%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU139+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 17:42:43 EDT 2023 % Result : Theorem 11.52s 2.39s % Output : Proof 14.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU139+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.33 % Computer : n009.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Wed Aug 23 13:36:36 EDT 2023 % 0.16/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.97/1.17 Prover 4: Preprocessing ... % 2.97/1.17 Prover 1: Preprocessing ... % 3.26/1.25 Prover 0: Preprocessing ... % 3.26/1.25 Prover 2: Preprocessing ... % 3.26/1.25 Prover 3: Preprocessing ... % 3.26/1.25 Prover 5: Preprocessing ... % 3.26/1.25 Prover 6: Preprocessing ... % 8.98/2.06 Prover 5: Proving ... % 8.98/2.08 Prover 1: Warning: ignoring some quantifiers % 8.98/2.16 Prover 6: Proving ... % 8.98/2.16 Prover 3: Warning: ignoring some quantifiers % 8.98/2.19 Prover 3: Constructing countermodel ... % 8.98/2.19 Prover 1: Constructing countermodel ... % 8.98/2.22 Prover 2: Proving ... % 10.36/2.27 Prover 4: Warning: ignoring some quantifiers % 10.36/2.34 Prover 0: Proving ... % 11.52/2.39 Prover 3: proved (1762ms) % 11.52/2.39 % 11.52/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.52/2.39 % 11.52/2.39 Prover 2: stopped % 11.52/2.39 Prover 6: stopped % 11.52/2.39 Prover 5: stopped % 11.52/2.39 Prover 0: stopped % 11.52/2.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.52/2.40 Prover 4: Constructing countermodel ... % 11.95/2.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.95/2.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.95/2.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.95/2.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.24/2.53 Prover 10: Preprocessing ... % 12.24/2.53 Prover 7: Preprocessing ... % 12.24/2.53 Prover 11: Preprocessing ... % 12.92/2.56 Prover 8: Preprocessing ... % 12.92/2.57 Prover 13: Preprocessing ... % 13.23/2.58 Prover 1: Found proof (size 16) % 13.23/2.59 Prover 1: proved (1975ms) % 13.23/2.59 Prover 4: stopped % 13.23/2.60 Prover 10: stopped % 13.23/2.61 Prover 7: stopped % 13.59/2.64 Prover 11: stopped % 13.59/2.65 Prover 13: stopped % 14.21/2.80 Prover 8: Warning: ignoring some quantifiers % 14.21/2.82 Prover 8: Constructing countermodel ... % 14.21/2.84 Prover 8: stopped % 14.21/2.84 % 14.21/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.21/2.84 % 14.21/2.84 % SZS output start Proof for theBenchmark % 14.64/2.85 Assumptions after simplification: % 14.64/2.85 --------------------------------- % 14.64/2.85 % 14.64/2.85 (d10_xboole_0) % 14.64/2.88 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | % 14.64/2.88 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] % 14.64/2.88 : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 14.64/2.88 % 14.64/2.88 (d8_xboole_0) % 14.64/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 14.64/2.88 (proper_subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ % 14.64/2.88 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.64/2.88 (proper_subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & % 14.64/2.88 subset(v0, v1) = 0)) % 14.64/2.88 % 14.64/2.88 (t60_xboole_1) % 14.64/2.88 ? [v0: $i] : ? [v1: $i] : (subset(v0, v1) = 0 & proper_subset(v1, v0) = 0 & % 14.64/2.88 $i(v1) & $i(v0)) % 14.64/2.88 % 14.64/2.88 (function-axioms) % 14.64/2.89 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.64/2.89 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 14.64/2.89 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.64/2.89 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 14.64/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.64/2.89 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 14.64/2.89 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.64/2.89 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 14.64/2.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.64/2.89 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 14.64/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.64/2.89 : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = % 14.64/2.89 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.64/2.89 $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 14.64/2.89 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 14.64/2.89 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 14.64/2.89 % 14.64/2.89 Further assumptions not needed in the proof: % 14.64/2.89 -------------------------------------------- % 14.64/2.89 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_xboole_0, % 14.64/2.89 commutativity_k3_xboole_0, d1_xboole_0, d2_xboole_0, d3_tarski, d3_xboole_0, % 14.64/2.89 d4_xboole_0, d7_xboole_0, dt_k1_xboole_0, dt_k2_xboole_0, dt_k3_xboole_0, % 14.64/2.89 dt_k4_xboole_0, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, % 14.64/2.89 idempotence_k2_xboole_0, idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, % 14.64/2.89 l32_xboole_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 14.64/2.89 symmetry_r1_xboole_0, t12_xboole_1, t17_xboole_1, t19_xboole_1, t1_boole, % 14.64/2.89 t1_xboole_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, % 14.64/2.89 t33_xboole_1, t36_xboole_1, t37_xboole_1, t39_xboole_1, t3_boole, t3_xboole_0, % 14.64/2.89 t3_xboole_1, t40_xboole_1, t45_xboole_1, t48_xboole_1, t4_boole, t4_xboole_0, % 14.64/2.89 t6_boole, t7_boole, t7_xboole_1, t8_boole, t8_xboole_1 % 14.64/2.89 % 14.64/2.89 Those formulas are unsatisfiable: % 14.64/2.89 --------------------------------- % 14.64/2.89 % 14.64/2.89 Begin of proof % 14.64/2.89 | % 14.64/2.89 | ALPHA: (d10_xboole_0) implies: % 14.64/2.89 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ % 14.64/2.89 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = % 14.64/2.89 | v2)) % 14.64/2.89 | % 14.64/2.89 | ALPHA: (d8_xboole_0) implies: % 14.64/2.89 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (proper_subset(v0, v1) = 0) | ~ $i(v1) % 14.64/2.89 | | ~ $i(v0) | ( ~ (v1 = v0) & subset(v0, v1) = 0)) % 14.64/2.89 | % 14.64/2.89 | ALPHA: (function-axioms) implies: % 14.64/2.89 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.64/2.89 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 14.64/2.89 | = v0)) % 14.64/2.90 | % 14.64/2.90 | DELTA: instantiating (t60_xboole_1) with fresh symbols all_57_0, all_57_1 % 14.64/2.90 | gives: % 14.64/2.90 | (4) subset(all_57_1, all_57_0) = 0 & proper_subset(all_57_0, all_57_1) = 0 % 14.64/2.90 | & $i(all_57_0) & $i(all_57_1) % 14.64/2.90 | % 14.64/2.90 | ALPHA: (4) implies: % 14.64/2.90 | (5) $i(all_57_1) % 14.64/2.90 | (6) $i(all_57_0) % 14.64/2.90 | (7) proper_subset(all_57_0, all_57_1) = 0 % 14.64/2.90 | (8) subset(all_57_1, all_57_0) = 0 % 14.64/2.90 | % 14.64/2.90 | GROUND_INST: instantiating (2) with all_57_0, all_57_1, simplifying with (5), % 14.64/2.90 | (6), (7) gives: % 14.64/2.90 | (9) ~ (all_57_0 = all_57_1) & subset(all_57_0, all_57_1) = 0 % 14.64/2.90 | % 14.64/2.90 | ALPHA: (9) implies: % 14.64/2.90 | (10) ~ (all_57_0 = all_57_1) % 14.64/2.90 | (11) subset(all_57_0, all_57_1) = 0 % 14.64/2.90 | % 14.64/2.90 | GROUND_INST: instantiating (1) with all_57_1, all_57_0, simplifying with (5), % 14.64/2.90 | (6), (8) gives: % 14.64/2.90 | (12) all_57_0 = all_57_1 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_57_0, % 14.64/2.90 | all_57_1) = v0) % 14.64/2.90 | % 14.64/2.90 | BETA: splitting (12) gives: % 14.64/2.90 | % 14.64/2.90 | Case 1: % 14.64/2.90 | | % 14.64/2.90 | | (13) all_57_0 = all_57_1 % 14.64/2.90 | | % 14.64/2.90 | | REDUCE: (10), (13) imply: % 14.64/2.90 | | (14) $false % 14.64/2.91 | | % 14.64/2.91 | | CLOSE: (14) is inconsistent. % 14.64/2.91 | | % 14.64/2.91 | Case 2: % 14.64/2.91 | | % 14.64/2.91 | | (15) ? [v0: int] : ( ~ (v0 = 0) & subset(all_57_0, all_57_1) = v0) % 14.64/2.91 | | % 14.64/2.91 | | DELTA: instantiating (15) with fresh symbol all_81_0 gives: % 14.64/2.91 | | (16) ~ (all_81_0 = 0) & subset(all_57_0, all_57_1) = all_81_0 % 14.64/2.91 | | % 14.64/2.91 | | ALPHA: (16) implies: % 14.64/2.91 | | (17) ~ (all_81_0 = 0) % 14.64/2.91 | | (18) subset(all_57_0, all_57_1) = all_81_0 % 14.64/2.91 | | % 14.64/2.91 | | GROUND_INST: instantiating (3) with 0, all_81_0, all_57_1, all_57_0, % 14.64/2.91 | | simplifying with (11), (18) gives: % 14.64/2.91 | | (19) all_81_0 = 0 % 14.64/2.91 | | % 14.64/2.91 | | REDUCE: (17), (19) imply: % 14.64/2.91 | | (20) $false % 14.64/2.91 | | % 14.64/2.91 | | CLOSE: (20) is inconsistent. % 14.64/2.91 | | % 14.64/2.91 | End of split % 14.64/2.91 | % 14.64/2.91 End of proof % 14.64/2.91 % SZS output end Proof for theBenchmark % 14.64/2.91 % 14.64/2.91 2314ms %------------------------------------------------------------------------------