%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU217+3 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 17:43:21 EDT 2023 % Result : Theorem 7.63s 1.85s % Output : Proof 8.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : SEU217+3 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n015.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Wed Aug 23 18:50:50 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/sandbox/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.20/1.12 Prover 4: Preprocessing ... % 2.20/1.13 Prover 1: Preprocessing ... % 2.82/1.16 Prover 5: Preprocessing ... % 2.82/1.16 Prover 6: Preprocessing ... % 2.82/1.17 Prover 0: Preprocessing ... % 2.82/1.17 Prover 3: Preprocessing ... % 2.82/1.17 Prover 2: Preprocessing ... % 5.59/1.58 Prover 1: Warning: ignoring some quantifiers % 5.59/1.61 Prover 2: Proving ... % 5.59/1.61 Prover 3: Warning: ignoring some quantifiers % 5.59/1.61 Prover 5: Proving ... % 5.59/1.62 Prover 6: Proving ... % 5.98/1.62 Prover 3: Constructing countermodel ... % 5.98/1.63 Prover 1: Constructing countermodel ... % 5.98/1.64 Prover 4: Warning: ignoring some quantifiers % 6.19/1.66 Prover 4: Constructing countermodel ... % 6.19/1.72 Prover 0: Proving ... % 7.63/1.85 Prover 3: proved (1189ms) % 7.63/1.85 % 7.63/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.63/1.85 % 7.63/1.85 Prover 6: stopped % 7.63/1.85 Prover 0: stopped % 7.63/1.85 Prover 5: stopped % 7.80/1.87 Prover 2: stopped % 7.80/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.80/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.80/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.80/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.80/1.89 Prover 8: Preprocessing ... % 7.80/1.89 Prover 1: Found proof (size 24) % 7.80/1.89 Prover 1: proved (1238ms) % 7.80/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.80/1.89 Prover 4: stopped % 7.80/1.90 Prover 10: Preprocessing ... % 7.80/1.90 Prover 7: Preprocessing ... % 7.80/1.92 Prover 10: stopped % 7.80/1.92 Prover 7: stopped % 8.20/1.92 Prover 13: Preprocessing ... % 8.20/1.93 Prover 11: Preprocessing ... % 8.20/1.95 Prover 13: stopped % 8.43/1.96 Prover 11: stopped % 8.43/1.98 Prover 8: Warning: ignoring some quantifiers % 8.43/1.98 Prover 8: Constructing countermodel ... % 8.43/1.99 Prover 8: stopped % 8.43/1.99 % 8.43/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.43/1.99 % 8.43/2.00 % SZS output start Proof for theBenchmark % 8.43/2.00 Assumptions after simplification: % 8.43/2.00 --------------------------------- % 8.43/2.00 % 8.43/2.00 (fc2_funct_1) % 8.43/2.03 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) | % 8.43/2.03 function(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = % 8.43/2.03 v1) | ~ $i(v0) | relation(v1) = 0) % 8.43/2.03 % 8.43/2.03 (t34_funct_1) % 8.80/2.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity_relation(v0) = v2) | % 8.80/2.03 ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 8.80/2.03 (relation_dom(v1) = v4 & relation(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | (( ~ % 8.80/2.03 (v4 = v0) | v2 = v1 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 8.80/2.03 apply(v1, v5) = v6 & in(v5, v0) = 0 & $i(v6) & $i(v5))) & ( ~ (v2 % 8.80/2.03 = v1) | (v4 = v0 & ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ % 8.80/2.03 (apply(v1, v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & % 8.80/2.03 in(v5, v0) = v7)))))))) % 8.80/2.03 % 8.80/2.03 (t35_funct_1) % 8.80/2.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) & % 8.80/2.03 apply(v2, v1) = v3 & identity_relation(v0) = v2 & in(v1, v0) = 0 & $i(v3) & % 8.80/2.03 $i(v2) & $i(v1) & $i(v0)) % 8.80/2.03 % 8.80/2.03 (function-axioms) % 8.80/2.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.80/2.04 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 8.80/2.04 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.80/2.04 (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.80/2.04 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.80/2.04 (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: % 8.80/2.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.80/2.04 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 8.80/2.04 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) % 8.80/2.04 | ~ (identity_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 8.80/2.04 : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! % 8.80/2.04 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 8.80/2.04 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.80/2.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 8.80/2.04 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.80/2.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 8.80/2.04 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 8.80/2.04 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 8.80/2.04 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: % 8.80/2.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.80/2.04 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 8.80/2.04 % 8.80/2.04 Further assumptions not needed in the proof: % 8.80/2.04 -------------------------------------------- % 8.80/2.04 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, dt_k6_relat_1, % 8.80/2.04 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, % 8.80/2.04 fc5_relat_1, fc7_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, % 8.80/2.04 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_relat_1, reflexivity_r1_tarski, % 8.80/2.04 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, % 8.80/2.04 t8_boole % 8.80/2.04 % 8.80/2.04 Those formulas are unsatisfiable: % 8.80/2.04 --------------------------------- % 8.80/2.04 % 8.80/2.04 Begin of proof % 8.80/2.04 | % 8.80/2.04 | ALPHA: (fc2_funct_1) implies: % 8.80/2.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 8.80/2.05 | $i(v0) | relation(v1) = 0) % 8.80/2.05 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 8.80/2.05 | $i(v0) | function(v1) = 0) % 8.80/2.05 | % 8.80/2.05 | ALPHA: (function-axioms) implies: % 8.80/2.05 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.80/2.05 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 8.80/2.05 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.80/2.05 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 8.80/2.05 | % 8.80/2.05 | DELTA: instantiating (t35_funct_1) with fresh symbols all_38_0, all_38_1, % 8.80/2.05 | all_38_2, all_38_3 gives: % 8.80/2.05 | (5) ~ (all_38_0 = all_38_2) & apply(all_38_1, all_38_2) = all_38_0 & % 8.80/2.05 | identity_relation(all_38_3) = all_38_1 & in(all_38_2, all_38_3) = 0 & % 8.80/2.05 | $i(all_38_0) & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) % 8.80/2.05 | % 8.80/2.05 | ALPHA: (5) implies: % 8.80/2.05 | (6) ~ (all_38_0 = all_38_2) % 8.80/2.05 | (7) $i(all_38_3) % 8.80/2.05 | (8) $i(all_38_2) % 8.80/2.05 | (9) $i(all_38_1) % 8.80/2.05 | (10) in(all_38_2, all_38_3) = 0 % 8.80/2.05 | (11) identity_relation(all_38_3) = all_38_1 % 8.80/2.05 | (12) apply(all_38_1, all_38_2) = all_38_0 % 8.80/2.05 | % 8.80/2.05 | GROUND_INST: instantiating (2) with all_38_3, all_38_1, simplifying with (7), % 8.80/2.05 | (11) gives: % 8.80/2.05 | (13) function(all_38_1) = 0 % 8.80/2.05 | % 8.80/2.05 | GROUND_INST: instantiating (1) with all_38_3, all_38_1, simplifying with (7), % 8.80/2.05 | (11) gives: % 8.80/2.05 | (14) relation(all_38_1) = 0 % 8.80/2.05 | % 8.80/2.05 | GROUND_INST: instantiating (t34_funct_1) with all_38_3, all_38_1, all_38_1, % 8.80/2.05 | simplifying with (7), (9), (11), (13) gives: % 8.80/2.06 | (15) ? [v0: any] : ? [v1: $i] : (relation_dom(all_38_1) = v1 & % 8.80/2.06 | relation(all_38_1) = v0 & $i(v1) & ( ~ (v0 = 0) | (v1 = all_38_3 & % 8.80/2.06 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (apply(all_38_1, v2) = % 8.80/2.06 | v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, % 8.80/2.06 | all_38_3) = v4))))) % 8.80/2.06 | % 8.80/2.06 | DELTA: instantiating (15) with fresh symbols all_65_0, all_65_1 gives: % 8.80/2.06 | (16) relation_dom(all_38_1) = all_65_0 & relation(all_38_1) = all_65_1 & % 8.80/2.06 | $i(all_65_0) & ( ~ (all_65_1 = 0) | (all_65_0 = all_38_3 & ! [v0: $i] % 8.80/2.06 | : ! [v1: $i] : (v1 = v0 | ~ (apply(all_38_1, v0) = v1) | ~ % 8.80/2.06 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_38_3) = v2)))) % 8.80/2.06 | % 8.80/2.06 | ALPHA: (16) implies: % 8.80/2.06 | (17) relation(all_38_1) = all_65_1 % 8.80/2.06 | (18) ~ (all_65_1 = 0) | (all_65_0 = all_38_3 & ! [v0: $i] : ! [v1: $i] : % 8.80/2.06 | (v1 = v0 | ~ (apply(all_38_1, v0) = v1) | ~ $i(v0) | ? [v2: int] % 8.80/2.06 | : ( ~ (v2 = 0) & in(v0, all_38_3) = v2))) % 8.80/2.06 | % 8.80/2.06 | GROUND_INST: instantiating (3) with 0, all_65_1, all_38_1, simplifying with % 8.80/2.06 | (14), (17) gives: % 8.80/2.06 | (19) all_65_1 = 0 % 8.80/2.06 | % 8.80/2.06 | BETA: splitting (18) gives: % 8.80/2.06 | % 8.80/2.06 | Case 1: % 8.80/2.06 | | % 8.80/2.06 | | (20) ~ (all_65_1 = 0) % 8.80/2.06 | | % 8.80/2.06 | | REDUCE: (19), (20) imply: % 8.80/2.06 | | (21) $false % 8.80/2.06 | | % 8.80/2.06 | | CLOSE: (21) is inconsistent. % 8.80/2.06 | | % 8.80/2.06 | Case 2: % 8.80/2.06 | | % 8.80/2.06 | | (22) all_65_0 = all_38_3 & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 8.80/2.06 | | (apply(all_38_1, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 8.80/2.06 | | 0) & in(v0, all_38_3) = v2)) % 8.80/2.06 | | % 8.80/2.06 | | ALPHA: (22) implies: % 8.80/2.06 | | (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (apply(all_38_1, v0) = v1) % 8.80/2.06 | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_38_3) = % 8.80/2.06 | | v2)) % 8.80/2.06 | | % 8.80/2.06 | | GROUND_INST: instantiating (23) with all_38_2, all_38_0, simplifying with % 8.80/2.06 | | (8), (12) gives: % 8.80/2.06 | | (24) all_38_0 = all_38_2 | ? [v0: int] : ( ~ (v0 = 0) & in(all_38_2, % 8.80/2.06 | | all_38_3) = v0) % 8.80/2.06 | | % 8.80/2.06 | | BETA: splitting (24) gives: % 8.80/2.06 | | % 8.80/2.06 | | Case 1: % 8.80/2.06 | | | % 8.80/2.06 | | | (25) all_38_0 = all_38_2 % 8.80/2.06 | | | % 8.80/2.06 | | | REDUCE: (6), (25) imply: % 8.80/2.06 | | | (26) $false % 8.80/2.06 | | | % 8.80/2.06 | | | CLOSE: (26) is inconsistent. % 8.80/2.06 | | | % 8.80/2.06 | | Case 2: % 8.80/2.06 | | | % 8.80/2.07 | | | (27) ? [v0: int] : ( ~ (v0 = 0) & in(all_38_2, all_38_3) = v0) % 8.80/2.07 | | | % 8.80/2.07 | | | DELTA: instantiating (27) with fresh symbol all_86_0 gives: % 8.80/2.07 | | | (28) ~ (all_86_0 = 0) & in(all_38_2, all_38_3) = all_86_0 % 8.80/2.07 | | | % 8.80/2.07 | | | ALPHA: (28) implies: % 8.80/2.07 | | | (29) ~ (all_86_0 = 0) % 8.80/2.07 | | | (30) in(all_38_2, all_38_3) = all_86_0 % 8.80/2.07 | | | % 8.80/2.07 | | | GROUND_INST: instantiating (4) with 0, all_86_0, all_38_3, all_38_2, % 8.80/2.07 | | | simplifying with (10), (30) gives: % 8.80/2.07 | | | (31) all_86_0 = 0 % 8.80/2.07 | | | % 8.80/2.07 | | | REDUCE: (29), (31) imply: % 8.80/2.07 | | | (32) $false % 8.80/2.07 | | | % 8.80/2.07 | | | CLOSE: (32) is inconsistent. % 8.80/2.07 | | | % 8.80/2.07 | | End of split % 8.80/2.07 | | % 8.80/2.07 | End of split % 8.80/2.07 | % 8.80/2.07 End of proof % 8.80/2.07 % SZS output end Proof for theBenchmark % 8.80/2.07 % 8.80/2.07 1432ms %------------------------------------------------------------------------------