%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU211+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 : n012.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 17:43:17 EDT 2023 % Result : Theorem 9.40s 2.15s % Output : Proof 11.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU211+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n012.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Aug 23 21:27:12 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.66 ________ _____ % 0.19/0.66 ___ __ \_________(_)________________________________ % 0.19/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.66 % 0.19/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.66 (2023-06-19) % 0.19/0.66 % 0.19/0.66 (c) Philipp Rümmer, 2009-2023 % 0.19/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.66 Amanda Stjerna. % 0.19/0.66 Free software under BSD-3-Clause. % 0.19/0.66 % 0.19/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.66 % 0.19/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.68 Running up to 7 provers in parallel. % 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.56/1.15 Prover 4: Preprocessing ... % 2.56/1.15 Prover 1: Preprocessing ... % 2.81/1.20 Prover 0: Preprocessing ... % 2.81/1.20 Prover 3: Preprocessing ... % 2.81/1.20 Prover 6: Preprocessing ... % 2.81/1.20 Prover 2: Preprocessing ... % 2.81/1.20 Prover 5: Preprocessing ... % 5.28/1.68 Prover 1: Warning: ignoring some quantifiers % 5.75/1.70 Prover 3: Warning: ignoring some quantifiers % 5.75/1.70 Prover 4: Warning: ignoring some quantifiers % 5.75/1.72 Prover 5: Proving ... % 5.75/1.72 Prover 2: Proving ... % 5.75/1.72 Prover 6: Proving ... % 5.75/1.73 Prover 1: Constructing countermodel ... % 5.75/1.73 Prover 3: Constructing countermodel ... % 5.75/1.73 Prover 4: Constructing countermodel ... % 6.71/1.78 Prover 0: Proving ... % 9.16/2.15 Prover 3: proved (1453ms) % 9.40/2.15 % 9.40/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.40/2.15 % 9.40/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.40/2.15 Prover 6: stopped % 9.40/2.15 Prover 2: stopped % 9.40/2.15 Prover 5: stopped % 9.40/2.16 Prover 0: stopped % 9.40/2.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.40/2.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.40/2.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.40/2.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.40/2.19 Prover 1: Found proof (size 31) % 9.40/2.19 Prover 1: proved (1508ms) % 9.40/2.19 Prover 4: stopped % 9.40/2.22 Prover 10: Preprocessing ... % 9.40/2.25 Prover 7: Preprocessing ... % 9.40/2.26 Prover 8: Preprocessing ... % 9.40/2.27 Prover 7: stopped % 9.40/2.27 Prover 13: Preprocessing ... % 9.40/2.28 Prover 10: stopped % 9.40/2.29 Prover 11: Preprocessing ... % 9.40/2.31 Prover 13: stopped % 9.40/2.32 Prover 11: stopped % 10.15/2.36 Prover 8: Warning: ignoring some quantifiers % 10.15/2.37 Prover 8: Constructing countermodel ... % 10.15/2.38 Prover 8: stopped % 10.15/2.38 % 10.15/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.15/2.38 % 10.15/2.38 % SZS output start Proof for theBenchmark % 10.15/2.39 Assumptions after simplification: % 10.15/2.39 --------------------------------- % 10.15/2.39 % 10.15/2.39 (d14_relat_1) % 10.88/2.42 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ? [v1: $i] : ! [v2: $i] % 10.88/2.42 : ! [v3: $i] : (v3 = v1 | ~ (relation_inverse_image(v0, v2) = v3) | ~ % 10.88/2.42 $i(v2) | ~ $i(v1) | ? [v4: $i] : ? [v5: any] : (in(v4, v1) = v5 & % 10.88/2.42 $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ % 10.88/2.42 (ordered_pair(v4, v6) = v7) | ~ (in(v7, v0) = 0) | ~ $i(v6) | ? % 10.88/2.42 [v8: int] : ( ~ (v8 = 0) & in(v6, v2) = v8))) & (v5 = 0 | ? [v6: % 10.88/2.42 $i] : ? [v7: $i] : (ordered_pair(v4, v6) = v7 & in(v7, v0) = 0 & % 10.88/2.42 in(v6, v2) = 0 & $i(v7) & $i(v6))))) & ! [v1: $i] : ! [v2: $i] : % 10.88/2.42 ( ~ (relation_inverse_image(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ( ! % 10.88/2.42 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 10.88/2.42 ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = v6) | ~ % 10.88/2.42 (in(v6, v0) = 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & % 10.88/2.42 in(v5, v1) = v7))) & ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ % 10.88/2.42 $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v3, v4) = v5 & % 10.88/2.42 in(v5, v0) = 0 & in(v4, v1) = 0 & $i(v5) & $i(v4))))))) % 10.88/2.42 % 10.88/2.42 (d3_tarski) % 10.88/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 10.88/2.42 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 10.88/2.42 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.88/2.42 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 10.88/2.42 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 10.88/2.42 % 10.88/2.42 (t178_relat_1) % 10.88/2.43 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.88/2.43 int] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & % 10.88/2.43 relation_inverse_image(v2, v1) = v4 & relation_inverse_image(v2, v0) = v3 & % 10.88/2.43 relation(v2) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.88/2.43 % 10.88/2.43 (function-axioms) % 10.88/2.43 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.88/2.43 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 10.88/2.43 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.88/2.43 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 10.88/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.88/2.43 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 10.88/2.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 10.88/2.43 ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 10.88/2.43 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.88/2.43 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 10.88/2.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.88/2.43 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 10.88/2.43 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 10.88/2.43 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 10.88/2.43 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: MultipleValueBool] % 10.88/2.43 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) % 10.88/2.43 | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.88/2.43 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 10.88/2.43 (empty(v2) = v0)) % 10.88/2.43 % 10.88/2.43 Further assumptions not needed in the proof: % 10.88/2.43 -------------------------------------------- % 10.88/2.43 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d5_tarski, % 10.88/2.43 dt_k10_relat_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, % 10.88/2.43 dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, % 10.88/2.43 fc1_zfmisc_1, fc2_subset_1, fc3_subset_1, fc4_relat_1, rc1_relat_1, % 10.88/2.43 rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0, % 10.88/2.43 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, % 10.88/2.43 t6_boole, t7_boole, t8_boole % 10.88/2.43 % 10.88/2.43 Those formulas are unsatisfiable: % 10.88/2.43 --------------------------------- % 10.88/2.43 % 10.88/2.43 Begin of proof % 10.88/2.43 | % 10.88/2.43 | ALPHA: (d3_tarski) implies: % 10.88/2.43 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 10.88/2.44 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1) % 10.88/2.44 | = 0)) % 10.88/2.44 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 10.88/2.44 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 10.88/2.44 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 10.88/2.44 | % 10.88/2.44 | ALPHA: (function-axioms) implies: % 10.88/2.44 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.88/2.44 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 10.88/2.44 | % 10.88/2.44 | DELTA: instantiating (t178_relat_1) with fresh symbols all_35_0, all_35_1, % 10.88/2.44 | all_35_2, all_35_3, all_35_4, all_35_5 gives: % 10.88/2.44 | (4) ~ (all_35_0 = 0) & subset(all_35_2, all_35_1) = all_35_0 & % 10.88/2.44 | subset(all_35_5, all_35_4) = 0 & relation_inverse_image(all_35_3, % 10.88/2.44 | all_35_4) = all_35_1 & relation_inverse_image(all_35_3, all_35_5) = % 10.88/2.44 | all_35_2 & relation(all_35_3) = 0 & $i(all_35_1) & $i(all_35_2) & % 10.88/2.44 | $i(all_35_3) & $i(all_35_4) & $i(all_35_5) % 10.88/2.44 | % 10.88/2.44 | ALPHA: (4) implies: % 10.88/2.44 | (5) ~ (all_35_0 = 0) % 10.88/2.44 | (6) $i(all_35_5) % 10.88/2.44 | (7) $i(all_35_4) % 10.88/2.44 | (8) $i(all_35_3) % 10.88/2.44 | (9) $i(all_35_2) % 10.88/2.44 | (10) $i(all_35_1) % 10.88/2.44 | (11) relation(all_35_3) = 0 % 10.88/2.44 | (12) relation_inverse_image(all_35_3, all_35_5) = all_35_2 % 10.88/2.44 | (13) relation_inverse_image(all_35_3, all_35_4) = all_35_1 % 10.88/2.44 | (14) subset(all_35_5, all_35_4) = 0 % 10.88/2.44 | (15) subset(all_35_2, all_35_1) = all_35_0 % 10.88/2.44 | % 10.88/2.44 | GROUND_INST: instantiating (d14_relat_1) with all_35_3, simplifying with (8), % 10.88/2.44 | (11) gives: % 10.88/2.45 | (16) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 10.88/2.45 | (relation_inverse_image(all_35_3, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 10.88/2.45 | | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = % 10.88/2.45 | 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 10.88/2.45 | v6) | ~ (in(v6, all_35_3) = 0) | ~ $i(v5) | ? [v7: int] : % 10.88/2.45 | ( ~ (v7 = 0) & in(v5, v1) = v7))) & (v4 = 0 | ? [v5: $i] : ? % 10.88/2.45 | [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, all_35_3) = 0 & % 10.88/2.45 | in(v5, v1) = 0 & $i(v6) & $i(v5))))) & ! [v0: $i] : ! [v1: % 10.88/2.45 | $i] : ( ~ (relation_inverse_image(all_35_3, v0) = v1) | ~ $i(v1) | % 10.88/2.45 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) = % 10.88/2.45 | v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 10.88/2.45 | (ordered_pair(v2, v4) = v5) | ~ (in(v5, all_35_3) = 0) | ~ % 10.88/2.45 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & ! % 10.88/2.45 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? % 10.88/2.45 | [v4: $i] : (ordered_pair(v2, v3) = v4 & in(v4, all_35_3) = 0 & % 10.88/2.45 | in(v3, v0) = 0 & $i(v4) & $i(v3))))) % 10.88/2.45 | % 10.88/2.45 | ALPHA: (16) implies: % 10.88/2.45 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_35_3, v0) % 10.88/2.45 | = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 % 10.88/2.45 | = 0 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: % 10.88/2.45 | $i] : ( ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, all_35_3) = % 10.88/2.45 | 0) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = % 10.88/2.45 | v6))) & ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? % 10.88/2.45 | [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & in(v4, % 10.88/2.45 | all_35_3) = 0 & in(v3, v0) = 0 & $i(v4) & $i(v3))))) % 10.88/2.45 | % 10.88/2.45 | GROUND_INST: instantiating (1) with all_35_5, all_35_4, simplifying with (6), % 10.88/2.45 | (7), (14) gives: % 10.88/2.45 | (18) ! [v0: $i] : ( ~ (in(v0, all_35_5) = 0) | ~ $i(v0) | in(v0, % 10.88/2.45 | all_35_4) = 0) % 10.88/2.45 | % 10.88/2.45 | GROUND_INST: instantiating (2) with all_35_2, all_35_1, all_35_0, simplifying % 10.88/2.45 | with (9), (10), (15) gives: % 10.88/2.45 | (19) all_35_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 10.88/2.45 | all_35_1) = v1 & in(v0, all_35_2) = 0 & $i(v0)) % 10.88/2.45 | % 10.88/2.45 | GROUND_INST: instantiating (17) with all_35_5, all_35_2, simplifying with (6), % 10.88/2.45 | (9), (12) gives: % 10.88/2.45 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_35_2) = v1) | ~ % 10.88/2.45 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 10.88/2.45 | | ~ (in(v3, all_35_3) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 10.88/2.45 | 0) & in(v2, all_35_5) = v4))) & ! [v0: $i] : ( ~ (in(v0, % 10.88/2.45 | all_35_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 10.88/2.45 | (ordered_pair(v0, v1) = v2 & in(v2, all_35_3) = 0 & in(v1, all_35_5) % 10.88/2.45 | = 0 & $i(v2) & $i(v1))) % 10.88/2.45 | % 10.88/2.45 | ALPHA: (20) implies: % 11.20/2.46 | (21) ! [v0: $i] : ( ~ (in(v0, all_35_2) = 0) | ~ $i(v0) | ? [v1: $i] : % 11.20/2.46 | ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_35_3) = 0 & % 11.20/2.46 | in(v1, all_35_5) = 0 & $i(v2) & $i(v1))) % 11.20/2.46 | % 11.20/2.46 | GROUND_INST: instantiating (17) with all_35_4, all_35_1, simplifying with (7), % 11.20/2.46 | (10), (13) gives: % 11.20/2.46 | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_35_1) = v1) | ~ % 11.20/2.46 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 11.20/2.46 | | ~ (in(v3, all_35_3) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 11.20/2.46 | 0) & in(v2, all_35_4) = v4))) & ! [v0: $i] : ( ~ (in(v0, % 11.20/2.46 | all_35_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 11.20/2.46 | (ordered_pair(v0, v1) = v2 & in(v2, all_35_3) = 0 & in(v1, all_35_4) % 11.20/2.46 | = 0 & $i(v2) & $i(v1))) % 11.20/2.46 | % 11.20/2.46 | ALPHA: (22) implies: % 11.20/2.46 | (23) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_35_1) = v1) | ~ % 11.20/2.46 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 11.20/2.46 | | ~ (in(v3, all_35_3) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 11.20/2.46 | 0) & in(v2, all_35_4) = v4))) % 11.20/2.46 | % 11.20/2.46 | BETA: splitting (19) gives: % 11.20/2.46 | % 11.20/2.46 | Case 1: % 11.20/2.46 | | % 11.20/2.46 | | (24) all_35_0 = 0 % 11.20/2.46 | | % 11.20/2.46 | | REDUCE: (5), (24) imply: % 11.20/2.46 | | (25) $false % 11.20/2.46 | | % 11.20/2.46 | | CLOSE: (25) is inconsistent. % 11.20/2.46 | | % 11.20/2.46 | Case 2: % 11.20/2.46 | | % 11.20/2.46 | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_35_1) = v1 & % 11.20/2.46 | | in(v0, all_35_2) = 0 & $i(v0)) % 11.24/2.46 | | % 11.24/2.46 | | DELTA: instantiating (26) with fresh symbols all_62_0, all_62_1 gives: % 11.24/2.46 | | (27) ~ (all_62_0 = 0) & in(all_62_1, all_35_1) = all_62_0 & in(all_62_1, % 11.24/2.46 | | all_35_2) = 0 & $i(all_62_1) % 11.24/2.46 | | % 11.24/2.46 | | ALPHA: (27) implies: % 11.24/2.46 | | (28) ~ (all_62_0 = 0) % 11.24/2.46 | | (29) $i(all_62_1) % 11.24/2.46 | | (30) in(all_62_1, all_35_2) = 0 % 11.24/2.46 | | (31) in(all_62_1, all_35_1) = all_62_0 % 11.24/2.46 | | % 11.24/2.46 | | GROUND_INST: instantiating (21) with all_62_1, simplifying with (29), (30) % 11.24/2.46 | | gives: % 11.24/2.47 | | (32) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_62_1, v0) = v1 & % 11.24/2.47 | | in(v1, all_35_3) = 0 & in(v0, all_35_5) = 0 & $i(v1) & $i(v0)) % 11.24/2.47 | | % 11.24/2.47 | | GROUND_INST: instantiating (23) with all_62_1, all_62_0, simplifying with % 11.24/2.47 | | (29), (31) gives: % 11.24/2.47 | | (33) all_62_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 11.24/2.47 | | (ordered_pair(all_62_1, v0) = v1) | ~ (in(v1, all_35_3) = 0) | ~ % 11.24/2.47 | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_35_4) = v2)) % 11.24/2.47 | | % 11.24/2.47 | | DELTA: instantiating (32) with fresh symbols all_73_0, all_73_1 gives: % 11.24/2.47 | | (34) ordered_pair(all_62_1, all_73_1) = all_73_0 & in(all_73_0, all_35_3) % 11.24/2.47 | | = 0 & in(all_73_1, all_35_5) = 0 & $i(all_73_0) & $i(all_73_1) % 11.24/2.47 | | % 11.24/2.47 | | ALPHA: (34) implies: % 11.24/2.47 | | (35) $i(all_73_1) % 11.24/2.47 | | (36) in(all_73_1, all_35_5) = 0 % 11.24/2.47 | | (37) in(all_73_0, all_35_3) = 0 % 11.24/2.47 | | (38) ordered_pair(all_62_1, all_73_1) = all_73_0 % 11.24/2.47 | | % 11.24/2.47 | | BETA: splitting (33) gives: % 11.24/2.47 | | % 11.24/2.47 | | Case 1: % 11.24/2.47 | | | % 11.24/2.47 | | | (39) all_62_0 = 0 % 11.24/2.47 | | | % 11.24/2.47 | | | REDUCE: (28), (39) imply: % 11.24/2.47 | | | (40) $false % 11.24/2.47 | | | % 11.24/2.47 | | | CLOSE: (40) is inconsistent. % 11.24/2.47 | | | % 11.24/2.47 | | Case 2: % 11.24/2.47 | | | % 11.24/2.47 | | | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_62_1, v0) = v1) % 11.24/2.47 | | | | ~ (in(v1, all_35_3) = 0) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 11.24/2.47 | | | = 0) & in(v0, all_35_4) = v2)) % 11.24/2.47 | | | % 11.24/2.47 | | | GROUND_INST: instantiating (18) with all_73_1, simplifying with (35), (36) % 11.24/2.47 | | | gives: % 11.24/2.47 | | | (42) in(all_73_1, all_35_4) = 0 % 11.24/2.47 | | | % 11.24/2.47 | | | GROUND_INST: instantiating (41) with all_73_1, all_73_0, simplifying with % 11.24/2.47 | | | (35), (37), (38) gives: % 11.24/2.47 | | | (43) ? [v0: int] : ( ~ (v0 = 0) & in(all_73_1, all_35_4) = v0) % 11.24/2.47 | | | % 11.24/2.47 | | | DELTA: instantiating (43) with fresh symbol all_92_0 gives: % 11.24/2.47 | | | (44) ~ (all_92_0 = 0) & in(all_73_1, all_35_4) = all_92_0 % 11.24/2.47 | | | % 11.24/2.47 | | | ALPHA: (44) implies: % 11.24/2.47 | | | (45) ~ (all_92_0 = 0) % 11.24/2.47 | | | (46) in(all_73_1, all_35_4) = all_92_0 % 11.24/2.47 | | | % 11.24/2.47 | | | GROUND_INST: instantiating (3) with 0, all_92_0, all_35_4, all_73_1, % 11.24/2.47 | | | simplifying with (42), (46) gives: % 11.24/2.47 | | | (47) all_92_0 = 0 % 11.24/2.47 | | | % 11.24/2.47 | | | REDUCE: (45), (47) imply: % 11.24/2.47 | | | (48) $false % 11.24/2.47 | | | % 11.24/2.47 | | | CLOSE: (48) is inconsistent. % 11.24/2.47 | | | % 11.24/2.47 | | End of split % 11.24/2.47 | | % 11.24/2.47 | End of split % 11.24/2.47 | % 11.24/2.47 End of proof % 11.24/2.47 % SZS output end Proof for theBenchmark % 11.24/2.47 % 11.24/2.47 1809ms %------------------------------------------------------------------------------