%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU158+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 : n010.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 17:42:52 EDT 2023 % Result : Theorem 12.89s 2.56s % Output : Proof 16.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU158+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n010.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 : Thu Aug 24 01:30:36 EDT 2023 % 0.14/0.36 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.51/1.18 Prover 4: Preprocessing ... % 3.51/1.18 Prover 1: Preprocessing ... % 3.51/1.21 Prover 5: Preprocessing ... % 3.51/1.21 Prover 6: Preprocessing ... % 3.51/1.21 Prover 2: Preprocessing ... % 3.51/1.21 Prover 3: Preprocessing ... % 3.51/1.21 Prover 0: Preprocessing ... % 10.08/2.14 Prover 1: Warning: ignoring some quantifiers % 10.59/2.19 Prover 5: Proving ... % 10.59/2.23 Prover 1: Constructing countermodel ... % 11.31/2.29 Prover 6: Proving ... % 11.31/2.31 Prover 3: Warning: ignoring some quantifiers % 11.68/2.33 Prover 4: Warning: ignoring some quantifiers % 11.68/2.34 Prover 3: Constructing countermodel ... % 11.68/2.38 Prover 2: Proving ... % 12.36/2.44 Prover 4: Constructing countermodel ... % 12.36/2.46 Prover 0: Proving ... % 12.89/2.56 Prover 3: proved (1889ms) % 12.89/2.56 % 12.89/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.89/2.56 % 12.89/2.56 Prover 5: stopped % 12.89/2.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.89/2.56 Prover 2: stopped % 13.52/2.58 Prover 6: stopped % 13.59/2.59 Prover 0: stopped % 13.59/2.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.59/2.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.59/2.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.59/2.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.59/2.70 Prover 8: Preprocessing ... % 13.59/2.71 Prover 1: Found proof (size 24) % 13.59/2.71 Prover 1: proved (2057ms) % 13.59/2.71 Prover 4: stopped % 13.59/2.71 Prover 10: Preprocessing ... % 13.59/2.72 Prover 11: Preprocessing ... % 13.59/2.73 Prover 13: Preprocessing ... % 13.59/2.74 Prover 7: Preprocessing ... % 14.96/2.78 Prover 10: stopped % 14.96/2.80 Prover 7: stopped % 14.96/2.81 Prover 13: stopped % 14.96/2.83 Prover 11: stopped % 15.63/2.91 Prover 8: Warning: ignoring some quantifiers % 15.86/2.94 Prover 8: Constructing countermodel ... % 15.86/2.95 Prover 8: stopped % 15.86/2.95 % 15.86/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.86/2.95 % 15.86/2.96 % SZS output start Proof for theBenchmark % 15.86/2.97 Assumptions after simplification: % 15.86/2.97 --------------------------------- % 15.86/2.97 % 15.86/2.97 (l2_zfmisc_1) % 15.86/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.86/2.99 (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 15.86/2.99 [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : % 15.86/2.99 ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | ~ $i(v1) | % 15.86/2.99 ~ $i(v0) | in(v0, v1) = 0) % 15.86/2.99 % 15.86/2.99 (t37_zfmisc_1) % 15.86/2.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 15.86/2.99 (singleton(v0) = v2 & subset(v2, v1) = v3 & in(v0, v1) = v4 & $i(v2) & $i(v1) % 15.86/2.99 & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 15.86/2.99 % 15.86/3.00 (function-axioms) % 15.86/3.00 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.86/3.00 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 15.86/3.00 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.86/3.00 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 15.86/3.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.86/3.00 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 15.86/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.86/3.00 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 15.86/3.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.86/3.00 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 15.86/3.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.86/3.00 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 15.86/3.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.86/3.00 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 15.86/3.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 15.86/3.00 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.86/3.00 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.86/3.00 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 15.86/3.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.86/3.00 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 15.86/3.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.86/3.00 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.86/3.00 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] % 15.86/3.00 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 15.86/3.00 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 15.86/3.00 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 15.86/3.01 % 15.86/3.01 Further assumptions not needed in the proof: % 15.86/3.01 -------------------------------------------- % 15.86/3.01 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 15.86/3.01 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, % 15.86/3.01 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski, % 15.86/3.01 d3_xboole_0, d4_tarski, d4_xboole_0, d5_tarski, d7_xboole_0, d8_xboole_0, % 15.86/3.01 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, % 15.86/3.01 dt_k2_zfmisc_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, % 15.86/3.01 fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 15.86/3.01 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, % 15.86/3.01 l25_zfmisc_1, l28_zfmisc_1, l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, % 15.86/3.01 l50_zfmisc_1, l55_zfmisc_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 15.86/3.01 symmetry_r1_xboole_0, t10_zfmisc_1, t12_xboole_1, t17_xboole_1, t19_xboole_1, % 15.86/3.01 t1_boole, t1_xboole_1, t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, % 15.86/3.01 t2_tarski, t2_xboole_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1, % 15.86/3.01 t39_xboole_1, t3_boole, t3_xboole_0, t3_xboole_1, t40_xboole_1, t45_xboole_1, % 15.86/3.01 t48_xboole_1, t4_boole, t4_xboole_0, t60_xboole_1, t63_xboole_1, t69_enumset1, % 15.86/3.01 t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_boole, % 15.86/3.01 t8_xboole_1, t8_zfmisc_1, t9_zfmisc_1 % 15.86/3.01 % 15.86/3.01 Those formulas are unsatisfiable: % 15.86/3.01 --------------------------------- % 15.86/3.01 % 15.86/3.01 Begin of proof % 15.86/3.01 | % 15.86/3.01 | ALPHA: (l2_zfmisc_1) implies: % 16.21/3.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ % 16.21/3.01 | (subset(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) = 0) % 16.21/3.01 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.21/3.01 | (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ % 16.21/3.01 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 16.21/3.01 | % 16.21/3.01 | ALPHA: (function-axioms) implies: % 16.21/3.01 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.21/3.01 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 16.21/3.01 | % 16.21/3.01 | DELTA: instantiating (t37_zfmisc_1) with fresh symbols all_89_0, all_89_1, % 16.21/3.01 | all_89_2, all_89_3, all_89_4 gives: % 16.21/3.01 | (4) singleton(all_89_4) = all_89_2 & subset(all_89_2, all_89_3) = all_89_1 % 16.21/3.01 | & in(all_89_4, all_89_3) = all_89_0 & $i(all_89_2) & $i(all_89_3) & % 16.21/3.01 | $i(all_89_4) & ((all_89_0 = 0 & ~ (all_89_1 = 0)) | (all_89_1 = 0 & ~ % 16.21/3.01 | (all_89_0 = 0))) % 16.21/3.01 | % 16.21/3.01 | ALPHA: (4) implies: % 16.21/3.01 | (5) $i(all_89_4) % 16.21/3.01 | (6) $i(all_89_3) % 16.21/3.02 | (7) in(all_89_4, all_89_3) = all_89_0 % 16.21/3.02 | (8) subset(all_89_2, all_89_3) = all_89_1 % 16.21/3.02 | (9) singleton(all_89_4) = all_89_2 % 16.21/3.02 | (10) (all_89_0 = 0 & ~ (all_89_1 = 0)) | (all_89_1 = 0 & ~ (all_89_0 = % 16.21/3.02 | 0)) % 16.21/3.02 | % 16.21/3.02 | GROUND_INST: instantiating (2) with all_89_4, all_89_3, all_89_2, all_89_1, % 16.21/3.02 | simplifying with (5), (6), (8), (9) gives: % 16.21/3.02 | (11) all_89_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_89_4, all_89_3) = % 16.21/3.02 | v0) % 16.21/3.02 | % 16.21/3.02 | BETA: splitting (10) gives: % 16.21/3.02 | % 16.21/3.02 | Case 1: % 16.21/3.02 | | % 16.21/3.02 | | (12) all_89_0 = 0 & ~ (all_89_1 = 0) % 16.21/3.02 | | % 16.21/3.02 | | ALPHA: (12) implies: % 16.21/3.02 | | (13) all_89_0 = 0 % 16.21/3.02 | | (14) ~ (all_89_1 = 0) % 16.21/3.02 | | % 16.21/3.02 | | REDUCE: (7), (13) imply: % 16.21/3.02 | | (15) in(all_89_4, all_89_3) = 0 % 16.21/3.02 | | % 16.21/3.02 | | BETA: splitting (11) gives: % 16.21/3.02 | | % 16.21/3.02 | | Case 1: % 16.21/3.02 | | | % 16.21/3.02 | | | (16) all_89_1 = 0 % 16.21/3.02 | | | % 16.21/3.02 | | | REDUCE: (14), (16) imply: % 16.21/3.02 | | | (17) $false % 16.21/3.02 | | | % 16.21/3.02 | | | CLOSE: (17) is inconsistent. % 16.21/3.02 | | | % 16.21/3.02 | | Case 2: % 16.21/3.02 | | | % 16.21/3.02 | | | (18) ? [v0: int] : ( ~ (v0 = 0) & in(all_89_4, all_89_3) = v0) % 16.21/3.02 | | | % 16.21/3.02 | | | DELTA: instantiating (18) with fresh symbol all_140_0 gives: % 16.21/3.02 | | | (19) ~ (all_140_0 = 0) & in(all_89_4, all_89_3) = all_140_0 % 16.21/3.02 | | | % 16.21/3.02 | | | ALPHA: (19) implies: % 16.21/3.02 | | | (20) ~ (all_140_0 = 0) % 16.21/3.02 | | | (21) in(all_89_4, all_89_3) = all_140_0 % 16.21/3.02 | | | % 16.21/3.02 | | | GROUND_INST: instantiating (3) with 0, all_140_0, all_89_3, all_89_4, % 16.21/3.02 | | | simplifying with (15), (21) gives: % 16.21/3.02 | | | (22) all_140_0 = 0 % 16.21/3.02 | | | % 16.21/3.02 | | | REDUCE: (20), (22) imply: % 16.21/3.02 | | | (23) $false % 16.21/3.02 | | | % 16.21/3.02 | | | CLOSE: (23) is inconsistent. % 16.21/3.02 | | | % 16.21/3.02 | | End of split % 16.21/3.02 | | % 16.21/3.02 | Case 2: % 16.21/3.02 | | % 16.21/3.02 | | (24) all_89_1 = 0 & ~ (all_89_0 = 0) % 16.21/3.02 | | % 16.21/3.02 | | ALPHA: (24) implies: % 16.21/3.02 | | (25) all_89_1 = 0 % 16.21/3.02 | | (26) ~ (all_89_0 = 0) % 16.21/3.02 | | % 16.21/3.02 | | REDUCE: (8), (25) imply: % 16.21/3.02 | | (27) subset(all_89_2, all_89_3) = 0 % 16.21/3.02 | | % 16.21/3.02 | | GROUND_INST: instantiating (1) with all_89_4, all_89_3, all_89_2, % 16.21/3.02 | | simplifying with (5), (6), (9), (27) gives: % 16.21/3.02 | | (28) in(all_89_4, all_89_3) = 0 % 16.21/3.02 | | % 16.21/3.02 | | GROUND_INST: instantiating (3) with all_89_0, 0, all_89_3, all_89_4, % 16.21/3.02 | | simplifying with (7), (28) gives: % 16.21/3.02 | | (29) all_89_0 = 0 % 16.21/3.02 | | % 16.21/3.02 | | REDUCE: (26), (29) imply: % 16.21/3.02 | | (30) $false % 16.21/3.02 | | % 16.21/3.02 | | CLOSE: (30) is inconsistent. % 16.21/3.02 | | % 16.21/3.02 | End of split % 16.21/3.02 | % 16.21/3.02 End of proof % 16.21/3.03 % SZS output end Proof for theBenchmark % 16.21/3.03 % 16.21/3.03 2391ms %------------------------------------------------------------------------------