%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU134+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 : n032.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 17:42:41 EDT 2023 % Result : Theorem 3.97s 1.22s % Output : Proof 4.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SEU134+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.31 % Computer : n032.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Thu Aug 24 01:13:41 EDT 2023 % 0.10/0.31 % CPUTime : % 0.16/0.52 ________ _____ % 0.16/0.52 ___ __ \_________(_)________________________________ % 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.52 % 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.52 (2023-06-19) % 0.16/0.52 % 0.16/0.52 (c) Philipp Rümmer, 2009-2023 % 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.52 Amanda Stjerna. % 0.16/0.52 Free software under BSD-3-Clause. % 0.16/0.52 % 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.52 % 0.16/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.53 Running up to 7 provers in parallel. % 0.16/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.55 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.46/0.86 Prover 4: Preprocessing ... % 1.46/0.86 Prover 1: Preprocessing ... % 1.92/0.90 Prover 3: Preprocessing ... % 1.92/0.90 Prover 6: Preprocessing ... % 1.92/0.90 Prover 2: Preprocessing ... % 1.92/0.90 Prover 0: Preprocessing ... % 1.92/0.90 Prover 5: Preprocessing ... % 2.97/1.08 Prover 1: Warning: ignoring some quantifiers % 2.97/1.09 Prover 2: Proving ... % 2.97/1.09 Prover 3: Warning: ignoring some quantifiers % 2.97/1.09 Prover 5: Proving ... % 2.97/1.10 Prover 3: Constructing countermodel ... % 2.97/1.10 Prover 6: Proving ... % 2.97/1.10 Prover 4: Constructing countermodel ... % 2.97/1.10 Prover 1: Constructing countermodel ... % 2.97/1.10 Prover 0: Proving ... % 3.97/1.22 Prover 3: proved (677ms) % 3.97/1.22 % 3.97/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.97/1.22 % 3.97/1.23 Prover 6: stopped % 3.97/1.23 Prover 0: proved (690ms) % 3.97/1.23 % 3.97/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.97/1.23 % 3.97/1.23 Prover 2: stopped % 3.97/1.23 Prover 5: proved (687ms) % 3.97/1.23 % 3.97/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.97/1.23 % 3.97/1.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.97/1.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.97/1.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.97/1.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.97/1.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.97/1.25 Prover 10: Preprocessing ... % 3.97/1.26 Prover 13: Preprocessing ... % 3.97/1.26 Prover 11: Preprocessing ... % 3.97/1.26 Prover 7: Preprocessing ... % 4.67/1.27 Prover 8: Preprocessing ... % 4.67/1.27 Prover 4: Found proof (size 28) % 4.67/1.27 Prover 4: proved (728ms) % 4.67/1.28 Prover 1: stopped % 4.67/1.28 Prover 13: stopped % 4.85/1.30 Prover 11: stopped % 4.85/1.30 Prover 10: Warning: ignoring some quantifiers % 4.85/1.31 Prover 10: Constructing countermodel ... % 4.85/1.31 Prover 7: Warning: ignoring some quantifiers % 4.85/1.31 Prover 10: stopped % 4.85/1.31 Prover 7: Constructing countermodel ... % 4.85/1.32 Prover 7: stopped % 4.85/1.32 Prover 8: Warning: ignoring some quantifiers % 4.85/1.33 Prover 8: Constructing countermodel ... % 4.85/1.33 Prover 8: stopped % 4.85/1.33 % 4.85/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.85/1.33 % 4.85/1.34 % SZS output start Proof for theBenchmark % 4.85/1.34 Assumptions after simplification: % 4.85/1.34 --------------------------------- % 4.85/1.34 % 4.85/1.34 (l32_xboole_1) % 4.85/1.38 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 4.85/1.38 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ % 4.85/1.38 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 4.85/1.38 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 4.85/1.38 $i] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3 & $i(v3))) & ! % 4.85/1.38 [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | ~ $i(v1) % 4.85/1.38 | ~ $i(v0) | subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 4.85/1.38 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) = % 4.85/1.38 empty_set) % 4.85/1.38 % 4.85/1.38 (t37_xboole_1) % 4.85/1.38 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 4.85/1.38 (set_difference(v0, v1) = v2 & subset(v0, v1) = v3 & $i(v2) & $i(v1) & $i(v0) % 4.85/1.38 & ((v3 = 0 & ~ (v2 = empty_set)) | (v2 = empty_set & ~ (v3 = 0)))) % 4.85/1.38 % 4.85/1.38 (function-axioms) % 4.85/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.85/1.39 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 4.85/1.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.85/1.39 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 4.85/1.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.85/1.39 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 4.85/1.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 4.85/1.39 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 4.85/1.39 % 4.85/1.39 Further assumptions not needed in the proof: % 4.85/1.39 -------------------------------------------- % 4.85/1.39 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k4_xboole_0, fc1_xboole_0, % 4.85/1.39 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, t3_boole, t4_boole, t6_boole, % 4.85/1.39 t7_boole, t8_boole % 4.85/1.39 % 4.85/1.39 Those formulas are unsatisfiable: % 4.85/1.39 --------------------------------- % 4.85/1.39 % 4.85/1.39 Begin of proof % 4.85/1.39 | % 4.85/1.39 | ALPHA: (l32_xboole_1) implies: % 4.85/1.39 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 4.85/1.39 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = empty_set) % 4.85/1.39 | & set_difference(v0, v1) = v3 & $i(v3))) % 4.85/1.39 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 4.85/1.39 | (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 4.85/1.39 | : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 4.85/1.39 | % 4.85/1.39 | ALPHA: (t37_xboole_1) implies: % 4.85/1.39 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 4.85/1.39 | (set_difference(v0, v1) = v2 & subset(v0, v1) = v3 & $i(v2) & $i(v1) & % 4.85/1.39 | $i(v0) & ((v3 = 0 & ~ (v2 = empty_set)) | (v2 = empty_set & ~ (v3 = % 4.85/1.39 | 0)))) % 4.85/1.39 | % 4.85/1.39 | ALPHA: (function-axioms) implies: % 4.85/1.40 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.85/1.40 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 4.85/1.40 | = v0)) % 4.85/1.40 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.85/1.40 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 4.85/1.40 | % 4.85/1.40 | DELTA: instantiating (3) with fresh symbols all_16_0, all_16_1, all_16_2, % 4.85/1.40 | all_16_3 gives: % 4.85/1.40 | (6) set_difference(all_16_3, all_16_2) = all_16_1 & subset(all_16_3, % 4.85/1.40 | all_16_2) = all_16_0 & $i(all_16_1) & $i(all_16_2) & $i(all_16_3) & % 4.85/1.40 | ((all_16_0 = 0 & ~ (all_16_1 = empty_set)) | (all_16_1 = empty_set & % 4.85/1.40 | ~ (all_16_0 = 0))) % 4.85/1.40 | % 4.85/1.40 | ALPHA: (6) implies: % 4.85/1.40 | (7) $i(all_16_3) % 4.85/1.40 | (8) $i(all_16_2) % 4.85/1.40 | (9) subset(all_16_3, all_16_2) = all_16_0 % 4.85/1.40 | (10) set_difference(all_16_3, all_16_2) = all_16_1 % 4.85/1.40 | (11) (all_16_0 = 0 & ~ (all_16_1 = empty_set)) | (all_16_1 = empty_set & % 4.85/1.40 | ~ (all_16_0 = 0)) % 4.85/1.40 | % 4.85/1.40 | GROUND_INST: instantiating (1) with all_16_3, all_16_2, all_16_0, simplifying % 4.85/1.40 | with (7), (8), (9) gives: % 4.85/1.40 | (12) all_16_0 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & % 4.85/1.40 | set_difference(all_16_3, all_16_2) = v0 & $i(v0)) % 4.85/1.40 | % 4.85/1.40 | GROUND_INST: instantiating (2) with all_16_3, all_16_2, all_16_1, simplifying % 4.85/1.40 | with (7), (8), (10) gives: % 4.85/1.41 | (13) all_16_1 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(all_16_3, % 4.85/1.41 | all_16_2) = v0) % 4.85/1.41 | % 4.85/1.41 | BETA: splitting (11) gives: % 4.85/1.41 | % 4.85/1.41 | Case 1: % 4.85/1.41 | | % 4.85/1.41 | | (14) all_16_0 = 0 & ~ (all_16_1 = empty_set) % 4.85/1.41 | | % 4.85/1.41 | | ALPHA: (14) implies: % 4.85/1.41 | | (15) all_16_0 = 0 % 4.85/1.41 | | (16) ~ (all_16_1 = empty_set) % 4.85/1.41 | | % 4.85/1.41 | | REDUCE: (9), (15) imply: % 4.85/1.41 | | (17) subset(all_16_3, all_16_2) = 0 % 4.85/1.41 | | % 4.85/1.41 | | BETA: splitting (13) gives: % 4.85/1.41 | | % 4.85/1.41 | | Case 1: % 4.85/1.41 | | | % 4.85/1.41 | | | (18) all_16_1 = empty_set % 4.85/1.41 | | | % 4.85/1.41 | | | REDUCE: (16), (18) imply: % 4.85/1.41 | | | (19) $false % 4.85/1.41 | | | % 4.85/1.41 | | | CLOSE: (19) is inconsistent. % 4.85/1.41 | | | % 4.85/1.41 | | Case 2: % 4.85/1.41 | | | % 4.85/1.41 | | | (20) ? [v0: int] : ( ~ (v0 = 0) & subset(all_16_3, all_16_2) = v0) % 4.85/1.41 | | | % 4.85/1.41 | | | DELTA: instantiating (20) with fresh symbol all_35_0 gives: % 4.85/1.41 | | | (21) ~ (all_35_0 = 0) & subset(all_16_3, all_16_2) = all_35_0 % 4.85/1.41 | | | % 4.85/1.41 | | | ALPHA: (21) implies: % 4.85/1.41 | | | (22) ~ (all_35_0 = 0) % 4.85/1.41 | | | (23) subset(all_16_3, all_16_2) = all_35_0 % 4.85/1.41 | | | % 4.85/1.41 | | | GROUND_INST: instantiating (4) with 0, all_35_0, all_16_2, all_16_3, % 4.85/1.41 | | | simplifying with (17), (23) gives: % 4.85/1.41 | | | (24) all_35_0 = 0 % 4.85/1.41 | | | % 4.85/1.41 | | | REDUCE: (22), (24) imply: % 4.85/1.41 | | | (25) $false % 4.85/1.41 | | | % 4.85/1.41 | | | CLOSE: (25) is inconsistent. % 4.85/1.41 | | | % 4.85/1.41 | | End of split % 4.85/1.41 | | % 4.85/1.41 | Case 2: % 4.85/1.41 | | % 4.85/1.41 | | (26) all_16_1 = empty_set & ~ (all_16_0 = 0) % 4.85/1.41 | | % 4.85/1.41 | | ALPHA: (26) implies: % 4.85/1.41 | | (27) all_16_1 = empty_set % 4.85/1.41 | | (28) ~ (all_16_0 = 0) % 4.85/1.41 | | % 4.85/1.41 | | REDUCE: (10), (27) imply: % 4.85/1.41 | | (29) set_difference(all_16_3, all_16_2) = empty_set % 4.85/1.41 | | % 4.85/1.41 | | BETA: splitting (12) gives: % 4.85/1.41 | | % 4.85/1.41 | | Case 1: % 4.85/1.41 | | | % 4.85/1.41 | | | (30) all_16_0 = 0 % 4.85/1.41 | | | % 4.85/1.41 | | | REDUCE: (28), (30) imply: % 4.85/1.41 | | | (31) $false % 4.85/1.41 | | | % 4.85/1.41 | | | CLOSE: (31) is inconsistent. % 4.85/1.41 | | | % 4.85/1.41 | | Case 2: % 4.85/1.41 | | | % 4.85/1.41 | | | (32) ? [v0: $i] : ( ~ (v0 = empty_set) & set_difference(all_16_3, % 4.85/1.41 | | | all_16_2) = v0 & $i(v0)) % 4.85/1.41 | | | % 4.85/1.41 | | | DELTA: instantiating (32) with fresh symbol all_35_0 gives: % 4.85/1.41 | | | (33) ~ (all_35_0 = empty_set) & set_difference(all_16_3, all_16_2) = % 4.85/1.41 | | | all_35_0 & $i(all_35_0) % 4.85/1.41 | | | % 4.85/1.41 | | | ALPHA: (33) implies: % 4.85/1.41 | | | (34) ~ (all_35_0 = empty_set) % 4.85/1.41 | | | (35) set_difference(all_16_3, all_16_2) = all_35_0 % 4.85/1.42 | | | % 4.85/1.42 | | | GROUND_INST: instantiating (5) with empty_set, all_35_0, all_16_2, % 4.85/1.42 | | | all_16_3, simplifying with (29), (35) gives: % 4.85/1.42 | | | (36) all_35_0 = empty_set % 4.85/1.42 | | | % 4.85/1.42 | | | REDUCE: (34), (36) imply: % 4.85/1.42 | | | (37) $false % 4.85/1.42 | | | % 4.85/1.42 | | | CLOSE: (37) is inconsistent. % 4.85/1.42 | | | % 4.85/1.42 | | End of split % 4.85/1.42 | | % 4.85/1.42 | End of split % 4.85/1.42 | % 4.85/1.42 End of proof % 4.85/1.42 % SZS output end Proof for theBenchmark % 4.85/1.42 % 4.85/1.42 895ms %------------------------------------------------------------------------------