preprocessing ... % 2.37/1.02 Prover 3: Preprocessing ... % 2.37/1.02 Prover 5: Preprocessing ... % 2.37/1.02 Prover 0: Preprocessing ... % 2.37/1.02 Prover 2: Preprocessing ... % 3.57/1.19 Prover 1: Warning: ignoring some quantifiers % 3.57/1.20 Prover 5: Proving ... % 3.57/1.20 Prover 2: Proving ... % 3.57/1.20 Prover 6: Proving ... % 3.57/1.20 Prover 3: Warning: ignoring some quantifiers % 3.57/1.21 Prover 4: Warning: ignoring some quantifiers % 3.57/1.22 Prover 1: Constructing countermodel ... % 3.57/1.22 Prover 0: Proving ... % 3.57/1.22 Prover 3: Constructing countermodel ... % 3.57/1.22 Prover 4: Constructing countermodel ... % 4.61/1.36 Prover 3: proved (722ms) % 4.61/1.37 % 4.61/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.61/1.37 % 4.61/1.37 Prover 5: stopped % 4.61/1.37 Prover 6: stopped % 4.61/1.38 Prover 2: stopped % 4.61/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.61/1.39 Prover 0: proved (732ms) % 4.61/1.39 % 4.61/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.61/1.39 % 4.61/1.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.61/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.61/1.39 Prover 7: Preprocessing ... % 4.61/1.39 Prover 10: Preprocessing ... % 4.61/1.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.61/1.39 Prover 8: Preprocessing ... % 4.61/1.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.61/1.40 Prover 13: Preprocessing ... % 4.61/1.40 Prover 11: Preprocessing ... % 4.61/1.41 Prover 10: Warning: ignoring some quantifiers % 4.61/1.42 Prover 7: Warning: ignoring some quantifiers % 4.61/1.42 Prover 4: Found proof (size 21) % 4.61/1.42 Prover 4: proved (783ms) % 4.61/1.42 Prover 1: stopped % 4.61/1.42 Prover 13: stopped % 4.61/1.43 Prover 7: Constructing countermodel ... % 4.61/1.43 Prover 7: stopped % 4.61/1.43 Prover 11: stopped % 4.61/1.43 Prover 10: Constructing countermodel ... % 4.61/1.44 Prover 10: stopped % 4.61/1.45 Prover 8: Warning: ignoring some quantifiers % 4.61/1.46 Prover 8: Constructing countermodel ... % 4.61/1.46 Prover 8: stopped % 4.61/1.46 % 4.61/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.61/1.46 % 4.61/1.46 % SZS output start Proof for theBenchmark % 4.61/1.47 Assumptions after simplification: % 4.61/1.47 --------------------------------- % 4.61/1.47 % 4.61/1.47 (d3_tarski) % 4.61/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.61/1.50 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 4.61/1.50 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 4.61/1.50 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 4.61/1.50 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 4.61/1.50 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 4.61/1.50 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 4.61/1.50 $i(v0) | in(v2, v1) = 0) % 4.61/1.50 % 4.61/1.50 (d4_tarski) % 4.61/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 % 4.61/1.51 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ~ % 4.61/1.51 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 4.61/1.51 in(v2, v4) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 4.61/1.51 : ! [v4: $i] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ % 4.61/1.51 (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 4.61/1.51 int] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 4.61/1.51 [v2: $i] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 4.61/1.51 | ~ $i(v0) | ? [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) & ? % 4.61/1.51 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~ % 4.61/1.51 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] % 4.61/1.51 : ? [v7: int] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ( ! % 4.61/1.51 [v8: $i] : ( ~ (in(v8, v1) = 0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = % 4.61/1.51 0) & in(v3, v8) = v9)) & ! [v8: $i] : ( ~ (in(v3, v8) = 0) | ~ % 4.61/1.51 $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, v1) = v9)))) & (v4 = 0 % 4.61/1.51 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) % 4.61/1.51 % 4.61/1.51 (l50_zfmisc_1) % 4.61/1.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 4.61/1.51 union(v1) = v2 & subset(v0, v2) = v3 & in(v0, v1) = 0 & $i(v2) & $i(v1) & % 4.61/1.51 $i(v0)) % 4.61/1.52 % 4.61/1.52 (function-axioms) % 4.61/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.61/1.52 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 4.61/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 4.61/1.52 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] % 4.61/1.52 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 4.61/1.52 v0)) % 4.61/1.52 % 4.61/1.52 Further assumptions not needed in the proof: % 4.61/1.52 -------------------------------------------- % 4.61/1.52 antisymmetry_r2_hidden, dt_k3_tarski, reflexivity_r1_tarski % 4.61/1.52 % 4.61/1.52 Those formulas are unsatisfiable: % 4.61/1.52 --------------------------------- % 4.61/1.52 % 4.61/1.52 Begin of proof % 4.61/1.52 | % 4.61/1.52 | ALPHA: (d3_tarski) implies: % 4.61/1.52 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 4.61/1.52 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 4.61/1.52 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 4.61/1.52 | % 4.61/1.52 | ALPHA: (d4_tarski) implies: % 4.61/1.53 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : % 4.61/1.53 | (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = % 4.61/1.53 | v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] % 4.61/1.53 | : ( ~ (v5 = 0) & in(v4, v0) = v5)) % 4.61/1.53 | % 4.61/1.53 | ALPHA: (function-axioms) implies: % 4.61/1.53 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.61/1.53 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.61/1.53 | % 4.61/1.53 | DELTA: instantiating (l50_zfmisc_1) with fresh symbols all_7_0, all_7_1, % 4.61/1.53 | all_7_2, all_7_3 gives: % 5.42/1.53 | (4) ~ (all_7_0 = 0) & union(all_7_2) = all_7_1 & subset(all_7_3, all_7_1) % 5.42/1.53 | = all_7_0 & in(all_7_3, all_7_2) = 0 & $i(all_7_1) & $i(all_7_2) & % 5.42/1.53 | $i(all_7_3) % 5.42/1.53 | % 5.42/1.53 | ALPHA: (4) implies: % 5.42/1.53 | (5) ~ (all_7_0 = 0) % 5.42/1.53 | (6) $i(all_7_3) % 5.42/1.53 | (7) $i(all_7_2) % 5.42/1.53 | (8) $i(all_7_1) % 5.42/1.53 | (9) in(all_7_3, all_7_2) = 0 % 5.42/1.53 | (10) subset(all_7_3, all_7_1) = all_7_0 % 5.42/1.53 | (11) union(all_7_2) = all_7_1 % 5.42/1.53 | % 5.42/1.53 | GROUND_INST: instantiating (1) with all_7_3, all_7_1, all_7_0, simplifying % 5.42/1.53 | with (6), (8), (10) gives: % 5.42/1.53 | (12) all_7_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 5.42/1.53 | all_7_1) = v1 & in(v0, all_7_3) = 0 & $i(v0)) % 5.42/1.53 | % 5.42/1.53 | BETA: splitting (12) gives: % 5.42/1.53 | % 5.42/1.54 | Case 1: % 5.42/1.54 | | % 5.42/1.54 | | (13) all_7_0 = 0 % 5.42/1.54 | | % 5.42/1.54 | | REDUCE: (5), (13) imply: % 5.42/1.54 | | (14) $false % 5.42/1.54 | | % 5.42/1.54 | | CLOSE: (14) is inconsistent. % 5.42/1.54 | | % 5.42/1.54 | Case 2: % 5.42/1.54 | | % 5.42/1.54 | | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_7_1) = v1 & % 5.42/1.54 | | in(v0, all_7_3) = 0 & $i(v0)) % 5.42/1.54 | | % 5.42/1.54 | | DELTA: instantiating (15) with fresh symbols all_22_0, all_22_1 gives: % 5.42/1.54 | | (16) ~ (all_22_0 = 0) & in(all_22_1, all_7_1) = all_22_0 & in(all_22_1, % 5.42/1.54 | | all_7_3) = 0 & $i(all_22_1) % 5.42/1.54 | | % 5.42/1.54 | | ALPHA: (16) implies: % 5.42/1.54 | | (17) ~ (all_22_0 = 0) % 5.42/1.54 | | (18) $i(all_22_1) % 5.42/1.54 | | (19) in(all_22_1, all_7_3) = 0 % 5.42/1.54 | | (20) in(all_22_1, all_7_1) = all_22_0 % 5.42/1.54 | | % 5.42/1.54 | | GROUND_INST: instantiating (2) with all_7_2, all_7_1, all_22_1, all_22_0, % 5.42/1.54 | | all_7_3, simplifying with (6), (7), (8), (11), (18), (19), (20) % 5.42/1.54 | | gives: % 5.42/1.54 | | (21) all_22_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_7_3, all_7_2) = % 5.42/1.54 | | v0) % 5.42/1.54 | | % 5.42/1.54 | | BETA: splitting (21) gives: % 5.42/1.54 | | % 5.42/1.54 | | Case 1: % 5.42/1.54 | | | % 5.42/1.54 | | | (22) all_22_0 = 0 % 5.42/1.54 | | | % 5.42/1.54 | | | REDUCE: (17), (22) imply: % 5.42/1.54 | | | (23) $false % 5.42/1.54 | | | % 5.42/1.54 | | | CLOSE: (23) is inconsistent. % 5.42/1.54 | | | % 5.42/1.54 | | Case 2: % 5.42/1.54 | | | % 5.42/1.54 | | | (24) ? [v0: int] : ( ~ (v0 = 0) & in(all_7_3, all_7_2) = v0) % 5.42/1.54 | | | % 5.42/1.54 | | | DELTA: instantiating (24) with fresh symbol all_35_0 gives: % 5.42/1.54 | | | (25) ~ (all_35_0 = 0) & in(all_7_3, all_7_2) = all_35_0 % 5.42/1.54 | | | % 5.42/1.54 | | | ALPHA: (25) implies: % 5.42/1.54 | | | (26) ~ (all_35_0 = 0) % 5.42/1.54 | | | (27) in(all_7_3, all_7_2) = all_35_0 % 5.42/1.54 | | | % 5.42/1.54 | | | GROUND_INST: instantiating (3) with 0, all_35_0, all_7_2, all_7_3, % 5.42/1.54 | | | simplifying with (9), (27) gives: % 5.42/1.54 | | | (28) all_35_0 = 0 % 5.42/1.54 | | | % 5.42/1.54 | | | REDUCE: (26), (28) imply: % 5.42/1.54 | | | (29) $false % 5.42/1.54 | | | % 5.42/1.54 | | | CLOSE: (29) is inconsistent. % 5.42/1.54 | | | % 5.42/1.54 | | End of split % 5.42/1.54 | | % 5.42/1.54 | End of split % 5.42/1.54 | % 5.42/1.54 End of proof % 5.42/1.54 % SZS output end Proof for theBenchmark % 5.42/1.54 % 5.42/1.54 926ms %------------------------------------------------------------------------------