%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU125+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 : n019.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 17:42:37 EDT 2023 % Result : Theorem 9.58s 2.02s % Output : Proof 12.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.15 % Problem : SEU125+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.37 % Computer : n019.cluster.edu % 0.13/0.37 % Model : x86_64 x86_64 % 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.37 % Memory : 8042.1875MB % 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.37 % CPULimit : 300 % 0.13/0.37 % WCLimit : 300 % 0.13/0.37 % DateTime : Wed Aug 23 13:28:28 EDT 2023 % 0.13/0.37 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.44/1.03 Prover 4: Preprocessing ... % 2.44/1.05 Prover 1: Preprocessing ... % 2.96/1.09 Prover 3: Preprocessing ... % 2.96/1.09 Prover 0: Preprocessing ... % 2.96/1.09 Prover 2: Preprocessing ... % 2.96/1.09 Prover 6: Preprocessing ... % 2.96/1.09 Prover 5: Preprocessing ... % 5.18/1.45 Prover 5: Proving ... % 5.18/1.48 Prover 1: Warning: ignoring some quantifiers % 5.18/1.51 Prover 3: Warning: ignoring some quantifiers % 5.18/1.52 Prover 2: Proving ... % 5.18/1.53 Prover 3: Constructing countermodel ... % 5.18/1.55 Prover 1: Constructing countermodel ... % 5.18/1.56 Prover 4: Warning: ignoring some quantifiers % 5.18/1.62 Prover 6: Proving ... % 6.05/1.66 Prover 4: Constructing countermodel ... % 7.44/1.72 Prover 0: Proving ... % 9.58/2.02 Prover 0: proved (1403ms) % 9.58/2.02 % 9.58/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.58/2.02 % 9.58/2.03 Prover 6: stopped % 9.58/2.03 Prover 5: stopped % 9.68/2.03 Prover 3: stopped % 9.68/2.03 Prover 2: stopped % 9.68/2.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.68/2.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.68/2.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.68/2.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.68/2.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.68/2.11 Prover 8: Preprocessing ... % 9.68/2.11 Prover 13: Preprocessing ... % 9.68/2.14 Prover 7: Preprocessing ... % 9.68/2.14 Prover 10: Preprocessing ... % 9.68/2.15 Prover 11: Preprocessing ... % 9.68/2.23 Prover 10: Warning: ignoring some quantifiers % 10.32/2.24 Prover 13: Warning: ignoring some quantifiers % 10.32/2.24 Prover 10: Constructing countermodel ... % 10.32/2.25 Prover 7: Warning: ignoring some quantifiers % 10.32/2.26 Prover 7: Constructing countermodel ... % 10.32/2.27 Prover 13: Constructing countermodel ... % 10.32/2.27 Prover 8: Warning: ignoring some quantifiers % 10.32/2.29 Prover 8: Constructing countermodel ... % 11.56/2.31 Prover 4: Found proof (size 41) % 11.56/2.31 Prover 4: proved (1688ms) % 11.56/2.31 Prover 8: stopped % 11.56/2.31 Prover 1: stopped % 11.56/2.31 Prover 13: stopped % 11.56/2.31 Prover 7: stopped % 11.56/2.31 Prover 10: stopped % 11.56/2.33 Prover 11: Warning: ignoring some quantifiers % 11.56/2.35 Prover 11: Constructing countermodel ... % 11.56/2.36 Prover 11: stopped % 11.56/2.36 % 11.56/2.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.56/2.36 % 11.56/2.36 % SZS output start Proof for theBenchmark % 11.56/2.37 Assumptions after simplification: % 11.56/2.37 --------------------------------- % 11.56/2.37 % 11.56/2.37 (commutativity_k2_xboole_0) % 11.56/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 11.56/2.39 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 11.56/2.39 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 11.56/2.39 | (set_union2(v1, v0) = v2 & $i(v2))) % 11.56/2.39 % 11.56/2.39 (d2_xboole_0) % 12.00/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.00/2.41 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 12.00/2.41 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) % 12.00/2.41 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : ! % 12.00/2.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 12.00/2.41 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 12.00/2.41 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & % 12.00/2.41 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 12.00/2.41 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = % 12.00/2.41 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 12.00/2.41 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 % 12.00/2.41 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.00/2.41 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | % 12.00/2.41 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 12.00/2.41 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = % 12.00/2.41 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 12.00/2.41 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 12.00/2.41 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, % 12.00/2.41 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & % 12.00/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) % 12.00/2.41 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 12.00/2.41 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 & % 12.00/2.41 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.00/2.41 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 12.00/2.41 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, % 12.00/2.41 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( % 12.00/2.41 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 12.00/2.41 % 12.00/2.41 (d3_tarski) % 12.00/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.00/2.41 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 12.00/2.41 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 12.00/2.41 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 12.00/2.41 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 12.00/2.41 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.00/2.41 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 12.00/2.41 $i(v0) | in(v2, v1) = 0) % 12.00/2.41 % 12.00/2.41 (t8_xboole_1) % 12.00/2.41 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 12.00/2.41 = 0) & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 & % 12.00/2.41 set_union2(v0, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.00/2.41 % 12.00/2.41 (function-axioms) % 12.00/2.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.00/2.42 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 12.00/2.42 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.00/2.42 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 12.00/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.00/2.42 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 12.00/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.00/2.42 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 12.00/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.00/2.42 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 12.00/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 12.00/2.42 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 12.00/2.42 % 12.00/2.42 Further assumptions not needed in the proof: % 12.00/2.42 -------------------------------------------- % 12.00/2.42 antisymmetry_r2_hidden, commutativity_k3_xboole_0, d10_xboole_0, d1_xboole_0, % 12.00/2.42 d3_xboole_0, d7_xboole_0, dt_k1_xboole_0, dt_k2_xboole_0, dt_k3_xboole_0, % 12.00/2.42 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 12.00/2.42 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 12.00/2.42 symmetry_r1_xboole_0, t1_boole, t1_xboole_1, t2_xboole_1, t3_xboole_0, % 12.00/2.42 t3_xboole_1, t4_xboole_0, t6_boole, t7_boole, t7_xboole_1, t8_boole % 12.00/2.42 % 12.00/2.42 Those formulas are unsatisfiable: % 12.00/2.42 --------------------------------- % 12.00/2.42 % 12.00/2.42 Begin of proof % 12.00/2.42 | % 12.00/2.42 | ALPHA: (commutativity_k2_xboole_0) implies: % 12.00/2.42 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 12.00/2.42 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 12.00/2.42 | % 12.00/2.42 | ALPHA: (d2_xboole_0) implies: % 12.00/2.42 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 12.00/2.42 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 12.00/2.42 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.00/2.42 | (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0))) % 12.00/2.42 | % 12.00/2.42 | ALPHA: (d3_tarski) implies: % 12.00/2.42 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 12.00/2.42 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 12.00/2.42 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 12.00/2.42 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.00/2.42 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 12.00/2.42 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 12.00/2.42 | % 12.00/2.42 | ALPHA: (function-axioms) implies: % 12.00/2.42 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.00/2.42 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 12.00/2.42 | % 12.00/2.42 | DELTA: instantiating (t8_xboole_1) with fresh symbols all_34_0, all_34_1, % 12.00/2.42 | all_34_2, all_34_3, all_34_4 gives: % 12.00/2.43 | (6) ~ (all_34_0 = 0) & subset(all_34_1, all_34_3) = all_34_0 & % 12.00/2.43 | subset(all_34_2, all_34_3) = 0 & subset(all_34_4, all_34_3) = 0 & % 12.00/2.43 | set_union2(all_34_4, all_34_2) = all_34_1 & $i(all_34_1) & $i(all_34_2) % 12.00/2.43 | & $i(all_34_3) & $i(all_34_4) % 12.00/2.43 | % 12.00/2.43 | ALPHA: (6) implies: % 12.00/2.43 | (7) ~ (all_34_0 = 0) % 12.00/2.43 | (8) $i(all_34_4) % 12.00/2.43 | (9) $i(all_34_3) % 12.00/2.43 | (10) $i(all_34_2) % 12.00/2.43 | (11) set_union2(all_34_4, all_34_2) = all_34_1 % 12.00/2.43 | (12) subset(all_34_4, all_34_3) = 0 % 12.00/2.43 | (13) subset(all_34_2, all_34_3) = 0 % 12.00/2.43 | (14) subset(all_34_1, all_34_3) = all_34_0 % 12.00/2.43 | % 12.00/2.43 | GROUND_INST: instantiating (1) with all_34_2, all_34_4, all_34_1, simplifying % 12.00/2.43 | with (8), (10), (11) gives: % 12.00/2.43 | (15) set_union2(all_34_2, all_34_4) = all_34_1 & $i(all_34_1) % 12.00/2.43 | % 12.00/2.43 | ALPHA: (15) implies: % 12.00/2.43 | (16) $i(all_34_1) % 12.00/2.43 | (17) set_union2(all_34_2, all_34_4) = all_34_1 % 12.00/2.43 | % 12.00/2.43 | GROUND_INST: instantiating (3) with all_34_1, all_34_3, all_34_0, simplifying % 12.00/2.43 | with (9), (14), (16) gives: % 12.00/2.43 | (18) all_34_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 12.00/2.43 | all_34_1) = 0 & in(v0, all_34_3) = v1 & $i(v0)) % 12.00/2.43 | % 12.00/2.43 | BETA: splitting (18) gives: % 12.00/2.43 | % 12.00/2.43 | Case 1: % 12.00/2.43 | | % 12.00/2.43 | | (19) all_34_0 = 0 % 12.00/2.43 | | % 12.00/2.43 | | REDUCE: (7), (19) imply: % 12.00/2.43 | | (20) $false % 12.00/2.43 | | % 12.00/2.43 | | CLOSE: (20) is inconsistent. % 12.00/2.43 | | % 12.00/2.43 | Case 2: % 12.00/2.43 | | % 12.00/2.43 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_34_1) = 0 & % 12.00/2.43 | | in(v0, all_34_3) = v1 & $i(v0)) % 12.00/2.43 | | % 12.00/2.43 | | DELTA: instantiating (21) with fresh symbols all_54_0, all_54_1 gives: % 12.00/2.43 | | (22) ~ (all_54_0 = 0) & in(all_54_1, all_34_1) = 0 & in(all_54_1, % 12.00/2.43 | | all_34_3) = all_54_0 & $i(all_54_1) % 12.00/2.43 | | % 12.00/2.43 | | ALPHA: (22) implies: % 12.00/2.43 | | (23) ~ (all_54_0 = 0) % 12.00/2.43 | | (24) $i(all_54_1) % 12.00/2.43 | | (25) in(all_54_1, all_34_3) = all_54_0 % 12.00/2.43 | | (26) in(all_54_1, all_34_1) = 0 % 12.00/2.43 | | % 12.00/2.43 | | GROUND_INST: instantiating (4) with all_34_2, all_34_3, all_54_1, all_54_0, % 12.00/2.43 | | simplifying with (9), (10), (13), (24), (25) gives: % 12.00/2.43 | | (27) all_54_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_54_1, all_34_2) % 12.00/2.43 | | = v0) % 12.00/2.44 | | % 12.00/2.44 | | GROUND_INST: instantiating (4) with all_34_4, all_34_3, all_54_1, all_54_0, % 12.00/2.44 | | simplifying with (8), (9), (12), (24), (25) gives: % 12.00/2.44 | | (28) all_54_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_54_1, all_34_4) % 12.00/2.44 | | = v0) % 12.00/2.44 | | % 12.00/2.44 | | GROUND_INST: instantiating (2) with all_34_2, all_34_4, all_34_1, all_54_1, % 12.00/2.44 | | simplifying with (8), (10), (16), (17), (24), (26) gives: % 12.00/2.44 | | (29) ? [v0: any] : ? [v1: any] : (in(all_54_1, all_34_2) = v0 & % 12.00/2.44 | | in(all_54_1, all_34_4) = v1 & (v1 = 0 | v0 = 0)) % 12.00/2.44 | | % 12.00/2.44 | | DELTA: instantiating (29) with fresh symbols all_82_0, all_82_1 gives: % 12.00/2.44 | | (30) in(all_54_1, all_34_2) = all_82_1 & in(all_54_1, all_34_4) = % 12.00/2.44 | | all_82_0 & (all_82_0 = 0 | all_82_1 = 0) % 12.00/2.44 | | % 12.00/2.44 | | ALPHA: (30) implies: % 12.00/2.44 | | (31) in(all_54_1, all_34_4) = all_82_0 % 12.00/2.44 | | (32) in(all_54_1, all_34_2) = all_82_1 % 12.00/2.44 | | (33) all_82_0 = 0 | all_82_1 = 0 % 12.00/2.44 | | % 12.00/2.44 | | BETA: splitting (28) gives: % 12.00/2.44 | | % 12.00/2.44 | | Case 1: % 12.00/2.44 | | | % 12.00/2.44 | | | (34) all_54_0 = 0 % 12.00/2.44 | | | % 12.00/2.44 | | | REDUCE: (23), (34) imply: % 12.00/2.44 | | | (35) $false % 12.00/2.44 | | | % 12.00/2.44 | | | CLOSE: (35) is inconsistent. % 12.00/2.44 | | | % 12.00/2.44 | | Case 2: % 12.00/2.44 | | | % 12.00/2.44 | | | (36) ? [v0: int] : ( ~ (v0 = 0) & in(all_54_1, all_34_4) = v0) % 12.00/2.44 | | | % 12.00/2.44 | | | DELTA: instantiating (36) with fresh symbol all_92_0 gives: % 12.00/2.44 | | | (37) ~ (all_92_0 = 0) & in(all_54_1, all_34_4) = all_92_0 % 12.00/2.44 | | | % 12.00/2.44 | | | ALPHA: (37) implies: % 12.00/2.44 | | | (38) ~ (all_92_0 = 0) % 12.00/2.44 | | | (39) in(all_54_1, all_34_4) = all_92_0 % 12.00/2.44 | | | % 12.00/2.44 | | | BETA: splitting (27) gives: % 12.00/2.44 | | | % 12.00/2.44 | | | Case 1: % 12.00/2.44 | | | | % 12.00/2.44 | | | | (40) all_54_0 = 0 % 12.00/2.44 | | | | % 12.00/2.44 | | | | REDUCE: (23), (40) imply: % 12.00/2.44 | | | | (41) $false % 12.00/2.44 | | | | % 12.00/2.44 | | | | CLOSE: (41) is inconsistent. % 12.00/2.44 | | | | % 12.00/2.44 | | | Case 2: % 12.00/2.44 | | | | % 12.00/2.44 | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & in(all_54_1, all_34_2) = v0) % 12.00/2.44 | | | | % 12.00/2.44 | | | | DELTA: instantiating (42) with fresh symbol all_103_0 gives: % 12.00/2.44 | | | | (43) ~ (all_103_0 = 0) & in(all_54_1, all_34_2) = all_103_0 % 12.00/2.44 | | | | % 12.00/2.44 | | | | ALPHA: (43) implies: % 12.00/2.44 | | | | (44) ~ (all_103_0 = 0) % 12.00/2.44 | | | | (45) in(all_54_1, all_34_2) = all_103_0 % 12.00/2.44 | | | | % 12.00/2.44 | | | | GROUND_INST: instantiating (5) with all_82_0, all_92_0, all_34_4, % 12.00/2.44 | | | | all_54_1, simplifying with (31), (39) gives: % 12.00/2.44 | | | | (46) all_92_0 = all_82_0 % 12.00/2.44 | | | | % 12.00/2.44 | | | | GROUND_INST: instantiating (5) with all_82_1, all_103_0, all_34_2, % 12.00/2.44 | | | | all_54_1, simplifying with (32), (45) gives: % 12.00/2.44 | | | | (47) all_103_0 = all_82_1 % 12.00/2.44 | | | | % 12.00/2.44 | | | | REDUCE: (44), (47) imply: % 12.00/2.44 | | | | (48) ~ (all_82_1 = 0) % 12.00/2.44 | | | | % 12.00/2.44 | | | | REDUCE: (38), (46) imply: % 12.00/2.44 | | | | (49) ~ (all_82_0 = 0) % 12.00/2.44 | | | | % 12.00/2.44 | | | | BETA: splitting (33) gives: % 12.00/2.44 | | | | % 12.00/2.44 | | | | Case 1: % 12.00/2.44 | | | | | % 12.00/2.44 | | | | | (50) all_82_0 = 0 % 12.00/2.44 | | | | | % 12.00/2.44 | | | | | REDUCE: (49), (50) imply: % 12.00/2.44 | | | | | (51) $false % 12.00/2.44 | | | | | % 12.00/2.44 | | | | | CLOSE: (51) is inconsistent. % 12.00/2.44 | | | | | % 12.00/2.44 | | | | Case 2: % 12.00/2.44 | | | | | % 12.00/2.44 | | | | | (52) all_82_1 = 0 % 12.00/2.44 | | | | | % 12.00/2.44 | | | | | REDUCE: (48), (52) imply: % 12.00/2.44 | | | | | (53) $false % 12.00/2.44 | | | | | % 12.00/2.44 | | | | | CLOSE: (53) is inconsistent. % 12.00/2.44 | | | | | % 12.00/2.44 | | | | End of split % 12.00/2.44 | | | | % 12.00/2.45 | | | End of split % 12.00/2.45 | | | % 12.00/2.45 | | End of split % 12.00/2.45 | | % 12.00/2.45 | End of split % 12.00/2.45 | % 12.00/2.45 End of proof % 12.00/2.45 % SZS output end Proof for theBenchmark % 12.00/2.45 % 12.00/2.45 1845ms %------------------------------------------------------------------------------