%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU217+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 : n003.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 17:43:20 EDT 2023 % Result : Theorem 6.60s 1.65s % Output : Proof 9.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU217+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Aug 24 01:48:22 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.62/1.05 Prover 1: Preprocessing ... % 2.62/1.06 Prover 4: Preprocessing ... % 2.88/1.09 Prover 5: Preprocessing ... % 2.88/1.09 Prover 6: Preprocessing ... % 2.88/1.09 Prover 0: Preprocessing ... % 2.88/1.09 Prover 2: Preprocessing ... % 2.88/1.09 Prover 3: Preprocessing ... % 4.60/1.39 Prover 3: Warning: ignoring some quantifiers % 4.60/1.39 Prover 1: Warning: ignoring some quantifiers % 4.60/1.41 Prover 3: Constructing countermodel ... % 4.60/1.41 Prover 1: Constructing countermodel ... % 4.60/1.41 Prover 2: Proving ... % 4.60/1.41 Prover 5: Proving ... % 4.60/1.43 Prover 6: Proving ... % 4.60/1.44 Prover 4: Warning: ignoring some quantifiers % 5.36/1.46 Prover 4: Constructing countermodel ... % 5.59/1.51 Prover 0: Proving ... % 6.60/1.65 Prover 3: proved (1018ms) % 6.60/1.65 % 6.60/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.60/1.65 % 6.60/1.65 Prover 2: stopped % 6.60/1.65 Prover 5: stopped % 6.60/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.60/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.60/1.65 Prover 0: stopped % 6.60/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.60/1.66 Prover 6: stopped % 6.98/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.98/1.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.98/1.69 Prover 8: Preprocessing ... % 6.98/1.69 Prover 7: Preprocessing ... % 6.98/1.70 Prover 13: Preprocessing ... % 6.98/1.70 Prover 10: Preprocessing ... % 6.98/1.71 Prover 11: Preprocessing ... % 7.58/1.78 Prover 7: Warning: ignoring some quantifiers % 7.82/1.79 Prover 7: Constructing countermodel ... % 7.82/1.80 Prover 10: Warning: ignoring some quantifiers % 7.82/1.81 Prover 10: Constructing countermodel ... % 8.21/1.83 Prover 8: Warning: ignoring some quantifiers % 8.21/1.84 Prover 1: Found proof (size 23) % 8.21/1.84 Prover 1: proved (1216ms) % 8.21/1.84 Prover 7: stopped % 8.21/1.84 Prover 13: Warning: ignoring some quantifiers % 8.21/1.84 Prover 10: stopped % 8.21/1.85 Prover 8: Constructing countermodel ... % 8.21/1.85 Prover 4: stopped % 8.37/1.85 Prover 13: Constructing countermodel ... % 8.37/1.85 Prover 8: stopped % 8.37/1.86 Prover 13: stopped % 8.37/1.91 Prover 11: Warning: ignoring some quantifiers % 8.37/1.92 Prover 11: Constructing countermodel ... % 8.37/1.93 Prover 11: stopped % 8.37/1.93 % 8.37/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.37/1.93 % 8.37/1.93 % SZS output start Proof for theBenchmark % 8.37/1.94 Assumptions after simplification: % 8.37/1.94 --------------------------------- % 8.37/1.94 % 8.37/1.94 (fc2_funct_1) % 8.37/1.97 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) | % 8.37/1.97 function(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = % 8.37/1.97 v1) | ~ $i(v0) | relation(v1) = 0) % 8.37/1.97 % 8.37/1.97 (t34_funct_1) % 8.37/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity_relation(v0) = v2) | % 8.37/1.97 ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 8.37/1.97 (relation_dom(v1) = v4 & relation(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | (( ~ % 8.37/1.97 (v4 = v0) | v2 = v1 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 8.37/1.97 apply(v1, v5) = v6 & in(v5, v0) = 0 & $i(v6) & $i(v5))) & ( ~ (v2 % 8.37/1.97 = v1) | (v4 = v0 & ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ % 8.37/1.97 (apply(v1, v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & % 8.37/1.97 in(v5, v0) = v7)))))))) % 8.37/1.97 % 8.37/1.97 (t35_funct_1) % 8.37/1.97 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) & % 8.37/1.97 apply(v2, v1) = v3 & identity_relation(v0) = v2 & in(v1, v0) = 0 & $i(v3) & % 8.37/1.97 $i(v2) & $i(v1) & $i(v0)) % 8.37/1.98 % 8.37/1.98 (function-axioms) % 8.37/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.37/1.98 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 8.37/1.98 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.37/1.98 (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.37/1.98 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.37/1.98 (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.37/1.98 $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ % 8.37/1.98 (identity_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 8.37/1.98 (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: % 8.37/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.37/1.98 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 8.37/1.98 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 8.37/1.98 ~ (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.37/1.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 8.37/1.98 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.37/1.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 8.37/1.98 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 8.37/1.98 % 8.37/1.98 Further assumptions not needed in the proof: % 8.37/1.98 -------------------------------------------- % 8.37/1.98 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, dt_k1_funct_1, dt_k1_relat_1, % 8.37/1.98 dt_k1_xboole_0, dt_k6_relat_1, dt_m1_subset_1, existence_m1_subset_1, % 8.37/1.98 fc12_relat_1, fc1_xboole_0, fc4_relat_1, fc5_relat_1, fc7_relat_1, rc1_funct_1, % 8.37/1.98 rc1_relat_1, rc1_xboole_0, rc2_relat_1, rc2_xboole_0, rc3_relat_1, t1_subset, % 8.37/1.98 t2_subset, t6_boole, t7_boole, t8_boole % 8.37/1.98 % 8.37/1.98 Those formulas are unsatisfiable: % 8.37/1.98 --------------------------------- % 8.37/1.98 % 8.37/1.98 Begin of proof % 8.37/1.98 | % 8.37/1.98 | ALPHA: (fc2_funct_1) implies: % 8.37/1.99 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 8.37/1.99 | $i(v0) | relation(v1) = 0) % 8.37/1.99 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 8.37/1.99 | $i(v0) | function(v1) = 0) % 8.37/1.99 | % 8.37/1.99 | ALPHA: (function-axioms) implies: % 8.37/1.99 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.37/1.99 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 8.37/1.99 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.37/1.99 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 8.37/1.99 | % 8.37/1.99 | DELTA: instantiating (t35_funct_1) with fresh symbols all_30_0, all_30_1, % 8.37/1.99 | all_30_2, all_30_3 gives: % 8.37/1.99 | (5) ~ (all_30_0 = all_30_2) & apply(all_30_1, all_30_2) = all_30_0 & % 8.37/1.99 | identity_relation(all_30_3) = all_30_1 & in(all_30_2, all_30_3) = 0 & % 8.37/1.99 | $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & $i(all_30_3) % 8.37/1.99 | % 8.37/1.99 | ALPHA: (5) implies: % 8.37/1.99 | (6) ~ (all_30_0 = all_30_2) % 8.37/1.99 | (7) $i(all_30_3) % 8.37/1.99 | (8) $i(all_30_2) % 8.37/1.99 | (9) $i(all_30_1) % 8.37/1.99 | (10) in(all_30_2, all_30_3) = 0 % 8.37/1.99 | (11) identity_relation(all_30_3) = all_30_1 % 8.37/1.99 | (12) apply(all_30_1, all_30_2) = all_30_0 % 8.37/1.99 | % 8.37/1.99 | GROUND_INST: instantiating (2) with all_30_3, all_30_1, simplifying with (7), % 8.37/1.99 | (11) gives: % 8.37/1.99 | (13) function(all_30_1) = 0 % 8.37/1.99 | % 8.37/1.99 | GROUND_INST: instantiating (1) with all_30_3, all_30_1, simplifying with (7), % 8.37/1.99 | (11) gives: % 8.37/1.99 | (14) relation(all_30_1) = 0 % 8.37/1.99 | % 8.37/2.00 | GROUND_INST: instantiating (t34_funct_1) with all_30_3, all_30_1, all_30_1, % 8.37/2.00 | simplifying with (7), (9), (11), (13) gives: % 8.37/2.00 | (15) ? [v0: any] : ? [v1: $i] : (relation_dom(all_30_1) = v1 & % 8.37/2.00 | relation(all_30_1) = v0 & $i(v1) & ( ~ (v0 = 0) | (v1 = all_30_3 & % 8.37/2.00 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (apply(all_30_1, v2) = % 8.37/2.00 | v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, % 8.37/2.00 | all_30_3) = v4))))) % 8.37/2.00 | % 8.37/2.00 | DELTA: instantiating (15) with fresh symbols all_57_0, all_57_1 gives: % 9.05/2.00 | (16) relation_dom(all_30_1) = all_57_0 & relation(all_30_1) = all_57_1 & % 9.05/2.00 | $i(all_57_0) & ( ~ (all_57_1 = 0) | (all_57_0 = all_30_3 & ! [v0: $i] % 9.05/2.00 | : ! [v1: $i] : (v1 = v0 | ~ (apply(all_30_1, v0) = v1) | ~ % 9.05/2.00 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_30_3) = v2)))) % 9.05/2.00 | % 9.05/2.00 | ALPHA: (16) implies: % 9.05/2.00 | (17) relation(all_30_1) = all_57_1 % 9.05/2.00 | (18) ~ (all_57_1 = 0) | (all_57_0 = all_30_3 & ! [v0: $i] : ! [v1: $i] : % 9.05/2.00 | (v1 = v0 | ~ (apply(all_30_1, v0) = v1) | ~ $i(v0) | ? [v2: int] % 9.05/2.00 | : ( ~ (v2 = 0) & in(v0, all_30_3) = v2))) % 9.05/2.00 | % 9.05/2.00 | GROUND_INST: instantiating (3) with 0, all_57_1, all_30_1, simplifying with % 9.05/2.00 | (14), (17) gives: % 9.05/2.00 | (19) all_57_1 = 0 % 9.05/2.00 | % 9.05/2.00 | BETA: splitting (18) gives: % 9.05/2.00 | % 9.05/2.00 | Case 1: % 9.05/2.00 | | % 9.05/2.00 | | (20) ~ (all_57_1 = 0) % 9.05/2.00 | | % 9.05/2.00 | | REDUCE: (19), (20) imply: % 9.05/2.00 | | (21) $false % 9.05/2.00 | | % 9.05/2.00 | | CLOSE: (21) is inconsistent. % 9.05/2.00 | | % 9.05/2.00 | Case 2: % 9.05/2.00 | | % 9.05/2.00 | | (22) all_57_0 = all_30_3 & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 9.05/2.00 | | (apply(all_30_1, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 9.05/2.00 | | 0) & in(v0, all_30_3) = v2)) % 9.05/2.00 | | % 9.05/2.00 | | ALPHA: (22) implies: % 9.05/2.00 | | (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (apply(all_30_1, v0) = v1) % 9.05/2.00 | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_30_3) = % 9.05/2.00 | | v2)) % 9.05/2.00 | | % 9.05/2.00 | | GROUND_INST: instantiating (23) with all_30_2, all_30_0, simplifying with % 9.05/2.00 | | (8), (12) gives: % 9.05/2.00 | | (24) all_30_0 = all_30_2 | ? [v0: int] : ( ~ (v0 = 0) & in(all_30_2, % 9.05/2.00 | | all_30_3) = v0) % 9.05/2.00 | | % 9.05/2.00 | | BETA: splitting (24) gives: % 9.05/2.00 | | % 9.05/2.00 | | Case 1: % 9.05/2.00 | | | % 9.05/2.00 | | | (25) all_30_0 = all_30_2 % 9.05/2.00 | | | % 9.05/2.01 | | | REDUCE: (6), (25) imply: % 9.05/2.01 | | | (26) $false % 9.05/2.01 | | | % 9.05/2.01 | | | CLOSE: (26) is inconsistent. % 9.05/2.01 | | | % 9.05/2.01 | | Case 2: % 9.05/2.01 | | | % 9.05/2.01 | | | (27) ? [v0: int] : ( ~ (v0 = 0) & in(all_30_2, all_30_3) = v0) % 9.05/2.01 | | | % 9.05/2.01 | | | DELTA: instantiating (27) with fresh symbol all_72_0 gives: % 9.05/2.01 | | | (28) ~ (all_72_0 = 0) & in(all_30_2, all_30_3) = all_72_0 % 9.05/2.01 | | | % 9.05/2.01 | | | ALPHA: (28) implies: % 9.05/2.01 | | | (29) ~ (all_72_0 = 0) % 9.05/2.01 | | | (30) in(all_30_2, all_30_3) = all_72_0 % 9.05/2.01 | | | % 9.05/2.01 | | | GROUND_INST: instantiating (4) with 0, all_72_0, all_30_3, all_30_2, % 9.05/2.01 | | | simplifying with (10), (30) gives: % 9.05/2.01 | | | (31) all_72_0 = 0 % 9.05/2.01 | | | % 9.05/2.01 | | | REDUCE: (29), (31) imply: % 9.05/2.01 | | | (32) $false % 9.05/2.01 | | | % 9.05/2.01 | | | CLOSE: (32) is inconsistent. % 9.05/2.01 | | | % 9.05/2.01 | | End of split % 9.05/2.01 | | % 9.05/2.01 | End of split % 9.05/2.01 | % 9.05/2.01 End of proof % 9.05/2.01 % SZS output end Proof for theBenchmark % 9.05/2.01 % 9.05/2.01 1400ms %------------------------------------------------------------------------------