%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU166+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 : n001.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 17:42:58 EDT 2023 % Result : Theorem 6.53s 1.53s % Output : Proof 7.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU166+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n001.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 15:27:09 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.56 ________ _____ % 0.19/0.56 ___ __ \_________(_)________________________________ % 0.19/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.56 % 0.19/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.56 (2023-06-19) % 0.19/0.56 % 0.19/0.56 (c) Philipp Rümmer, 2009-2023 % 0.19/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.56 Amanda Stjerna. % 0.19/0.56 Free software under BSD-3-Clause. % 0.19/0.56 % 0.19/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.56 % 0.19/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.57 Running up to 7 provers in parallel. % 0.19/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.00/0.94 Prover 1: Preprocessing ... % 2.00/0.94 Prover 4: Preprocessing ... % 2.62/0.98 Prover 5: Preprocessing ... % 2.62/0.98 Prover 0: Preprocessing ... % 2.62/0.98 Prover 6: Preprocessing ... % 2.62/0.98 Prover 3: Preprocessing ... % 2.62/0.98 Prover 2: Preprocessing ... % 4.16/1.21 Prover 6: Proving ... % 4.16/1.21 Prover 1: Warning: ignoring some quantifiers % 4.16/1.22 Prover 3: Warning: ignoring some quantifiers % 4.16/1.22 Prover 4: Warning: ignoring some quantifiers % 4.16/1.23 Prover 3: Constructing countermodel ... % 4.16/1.23 Prover 1: Constructing countermodel ... % 4.16/1.24 Prover 5: Proving ... % 4.16/1.24 Prover 4: Constructing countermodel ... % 4.16/1.25 Prover 0: Proving ... % 4.94/1.29 Prover 2: Proving ... % 6.53/1.53 Prover 0: proved (948ms) % 6.53/1.53 % 6.53/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.53/1.53 % 6.53/1.53 Prover 3: stopped % 6.53/1.54 Prover 5: stopped % 6.53/1.54 Prover 2: stopped % 6.53/1.55 Prover 6: stopped % 6.53/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.53/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.53/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.53/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.53/1.56 Prover 10: Preprocessing ... % 6.53/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.53/1.57 Prover 7: Preprocessing ... % 6.53/1.58 Prover 8: Preprocessing ... % 6.53/1.58 Prover 13: Preprocessing ... % 7.02/1.61 Prover 10: Warning: ignoring some quantifiers % 7.02/1.61 Prover 11: Preprocessing ... % 7.02/1.61 Prover 10: Constructing countermodel ... % 7.02/1.62 Prover 7: Warning: ignoring some quantifiers % 7.02/1.63 Prover 7: Constructing countermodel ... % 7.02/1.66 Prover 8: Warning: ignoring some quantifiers % 7.02/1.66 Prover 4: Found proof (size 52) % 7.02/1.66 Prover 4: proved (1078ms) % 7.02/1.66 Prover 7: stopped % 7.02/1.66 Prover 10: gave up % 7.02/1.66 Prover 1: stopped % 7.02/1.66 Prover 8: Constructing countermodel ... % 7.02/1.66 Prover 13: Warning: ignoring some quantifiers % 7.65/1.67 Prover 8: stopped % 7.65/1.67 Prover 13: Constructing countermodel ... % 7.65/1.67 Prover 13: stopped % 7.65/1.68 Prover 11: Warning: ignoring some quantifiers % 7.73/1.68 Prover 11: Constructing countermodel ... % 7.73/1.69 Prover 11: stopped % 7.73/1.69 % 7.73/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.73/1.69 % 7.73/1.70 % SZS output start Proof for theBenchmark % 7.73/1.70 Assumptions after simplification: % 7.73/1.70 --------------------------------- % 7.73/1.70 % 7.73/1.70 (d2_zfmisc_1) % 7.97/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 7.97/1.73 $i] : ! [v6: $i] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ % 7.97/1.73 (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ~ $i(v6) | ~ $i(v5) | % 7.97/1.73 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] % 7.97/1.73 : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 7.97/1.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.97/1.73 (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 7.97/1.73 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : % 7.97/1.73 (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) & % 7.97/1.73 $i(v4))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = % 7.97/1.73 v0 | ~ (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.97/1.73 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 7.97/1.73 int] : ? [v9: int] : ? [v10: $i] : (in(v4, v0) = v5 & $i(v7) & $i(v6) & % 7.97/1.73 $i(v4) & ( ~ (v5 = 0) | ! [v11: $i] : ! [v12: $i] : ( ~ % 7.97/1.73 (ordered_pair(v11, v12) = v4) | ~ $i(v12) | ~ $i(v11) | ? [v13: % 7.97/1.73 any] : ? [v14: any] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ % 7.97/1.73 (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = % 7.97/1.73 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) % 7.97/1.73 % 7.97/1.74 (d3_tarski) % 7.97/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.97/1.74 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 7.97/1.74 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 7.97/1.74 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 7.97/1.74 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 7.97/1.74 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 7.97/1.74 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 7.97/1.74 $i(v0) | in(v2, v1) = 0) % 7.97/1.74 % 7.97/1.74 (t118_zfmisc_1) % 7.97/1.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.97/1.74 any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (subset(v6, v7) = v8 & % 7.97/1.74 subset(v3, v4) = v5 & subset(v0, v1) = 0 & cartesian_product2(v2, v1) = v7 & % 7.97/1.74 cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v4 & % 7.97/1.74 cartesian_product2(v0, v2) = v3 & $i(v7) & $i(v6) & $i(v4) & $i(v3) & $i(v2) % 7.97/1.74 & $i(v1) & $i(v0) & ( ~ (v8 = 0) | ~ (v5 = 0))) % 7.97/1.74 % 7.97/1.74 (function-axioms) % 7.97/1.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.97/1.74 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 7.97/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.97/1.75 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 7.97/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.97/1.75 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 7.97/1.75 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, % 7.97/1.75 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 7.97/1.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 7.97/1.75 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 7.97/1.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.97/1.75 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 7.97/1.75 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 7.97/1.75 % 7.97/1.75 Further assumptions not needed in the proof: % 7.97/1.75 -------------------------------------------- % 7.97/1.75 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, dt_k1_tarski, % 7.97/1.75 dt_k2_tarski, dt_k2_zfmisc_1, dt_k4_tarski, fc1_zfmisc_1, rc1_xboole_0, % 7.97/1.75 rc2_xboole_0, reflexivity_r1_tarski % 7.97/1.75 % 7.97/1.75 Those formulas are unsatisfiable: % 7.97/1.75 --------------------------------- % 7.97/1.75 % 7.97/1.75 Begin of proof % 7.97/1.75 | % 7.97/1.75 | ALPHA: (d2_zfmisc_1) implies: % 7.97/1.75 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.97/1.75 | (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | % 7.97/1.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : % 7.97/1.75 | (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) % 7.97/1.75 | & $i(v4))) % 7.97/1.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 7.97/1.75 | ! [v5: $i] : ! [v6: $i] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = % 7.97/1.75 | v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ~ % 7.97/1.75 | $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 7.97/1.75 | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ % 7.97/1.75 | (v8 = 0) | ~ (v7 = 0)))) % 7.97/1.75 | % 7.97/1.75 | ALPHA: (d3_tarski) implies: % 7.97/1.75 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 7.97/1.75 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = % 7.97/1.75 | 0) % 7.97/1.75 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 7.97/1.75 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 7.97/1.75 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 7.97/1.75 | % 7.97/1.75 | ALPHA: (function-axioms) implies: % 7.97/1.75 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.97/1.75 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 7.97/1.75 | % 7.97/1.75 | DELTA: instantiating (t118_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 7.97/1.75 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7, all_14_8 % 7.97/1.75 | gives: % 7.97/1.75 | (6) subset(all_14_2, all_14_1) = all_14_0 & subset(all_14_5, all_14_4) = % 7.97/1.75 | all_14_3 & subset(all_14_8, all_14_7) = 0 & % 7.97/1.75 | cartesian_product2(all_14_6, all_14_7) = all_14_1 & % 7.97/1.75 | cartesian_product2(all_14_6, all_14_8) = all_14_2 & % 7.97/1.75 | cartesian_product2(all_14_7, all_14_6) = all_14_4 & % 7.97/1.75 | cartesian_product2(all_14_8, all_14_6) = all_14_5 & $i(all_14_1) & % 7.97/1.75 | $i(all_14_2) & $i(all_14_4) & $i(all_14_5) & $i(all_14_6) & % 7.97/1.75 | $i(all_14_7) & $i(all_14_8) & ( ~ (all_14_0 = 0) | ~ (all_14_3 = 0)) % 7.97/1.75 | % 7.97/1.75 | ALPHA: (6) implies: % 7.97/1.76 | (7) $i(all_14_8) % 7.97/1.76 | (8) $i(all_14_7) % 7.97/1.76 | (9) $i(all_14_6) % 7.97/1.76 | (10) $i(all_14_5) % 7.97/1.76 | (11) $i(all_14_4) % 7.97/1.76 | (12) $i(all_14_2) % 7.97/1.76 | (13) $i(all_14_1) % 7.97/1.76 | (14) cartesian_product2(all_14_8, all_14_6) = all_14_5 % 7.97/1.76 | (15) cartesian_product2(all_14_7, all_14_6) = all_14_4 % 7.97/1.76 | (16) cartesian_product2(all_14_6, all_14_8) = all_14_2 % 7.97/1.76 | (17) cartesian_product2(all_14_6, all_14_7) = all_14_1 % 7.97/1.76 | (18) subset(all_14_8, all_14_7) = 0 % 7.97/1.76 | (19) subset(all_14_5, all_14_4) = all_14_3 % 7.97/1.76 | (20) subset(all_14_2, all_14_1) = all_14_0 % 7.97/1.76 | (21) ~ (all_14_0 = 0) | ~ (all_14_3 = 0) % 7.97/1.76 | % 7.97/1.76 | GROUND_INST: instantiating (4) with all_14_5, all_14_4, all_14_3, simplifying % 7.97/1.76 | with (10), (11), (19) gives: % 7.97/1.76 | (22) all_14_3 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 7.97/1.76 | all_14_4) = v1 & in(v0, all_14_5) = 0 & $i(v0)) % 7.97/1.76 | % 7.97/1.76 | GROUND_INST: instantiating (4) with all_14_2, all_14_1, all_14_0, simplifying % 7.97/1.76 | with (12), (13), (20) gives: % 7.97/1.76 | (23) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 7.97/1.76 | all_14_1) = v1 & in(v0, all_14_2) = 0 & $i(v0)) % 7.97/1.76 | % 7.97/1.76 | BETA: splitting (21) gives: % 7.97/1.76 | % 7.97/1.76 | Case 1: % 7.97/1.76 | | % 7.97/1.76 | | (24) ~ (all_14_0 = 0) % 7.97/1.76 | | % 7.97/1.76 | | BETA: splitting (23) gives: % 7.97/1.76 | | % 7.97/1.76 | | Case 1: % 7.97/1.76 | | | % 7.97/1.76 | | | (25) all_14_0 = 0 % 7.97/1.76 | | | % 7.97/1.76 | | | REDUCE: (24), (25) imply: % 7.97/1.76 | | | (26) $false % 7.97/1.76 | | | % 7.97/1.76 | | | CLOSE: (26) is inconsistent. % 7.97/1.76 | | | % 7.97/1.76 | | Case 2: % 7.97/1.76 | | | % 7.97/1.76 | | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_1) = v1 % 7.97/1.76 | | | & in(v0, all_14_2) = 0 & $i(v0)) % 7.97/1.76 | | | % 7.97/1.76 | | | DELTA: instantiating (27) with fresh symbols all_29_0, all_29_1 gives: % 7.97/1.76 | | | (28) ~ (all_29_0 = 0) & in(all_29_1, all_14_1) = all_29_0 & % 7.97/1.76 | | | in(all_29_1, all_14_2) = 0 & $i(all_29_1) % 7.97/1.76 | | | % 7.97/1.76 | | | ALPHA: (28) implies: % 7.97/1.76 | | | (29) ~ (all_29_0 = 0) % 7.97/1.76 | | | (30) $i(all_29_1) % 7.97/1.76 | | | (31) in(all_29_1, all_14_2) = 0 % 7.97/1.77 | | | (32) in(all_29_1, all_14_1) = all_29_0 % 7.97/1.77 | | | % 7.97/1.77 | | | GROUND_INST: instantiating (1) with all_14_6, all_14_8, all_14_2, % 7.97/1.77 | | | all_29_1, simplifying with (7), (9), (12), (16), (30), (31) % 7.97/1.77 | | | gives: % 7.97/1.77 | | | (33) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_29_1 & % 7.97/1.77 | | | in(v1, all_14_8) = 0 & in(v0, all_14_6) = 0 & $i(v1) & $i(v0)) % 7.97/1.77 | | | % 7.97/1.77 | | | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1 gives: % 7.97/1.77 | | | (34) ordered_pair(all_38_1, all_38_0) = all_29_1 & in(all_38_0, % 7.97/1.77 | | | all_14_8) = 0 & in(all_38_1, all_14_6) = 0 & $i(all_38_0) & % 7.97/1.77 | | | $i(all_38_1) % 7.97/1.77 | | | % 7.97/1.77 | | | ALPHA: (34) implies: % 7.97/1.77 | | | (35) $i(all_38_1) % 7.97/1.77 | | | (36) $i(all_38_0) % 7.97/1.77 | | | (37) in(all_38_1, all_14_6) = 0 % 7.97/1.77 | | | (38) in(all_38_0, all_14_8) = 0 % 7.97/1.77 | | | (39) ordered_pair(all_38_1, all_38_0) = all_29_1 % 7.97/1.77 | | | % 7.97/1.77 | | | GROUND_INST: instantiating (3) with all_14_8, all_14_7, all_38_0, % 7.97/1.77 | | | simplifying with (7), (8), (18), (36), (38) gives: % 7.97/1.77 | | | (40) in(all_38_0, all_14_7) = 0 % 7.97/1.77 | | | % 7.97/1.77 | | | GROUND_INST: instantiating (2) with all_14_6, all_14_7, all_14_1, % 7.97/1.77 | | | all_29_1, all_29_0, all_38_1, all_38_0, simplifying with (8), % 7.97/1.77 | | | (9), (13), (17), (30), (32), (35), (36), (39) gives: % 7.97/1.77 | | | (41) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_38_0, % 7.97/1.77 | | | all_14_7) = v1 & in(all_38_1, all_14_6) = v0 & ( ~ (v1 = 0) | % 7.97/1.77 | | | ~ (v0 = 0))) % 7.97/1.77 | | | % 7.97/1.77 | | | BETA: splitting (41) gives: % 7.97/1.77 | | | % 7.97/1.77 | | | Case 1: % 7.97/1.77 | | | | % 7.97/1.77 | | | | (42) all_29_0 = 0 % 7.97/1.77 | | | | % 7.97/1.77 | | | | REDUCE: (29), (42) imply: % 7.97/1.77 | | | | (43) $false % 7.97/1.77 | | | | % 7.97/1.77 | | | | CLOSE: (43) is inconsistent. % 7.97/1.77 | | | | % 7.97/1.77 | | | Case 2: % 7.97/1.77 | | | | % 7.97/1.77 | | | | (44) ? [v0: any] : ? [v1: any] : (in(all_38_0, all_14_7) = v1 & % 7.97/1.77 | | | | in(all_38_1, all_14_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 7.97/1.77 | | | | % 7.97/1.77 | | | | DELTA: instantiating (44) with fresh symbols all_58_0, all_58_1 gives: % 7.97/1.77 | | | | (45) in(all_38_0, all_14_7) = all_58_0 & in(all_38_1, all_14_6) = % 7.97/1.77 | | | | all_58_1 & ( ~ (all_58_0 = 0) | ~ (all_58_1 = 0)) % 7.97/1.77 | | | | % 7.97/1.77 | | | | ALPHA: (45) implies: % 7.97/1.77 | | | | (46) in(all_38_1, all_14_6) = all_58_1 % 7.97/1.77 | | | | (47) in(all_38_0, all_14_7) = all_58_0 % 7.97/1.77 | | | | (48) ~ (all_58_0 = 0) | ~ (all_58_1 = 0) % 7.97/1.77 | | | | % 7.97/1.77 | | | | GROUND_INST: instantiating (5) with 0, all_58_1, all_14_6, all_38_1, % 7.97/1.77 | | | | simplifying with (37), (46) gives: % 7.97/1.77 | | | | (49) all_58_1 = 0 % 7.97/1.77 | | | | % 7.97/1.77 | | | | GROUND_INST: instantiating (5) with 0, all_58_0, all_14_7, all_38_0, % 7.97/1.77 | | | | simplifying with (40), (47) gives: % 7.97/1.77 | | | | (50) all_58_0 = 0 % 7.97/1.77 | | | | % 7.97/1.77 | | | | BETA: splitting (48) gives: % 7.97/1.77 | | | | % 7.97/1.77 | | | | Case 1: % 7.97/1.77 | | | | | % 7.97/1.77 | | | | | (51) ~ (all_58_0 = 0) % 7.97/1.77 | | | | | % 7.97/1.77 | | | | | REDUCE: (50), (51) imply: % 7.97/1.77 | | | | | (52) $false % 7.97/1.77 | | | | | % 7.97/1.77 | | | | | CLOSE: (52) is inconsistent. % 7.97/1.77 | | | | | % 7.97/1.77 | | | | Case 2: % 7.97/1.77 | | | | | % 7.97/1.77 | | | | | (53) ~ (all_58_1 = 0) % 7.97/1.77 | | | | | % 7.97/1.77 | | | | | REDUCE: (49), (53) imply: % 7.97/1.77 | | | | | (54) $false % 7.97/1.77 | | | | | % 7.97/1.77 | | | | | CLOSE: (54) is inconsistent. % 7.97/1.77 | | | | | % 7.97/1.77 | | | | End of split % 7.97/1.77 | | | | % 7.97/1.78 | | | End of split % 7.97/1.78 | | | % 7.97/1.78 | | End of split % 7.97/1.78 | | % 7.97/1.78 | Case 2: % 7.97/1.78 | | % 7.97/1.78 | | (55) ~ (all_14_3 = 0) % 7.97/1.78 | | % 7.97/1.78 | | BETA: splitting (22) gives: % 7.97/1.78 | | % 7.97/1.78 | | Case 1: % 7.97/1.78 | | | % 7.97/1.78 | | | (56) all_14_3 = 0 % 7.97/1.78 | | | % 7.97/1.78 | | | REDUCE: (55), (56) imply: % 7.97/1.78 | | | (57) $false % 7.97/1.78 | | | % 7.97/1.78 | | | CLOSE: (57) is inconsistent. % 7.97/1.78 | | | % 7.97/1.78 | | Case 2: % 7.97/1.78 | | | % 7.97/1.78 | | | (58) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_4) = v1 % 7.97/1.78 | | | & in(v0, all_14_5) = 0 & $i(v0)) % 7.97/1.78 | | | % 7.97/1.78 | | | DELTA: instantiating (58) with fresh symbols all_29_0, all_29_1 gives: % 7.97/1.78 | | | (59) ~ (all_29_0 = 0) & in(all_29_1, all_14_4) = all_29_0 & % 7.97/1.78 | | | in(all_29_1, all_14_5) = 0 & $i(all_29_1) % 7.97/1.78 | | | % 7.97/1.78 | | | ALPHA: (59) implies: % 7.97/1.78 | | | (60) ~ (all_29_0 = 0) % 7.97/1.78 | | | (61) $i(all_29_1) % 7.97/1.78 | | | (62) in(all_29_1, all_14_5) = 0 % 7.97/1.78 | | | (63) in(all_29_1, all_14_4) = all_29_0 % 7.97/1.78 | | | % 7.97/1.78 | | | GROUND_INST: instantiating (1) with all_14_8, all_14_6, all_14_5, % 7.97/1.78 | | | all_29_1, simplifying with (7), (9), (10), (14), (61), (62) % 7.97/1.78 | | | gives: % 7.97/1.78 | | | (64) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_29_1 & % 7.97/1.78 | | | in(v1, all_14_6) = 0 & in(v0, all_14_8) = 0 & $i(v1) & $i(v0)) % 7.97/1.78 | | | % 7.97/1.78 | | | DELTA: instantiating (64) with fresh symbols all_38_0, all_38_1 gives: % 7.97/1.78 | | | (65) ordered_pair(all_38_1, all_38_0) = all_29_1 & in(all_38_0, % 7.97/1.78 | | | all_14_6) = 0 & in(all_38_1, all_14_8) = 0 & $i(all_38_0) & % 7.97/1.78 | | | $i(all_38_1) % 7.97/1.78 | | | % 7.97/1.78 | | | ALPHA: (65) implies: % 7.97/1.78 | | | (66) $i(all_38_1) % 7.97/1.78 | | | (67) $i(all_38_0) % 7.97/1.78 | | | (68) in(all_38_1, all_14_8) = 0 % 7.97/1.78 | | | (69) in(all_38_0, all_14_6) = 0 % 7.97/1.78 | | | (70) ordered_pair(all_38_1, all_38_0) = all_29_1 % 7.97/1.78 | | | % 7.97/1.78 | | | GROUND_INST: instantiating (3) with all_14_8, all_14_7, all_38_1, % 7.97/1.78 | | | simplifying with (7), (8), (18), (66), (68) gives: % 7.97/1.78 | | | (71) in(all_38_1, all_14_7) = 0 % 7.97/1.78 | | | % 7.97/1.78 | | | GROUND_INST: instantiating (2) with all_14_7, all_14_6, all_14_4, % 7.97/1.78 | | | all_29_1, all_29_0, all_38_1, all_38_0, simplifying with (8), % 7.97/1.78 | | | (9), (11), (15), (61), (63), (66), (67), (70) gives: % 7.97/1.78 | | | (72) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_38_0, % 7.97/1.78 | | | all_14_6) = v1 & in(all_38_1, all_14_7) = v0 & ( ~ (v1 = 0) | % 7.97/1.78 | | | ~ (v0 = 0))) % 7.97/1.78 | | | % 7.97/1.78 | | | BETA: splitting (72) gives: % 7.97/1.78 | | | % 7.97/1.78 | | | Case 1: % 7.97/1.78 | | | | % 7.97/1.78 | | | | (73) all_29_0 = 0 % 7.97/1.78 | | | | % 7.97/1.78 | | | | REDUCE: (60), (73) imply: % 7.97/1.78 | | | | (74) $false % 7.97/1.78 | | | | % 7.97/1.78 | | | | CLOSE: (74) is inconsistent. % 7.97/1.78 | | | | % 7.97/1.78 | | | Case 2: % 7.97/1.78 | | | | % 7.97/1.78 | | | | (75) ? [v0: any] : ? [v1: any] : (in(all_38_0, all_14_6) = v1 & % 7.97/1.78 | | | | in(all_38_1, all_14_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 7.97/1.78 | | | | % 7.97/1.78 | | | | DELTA: instantiating (75) with fresh symbols all_58_0, all_58_1 gives: % 7.97/1.78 | | | | (76) in(all_38_0, all_14_6) = all_58_0 & in(all_38_1, all_14_7) = % 7.97/1.78 | | | | all_58_1 & ( ~ (all_58_0 = 0) | ~ (all_58_1 = 0)) % 7.97/1.78 | | | | % 7.97/1.78 | | | | ALPHA: (76) implies: % 7.97/1.78 | | | | (77) in(all_38_1, all_14_7) = all_58_1 % 7.97/1.78 | | | | (78) in(all_38_0, all_14_6) = all_58_0 % 7.97/1.78 | | | | (79) ~ (all_58_0 = 0) | ~ (all_58_1 = 0) % 7.97/1.78 | | | | % 7.97/1.79 | | | | GROUND_INST: instantiating (5) with 0, all_58_1, all_14_7, all_38_1, % 7.97/1.79 | | | | simplifying with (71), (77) gives: % 7.97/1.79 | | | | (80) all_58_1 = 0 % 7.97/1.79 | | | | % 7.97/1.79 | | | | GROUND_INST: instantiating (5) with 0, all_58_0, all_14_6, all_38_0, % 7.97/1.79 | | | | simplifying with (69), (78) gives: % 7.97/1.79 | | | | (81) all_58_0 = 0 % 7.97/1.79 | | | | % 7.97/1.79 | | | | BETA: splitting (79) gives: % 7.97/1.79 | | | | % 7.97/1.79 | | | | Case 1: % 7.97/1.79 | | | | | % 7.97/1.79 | | | | | (82) ~ (all_58_0 = 0) % 7.97/1.79 | | | | | % 7.97/1.79 | | | | | REDUCE: (81), (82) imply: % 7.97/1.79 | | | | | (83) $false % 7.97/1.79 | | | | | % 7.97/1.79 | | | | | CLOSE: (83) is inconsistent. % 7.97/1.79 | | | | | % 7.97/1.79 | | | | Case 2: % 7.97/1.79 | | | | | % 7.97/1.79 | | | | | (84) ~ (all_58_1 = 0) % 7.97/1.79 | | | | | % 7.97/1.79 | | | | | REDUCE: (80), (84) imply: % 7.97/1.79 | | | | | (85) $false % 7.97/1.79 | | | | | % 7.97/1.79 | | | | | CLOSE: (85) is inconsistent. % 7.97/1.79 | | | | | % 7.97/1.79 | | | | End of split % 7.97/1.79 | | | | % 7.97/1.79 | | | End of split % 7.97/1.79 | | | % 7.97/1.79 | | End of split % 7.97/1.79 | | % 7.97/1.79 | End of split % 7.97/1.79 | % 7.97/1.79 End of proof % 7.97/1.79 % SZS output end Proof for theBenchmark % 7.97/1.79 % 7.97/1.79 1225ms %------------------------------------------------------------------------------