%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU134+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 : 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 : Thu Aug 31 17:42:41 EDT 2023 % Result : Theorem 12.27s 2.56s % Output : Proof 15.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SEU134+2 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n004.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 15:13:38 EDT 2023 % 0.14/0.35 % CPUTime : % 0.22/0.66 ________ _____ % 0.22/0.66 ___ __ \_________(_)________________________________ % 0.22/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.66 % 0.22/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.66 (2023-06-19) % 0.22/0.66 % 0.22/0.66 (c) Philipp Rümmer, 2009-2023 % 0.22/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.66 Amanda Stjerna. % 0.22/0.66 Free software under BSD-3-Clause. % 0.22/0.66 % 0.22/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.66 % 0.22/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.68 Running up to 7 provers in parallel. % 0.22/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.22/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.18/1.20 Prover 1: Preprocessing ... % 3.18/1.20 Prover 4: Preprocessing ... % 3.18/1.26 Prover 2: Preprocessing ... % 3.18/1.26 Prover 0: Preprocessing ... % 3.18/1.27 Prover 5: Preprocessing ... % 3.18/1.27 Prover 6: Preprocessing ... % 3.18/1.27 Prover 3: Preprocessing ... % 8.55/2.09 Prover 5: Proving ... % 9.28/2.12 Prover 1: Warning: ignoring some quantifiers % 10.01/2.20 Prover 1: Constructing countermodel ... % 10.01/2.20 Prover 6: Proving ... % 10.01/2.25 Prover 3: Warning: ignoring some quantifiers % 10.01/2.28 Prover 3: Constructing countermodel ... % 10.01/2.32 Prover 2: Proving ... % 11.03/2.43 Prover 4: Warning: ignoring some quantifiers % 11.03/2.48 Prover 4: Constructing countermodel ... % 12.27/2.53 Prover 0: Proving ... % 12.27/2.55 Prover 6: proved (1856ms) % 12.27/2.55 Prover 5: proved (1855ms) % 12.27/2.56 % 12.27/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.27/2.56 % 12.27/2.56 % 12.27/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.27/2.56 % 12.27/2.56 Prover 3: stopped % 12.27/2.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.27/2.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.27/2.59 Prover 2: stopped % 12.27/2.59 Prover 0: stopped % 12.27/2.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.27/2.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.83/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.83/2.68 Prover 7: Preprocessing ... % 13.37/2.70 Prover 11: Preprocessing ... % 13.37/2.70 Prover 8: Preprocessing ... % 13.37/2.72 Prover 10: Preprocessing ... % 13.37/2.75 Prover 13: Preprocessing ... % 13.94/2.78 Prover 1: Found proof (size 25) % 13.94/2.78 Prover 1: proved (2096ms) % 13.94/2.78 Prover 10: stopped % 13.94/2.79 Prover 4: stopped % 13.94/2.79 Prover 7: stopped % 13.94/2.79 Prover 11: stopped % 13.94/2.84 Prover 13: stopped % 14.81/2.94 Prover 8: Warning: ignoring some quantifiers % 14.81/2.96 Prover 8: Constructing countermodel ... % 14.81/2.98 Prover 8: stopped % 14.81/2.98 % 14.81/2.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.81/2.98 % 14.81/2.98 % SZS output start Proof for theBenchmark % 14.81/2.99 Assumptions after simplification: % 14.81/2.99 --------------------------------- % 14.81/2.99 % 14.81/2.99 (l32_xboole_1) % 15.16/3.03 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 15.16/3.03 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ % 15.16/3.03 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.16/3.03 (set_difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | subset(v0, % 15.16/3.03 v1) = 0) % 15.16/3.03 % 15.16/3.03 (t37_xboole_1) % 15.16/3.04 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 15.16/3.04 (set_difference(v0, v1) = v2 & subset(v0, v1) = v3 & $i(v2) & $i(v1) & $i(v0) % 15.16/3.04 & ((v3 = 0 & ~ (v2 = empty_set)) | (v2 = empty_set & ~ (v3 = 0)))) % 15.16/3.04 % 15.16/3.04 (function-axioms) % 15.16/3.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.16/3.04 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 15.16/3.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.16/3.04 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 15.16/3.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.16/3.04 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 15.16/3.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.16/3.04 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 15.16/3.04 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.16/3.04 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 15.16/3.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.16/3.04 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 15.16/3.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.16/3.04 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 15.16/3.04 % 15.16/3.04 Further assumptions not needed in the proof: % 15.16/3.04 -------------------------------------------- % 15.16/3.05 antisymmetry_r2_hidden, commutativity_k2_xboole_0, commutativity_k3_xboole_0, % 15.16/3.05 d10_xboole_0, d1_xboole_0, d2_xboole_0, d3_tarski, d3_xboole_0, d4_xboole_0, % 15.16/3.05 d7_xboole_0, dt_k1_xboole_0, dt_k2_xboole_0, dt_k3_xboole_0, dt_k4_xboole_0, % 15.16/3.05 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 15.16/3.05 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 15.16/3.05 symmetry_r1_xboole_0, t12_xboole_1, t17_xboole_1, t19_xboole_1, t1_boole, % 15.16/3.05 t1_xboole_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, % 15.16/3.05 t33_xboole_1, t36_xboole_1, t3_boole, t3_xboole_0, t3_xboole_1, t4_boole, % 15.16/3.05 t4_xboole_0, t6_boole, t7_boole, t7_xboole_1, t8_boole, t8_xboole_1 % 15.16/3.05 % 15.16/3.05 Those formulas are unsatisfiable: % 15.16/3.05 --------------------------------- % 15.16/3.05 % 15.16/3.05 Begin of proof % 15.16/3.05 | % 15.16/3.05 | ALPHA: (l32_xboole_1) implies: % 15.16/3.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | % 15.16/3.05 | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0) % 15.16/3.05 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 15.16/3.05 | (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 15.16/3.05 | : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 15.16/3.05 | % 15.16/3.05 | ALPHA: (t37_xboole_1) implies: % 15.16/3.05 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 15.16/3.05 | (set_difference(v0, v1) = v2 & subset(v0, v1) = v3 & $i(v2) & $i(v1) & % 15.16/3.05 | $i(v0) & ((v3 = 0 & ~ (v2 = empty_set)) | (v2 = empty_set & ~ (v3 = % 15.16/3.06 | 0)))) % 15.16/3.06 | % 15.16/3.06 | ALPHA: (function-axioms) implies: % 15.16/3.06 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.16/3.06 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 15.16/3.06 | = v0)) % 15.16/3.06 | % 15.16/3.06 | DELTA: instantiating (3) with fresh symbols all_50_0, all_50_1, all_50_2, % 15.16/3.06 | all_50_3 gives: % 15.16/3.06 | (5) set_difference(all_50_3, all_50_2) = all_50_1 & subset(all_50_3, % 15.16/3.06 | all_50_2) = all_50_0 & $i(all_50_1) & $i(all_50_2) & $i(all_50_3) & % 15.16/3.06 | ((all_50_0 = 0 & ~ (all_50_1 = empty_set)) | (all_50_1 = empty_set & % 15.16/3.06 | ~ (all_50_0 = 0))) % 15.16/3.06 | % 15.16/3.06 | ALPHA: (5) implies: % 15.16/3.06 | (6) $i(all_50_3) % 15.16/3.06 | (7) $i(all_50_2) % 15.16/3.06 | (8) subset(all_50_3, all_50_2) = all_50_0 % 15.16/3.06 | (9) set_difference(all_50_3, all_50_2) = all_50_1 % 15.16/3.06 | (10) (all_50_0 = 0 & ~ (all_50_1 = empty_set)) | (all_50_1 = empty_set & % 15.16/3.06 | ~ (all_50_0 = 0)) % 15.16/3.06 | % 15.16/3.07 | GROUND_INST: instantiating (2) with all_50_3, all_50_2, all_50_1, simplifying % 15.16/3.07 | with (6), (7), (9) gives: % 15.16/3.07 | (11) all_50_1 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(all_50_3, % 15.16/3.07 | all_50_2) = v0) % 15.16/3.07 | % 15.16/3.07 | BETA: splitting (10) gives: % 15.16/3.07 | % 15.16/3.07 | Case 1: % 15.16/3.07 | | % 15.16/3.07 | | (12) all_50_0 = 0 & ~ (all_50_1 = empty_set) % 15.16/3.07 | | % 15.16/3.07 | | ALPHA: (12) implies: % 15.16/3.07 | | (13) all_50_0 = 0 % 15.16/3.07 | | (14) ~ (all_50_1 = empty_set) % 15.16/3.07 | | % 15.16/3.07 | | REDUCE: (8), (13) imply: % 15.16/3.07 | | (15) subset(all_50_3, all_50_2) = 0 % 15.16/3.07 | | % 15.16/3.07 | | BETA: splitting (11) gives: % 15.16/3.07 | | % 15.16/3.07 | | Case 1: % 15.51/3.07 | | | % 15.51/3.07 | | | (16) all_50_1 = empty_set % 15.51/3.07 | | | % 15.51/3.07 | | | REDUCE: (14), (16) imply: % 15.51/3.07 | | | (17) $false % 15.51/3.07 | | | % 15.51/3.07 | | | CLOSE: (17) is inconsistent. % 15.51/3.07 | | | % 15.51/3.07 | | Case 2: % 15.51/3.07 | | | % 15.51/3.07 | | | (18) ? [v0: int] : ( ~ (v0 = 0) & subset(all_50_3, all_50_2) = v0) % 15.51/3.07 | | | % 15.51/3.07 | | | DELTA: instantiating (18) with fresh symbol all_84_0 gives: % 15.51/3.07 | | | (19) ~ (all_84_0 = 0) & subset(all_50_3, all_50_2) = all_84_0 % 15.51/3.07 | | | % 15.51/3.07 | | | ALPHA: (19) implies: % 15.51/3.07 | | | (20) ~ (all_84_0 = 0) % 15.51/3.07 | | | (21) subset(all_50_3, all_50_2) = all_84_0 % 15.51/3.07 | | | % 15.51/3.07 | | | GROUND_INST: instantiating (4) with 0, all_84_0, all_50_2, all_50_3, % 15.51/3.07 | | | simplifying with (15), (21) gives: % 15.51/3.08 | | | (22) all_84_0 = 0 % 15.51/3.08 | | | % 15.51/3.08 | | | REDUCE: (20), (22) imply: % 15.51/3.08 | | | (23) $false % 15.51/3.08 | | | % 15.51/3.08 | | | CLOSE: (23) is inconsistent. % 15.51/3.08 | | | % 15.51/3.08 | | End of split % 15.51/3.08 | | % 15.51/3.08 | Case 2: % 15.51/3.08 | | % 15.51/3.08 | | (24) all_50_1 = empty_set & ~ (all_50_0 = 0) % 15.51/3.08 | | % 15.51/3.08 | | ALPHA: (24) implies: % 15.51/3.08 | | (25) all_50_1 = empty_set % 15.51/3.08 | | (26) ~ (all_50_0 = 0) % 15.51/3.08 | | % 15.51/3.08 | | REDUCE: (9), (25) imply: % 15.51/3.08 | | (27) set_difference(all_50_3, all_50_2) = empty_set % 15.51/3.08 | | % 15.51/3.08 | | GROUND_INST: instantiating (1) with all_50_3, all_50_2, simplifying with % 15.51/3.08 | | (6), (7), (27) gives: % 15.51/3.08 | | (28) subset(all_50_3, all_50_2) = 0 % 15.51/3.08 | | % 15.51/3.08 | | GROUND_INST: instantiating (4) with all_50_0, 0, all_50_2, all_50_3, % 15.51/3.08 | | simplifying with (8), (28) gives: % 15.51/3.08 | | (29) all_50_0 = 0 % 15.51/3.08 | | % 15.51/3.08 | | REDUCE: (26), (29) imply: % 15.51/3.08 | | (30) $false % 15.51/3.08 | | % 15.51/3.08 | | CLOSE: (30) is inconsistent. % 15.51/3.08 | | % 15.51/3.08 | End of split % 15.51/3.08 | % 15.51/3.08 End of proof % 15.51/3.08 % SZS output end Proof for theBenchmark % 15.51/3.08 % 15.51/3.08 2417ms %------------------------------------------------------------------------------